Houston Independent School District



Introduction Overview / RationaleFor new and seasoned professionals alike, the beginning of the school year is the time to teach and re-teach classroom routines and procedures. While it may take several weeks for these routines and procedures to become firmly established, the initial time invested pays significant dividends throughout the year. Routines and procedures are the backbone of daily classroom life. They facilitate teaching and learning and save valuable classroom time when implemented early and consistently. Efficient routines and procedures maximize instructional time, thereby making it easier for students to learn. For students, a successful experience in mathematics begins with the basics: how to think like an active mathematician, how to speak mathematically, and how to record and share one’s ideas. Routines and procedures, once taught, need to be practiced with the whole class in order for effective implementation to occur. Doing so allows students an opportunity to demonstrate they know and understand what is expected of them. Clear statements and demonstrations of both student and teacher roles need to be explicit.The HISD First 25 Days of Math implementation guide is intended for use with students in grades K-5. Each day of the guide includes grade-level differentiation to support individual teacher and student needs. As you prepare to implement the First 25 Days of Math during the 90-minute math block, keep in mind that flexibility is key. This guide is intended to provide support in establishing routines and procedures through short 5 to 20 minute mini-lessons that are embedded in the daily lesson. To support professional learning communities (PLCs) at the campus level, it is recommended that grade-level teams meet periodically to monitor and adjust progress of implementation. All points and aspects of this guide need to be repeated, and consistently referred to, during instruction. Goals ImplementationThis document has been designed to: Support student academic thinking and speaking and develop students’ problem-solving skillsEstablish consistent classroom routines and procedures to support teaching and learningSupport the use of the mathematical process standards, so as to increase instructional rigor as students explore, express, and better understand content standards Support teachers as they implement math stations and facilitate small-group instruction The structures and strategies provided in this guide are to be embedded within the content lessons of the first 25 days of instruction. As such, utilize the recommendations in this guide in conjunction with the HISD curriculum documents (e.g., unit planning guides, formative assessments, and snapshot teacher outlines) following the recommended 90-minute math block (*See page 2). To the greatest extent possible, embed the objective of the day within your 5 to 20 minute First 25 Days of Math mini-lesson to connect daily routines and procedures to the math content of the day.Each component of the First 25 Days of Math is listed here according to the HISD academic calendar. While flexibility may be necessary to ensure effective implementation, the expectation is teachers begin to fully implement small-group instruction and math stations by the beginning of October 2015. AUGUST 2015 MONDAYTUESDAYWEDNESDAYTHURSDAYFRIDAY24 Number of the Day25 Number Talks26Anchor Charts27Math Vocabulary Word Wall28Number Strings31Interactive Math NotebooksSEPTEMBER 2015MONDAYTUESDAYWEDNESDAYTHURSDAYFRIDAY 1Collaborative Groups2Self-Monitoring Skills3Math Think-Aloud4The Problem Solving Model7Labor Day—No School8Problem Solving Journal9Math Rubric 10Data-Driven TEKS Warm-Up 11Multiple Representations 14Justification & Reasonableness15Making Connections16Accountable Talk17Evaluating the Problem-Solving Process18Teach Backs21Math Stations22Manipulatives Management & Organization 23SCHOOL HOLIDAY24Management Board & Tight Transitions25Math Data Folders28Small Group Instruction I29Small Group Instruction II*The calendar above is only a suggestion for the pacing and order of implementation for the components of this document. Teachers and campuses have the flexibility to modify this calendar according to their needs. Introduction Connection to Houston ISD 5E Math Block 12636597694This document offers suggestions for implementing routines and procedures; however, it does not replace the HISD Planning Guides. Please reference the HISD Unit Planning Guides to plan for daily math lessons.00This document offers suggestions for implementing routines and procedures; however, it does not replace the HISD Planning Guides. Please reference the HISD Unit Planning Guides to plan for daily math lessons.Day 1—Number of the DayTeacher ConsiderationsA number of the day is a simple math routine focused on just one number, where students create multiple representations of and make multiple connections to the number. According to the recommended 90-minute math block, the Number of the Day is one option of choice for teachers in developing their students’ numerical fluency. The Number of the Day is typically done before the daily lesson objective is taught and can be combined with a problem of the day or a spiral-review activity. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 5 to 8 minutes of class time.Rationale Exemplar The Number of the Day: Helps build numerical fluency and develops number senseSupports students with making connections from numbers to mathematical conceptsProvides structures for students to experience multiple computational strategies needed to solve diverse problemsSupports students in making sense of mathematics ImplementationDuring planning, identify the number you wish to talk about. Predict and then create a list of possible student responses for when they will be prompted to represent the number in a variety of ways. Identify and explain to students the procedure for gathering together and/or following along (e.g., determine where in the room students will gather for Number of the Day and what they will use to record their thinking). Pre-determine where and how you will display the Number of the Day (e.g., chart paper, anchor chart, student worksheet, bulletin board, etc.). To begin this routine, bring students to the pre-determined gathering place and ensure they have the materials needed to participate (e.g., pencils, sticky notes, dry-erase board/marker, etc.).Explain to students that they will be participating in a math routine that will ask them to think about numbers.Display the number of the day and ask students to think about different ways to represent it.Instruct students to record their thinking. For no more than 1 to 2 minutes, instruct students to write as many different representations as they can for the number. (*Note: You can utilize a number within a given concept for math, such as measurement, in order to connect your Number of the Day for the concept of the lesson.)Next have students turn to a partner and talk about their representations for no more than 1 minute. After time is up, engage with students in whole-group sharing about their representations. Ask each student to choose his/her favorite representation and record it according to your directions (e.g., record number on sticky note and place it on chart paper, or teacher scribes what students share aloud). To close out the number of the day activity, discuss a few of the students’ recorded ideas, highlighting any of the representations which align to the daily lesson objective. Extension: Consider preparing in advance 3 to 6 categories into which students sort their varied representations generated during step 9. Before having students turn and talk to a partner (step 10), show them the categories and ask that they continue brainstorming to ensure that they have at least one representation per category. Recommended MaterialsChart paper/markers or white boardNumber for the day (chosen in advance)Dry-erase boards/markers Sticky notes, pencils, scratch paper, etc.Optional: Categories or concepts that connect chosen number to math content of the dayAdditional ResourcesNumber Sense Routines Book: Building Numerical Literacy Every Day in Grades K-3 by Jessica Shumway (2011)HISD Video Exemplar: Number of the Day HISD Number Concept MapsNumber of the Day SamplesPinterest Ideas for Number of the DayHYPERLINK ""Interactive Number of the DayInstructional Practice (IP) Rubric ConnectionsI-3 Differentiates instruction for student needs by employing a variety of instructional strategies I-6 Communicates content and concepts to students I-8 Students actively participate in lesson activitiesGrade-Level Differentiation Early Childhood: Use dot cards (structured and random) to help students develop subitizing skills (i.e., the automatic and rapid identification of small number quantities). Utilize ten frames to provide a structure for students to compose and decompose numbers to 10. In the early grades, the Number of Day should focus on concrete and/or pictorial representations. Intermediate: Use multiple representations (e.g., ten frames, base-10 blocks, hundred boards, hundredths/thousandths grids, number lines, etc.) to make connections to grade-level content standards. Day 2—Number TalksTeacher ConsiderationsA Number Talk is a daily-math routine where work by students is done mentally. Number talks help build students’ number sense and mental math strategies. According to the recommended 90-minute math block, a Number Talk is one option of choice for teachers in developing their students’ computational fluency. In order for Number Talks to be effective, it is recommended for teachers to implement them frequently. Unlike Number of the Day, Number Talks promote mental math strategies and therefore students do not record individual responses. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 5 to 8 minutes of class time. Rationale ExemplarNumber Talks:Help teachers create a classroom environment that develops numerical efficiency, flexibility, and accuracy Build key foundational ideas in mathematics (e.g., composition and decomposition of numbers, systems of tens, application of properties, etc.)Foster students’ ability to reason and justify their thinking in math Provide structures for students to experience multiple computational strategies while solving problems mentally3168519525000 3105009715500ImplementationDuring planning, identify the numerical expression (number sentence) you will present for students to solve mentally.Predict and then create a list of possible student responses for the numerical expression.Identify a designated location to hold your number talk that helps you maintain close proximity with your students (e.g., rug, small group circle).When introducing number talks, be sure to set the tone that all answers are considered and respected. It is important for teachers to understand that wrong answers are often rooted in misconceptions and provide a rich opportunity to give meaningful feedback. Display a numerical expression (number sentence) and give students an opportunity to solve it mentally. Let them know that they will be expected to explain how they arrived at their solution. Model the response signal students should use when they have arrived at a solution and can explain their thinking (e.g., two fingers in the air). Remember, students do not use paper and pencil to solve. Provide 1 to 2 minutes of wait time to ensure the majority of students have processed the problem and are able to explain how they arrived at their solution. For students who finish early, consider having them think of a different way to solve the problem.After time is up, tell students that you will be sharing your own thinking for how you solved the problem. Model for students your expectations for how they interact when talking to their partners about their own solution strategies. Teachers might consider sharing an uncommon solution during role-play.Next, have students turn to a partner and talk about how they arrived at their solution.When time is up, engage the students in a whole-group share-out about their thinking. Select a few students to share their thinking, remembering that you may have to support students as they attempt to communicate their thinking verbally. Record student responses exactly how they are explained. To close out the Number Talk, discuss a few of the students’ recorded ideas, highlighting any possible misconceptions and alignment to the daily lesson objective. Recommended MaterialsChart Paper/Chalk Board/White Board/Overhead ProjectorMarkersTen Frame Hundreds Chart Number Line Additional ResourcesNumber Talks, Sherry ParrishHISD Video Exemplar: Number TalksNumber Talk VideoNumber Talk OverviewInstructional Practice (IP) Rubric ConnectionsI-4 Engages students in work that develop higher level thinking skillsI-8 Students actively participating in lesson activitiesI-10 Builds a positive and respectful classroom environmentGrade-Level Differentiation Early Childhood: Consider introducing pictorial representations and structures (e.g., object, animals, ten frames, etc.) before introducing numerical expressions (e.g., 2 and 3 is the same as ___, 5 + 27, etc.). Ensure the number sentence is grade level appropriate.Intermediate: Consider using other representations outside of numerical expressions (e.g., geometric figures, equations, etc.). Utilize a variety of positive rational numbers (i.e., whole numbers, fractions, and decimals). Day 3—Anchor ChartsTeacher ConsiderationsAnchor charts are large, hand-written charts created by teachers and students together to make the learning of a concept or a skill visible. Anchor charts make learning accessible by providing students a tool they can use to answer questions. Anchor charts contain only the most relevant or important information of a given concept or skill. Charts should be neat and organized, with simple icons and graphics to enhance their usefulness. Anchor charts should have a single focus, reflect recent math lessons needing continued support and scaffolding, help students remember the process of a skill or strategy, support the development of precise math language, and be organized and accurate. Depending on the grade level, the full implementation of this mini-lesson will require teachers to spend approximately 10-15 minutes of class time.Rationale ExemplarAnchor charts: Make thinking visible by recording content, strategies, processes, cues, and guidelines during the learning process.Keep relevant and current content accessible to students to remind them of prior learning, supporting them to make connections with new learning.Expand ideas and contribute to classroom instruction, discussions, and problem solving. Act as a reference to support ideas during class