6th Grade Mathematics
Kindergarten Mathematics
Numbers to 10 to 20
Count to 100 By Tens and Ones
Unit IV Curriculum Map: April 7th, 2017-June 19, 2017
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Kindergarten Unit IV Table of Contents
|I. |Mathematics Mission Statement |p. 2 |
|II. |Mathematical Teaching Practices |p. 3 |
|III. |Mathematical Goal Setting |p. 4 |
|IV. |Reasoning and Problem Solving |p. 6 |
|V. |Mathematical Representations |p. 7 |
|VI. |Mathematical Discourse |p. 9 |
|VII. |Conceptual Understanding |p. 14 |
|VIII. |Evidence of Student Thinking |p. 15 |
|IX. |ELL and SPED Considerations |p. 17 |
|X. |Kindergarten Unit IV NJSLS |p. 21 |
|XI. |Eight Mathematical Practices |p. 27 |
|XII. |Ideal Math Block |p. 29 |
|XIII. |Math In Focus Lesson Structure |p. 33 |
|XIX. |Ideal Math Block Planning Template |p. 36 |
|XX. |Planning Calendar |p. 39 |
|XXI. |Instructional and Assessment Framework |p. 41 |
|XXII. |PLD Rubric |p. 48 |
|XXIII. |Data Driven Instruction |p. 49 |
|XXIV. |Math Portfolio Expectations |p. 51 |
|XXV. |Resources |p. 53 |
Office of Mathematics Mission Statement
The Office of Mathematics exists to provide the students it serves with a mathematical ‘lens’-- allowing them to better access the world with improved decisiveness, precision, and dexterity; facilities attained as students develop a broad and deep understanding of mathematical content. Achieving this goal defines our work - ensuring that students are exposed to excellence via a rigorous, standards-driven mathematics curriculum, knowledgeable and effective teachers, and policies that enhance and support learning.
Office of Mathematics Objective
By the year 2021, Orange Public School students will demonstrate improved academic achievement as measured by a 25% increase in the number of students scoring at or above the district’s standard for proficient (college ready (9-12); on track for college and career (K-8)) in Mathematics.
Rigorous, Standards-Driven Mathematics Curriculum
The Grades K-8 mathematics curriculum was redesigned to strengthen students’ procedural skills and fluency while developing the foundational skills of mathematical reasoning and problem solving that are crucial to success in high school mathematics. Our curriculum maps are Unit Plans that are in alignment with the New Jersey Student Learning Standards for Mathematics.
Office of Mathematics Department Handbook
Research tells us that teacher knowledge is one of the biggest influences on classroom atmosphere and student achievement (Fennema & Franke, 1992). This is because of the daily tasks of teachers, interpreting someone else’s work, representing and forging links between ideas in multiple forms, developing alternative explanations, and choosing usable definitions. (Ball, 2003; Ball, et al., 2005; Hill & Ball, 2009). As such, the Office of Mathematics Department Handbook and Unit Plans were intentionally developed to facilitate the daily work of our teachers; providing the tools necessary for the alignment between curriculum, instruction, and assessment. These document helps to (1) communicate the shifts (explicit and implicit) in the New Jersey Student Learning Standards for elementary and secondary mathematics (2) set course expectations for each of our courses of study and (3) encourage teaching practices that promote student achievement. These resources are accessible through the Office of Mathematics website.
Curriculum Unit Plans
Designed to be utilized as a reference when making instructional and pedagogical decisions, Curriculum Unit Plans include but are not limited to standards to be addressed each unit, recommended instructional pacing, best practices, as well as an assessment framework.
Mathematical Teaching Practices
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Mathematical Goal Setting:
• What are the math expectations for student learning?
• In what ways do these math goals focus the teacher’s interactions with students throughout the lesson?
Learning Goals should:
• Clearly state what students are to learn and understand about mathematics as the result of instruction.
• Be situated within learning progressions.
• Frame the decisions that teachers make during a lesson.
Example:
New Jersey Student Learning Standards:
K.OA.1
Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
K.OA.2
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
K.OA.5
Fluently add and subtract within 5.
Learning Goal(s):
Students will use multiple representations to solve addition and/or subtraction situations (K.OA.1-2) and explain their solution paths.