discussions. ImplementationDuring planning, sketch on a piece of paper what the completed anchor chart will look like for the concept being covered. Some components of the anchor chart may be pre-drawn on the chart to save instructional time (e.g. title, graphic organizer, prompts, guiding questions, etc.). Determine where in the classroom you will create the anchor chart with your students, as well as the location where it will later be posted for students to reference. During whole group, tell the class you will be creating an Anchor Chart to make their thinking visible, record their current understanding, and support their work during independent and small-group activities. Begin by telling students the title of the anchor chart and by explaining the focus of the day’s learning. Co-create the anchor chart with students. Ask students to share their ideas on what should be added, and record the shared ideas on the anchor chart. Post anchor chart in pre-determined location and remind students to reference the chart often, as needed. Tell students that they may add ideas to the anchor chart as they apply new learning, discover interesting ideas, or develop useful strategies for problem-solving or skill application. (NOTE: Adding to the chart can occur during the initial stage of creation or afterwards, as students continue building understanding.)EXTENSION: As students familiarize themselves with the expectations of an anchor chart, they can create their own charts during small group or independent practice. Thereafter, students can share or present their charts with the rest of the class.MaterialsChart Paper MarkersPost-It NotesSentence Strips Manipulatives Student Work and/or Ideas Additional ResourcesHISD Video Exemplar: Anchor ChartsAnchor Chart Ideas Anchor Chart PicturesInstructional Practice (IP) Rubric ConnectionsI-1 Facilitates organized, student-centered, objective driven lessonsI-6 Communicates content and concepts to students I-8 Students actively participating in lesson activities Grade-Level Differentiation Early Childhood: In the lower grades, anchor charts should contain visuals and graphics to support students’ acquisition of sight words and academic math vocabulary. The use of sentence stems supports language development and should be used in Kindergarten and First grade classrooms extensively. Intermediate: As appropriate, provide supports to help students regularly create their own anchor charts.Day 4—Math Vocabulary Word WallTeacher ConsiderationsA?math word wall?is an ongoing, organized display of words?that provides a visual reference for students throughout a unit of study. Math words selected to be placed on the word wall?should be ones used regularly by the teacher during instruction. These words are to be promoted for student use during activities in all forms of communication, both written and verbal. Math walls help support students develop a robust academic vocabulary. A math word wall should be on-going, updated, and referenced daily. Understanding that students have a limited capacity for learning new words, it is important for teachers to carefully select which words they will highlight on the wall, as well as determine when to update and/or replace the words displayed on the wall.Depending on the grade level, the full implementation of this mini-lesson will require teachers to spend approximately 15-20 minutes of class time. Rationale ExemplarMath word walls: Allow students to communicate orally using appropriate academic math vocabulary.Help students identify new words and phrases needed for learning new mathematical concepts. Support the integration of reading and writing in mathematics. -400051825400ImplementationWhen setting up your classroom, determine which wall you will use to display the math word wall, remembering that it must be located in an area accessible and viewable by students. Identify the academic math vocabulary you will introduce during your unit of instruction. It is recommended that you reference the HISD curriculum documents for academic math vocabulary words and definitions.In order to help students make connections to new, unfamiliar vocabulary words, carefully select relevant real-world objects, pictures, and/or diagrams that can aid you in introducing new terms. Design an interactive activity that utilizes the real-world objects or pictures, and create an exemplar of the final product you want students to complete. Select interactive activity for students to engage in utilizing the new academic math vocabulary words. When first introducing the math vocabulary word wall, let students know the word wall is a tool to learn, engage, and reference academic math vocabulary. Introduce the new academic math words and their definitions. (For example, you might show the written word and accompanying visual, pronounce it, define it, use it in a sentence, and then say the word again). After introducing the academic math vocabulary words, post them on the Math Vocabulary Word Wall. To engage students in utilizing the new academic math vocabulary words, model the pre-selected interactive activity and pre-created exemplar. For activity ideas, reference this link.Allow students time to engage in the pre-selected activity. After completing the activity, bring students together to share learning in whole group. Consider utilizing interactive math vocabulary activities during workstations for continued reinforcement. MaterialsIndex cardsSentence stripsMarkersPocket chart (optional)Bulletin Board (optional)Additional ResourcesHISD Video Exemplar: Math Vocabulary Word Wall HYPERLINK "" Math Word Wall ActivitiesPinterest Word Wall IdeasUsing a Word Wall VideoWord Wall Activity Video Instructional Practice (IP) Rubric ConnectionsI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-6 Communicates content and concepts to students I-7 Promotes high academic expectations for studentsI-8 Students actively participating in lesson activitiesI-10 Builds a positive and respectful classroom environmentGrade-Level Differentiation Early Childhood: Utilize pictures, organizers, songs, kinesthetic movements, and bright colors to increase student engagement.Intermediate: Allow students choice when selecting which activity they will complete. Use writing to help students make connections between new academic math vocabulary and their every-day experiences. Day 5—Number StringsTeacher ConsiderationsNumber strings are a set of number patterns or stories crafted to support students’ construction of big ideas. Students make connections with various operations and build their own strategies to solve given Number Strings. Students should first determine the pattern and/or solution mentally and then share it with the class. While students share, the teacher should represent students’ strategies and facilitate conversation among them. According to the recommended 90-minute math block, Number Strings are one option of choice for teachers in developing their students’ numerical fluency. Number Strings are typically done before the daily lesson objective is taught and can be combined with a problem of the day or a spiral-review activity. ?Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 5 to 8 minutes of class time.Rationale ExemplarNumber Strings:Allow students to use number relationships to solve problemsHelp students build numerical fluency by using known facts and relationships to determine unknown facts and solutionsSupport students as they learn to develop and test conjectures helpAid students in making generalizations about mathematical relationships, operations, and properties1049398219081600-273053810000ImplementationDuring planning, identify the number strings you will present for students to solve mentally. For example, you might provide a ?number pattern (e.g., 8 x 13, 8 x 23, 8 x 33, 8 x 43, etc., or 15 + 25 = 18 + __, 15 + 25 = 19 + __, 15 + 25 = 20 + ___, etc..) or a number story (e.g., Start with the number that is odd: 18 or 19, add the number of minutes in a quarter of an hour, subtract the number equal to 4 + 4. What is 100 more? Subtract the number of pennies equal to a nickel. What is your number?) Predict and then create a list of possible student responses for the number strings.Identify a designated location in your classroom to hold your number strings that helps you maintain close proximity with your students (e.g., rug, small-group circle, etc.).Display the pre-planned number strings, and give students an opportunity to solve it mentally. Let students know they will be expected to explain how they arrived at their solution and what strategies they used. Model the response signal students should use when they have arrived at a solution and can explain their thinking (e.g., hold two fingers in the air). Remember, students do not use paper and pencil to solve.Provide 1 to 2 minutes of wait time to ensure the majority of students have worked through?the number strings and are able to explain how they arrived at their solution. For students who finish early, consider having them think of a different strategy to solve the problem.Have students turn to a partner and talk about how they arrived at their solution.When time is up, engage the students in a whole-group share-out about their thinking. Select a few students to share their thinking, remembering that you may need to support students as they attempt to communicate their thinking verbally. ?Record student responses exactly how they are explained.To close out the Number Strings, discuss a few of the students’ recorded ideas, highlighting any possible misconceptions and connections.Recommended MaterialsChart Paper/Chalk Board/White Board/Overhead ProjectorMarkersTen Frame Hundreds Chart Number Line Additional ResourcesNumber Talks, by Sherry ParrishInstructional Practice (IP) Rubric ConnectionsI-1 Facilitates organized, student-centered, objective driven lessons I-6 Communicates content and concepts to students Grade-Level Differentiation Early Childhood: Use dot cards (structured and random) to help students develop skills with recognizing patterns or combinations of number. Utilize ten frames to provide a structure for students to compose and decompose numbers to 10. In the early grades, Number Strings should initially focus on concrete and/or pictorial representations. Intermediate: Use multiple representations (e.g., ten frames, base-10 blocks, hundred boards, hundredths/thousandths grids, number lines, etc.) to make connections to grade-level content standards. Day 6—Interactive Math NotebookTeacher ConsiderationsInteractive math notebooks are introduced on the first day of instruction and can be used daily in conjunction with the 5E math block. It is recommended that the teacher create an interactive notebook along with students to serve as an exemplar. Students are encouraged to utilize their interactive math notebook as a learning tool throughout the math block. The steps for implementation outlined below focus on how to set up interactive math notebooks. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 15-20 minutes of class time.Rationale ExemplarAn interactive math notebook:Allows students to express their own ideas in order to process, organize, apply, and synthesize information and skills bines instructional strategies, such as note-taking, concept-mapping, foldables and other strategies based on brain research, multiple intelligences, and learning styles, in order to optimize support for student learning. NOTE: It is ok if teachers decide to switch the input and output sides as long as they are consistent with the placement from the beginning.ImplementationWhen first introducing Interactive Math Notebooks with students, let them know their notebook is a tool they will use to represent their learning and experiences this year in mathematics. Explain that the Interactive Math Notebook will be used daily. Set the expectation that, in case of an absence, students refer to the teacher’s exemplar notebook and then update their individual notebook accordingly. Ensure that all materials needed for set-up are available to students. (*See recommended materials list.)Model for students how to personalize the cover of their interactive math notebook. As you model for students, instruct them to follow along by personalizing the cover of their own notebook. Establish or provide written expectations for the use of the interactive math notebook and have the students write in, or insert, the expectations on one of the first pages in their own notebook. Supply blank pre-created table of content pages, or instruct students to create their own table of contents in the beginning pages of their notebook. With the students, number the first 30 pages of the notebook. Explain to students that they will continue numbering the pages during math instruction, as needed.Explain the input/output structure of the notebook by showing students the exemplar graphic pictured above. Consider providing students a copy of the input/output handout as a reference or post it in the room as a reminder. Let students know that they will now use the interactive math notebook for the first time during the day’s math lesson. (*Note: It is recommended that students write the math objective in their interactive math notebook)Recommended MaterialsComposition book (appropriate for grade-level)Pencil Colored pencilsHighlightersGlue sticks and/or scotch tapeDuct Tape (variety of colors recommended) or Clear Large TapeScissorsPost-it notesAdditional ResourcesHISD Video Exemplar: Interactive Math NotebookGetting Started with Math Interactive NotebooksSample Interactive Notebook PagesInteractive Math Notebook Ideas & ExamplesInstructional Practice (IP) Rubric ConnectionsI-1 Facilitates organized, student-centered, objective driven lessons I-6 Communicates content and concepts to students Grade-Level Differentiation Early Childhood: Primary composition notebooks should be used in the lower grades. The pages of these notebooks include both open, white space for drawing pictures and over-sized handwriting lines to support initial writing skills.Intermediate: In the upper grades, the interactive math notebook should be an integral part of students’ note-taking, recording, justification of ideas/reasoning, and daily problem solving. The interactive notebook is an organized structure that should be utilized for student self-reflection and display of learning, as well as for review of important concepts before assessments.Day 7—Collaborative GroupsTeacher ConsiderationsCollaborative groups provide students an opportunity to learn from each other, develop cultural awareness, practice mutual respect, and learn the skills necessary to work with a team. Collaborative groups need to be heterogeneous, with a mix of student personality traits, learning styles, and achievement levels. Collaborative groups can be used strategically during different times throughout the math block (e.g., daily math routines, engage and explore activities, workstations, etc.). Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10-15 minutes of class time. Rationale ExemplarCollaborative Groups:“Improve a range of social skills (e.g., listening, peer learning, leadership, problem solving, conflict resolution, and helping others)” (Kagan, 2009)Promote healthy relationships and result in higher levels of classroom engagement, minimizing discipline problemsAllow students to organize and express their thoughts in a less threatening context, helping them more fully engage later in whole-group discussions 116783623910035560016656600016897634149600ImplementationBefore the lesson, rearrange desks to accommodate an environment that will support group interactions (e.g., tables arranged in groups of 4), and prepare a math-specific group activity to use during step 7 below.During planning, create a handout and/or an anchor chart that displays expectations for group work. This might include individual student roles and responsibilities, as well as randomizing assignments (e.g., each student in a group is assigned a letter and as different tasks are assigned, the teacher randomly appoints responsibilities according to letter).In addition, create a reference for students to manage volume levels, and consider creating a universal silence signal (e.g., hand signal, sign, hand clap, etc.).During the mini-lesson, help students understand how to work effectively in groups according to assigned roles, manage their volume levels, and respond to your quiet signal. Practice each expectation with students and reinforce each expectation consistently. Consider recording classroom expectations on chart paper to remind students how to behave during collaborative group work.Engage students in a practice session for how to work in collaborative groups. Provide students with a prompt (e.g., “Talk about an activity you did this summer.”). Reinforce each role and what that person is assigned to do during the practice session (e.g., scribes will record key points shared by each person, the time-keeper will monitor time to ensure all to participate, etc.). Consider modeling both desirable and undesirable behaviors, asking students to determine if each behavior is appropriate.After students have engaged in the practice session, bring them back using the quiet signal. Point out students who participated effectively, and name what they did that was effective.Next, provide students with a math-specific collaborative group activity on content they are familiar with, and allow them practice each role according to assignments.Bring the students back together using the quiet signal. Closure: On chart paper, record students’ reflection on what was effective about their collaborative group work. Recommended MaterialsChart PaperMarkersManagement mat Additional ResourcesKagan Cooperative Learning, Spencer Kagan Collaborating to Develop Mathematical Ideas (Video) Instructional Practice (IP) Rubric ConnectionsI-8 Students actively participating in lesson activitiesI-9 Sets and implements discipline management proceduresI-10 Builds a positive and respectful classroom environment Grade-Level Differentiation Early Childhood: When explaining how collaborative groups will be used in the classroom, allow students time to practice each role or responsibility in isolation of each other. Between each individual practice session, reinforce behavioral expectations and the silent signal. Use kinesthetic and/or visual cues to reinforce expectations. Students should not be limited to working at desks during collaborative group work (for example, they might work collaborative at the rug or during stations). Intermediate: Give students an opportunity to move about the room and explore in groups instead of working only at their tables. Provide clear expectations for mutual respect and how you expect them to manage disagreements during collaboration. Group students heterogeneously, with a mix of ability levels, personality types, and learning styles. Day 8—Self-Monitoring SkillsTeacher ConsiderationsSelf-monitoring skills are strategies students can be taught that help them develop self-regulation during independent work time. In order for students to develop effective self-monitoring skills, teachers need to be explicit with their instruction and provide opportunities for students to learn and practice a variety of self-monitoring strategies. Teachers should consistently model the skills and behaviors they expect students to emulate during independent practice. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 15-20 minutes of class time.Rationale ExemplarSelf-Monitoring Skills:Enable students to oversee the quality and pace of their own workSupport students in modifying ineffective strategies or actions when solving math problemsHelp students evaluate the effectiveness of their selected strategy after arriving at a solution -41783142200ImplementationSelect a word problem within the students’ zone of proximal development (i.e., a question with content students already know, but that will present a moderate challenge. Some teacher scaffolding may be required for students to be successful). Either create or find two different student work samples, one with the correct solution and one with the incorrect solution. Both samples should show sufficient detail so as to allow students the opportunity to evaluate the problem solving process. List out the thinking behind both solutions, including the misconceptions behind why the incorrect solution was attained and possible strategies and self-monitoring questions that could be utilized to avoid such errors. Present students with the pre-determined word problem and ask them to solve it. As students solve, instruct them to record as much of their thinking around the steps they took to arrive at their solution. Tell students to turn over their papers so that they can’t see their own work. Provide each student or pair of students with the two pre-created work samples. Allow students time to analyze and evaluate the two different solutions and identify the correct steps and/or errors found in the samples. This can be done through a think-pair-share, allowing students time to evaluate on their own, pair with a partner to discuss, and then share with the group at large.As students analyze, prompt them by saying, “What questions might you ask this student to get information about their thinking?” “What could you ask this student to understand why they did what they did?”In whole group, ask students to share the questions they would ask and identify the steps/errors they found during their analysis. As needed, be prepared to guide students’ thinking using the list created in step 3.?As students share, create an anchor chart that lists strategies and self-monitoring questions students need to develop in order to self-monitor their work. With the anchor chart created, have students evaluate the effectiveness of their own work using the strategies and questions listed on the chart.Later, use the information from the anchor chart to create a self-monitoring document, inclusive of a checklist and explicit self-monitoring questions students can utilize while solving problems independently. Recommended MaterialsSelf-monitoring checklistMath problem-solving boardChart paperMarkersStudent work samplesAdditional ResourcesHow to Guide for Self-Monitoring ArticleIntervention Central Sample Checklist Instructional Practice (IP) Rubric ConnectionsI-4 Engages students in work that develop higher level thinking skillsI-7 Promotes high academic expectations for studentsI-8 Students actively participating in lesson activitiesI-10 Builds a positive and respectful classroom environmentGrade-Level Differentiation Early Childhood: Consider providing students with a pictorial checklist and questions or prompts presented using partially completed sentence stems. Intermediate: Consider using a problem-solving board that encourages students to check answers, analyze and explain their own thinking, and justify their conclusions and the reasonableness of their solutions. Day 9—Math Think-AloudTeacher ConsiderationsA math think-aloud is a strategy both teachers and students can utilize when solving problems. During a think-aloud, the person solving the problem verbalizes his/her thinking about the problem-solving process, making explicit the reasons behind each step followed. A think-aloud helps students develop reading strategies and problem solving skills as they learn to make sense of problems. Teachers should allow for collaborative grouping in the classroom, model the thinking needed to make sense of various problems, and encourage students to listen to the thinking and questions others ask themselves during think-alouds. Doing so enables students to learn additional strategies from others. Teachers should model mathematical thinking out loud on a regular basis to help scholars learn to communicate their processes and ideas more clearly and succinctly. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10-15 minutes of class time.Rationale ExemplarA Math Think-Aloud: Helps students visualize a situation or problemClarifies vocabulary and develops important mathematical concepts and connectionsModels strategies for solving problemsSupports students with their problem-solving abilities as they transfer from group or partner work to independent work ImplementationChoose a problem that aligns with the learning objective of the day.Plan a think-aloud script that makes explicit key moves you will execute during the problem solving process. Scribe specific guiding questions you will ask yourself, making sure to anticipate misconceptions and distractors and how to overcome them (e.g., Who/What is the problem about? What actions are occurring in the problem? What do I know? What do I not know? What picture or model can I draw to represent the problem? What can I do first to begin solving? What should I do next? )Bring the students to the location in the classroom where you will model the think aloud. Tell the students you will be solving a problem and explain that their role is to listen to the questions you ask yourself and pay attention to the process you follow as you work toward a solution to the problem. Tell the students that they are not allowed to interact with you while you are solving the problem.Read the problem aloud, asking yourself questions as you encounter misconceptions, distractors, and difficulties (as outlined in the think-aloud script you pre-planned). After solving the problem, tell the students that together they will now discuss what they observed. Explain to students that what they just experienced is called a “think aloud.” Ask the students what strategies or processes they saw you use while solving the problem. Record student responses on white board or, if time permits, create an anchor chart so students will be able to reference specific strategies or key processes they can use while solving problems independently. Allow students time to practice a think-aloud with a partner while solving a new problem. Monitor and provide support as needed to ensure students are utilizing the processes and strategies brainstormed during step 6.MaterialsChart paper or white boardWord Problem (chosen in advance)Regular or Dry Erase Marker (to scribe student responses)Additional ResourcesScholastic Think-Aloud ActivitiesInstructional Practice (IP) Rubric ConnectionsPL-3 Designs effective lesson plans, units, and assessments I-1 Facilitates organized, student-centered, objective driven lessonsI-2 Checks for student understanding and responds to student misunderstandingI-4 Engages students in work that develop higher level thinking skillsI-6 Communicates content and concepts to studentsGrade-Level Differentiation Early Childhood: Provide students with manipulatives, concrete objects, story boards, and pictures/models to help them visualize the verbalization used during a think-aloud. Teachers should also consider modeling the think-aloud in parts, allowing students time to practice each separate part of the process.Intermediate: Use grade level appropriate problems of high student interest to increase student engagement.Day 10—The Problem Solving ModelTeacher ConsiderationsDuring the Daily Math Routines portion of the math block, it is recommended teachers engage students in a problem of the day to reinforce how to utilize an effective problem solving model. Teaching students how to problem solve increases their ability to think critically, which supports them in being deliberate in the ways they approach problem solving tasks. According to the Mathematical Process Standard 1B, students are to “use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.” As such, teachers must consistently demonstrate how to do this in order for students to become efficient problem solvers. Teachers need to reinforce and encourage students to use the problem-solving model regularly during each component of the math block. Depending on the grade level, the full implementation of this mini-lesson should take approximately 15 to 20 minutes.Rationale ExemplarThe Problem Solving Model:Supports students in organizing their thinking in order to process, organize, apply, and synthesize information in word problemsIncorporates analyzing information, formulating a plan, determining a solution, justifying the solution, evaluating the problem-solving process, and the reasonableness of the solutionSupports students as they apply mathematics to the real-world and make connections between various mathematical conceptsImplementationDuring planning, select a grade-level-appropriate problem on a concept with which students are already familiar. Students need to be exposed to multistep problems that require them to use a variety of problem solving strategies.Predict and create a list of exemplar student responses for the problem you chose. This can be done by solving problems using the problem solving board you will use in your class.Explain to the students that the first step in becoming a good problem solver is learning how to analyze word problems. Create an anchor chart with the students using a list of guiding questions to help them analyze the information in the problem. Record the following guiding questions on the anchor chart:What information is needed to solve this problem? What does the number ___ represent?What do I know? / What do I not know?Who is this problem about? / What is the question asking me to find out?Explain the remaining steps to the problem-solving process, as outlined by Mathematical Process Standard 1B, adding each to the anchor chart.Model with the students how to restate the question as a statement to check for understanding. (e.g., How many marbles does Tanya have? Tanya has ____ marbles.) Allow students time to brainstorm in groups a plan or strategy they would utilize to solve the problem. Instruct groups to follow their plan utilizing problem solving strategies. Encourage students to represent the problem with symbols, words, number sentences, and pictorial models. Encourage students to justify their answers by writing how they know their answer is reasonable.After solving the problem, have student groups present their plan, selected strategies, and solution. Students need to justify their solution in words and explain how they know their solution is reasonable. *Note: If students do not elicit any of the key strategies you identified through your exemplar student responses in step 2, present these additional strategies to the class. You can tell the students that the exemplar work was completed by a student in another class or from a previous year. After groups have finished presenting their work, guide the class to evaluate (respectfully) the different problem-solving processes. Was one strategy the most efficient? Was one plan of action more effective than another?Provide closure by reviewing the anchor chart created during step 4. MaterialsAnchor Chart PaperMarkersProblem Solving BoardAdditional ResourcesProblem Solving ArticleNCTM Problem Solving Brief Randall, Charles. Problem Solving Experiences in Mathematics (1985) Addison-Wesley Publishing Company K-5 SeriesHISD Problem Solving Journal (Grades 3-5)Instructional Practice (IP) Rubric ConnectionsI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-4 Engages students in work that develop higher level thinking skillsI-7 Promotes high academic expectations for studentsI-8 Students actively participating in lesson activitiesGrade-Level Differentiation Early Childhood: Students need ample opportunity acting out and modeling problems using concrete materials. All problems used should be contextual and relevant to the lives of the students. Intermediate: Expose students to a variety of representations using concrete and pictorial representations. Avoid moving too quickly to abstract representations. Allow students time to think of problem solving strategies on their own and encourage multiple representations and ideas. Students should develop a repertoire of effective strategies, learning that there are many possible ways to solve a problem. Day 11—Problem Solving JournalTeacher ConsiderationsProblem solving journals provide a structure for students to record their math thinking and should follow the steps outlined by Mathematical Process Standard 1B (i.e., students are to “use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.”). When used consistently, problem solving journals provide teachers with a window into how students think by illuminating what misconceptions they have. In addition, problem solving journals act as a record for tracking students’ growth with problem solving skills over the course of a school year. For grades 3-5 teachers using the HISD Problem Solving Journal, it is recommended to use one question per day during the Daily Math Routines section of the math block. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize 10 to 15 minutes of class time.Rationale ExemplarProblem Solving Journals: Allow students space to record their mathematical thinking using pictures, numbers, and words Allow teachers to identify misconceptions and provide immediate written and/or oral feedbackProvide teachers insight on how student thinking evolves throughout the school yearProvide a structure to help guide students in following Mathematical Process Standard 1B-643496985001835694000ImplementationIntroduce the Problem Solving Journal to students by letting them know it will be a tool used to represent their learning and experiences this year while problem solving in mathematics. Explain to students how the journal will be used daily. (*Note: The HISD problem solving journal provides one question per day in grades 3-5, not including Extend, Review, Assess, Reteach days). Explain to students that, in case of an absence, they are still responsible for completing the problem on the day they missed. Consider creating a system for missed work, including a way for the students to verify their make-up work against an exemplar. Make sure students have a composition notebook or HISD problem solving journal, pencils, and colored pencils/markers.Establish your expectations for how students are to record their work in the problem solving journal. Consider posting these expectations on a classroom wall.Following the recommendations outlined on Day 11 of this document, allow students to solve the first problem in the problem solving journal. Facilitate for students how to complete each section of a page in their journal. This may mean using a problem solving board and helping students understand how to complete each component on the board. Show students a teacher or student exemplar and post it with the problem solving journal expectations from step 4.Explain to students your system for providing feedback on their work. Provide closure by asking students to re-state expectations for how they are to complete each section of the problem solving board included in their problem solving journals. Remind students of your expectations for how they will begin work in their journals beginning tomorrow. MaterialsComposition book (appropriate for grade-level) or HISD problem-solving journal (available grades 3-5)Pencil Colored pencilsHighlightersAdditional ResourcesPinterest_Math Problem Solving Journals Graphic Organizer Problem Solving Templates HISD Problem Solving Journal (Grades 3-5)Instructional Practice (IP) Rubric ConnectionsI-4 Engages students in work that develop higher level thinking skillsI-7 Promotes high academic expectations for studentsI-8 Students actively participating in lesson activitiesGrade-Level Differentiation Early Childhood: Use lined paper or primary composition notebooks. Problems can be written, but problem solving should be acted out, described verbally, modeled concretely, and represented pictorially. At the beginning of the year, teachers can scribe student responses and over the course of the year, students can take more ownership is recording their own thinking. Intermediate: Use either the HISD problem solving journal or a composition notebook. Ensure manipulatives are available for students to access as needed. Vary the way in which the problem of the day is enacted, including opportunities for partner and group work. Day 12—Math RubricTeacher ConsiderationsA math rubric is a tool used to guide the evaluation of rich, open-ended problems. Rubrics help teachers focus their feedback on specific elements of the problem solving process, such as on evaluating whether or not students demonstrated an understanding of the concept and whether or not their work met the expectation outlined by the task. Since the questions used in conjunction with a math rubric are typically rich in content and open-ended, fewer items are assessed with the rubric and they are usually of a much higher quality than multiple-choice or drill & practice questions. This means that with just one quality problem-solving question, teachers can learn to provide helpful feedback to students without having to create and administer an excess of additional items. Depending on the grade level, the full implementation of this mini-lesson should take approximately 15 to 20 minutes.Rationale MaterialsA math rubric: Provides teachers a way to efficiently, effectively, and more objectively give feedback to students on open-ended workAllows students to know ahead of time the expectations of a given task and how to perform to meet an acceptable standardSupports the use of the Mathematical Process Standards, including the expectations for effective communicationCommunicates to students what things they can improve upon in order to more fully meet the expectations of the taskCan include opportunities for students to revise their work when they do not fully meet the standard of expectation on their first attempt at solving a problemHISD Elementary Mathematics Open-Ended Question Scoring RubricTwo, grade-level-specific problem solving questionsImplementationPrior to the mini-lesson, access the HISD Elementary Mathematics Open-Ended Question Scoring Rubric available at the front of the HISD problem solving journals. Select two open-ended problems students have learned the content for and should be successful in solving. Solve one of the selected questions four different times, at each of the four different levels indicated by the rubric, thus creating an example 4, 3, 2, and 1 response. Make enough copies of the question samples for each group or pair of students to receive a complete set of responses. Make enough copies of the scoring rubric and the second open-ended problem for each student to have a copy.Engage students by presenting them with the problem. Explain each of the levels on the rubric (4, 3, 2, and 1) in relation to the problem, but without being overly specific. As needed, adjust the wording on the rubric to a level appropriate for student understanding. Provide student groups (or pairs) with the four different examples of worked-out solutions to the problem. Encourage the students to work together to analyze each of the solutions in comparison to the rubric. Ask students to identify which work sample they believe best matches each of the four levels on the rubric. Debrief students’ thinking in whole group, highlighting which examples, respectively, matched each of the four different levels on the rubric and why. Provide student groups (or pairs) with the second open-ended problem and explain that, working together, they will now create sample responses to the question at each of the four levels indicated on the rubric. *Note: This step may be modified according to grade-level by referencing the differentiation section at the bottom of this page. After student groups finish creating samples of the solution at each level, allow them to trade their four solution examples with another group. Each group reviews the sample solutions received and works to classify each response according to level (4, 3, 2, or 1). Groups discuss classifications and make modifications to work samples as needed after receiving feedback. Groups repeat with other groups as time permits. To close, explain to students when you will be using a rubric to evaluate their thinking on future tasks (e.g., twice a week using the HISD Problem Solving Journal questions), and post the rubric and example work on a wall in the room for future reference. Additional ResourcesStutzman, R. Y., & Race, K. H. (2004). EMRF: Everday rubric grading. The Mathematics Teacher, 97 (1), pp. 34-39.Instructional Practice (IP) Rubric ConnectionsI-2 Checks for student understanding and responds to student misunderstandingI-4 Engages students in work that develop higher level thinking skillsI-6 Communicates content and concepts to studentsI-7 Promotes high academic expectations for studentsGrade-Level Differentiation Early Childhood: Modify the rubric using pictures and age-appropriate language to assist students in understanding the expectation of each level. For step 6 above, scaffold for the students by solving the second problem with them. Talk out loud about the thinking needed at each of the rubric levels, beginning with a level 1 example and moving to a level 4 example. Intermediate: Provide students with a copy of the rubric (modify language, if needed), and ask them to evaluate their own work after completing a given problem. Allow students to hold conferences with each other before submitting their work for evaluation. During the conferences, students use the rubric to guide their conversation around elements of the problem solving model that may be missing. Day 13—Data-Driven TEKS Warm-UpTeacher ConsiderationsData-Driven TEKS Warm-Ups are teacher-created “Do Now” activities designed to review and/or pre-assess specific TEKS at the beginning of the lesson. It is recommended that Data-Driven TEKS Warm-Ups be approximately five questions in length and consist of a mix of question formats (e.g., multiple choice, short answer, griddable, open-ended, etc.). Since it is recommended that this warm-up be timed, teachers should organize questions by TEKS according to rigor-level, beginning with easier questions and ending with more rigorous questions. Approximately three questions should be over TEKS that were previously taught but not mastered. Before including any such spiral TEKS in a Data-Driven TEKS Warm-Up, the teacher should have already re-taught the specific components of the standard students have yet to master. The remaining questions should be over previously-mastered TEKS to support spiral review, and/or should preview (pre-assess) upcoming TEKS. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10 to 15 minutes of class time.Rationale ExemplarData-Driven TEKS Warm-Ups:Provide teachers with immediate data to assess whether or not the adjustments are needed in their instructionProvide teachers a tool for assessing re-taught content and pre-assessing upcoming contentAllow teachers to plan for preconceptions to better inform their Tier I instruction-409431177100ImplementationDuring planning, review data from formative assessments and determine re-teaching plan. After re-teaching a particular concept, create approximately 3 questions with varied levels of rigor to include in the Data-Driven TEKS Warm-Up. Next, create approximately 2 questions from TEKS you will spiral (from previously taught curriculum) and/or will be teaching soon. Solve each question and create exemplar answers/responses. Identify and list possible misconceptions students may have when solving the warm up. Use this information to design probing questions to ask students after they’ve completed the warm up. Develop teacher and student tracking sheets to monitor student performance on the TEKS included in the warm-up. Follow this link for example “Measuring my Growth by TEKS” tracking sheet. Determine how students will keep their tracking sheets organized for use over time. To begin the mini-lesson, pass out the Data-Driven TEKS Warm-Up. Explain to students they will have 5-8 minutes to work independently and that you will be selecting one or two questions for review after time is up. As students complete the warm-up, monitor and make note of various solution strategies, misconceptions, and/or preconceptions in student work. When time is up, stop the students and bring them back together. Provide students with correct answers.Based on your notes from step 7, select one or two questions for students to review with partners or with their table groups.As you monitor group work, use the probing questions developed in step 4 to facilitate student conversation around identified misconceptions. Distribute tracking sheets and explain to students how they will utilize the tracker to monitor their own progress over time. Walk students through completing the form and explain how and where they will store the tracking sheet. Closure: Restate expectations for Data-Driven TEKS Warm-Ups and ask students to share what they learned by completing the data tracker. MaterialsStudent tracking sheetsFormative assessment dataWarm-up sheet for each studentAdditional ResourcesMeasuring my Growth by TEKSDriven by Data: A Practical Guide to Improve Instruction, Paul Bambrick-SantoyoLeverage Leadership: A Practical Guide to building Exceptional Schools, by Paul Bambrick-SantoyoInstructional Practice (IP) Rubric ConnectionsPL-2 Collects, tracks, and uses student data to drive instructionI-1 Facilitates organized, student-centered, objective driven lessons I-2 Checks for student understanding and responds to student misunderstandingI-6 Communicates content and concepts to studentsGrade-Level Differentiation Early Childhood: Consider administering formative assessments and/or warm-ups in small groups. Provide students materials (e.g., snap cubes, counters, ten frames, etc.) and allow them to use materials while solving questions posed aloud. In lieu of student trackers, teachers can utilize student checklists and record notes during small group sessions. Intermediate: Expand student trackers to include data on other assessments utilized in class. Consider allowing students the opportunity to create TEKS-specific questions that can be included on future warm-ups for previously mastered content. Day 14—Multiple RepresentationsTeacher ConsiderationsMathematical concepts can be represented in a number of different ways, and Mathematical Process Standard 1D indicates students are to “communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language.” This means teachers should consistently provide opportunities for students to represent their thinking with concrete objects, pictorial models, symbolic abstractions, and verbal/written explanations. Multiple representations allow students to make connections and establish a repertoire of strategies for organizing, recording, and communicating their mathematical ideas (See Mathematical Process Standard 1E). It is well established that students who experience learning in a variety of different ways form stronger neural connections as they acquire new knowledge. By encouraging and supporting students in using multiple representations, teachers provide them an opportunity to “display, explain, and justify their mathematical thinking and arguments using precise mathematical language in written or oral communication” (Mathematical Process Standard 1G). The full implementation of this mini-lesson should take approximately 10-15 minutes of class time.Rationale ExemplarMultiple Representations: Increase the depth of students’ understanding Expose students to various ways of thinking about a particular concept Allow multiple access points through which students can begin to understand and engage in a particular concept Increase students’ engagement and motivation to learn new conceptsProvide a means to differentiate instruction for students-504213810001525824383800ImplementationPrior to the mini-lesson, select a grade-level appropriate number or number sentence (e.g., 14 or 24 + 15 = 39) or word problem. Select a graphic organizer you will use to help students represent their number or number sentence in multiple ways (See, for example, HISD Number Concept Maps). Determine beforehand which manipulatives or forms of representation you will highlight with your students. For example, you might decide to use hundreds charts, ten frames, counters, base-10 blocks, colored rods, open number lines, bar models, part-part whole diagrams, pattern blocks, geometric shapes/solids, money, and/or graph paper to represent the number, number sentence, or word problem. Before the mini-lesson, prepare student work areas with the materials selected during step 2. Present the number, number sentence, or word problem to the students and ask, for example, “Similar to how we think about numbers during Number of the Day, I want you to represent 24 + 15 = 39 in as many different ways as you can think of?” Allow students time to work on representing the number, number sentence, or word problem. If using a graphic organizer, present this to the students at this point. Remind the students of the materials at their work areas they have access to, and encourage them to consider multiple ways to represent their thinking.Create an anchor chart by listing the multiple representations students were able to generate. If students were unable to generate the pre-identified, critical representations from step 2, provide examples for how these representations can also be used. Explain each representation and the thinking behind utilizing them. Provide closure by asking students to share what new representations they will consider using in the future and why, as well as similarities and differences between the representations highlighted on the anchor chart.Post the anchor in the classroom for students to reference during classroom instruction.MaterialsCountersLaminated cut out large circlesColor pencils\markers\ crayonsFrayer ModelAdditional ResourcesPinterest: Multiple Representations in MathIntegrating Technology Representations Developing Primary Visual Representations StudyHISD Number Concept MapsInstructional Practice (IP) Rubric ConnectionsI-1 Facilitates organized, student-centered, objective driven lessonsI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-6 Communicates content and concepts to studentsI-8 Students actively participating in lesson activitiesGrade-Level Differentiation Early Childhood: For younger students, multiple ways of explaining and describing one’s thinking about a number or problem verbally can constitute use of multiple representations. It is essential students are provided with concrete objects and/or manipulatives to represent their thinking before being expected to represent ideas pictorially or abstractly. Intermediate: Older students need to see and understand multiple representations and ways of thinking in all of the work they complete in a mathematics classroom. In addition, students should be facile with justifying, explaining, and mathematical arguing their ideas using mathematical language and concrete, pictorial, and symbolic representations. Day 15—Justification and ReasonablenessTeacher ConsiderationsJustification is the process by which students prove their thinking around a given mathematical problem using precise mathematical language. In doing so, students are required to display, explain, and argue mathematically their ideas in both written and verbal communication. In order for students to fully justify their thinking, they must consider whether or not their solution is reasonable. Reasonableness is a multi-faceted skill, one in which students must first consider the context of the problem and then determine if their solution is realistic within the given context. Reasonableness goes hand in hand with estimation, number sense, and the application of mathematics to real-world problems. In general, it’s often easier to consider an approximate solution to a problem and then compare one’s final solution to the estimation. Learning to justify and defend their solutions based on reasonableness supports students as they develop their confidence in solving problems and explaining their thinking. Students should be given opportunities to struggle through problems, explain how they used specific strategies to arrive at their solution, and defend their solution with precise mathematical language. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10 to 15 minutes of class time.Rationale ExemplarUsing Justification and Reasonableness in the classroom:Allows students to display, explain, and prove their thinkingExposes students to different ways of solving a problemTeaches students to consider whether their solution is realistic-476251603600ImplementationDuring planning, choose a word problem students have solved successfully. Create a list of probing questions focused on justification and reasonableness. Example probing questions for justification might include: “What steps would someone need to follow to get the correct solution?” “How would they know those steps were correct?” “How can you use words, pictures, and numbers to represent and prove your thinking?” “What’s another way to prove the answer is correct?” Example probing questions for reasonableness might include: “In considering this story, how do you know your solution makes sense?” “Is your answer realistic?” “What connections can you make to this problem that help you determine if the solution is reasonable?”Create exemplar responses for each probing question, considering how you would justify your thinking and the reasonableness of your solution. Consider referencing the HISD Elementary Mathematics Open-Ended Question Scoring Rubric to guide your thinking. To begin the mini-lesson, provide each student group (or pairs) with the word problem and solution—but do not provide them with any work showing how the solution was derived. For instance, give students the word problem and tell them, “The answer is 12.” Tell the students they will be justifying the given solution to the problem, as well as defending its reasonableness. Provide students with the following sentence stems: I know the answer _____ is correct because________________________. I know the answer _____ is reasonable because ____________________. Allow students to work together to justify the solution and explain why the answer is reasonable. Prompt students by asking previously-designed probing questions (created in step 1). Encourage students to justify their thinking in as many ways as possible. Remind students to generate reasons around why the solution is reasonable. In whole group, ask students to share their completed sentence stems. As students share, create an anchor chart (or two) to display their thinking for both justification and reasonableness. Consider adding additional ideas to the anchor chart if they are not elicited by student responses. Provide closure by stating your expectations for students’ work around justification and reasonableness. MaterialsChart PaperPreviously-solved problemMarkers/Pens/PencilsAdditional ResourcesMathSteps—Justifying Answers, What is it? Maximizing Student Mathematical Learning in the Early YearsInstructional Practice (IP) Rubric ConnectionsI-2 Checks for student understanding and responds to student misunderstandingI-4 Engages students in work that develop higher level thinking skillsGrade-Level Differentiation Early Childhood: Encourage students to act out and describe with words their thinking when solving problems. To develop skills in reasonableness, model for students how to estimate, solve, and then check their estimation.Intermediate: Students should be expected to justify their thinking using two or more different strategies. Students need ample opportunity arguing mathematically to defend/refute their own and others’ thinking. Students should be expected to use precise mathematical language in both written and oral forms of communication daily. Use this link to visit an article on Maximizing Student Mathematical Learning in the Early YearsDay 16—Making ConnectionsTeacher ConsiderationsA true understanding of mathematics means that one is able to make connections between mathematical concepts and everyday life. According to Mathematical Process Standard 1A, students are expected to “apply mathematics to problems arising in everyday life, society, and the workplace.” This indicates students must make connections between the “informal” mathematics they experience outside of school and the more “formal” mathematics they experience in the classroom. Teachers should consistently embed real-world mathematical examples into their instruction. As such, it is critical teachers consider the question, “When will we use this in the real world?” during their planning sessions as well as during the delivery of instruction. Building connections between and among mathematical concepts, as well as connecting learning to everyday experiences, should begin in the early grades and extend throughout the years. This means teachers should teach through the lens of real-world problem solving every day, even when the focus is on building numerical fluency and/or skills. When students can connect mathematical ideas, they develop a deeper, longer-lasting, and more conceptual understanding of mathematics. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10 to 15 minutes of class time. Rationale ExemplarMaking Connections:Fosters long-lasting, conceptual understanding of mathematical ideasSupports students as they apply mathematical to problems arising in everyday life, society, and the workplaceSupports students in their ability to transfer mathematical skills to different contexts and scenarios -606292095500ImplementationDuring planning, select a grade-level appropriate word problem and post it in a location visible to all. Create sentence stems with the information found in step 10. Create an anchor chart with the title Making Connections. Create 3 columns labeled as: Math to Self, Math to Math and Math to World. Create a graphic organizer that includes the word problem at the top, a miniature 3-column Making Connections table titled the same as the anchor chart, and blank space for students to work out the problem. Give each student the graphic organizer and, together, read the word problem.Explain to the students that today they will be discussing different ways in which they can make connections to math word problems.Point to the Math-to-Self section of the anchor chart and ask, “What does it mean to connect math to one’s self?” Collect student responses and record their ideas in the Math-to-Self section of the anchor chart. Refer back to the word problem and ask, “Does anyone relate to this math problem?” Collect student responses and record their ideas in the Math-to-Self section of the anchor chart. Prompt students to complete the corresponding column in the Math Connections table on their graphic organizer.Next, point to the Math-to-Math section and ask, “Where in math have we seen this type of problem before? Does this type of problem connect to work we’ve done before? What strategies have we used in the past when solving similar problems?” Collect student responses and record their ideas in the Math-to-Math section of the anchor chart. Prompt students to complete the corresponding column in the Math Connections table on their graphic organizer.Continue to the Math-to-World section of the anchor chart and ask, “How does this problem relate to the real world? Where in the real-world will we need to solve a problem similar to this? Has anyone ever used the math needed to solve this problem outside of the classroom?” Collect and record student responses, and prompt students to complete the final column in their graphic organizer.Prompt students to now solve the problem on their own. When finished review solution with students.Provide closure by posting pre-created sentence stems on the anchor chart. Tell students these sentence stems can help frame their thinking about connections in mathematics. Math-to-Self: I personally connect to this problem because _______. This problem makes me think of a time when I ____________. Math-to-Math: I have worked on math problems like this before when I __________. I can solve this problem by using the same strategies I learned when I _____________. Math-to-World: This relates to the real world because _______. I will use this type of thinking in the real world when I _____________.MaterialsMath Word ProblemChart PaperMarkersGraphic OrganizerAdditional ResourcesConnections Standard, principles and Standards for School Mathematics (Grades 3-5)Connections Standard, Principles and Standards for School Mathematics (Grades PreK-2) Instructional Practice (IP) Rubric ConnectionsPL-3 Designs effective lesson plans, units, and assessmentsI-3 Facilitates organized, student-centered, objective-driven lessonsI-6 Communicates content and concepts to students I-8 Students actively participating in lesson activitiesGrade-Level Differentiation Early Childhood: Use concrete and pictorial models when solving the problem and allow students to act out their thinking. Intermediate: Allow students to generate problems from their own life and ask them to bring in examples of how they are using math outside of the classroom or in other content areas. Day 17—Accountable TalkTeacher ConsiderationsAccountable Talk is a structure by which teachers provide students with sentence stems or question prompts that allow them to effectively engage in conversations and debate with others in the classroom. The Accountable Talk structure provides students with appropriate ways in which to agree, disagree, clarify, confirm, extend, and/or express confusion to someone else in the math classroom. As with all effective math practices, the teacher needs to model each sentence stem or question prompt with students, providing reasons and examples for their use, and allowing students time to practice both asking and responding to others in a safe environment. The Accountable Talk structure provides students with a way to hold one another accountable for the learning of math content, as well as protocols for how to effectively, and respectfully, communicate their thinking about math ideas. This practice can be embedded throughout your math block, including during partner- and group-work times. Depending on the grade level, the full implementation of this mini-lesson will require teacher to utilize approximately 15-20 minutes of class time. Rationale ExemplarThe Accountable Talk Structure:Helps students develop an understanding of mathematical ideas through expression and communicationAllows teachers to better understand students’ thinking, specifically what they know and don’t knowBrings misconceptions forward as students explain their thinkingHelps students effectively communicate mathematical ideas and reasoningProvides a channel for students to explain, justify, and defend/refute mathematical arguments using effective verbal communication skills11703051698400-52772124050ImplementationDuring planning, find and solve an on-grade-level word problem using two or three different strategies, with at least one strategy resulting in an incorrect solution. Label each of the different solution strategies with a student pseudonym (e.g., Strategy 1 was solved by “Betsy”). Display the different solution strategies so as to be visible to all students. Create ahead of time an anchor chart with sentence stems and question prompts. Click this link to view Sample Accountable Talk Anchor Chart. Read the word problem to students and tell them that two (or three) students from another school already solved the problem. Ask the students to listen closely and review each student’s written work as you read the different solutions aloud (e.g., “Betsy solved the problem by…”). Tell the students that today they will be learning about Accountable Talk. Explain to students that Accountable Talk is used to help them agree, disagree, clarify, confirm, extend, and/or express confusion to someone else during math class. Present the pre-created anchor chart to students, and explain each different title on the chart. Engage the students in a role play activity where they utilize the sentence stems or question prompts to express their thinking to the teacher (who will act like he/she is one of the students who solved the problem). For example, a student might practice “agreeing” with Betsy and would follow the prompts on the anchor chart to express his/her ideas to the “Betsy” (i.e., the teacher). Move students through each of the different sections of the anchor chart, asking different students to role play the various forms of expression (e.g., agreement, disagreement, confusion, clarification, extension, etc.) After engaging in the role play, explain that often during math class you will be asking students questions to hold them and others accountable for their thinking. Share some example question prompts with students. Such as, “Does anyone have evidence they can use to support _____’s idea/solution?”, “Does anyone have another point of view?”, “Who agrees/disagrees? Why?”, and/or “Can you explain your thinking?” During closure, explain where you will post the Accountable Talk anchor chart and tell students your expectations aligned to the Instructional Practice (IP) Rubric I-10. MaterialsChart paper/markers Sentence Stems/Question PromptsAdditional ResourcesClassroom Discussions: Using Math Talk to Help Students Learn by Chapin, O’Connor, & AndersonSample Accountable Talk Anchor ChartAccountable Talk In the Elementary Math ClassroomMath Talk on PinterestInstructional Practice (IP) Rubric ConnectionsI-4 Engages students in worth that develops higher-level thinking skillsI-8 Students actively participating in lesson activitiesI-10 Builds a positive and respectful classroom environmentGrade-Level Differentiation Early childhood: Consider providing students with picture cards with icons representing different forms of expression, and allow them to hold up the cards to initiate their thinking. Students should be allowed to act out and/or use manipulatives to express their ideas. Intermediate: Provide opportunities for students to debate and defend arguments using precise mathematical language. Day 18—Evaluating the Problem-Solving ProcessTeacher ConsiderationsWhen students evaluate the process by which a given problem was solved, they must engage in reflection and metacognition around the steps taken to arrive at a solution. As part of using a problem-solving model, students are expected to evaluate the process by which a given problem was solved. Students must learn to ask themselves questions regarding the efficiency, effectiveness, and practicality of the process used when arriving at a solution. For this to take place, students must develop a critical eye in evaluating their own work and asking themselves the question, “Did I solve this problem in the most efficient way possible?” Teachers should consistently ask students to reflect on how they arrived at their solution and then compare the process they followed to others in the classroom. Teachers should model reflective metacognition during think-alouds, teacher-led lessons, and problem-solving and make their thinking about the effectiveness of the process used to arrive at their solution explicit to students. Depending on the grade level, the full implementation of this mini-lesson will require teacher to utilize approximately 15-20 minutes of class time.Rationale MaterialsEvaluating the Problem-Solving Process: Allows students the opportunity to reflect on the efficiency of the process followed when solving a problem Provides students an opportunity to learn varied solution strategies Builds students capacity to determine the most effective, efficient, and practical way to solve a problem Previously-solved problemMarkers/Pens/PencilsImplementationDuring planning, find and solve an on-grade-level word problem using four or five different strategies, with all strategies resulting in the correct solution. Label each of the different solution strategies with a letter (e.g., A, B, C, D, E) and make enough copies for each group (or pair) to receive a complete set.Create a list of probing questions focused on helping students learn how to evaluate the thinking and processes used to arrive at a solution. Example probing questions: “What steps were followed to get this solution?” “How many steps did it take to arrive at the solution?” “Was there a faster way to arrive at the same solution?” “Which strategy was the easiest to follow when solving the problem? The hardest?” “What was the most difficult part of the process?” “How can you make the difficult parts in the process easier?” “Would the process used still be easy if the numbers were larger?” To begin the mini-lesson, provide each student group (or pairs) with the word problem and solutions. Read the problem together with the students. Tell the students they will be analyzing different strategies used to solve the problem and then determining which strategy was the “best.” Instruct students to rank-order the solution strategies from “most efficient” to “least efficient” and to prepare an explanation to defend their rankings. Prompt students by asking previously-designed probing questions (created in step 2). After students have finished ranking the solution strategies, have them display the strategies in order on their table. Instruct student groups to rotate around the room viewing the other groups’ work. Tell the students they may not change the other groups’ rankings. Allow students to return to their own group and discuss any changes they may want to make to their own group’s ranking. In whole-group, ask students to share their rankings and reasons for the orders they selected. As a class, create a list of reasons why certain strategies were more efficient than others. During closure, discuss the process behind evaluating one’s own thinking when arriving at a given solution. Explain that although students may arrive at the right answer, there might have been a faster, easier way to get the answer. Tell the students that listening to others explain their thinking, provides them an opportunity to decide if their peer’s solution strategy was more efficient than their own. Additional ResourcesEvaluating Problem Solving in Mathematics, ASCD article by Szetela & NicolInstructional Practice (IP) Rubric ConnectionsI-2 Checks for student understanding and responds to student misunderstandingI-4 Engages students in work that develop higher level thinking skillsI-6 Communicates content and concepts to studentsI-7 Promotes high academic expectations for studentsGrade-Level Differentiation Early Childhood: Consider posing a question for the students and acting out 3 different ways of solving the problem and arriving at the correct solution. Ask students to use words to explain which solution was the “best” and why. Intermediate: Consider instructing students to solve problems with 2 different strategies and then evaluating which solution strategy was the most efficient and why. Day 19—Teach BacksTeacher ConsiderationsA Teach Back is when a student is given the opportunity to act as the teacher in explaining a concept to the class or a small group. Teach Backs provide students the opportunity to verbalize their thinking, communicate using academic language, and explain mathematical concepts at mastery level. Teachers can more fully gauge the understanding level of their students as they listen to them teach a particular concept. Teach Backs allow the teacher to hear student misconceptions and provide intervention through questioning. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10 to 15 minutes of class time. Rationale ExemplarTeach Backs:Allow the teacher to evaluate student understanding of a given conceptSupport students in more efficiently communicating their mathematical ideasHelp students retain information about a given concept ImplementationDetermine the concept or skill in your lesson you want students to Teach Back. The selected concept/skill should be something students have learned well, to the point of mastery or near mastery. Tell students you will be teaching them a very specific concept or skill. Ask students to pay close attention and record important details they think are necessary in order to teach back this same skill or concept to a partner. Tell students they will be teaching back what they see you teach to a partner.Spend approximately 1 to 3 minutes teaching a specific skill or concept. Remind students to pay attention and record notes as you teach.Once finished, ask the students to turn to each other to engage in the Teach Back. One student acts as the teacher, while the other records notes as the student. Partner pairs then switch roles and repeat. Tell students to record 2 effective things their partner did while teaching and 1 recommendation for improvement. While students practice, monitor and record notes of effective practices or strategies you see them utilize. As students finish, ask them to share with their partner the 2 effective things done while teaching, as well as the 1 recommendation for improvement. Bring students together for whole group. Ask students to share out some of the effective things their partners did during their teach backs. Ask students to share ways in which the teaching could have been improved. Record both effective practices and suggestions for improvement on an anchor chart. Highlight any additional effective practices and strategies you noted during step 6 that were not elicited by the students.Closure: Explain to students that Teach Backs are a great way for them to demonstrate mastery of a given concept. Tell the students that as they practice doing Teach Backs in class, they should always ask for feedback for improvement. MaterialsChart paperMarkers Sticky notes PencilsScratch paperAdditional ResourcesHISD PSD Teach BackLemov, D. (2010). Teach like a champion: 49 techniques that put students on the path to college. San Francisco, CA: Jossey-Bass.Marzano, R. J., Pickering, D. J., & Heflebower, T. (2011). The highly engaged classroom. Bloomington, IN: Marzano Research Laboratory.Himmele, P., & Himmele, W. (2011). Total participation techniques: Making every student an active learner. Alexandria, VA: ASCD.Instructional Practice (IP) Rubric ConnectionsI-2 Checks for student understanding and responds to student misunderstandingI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-5 Maximizes Instructional timeI-6 Communicates content and concepts to studentsGrade-Level Differentiation Early Childhood: Consider isolating skills to 1 or 2 steps at maximum. Provide students with sentence stems to guide their teaching around a particular concept. Ensure concrete manipulatives are available to assist students as they explain concepts. Intermediate: Consider utilizing a “jig-saw”-type Teach Back activity, where groups of students design a mini-lesson to teach about a given concept as experts. Groups then split up and form new groups, where each member is an expert on a different, but related, concept/skill. Each group member teaches the others, who record notes and then provide feedback. Day 20—Math StationsTeacher ConsiderationsMath Stations are designed to spiral previously-taught content, and students engage in stations either independently, with partners, or in small groups. Teachers should design station activities based on critical-need-areas after analyzing data. Teachers need to design a way to hold students accountable for the work accomplished during math stations and should use student work to both inform small-group instruction and modify future stations according to students’ needs. The steps to effectively implement a new workstation are: 1) teach the station expectations explicitly to the whole class, 2) model what it does and doesn’t look like to successfully work through the station activities, and 3) provide students an opportunity to practice the station before including it as part of the math block. Teachers should create purposeful recording sheets for each station that hold students accountable for their math work. Teachers can consider creating an “I-Can” list to help students remember what to do to complete the station. It is recommended that stations be introduced one at a time. Teachers should label stations around the room and designate storage spaces so students know where to go to retrieve station materials. Depending on the grade level, the full implementation of this mini-lesson will require teachers to utilize approximately 10 to 15 minutes of class time. Rationale ExemplarMath Stations:Provide an opportunity for students to practice and apply skills and strategies taught within the classroomEngage students in purposeful activities, providing them additional opportunities to practice specific skills or master conceptsAllow teachers the opportunity to work in flexible groups to meet the individual needs of students-599860164368512255500ImplementationWhen planning for this mini-lesson, choose a standard that has already been taught. Prepare a math station activity that aligns to the standard and can be used during workstation time. Station activities should require higher-level thinking and embed the Mathematical Process Standards. Create a list of expectations for student behavior during work stations.To begin the mini-lesson, bring students to a pre-determined meeting place and tell them they will be learning about a math station activity. Review your expectations for student behavior created in step 1 and introduce math station activity. Consider posting a chart that lists student expectations. Depending on the activity, explain to students who they will be working on during the math workstation (e.g., individual, partner, small group). Tell students where station materials are stored and how they are to retrieve and return materials. Model the activity in whole group and explain how students are to record their learning on the recording sheet. Provide time for students to practice. Ensure students are meeting the behavioral expectations and completing the activity correctly. Remind students to complete the recording sheet. After practice time is over, bring students back to whole group and create an “I-Can” list to review the steps required to complete the workstation successfully. Closure: Ask students to share what it both looks like and sounds like to successfully complete the session activity. Ask students if they have any questions about the station. Tell students when, where, and for how long they will complete the station activity. Post I-Can chart at station location and ensure materials and recording sheets are ready for student use. MaterialsChart PaperMarkersManipulativesStation materialsAdditional ResourcesIntroducing Math Stations IdeasHISD Planning Guide (reference)Math Work Stations, Debbie DillerDeveloping Number Concepts (Books 1, 2, & 3), Kathy RichardsonInstructional Practice (IP) Rubric ConnectionsI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-9 Sets and implements discipline management proceduresI-10 Builds a positive and respectful classroom environmentGrade-Level Differentiation Early Childhood: Stations should be an integral part of the early childhood classroom. Students should engage with concrete objects and represent their thinking with pictures, numbers, and words. Ensure students have had multiple opportunities to successfully complete a station before replacing with a new one. Intermediate: Consider using TEKS-specific tracking sheets to monitor student success for critical concepts and skills. Consider allowing students to collaborate with a partner when evaluating their recording sheets and make corrections as needed. Day 21—Manipulatives Management & OrganizationTeacher ConsiderationsEffectively organizing manipulatives and creating a systematic approach to storing and retrieving materials will allow for smooth transitions in the classroom during workstation activities. Students should be taught and have time to practice both retrieving, dispersing, collecting, and returning manipulatives and other materials to the appropriate location(s) before engaging in activities at workstations. The ultimate goal of a manipulative management and organization system is to establish a classroom where students know how to access materials for use during math work time, can access them without disruption to the pacing of the lesson, can avoid interrupting the learning of others, and can correctly return them so they are ready for use by others in the future. Depending on the grade level, the full implementation of this mini-lesson will require teachers to spend approximately 10-15 minutes of class time. Rationale ExemplarManipulative Management & Organization:Enables both students and teachers to have quick access to the correct materials with minimum disruption to learningProvides a consistent structure to support teachers with maximizing instructional timeAllows for smooth transitions during workstation time399031397000 ImplementationIdentify the location(s) in the classroom where materials will be stored. The chosen location(s) should be easily accessible by both teacher and students. Select a new workstation to compliment the workstation presented yesterday, or simply repeat workstation work from yesterday.Create a voice-level tracking chart (e.g., 0 = no voice, 1 = whisper voice, 2 = partner voice, 3 = group voice, 4 = presentation voice, 5 = outside voice). Set the expectation for classroom voice level while materials are being distributed. A voice level 0, or no talking, is recommended to ensure students are able to hear all directions.To begin mini-lesson, introduce the day’s math activity determined in step 2 above. (See Day 20 for step-by-step directions). Introduce the voice-level tracking chart you created in step 3. Model and have students practice each voice-level. Tell students they need to be at level 0 (“no voice”) when materials are being retrieved and distributed.Assign a materials manager for each group. Tell students the materials manager’s responsibility includes retrieving and distributing manipulatives for their assigned station activity and then returning them to their correct location.Model for students how the materials manager will gather and distribute manipulatives. As needed, remind students of the expectations for movement during transition time (e.g., group members sitting or standing before rotation; materials manager walking to and from storage location, etc.).Have the materials managers practice retrieving manipulatives from the designated holding area. Then, have the materials manager practice distributing the manipulatives to the group.Establish how you will get students’ attention while they are working (e.g., hand in the air as a silencing signal). Allow students 30 to 60 seconds to work with the manipulatives, and then practice getting their attention. Model for students how the collection of manipulatives will look. Remind all students they are responsible for gathering materials at their station. Practice collecting and returning manipulatives to the designated holding area. (*Note: Remind students of voice level and movement expectations.) Remind students to move through the transition as quickly as possible while still managing the materials in a responsible way.Closure: Reinforce expectations regarding manipulatives management and organization as students engage in the workstation(s).MaterialsStorage containers or tubsLabels for manipulativesAdditional ResourcesOrganization IdeasManipulative labelsPinterest manipulative labels Pinterest manipulative organizationInstructional Practice (IP) Rubric ConnectionsI-5 Maximizes Instructional timeI-10 Builds a positive and respectful classroom environmentGrade-Level Differentiation Early Childhood: Labels for manipulative and storage containers in the early grades should include words as well as pictorial representations of the materials inside. It is recommended teachers scaffold the collection and distribution of manipulatives by first preparing and distributing the materials for the stations and then gradually releasing responsibility to students to manage the materials on their own. Intermediate: Manipulative management at this level should be student orchestrated to the greatest extent possible. Assign each group a materials manager and assistant materials manager. As needed, determine additional roles students can be assigned to help smooth the transitions between activities during workstation time. In addition, including labels with both words and pictures on storage containers can benefit English language learners, as well as those who may be unfamiliar with the manipulative in question.Day 22—Management Board & Tight TransitionsTeacher ConsiderationsA management board is posted on the classroom wall and serves as a visual reminder to students of station names and rotation sequences, as well as student grouping information. Utilizing a management board is one of the most critical elements to successfully implementing workstation routines and developing a seamless procedure for transitions. Be sure to post the chart in a location accessible to both students and teacher. Teachers should explain the purpose of the management board, how the board is read, and how the board indicates station rotations. Stations should only be placed in the management chart after content has been taught and activity has been modeled. It is highly recommended teachers use a timer when implementing tight transitions and practice all expectations with students before independent workstation time. Transition time must become routine in order for students to successfully maximize learning. Depending on the grade level, the full implementation of this mini-lesson will require teachers to spend approximately 10-15 minutes of class time.Rationale ExemplarManagement Board and Tight Transitions:Direct students as they rotate through stations Provide a consistent structure to support teachers as they implement workstationsAllow for smooth transitions, thus maximizing instructional time?-56236485100ImplementationDetermine the math station activities students will engage in as you introduced the management board and tight transitions between activities. It is recommended you utilize 2 or 3 stations to begin. Ensure the activities selected align to TEKS that have already been taught, modeled, and practiced. Create a management board that includes station names or labels, number of rotations, and student names and/or student pairs or groupings. On a chart poster, create a list of the steps you want students to follow as they transition from desks/tables to stations and as they transition from station to station during workstation time. Consider creating a checklist for the behaviors and steps students are to follow during transitions. See HISD Effective Practice: Tight Transitions To begin mini-lesson, introduce the new math station activity determined in step 1 above, if needed, utilizing the same steps from Day 20.Introduce management board to students. Tell them they have already been working in stations, but that today they will practice how to rotate through more than one station at a time.Review all components of the management board with students in small chunks, and check for understanding as you review activities, student grouping arrangements, and rotation sequences.Ask students to find their name and tell a friend what their first and second math activity will be when they go to workstations. Clarify student confusion misunderstandings. Show students the list of transition steps created in step 3 above. Review steps with students and ask them to think about what behaviors and voice-level(s) should be used during transitions between stations. Remind students of tight transition expectations (e.g., standing, sitting, walking, etc.) Consider adding additional student responses to the expectations already listed on chart. Post transition chart near management board to serve as a reminder for students. Provide students with an opportunity to practice following the directions on the management board by practicing moving from station to station before beginning any activities. Monitor students and provide guidance to support expectations. Repeat as needed. Use a timer to minimize time spent in transitions. Closure: Ask students to turn to their shoulder partner and complete the following sentence stem: “One thing I must remember while making a transition during station time is _______________________.” Highlight key ideas and tell students when they will begin station work. MaterialsManagement board (pocket chart, chart poster)Post-it notes, Strips of colored paperTimerFlash cards, labeling material Activities with recording sheetsManipulatives Additional ResourcesHISD Planning GuideHISD Effective Practice: Tight TransitionsMath Work Stations, Debbie DillerDeveloping Number Concepts (Book 1, 2, & 3), Kathy Richardson Instructional Practice (IP) Rubric ConnectionsI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesGrade-Level Differentiation Early Childhood: Teachers should use pictures and words on the management board. Students should be reminded consistently of the steps to follow for tight transitions. Intermediate: Consider assigning a student to assist in running the management chart. For assigned roles and responsibilities (e.g., materials manager, assistant materials manager, etc.), rotate students through assignments to ensure everyone has the opportunity to manage different components of station work. Day 23—Math Data FoldersTeacher ConsiderationsMath Data Folders help students take ownership of their learning by providing them with tools to track their own progress on grade-level standards. Math data folders can be used to track unit, weekly, snapshot, and benchmark assessments, as well as independent work and classroom assignments. Teachers should create a class-wide data folder of their own and support students in developing and maintaining individual math data folders as well. Students use math data folders to track individual progress on content and skills throughout the year. Data organized using data trackers can be helpful for students in developing and monitoring progress towards individual learning goals. It is highly recommended teachers schedule check-points with students and hold individual conferences to allow opportunity for celebration and reflection, as well as to determine areas for improvement and time lines for accomplishing goals. Depending on the grade-level, the full implementation of this mini-lesson will require teachers to spend approximately 10-15 minutes of class time.Rationale ExemplarMath Data Folders:Allow teachers and students to track the progress of student learning throughout the school yearProvide the students a clear picture of their progress on specific concepts and skills Can provide support for goal-setting and student conferences based on actual data 654053657600ImplementationDuring pre-planning, select a previously-scored student work product (e.g., graded formative assessment, exit ticket, or performance task).Create or find an individual student data tracker. Consider utilizing the Student Learning Reports available on the Lead4ward Resource page. Organize data trackers in individual student folders and determine a system for storing folders. Determine how you will collect and record class data. Review resources available for HYPERLINK "" HISD Instructional Practice PL-2 on the webpage. To begin mini-lesson, show a sample math folder to students. Tell students math folders will be used as a tool for celebrations, self-reflection, goal-setting, and will provide evidence of their academic progress. Provide students with previously-scored student work product you selected in step 1 and individual student data tracker from step 2. Model how to use the data from the scored student work sample to complete the data tracker. Consider using different colors to show mastery levels.Discuss the goals section of the tracker and how students will use the tracker to chart progress. Explain process for retrieving individual student folders, and instruct materials managers to retrieve folders for their group. Ask students to identify a goal for themselves and to complete the goal section of their tracker. Closure: Tell students they will use their math data folders throughout the year to monitor their academic progress and to review and set new learning goals. MaterialsFile or pocket folders (One for each student)Previously-scored student work productStudent data trackers Markers, colored pencils, or pencilsAdditional ResourcesHISD Student Self-Reflection forms (Last page of Snapshot assessment)PL-2 on the Lead4ward Resource: Student Learning ReportsPinterest Data Folder ExamplesInstructional Practice (IP) Rubric ConnectionsPL-2 Collects, tracks, and uses student data to drive instructionGrade-Level Differentiation Early Childhood: Consider using a simplified tracker, which may include grade-level appropriate language and colored stickers indicating varying levels of progress. Students may need to verbally communicate their goals to teachers, who will then write goals and accomplishments in the tracker.Intermediate: Data folders should be an integral part of students’ self-reflection and progress monitoring, as well as a communication tool between students, parents, and teacher. Day 24—Small Group Instruction ITeacher ConsiderationsSmall group instruction provides students with individualized content support at differentiated levels. Small group instruction is teacher-led, as well as data-driven. The small group structure allows for teachers to meet students where they are academically and provide strategic intervention for mastery of key concepts and skills. Small group instruction should be designed to explicitly address student misconceptions and gaps in understanding. Small group instruction should occur on a consistent basis, allow for flexible grouping, and include frequent and systematic checks for understanding. Small groups should not remain the same throughout the year, or even throughout a given unit of instruction. Students should not feel ostracized or trapped in a given group. Teachers and students should be constantly questioning, exploring, sharing, and engaging in hands-on, minds-on learning during small group instruction. Depending on the grade-level, the full implementation of this mini-lesson will require teachers to spend approximately 10-15 minutes of class time. Rationale ExemplarSmall Groups:Provide opportunities for students to make progress towards mastery in flexible groups based on students’ levels of understandingSupport teachers in differentiating their instruction, including extensions for advanced learnersProvide a structure for implementing response to intervention at the Tier 2 and Tier 3 levels-558801935500 .ImplementationDuring pre-planning, add a small group station to the management chart created on Day 23, but note that students will not rotate into the small group station until Day 25. Create a list of steps students should take if they need help and/or support during workstations when the teacher is leading a small group. For example, utilize the “Ask 3 before me” strategy or assign a workstation manager(s) who will be available to help students stay on task and answer questions.To begin mini lesson, review management board taught on Day 23. Explicitly show where you have added a station rotation for small group instruction with the teacher. Review for students the math station activities they will engage in and how they will rotate through the stations while small group instruction is taking place. Explain the transition process for students who will be entering or exiting the small-group setting. Review behavior expectations for workstations, remind materials managers of assignments, and briefly review tight transitions. Tell students small group instruction is uninterrupted time for the teacher and a select group of students to engage in deep mathematical learning. As such, the teacher and students at the small group table should not be disturbed. Tell students how they will receive help or ask questions during workstation time when small groups are taking place by reviewing your list created in step 3. Engage students in a practice session by pulling together a mock small group, assigning groups to stations, naming the workstation manager(s), and allowing students to move through the stations without actually completing activities. Remind students of the steps identified in step 8 and allow a student to model how to ask a question or receive help. After 2 to 4 minutes of practice, instruct students to return to their seats. Closure: Review expectations for what students should do when the teacher is working with a small group. Clarify any misunderstandings, and tell students that tomorrow will be the first day of small group instruction. MaterialsManipulativesResponse cards Dry-erase boards/markers (per student)Stick notes, pencils, paper, etc.Math activitiesAdditional ResourcesMaking the Most of Small Groups: Differentiation for All, Debbie DillerHMH GoMath! RTI Guide Tier 1, 2, 3 Instructional Practice (IP) Rubric ConnectionsI-2 Checks for student understanding and responds to student misunderstandingI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-6 Communicates content and concepts to students I-8 Students actively participate in lesson activities I-7 Promotes high academic expectations for students Grade-Level Differentiation Early Childhood: Utilize concrete materials during workstations to allow students to develop conceptual understandings of concepts. Consider shortening small-group instructional time to maximize students’ focus while engaged in station and small-group work. To ensure all students are fully engaged and meeting expectations at workstations, consider starting all students at a station and then initiate the first small group session during the second rotation.Intermediate: Utilize concrete materials during workstations before moving to pictorial and abstract representations. Small group instruction should provide teachers the opportunity to analyze student understanding at a conceptual level. Teachers should provide a short, yet meaningful, performance task or formative assessment to determine students’ mastery of concept/skill addressed during small group time (e.g., provide a two-question exit ticket or reflection slip during the last 3 minutes of small group time). Day 25—Small Group Instruction IITeacher ConsiderationsSee Day 24 for additional Teacher Considerations.Depending on the grade-level, the full implementation of this mini-lesson will require teachers to spend approximately 10-15 minutes of class time. Rationale ExemplarSmall Groups:Provide opportunities for students to make progress towards mastery in flexible groups based on students’ levels of understandingSupport teachers in differentiating their instruction, including extensions for advanced learnersProvide a structure for implementing response to intervention at the Tier 2 and Tier 3 levels169545317500 ImplementationDuring pre-planning, use formative assessment data to identify skills or concepts that need re-teaching. Use data to consider how students will be grouped when re-addressing the identified skill or concept.Identify aligned, rigorous activities to support the needs of students based on data. In order to re-assess student mastery of identified skill/concept, develop a student performance task or other formative assessment to accompany the small group lesson/activity. Consider using the HISD Elementary Mathematics Open-Ended Question Scoring Rubric to outline expectations for exemplar responses to the task or assessment.Brainstorm and record a list of student expectations for when students arrive at small group. Your list of expectations should include specific references to the day’s pre-planned activities. To begin the mini-lesson, explain to the class which students will be rotating through the small-group portion of the day’s station rotation (and when) by referencing the management board. Remind students of expectations explained during Day 24.Tell the students what they can expect when they arrive at small group. Highlight at least three specific components of the day’s activities students will engage in, and review the list of expectations created in step 3 above. Ask students to share with a shoulder partner three things they can expect to encounter while engaging in activities during small group instruction. Have students share out responses. Ask students to move to their first rotation, as identified on the management board. Instruct students to begin station work.With your small group of students, briefly review small-group expectations. Engage small group in prepared activity. At the conclusion of the activity/lesson, present students with performance task or formative assessment. Keep anecdotal notes of student progress and misconceptions, as well as notes for future small-group activities based on student needs. Consider allowing students the opportunity to track their own progress for the specified concept/skill using their student data folders. At the conclusion of rotation 1, ensure students in small group successfully transition to their next workstation activity. As necessary, remind students to review the management board to determine when they will move to small group with the teacher. Repeat steps 8 and 9 for each small group. *Note that it may not be possible to rotate every group of students into small group each day. As such, consider creating a weekly or bi-daily rotation schedule that ensures all students participate in small group instruction. MaterialsManipulativesResponse cards Dry-erase boards/markers (per student)Stick notes, pencils, paper, etc.Math activitiesAdditional ResourcesMaking the Most of Small Groups: Differentiation for All, Debbie DillerHMH GoMath! RTI Guide Tier 1, 2, 3HISD Elementary Mathematics Open-Ended Question Scoring RubricInstructional Practice (IP) Rubric ConnectionsI-2 Checks for student understanding and responds to student misunderstandingI-3 Differentiates instruction for student needs by employing a variety of instructional strategiesI-6 Communicates content and concepts to students I-8 Students actively participate in lesson activities I-7 Promotes high academic expectations for studentsGrade-Level Differentiation Early Childhood: Utilize concrete materials during workstations to allow students to develop conceptual understandings of concepts. Consider shortening small-group instructional time to maximize students’ focus while engaged in station and small-group work. To ensure all students are fully engaged and meeting expectations at workstations, consider starting all students at a station and then initiate the first small-group session during the second rotation.Intermediate: Utilize concrete materials during workstations before moving to pictorial and abstract representations. Small group instruction should provide teachers the opportunity to analyze student understanding at a conceptual level. Teachers should provide a short, yet meaningful, performance task or formative assessment to determine students’ mastery of concept/skill addressed during small group time (e.g., provide a two-question exit ticket or reflection slip during the last 3 minutes of small group time). ................
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