Student Friendly Version:
We are learning to act out and solve addition and/ or subtraction situations.
We are will also be able to explain how we solved different situations.
Lesson Implementation:
As students reason through their selected solution paths, educators use of questioning facilitates the accomplishment of the identified math goal. Students’ level of understanding becomes evident in what they produce and are able to communicate. Students can also assess their level of goal attainment and that of their peers through the use of a student friendly rubric (MP3).
Student Name: __________________________________________ Task: ______________________________ School: ___________ Teacher: ______________ Date: ___________
| | | |
|“I CAN…..” |STUDENT FRIENDLY RUBRIC |SCORE |
| | | |
| | | | | | |
| |…a start |…getting there |…that’s it |WOW! | |
| |1 |2 |3 |4 | |
|Solve |I am unable to use a strategy. |I can start to use a strategy. |I can solve it more than one way. |I can use more than one strategy and | |
| | | | |talk about how they get to the same | |
| | | | |answer. | |
|Say |I am unable to say or write. |I can write or say some of what I did. |I can write and talk about what I did. |I can write and say what I did and why I| |
|or | | | |did it. | |
|Write | | |I can write or talk about why I did it. | | |
| |I am not able to draw or show my |I can draw, but not show my thinking; |I can draw and show my thinking |I can draw, show and talk about my | |
|Draw |thinking. |or | |thinking. | |
|or | |I can show but not draw my thinking; | | | |
|Show | | | | | |
| | | | | | |
Reasoning and Problem Solving Mathematical Tasks
The benefits of using formative performance tasks in the classroom instead of multiple choice, fill in the blank, or short answer questions have to do with their abilities to capture authentic samples of students' work that make thinking and reasoning visible. Educators’ ability to differentiate between low-level and high-level demand task is essential to ensure that evidence of student thinking is aligned and targeted to learning goals. The Mathematical Task Analysis Guide serves as a tool to assist educators in selecting and implementing tasks that promote reasoning and problem solving.
Use and Connection of Mathematical Representations
The Lesh Translation Model
Each oval in the model corresponds to one way to represent a mathematical idea.
Visual: When children draw pictures, the teacher can learn more about what they understand about a particular mathematical idea and can use the different pictures that children create to provoke a discussion about mathematical ideas. Constructing their own pictures can be a powerful learning experience for children because they must consider several aspects of mathematical ideas that are often assumed when pictures are pre-drawn for students.
Physical: The manipulatives representation refers to the unifix cubes, base-ten blocks, fraction circles, and the like, that a child might use to solve a problem. Because children can physically manipulate these objects, when used appropriately, they provide opportunities to compare relative sizes of objects, to identify patterns, as well as to put together representations of numbers in multiple ways.
Verbal: Traditionally, teachers often used the spoken language of mathematics but rarely gave students opportunities to grapple with it. Yet, when students do have opportunities to express their mathematical reasoning aloud, they may be able to make explicit some knowledge that was previously implicit for them.
Symbolic: Written symbols refer to both the mathematical symbols and the written words that are associated with them. For students, written symbols tend to be more abstract than the other representations. I tend to introduce symbols after students have had opportunities to make connections among the other representations, so that the students have multiple ways to connect the symbols to mathematical ideas, thus increasing the likelihood that the symbols will be comprehensible to students.
Contextual: A relevant situation can be any context that involves appropriate mathematical ideas and holds interest for children; it is often, but not necessarily, connected to a real-life situation.
The Lesh Translation Model: Importance of Connections
As important as the ovals are in this model, another feature of the model is even more important than the representations themselves: The arrows! The arrows are important because they represent the connections students make between the representations. When students make these connections, they may be better able to access information about a mathematical idea, because they have multiple ways to represent it and, thus, many points of access.
Individuals enhance or modify their knowledge by building on what they already know, so the greater the number of representations with which students have opportunities to engage, the more likely the teacher is to tap into a student’s prior knowledge. This “tapping in” can then be used to connect students’ experiences to those representations that are more abstract in nature (such as written symbols). Not all students have the same set of prior experiences and knowledge. Teachers can introduce multiple representations in a meaningful way so that students’ opportunities to grapple with mathematical ideas are greater than if their teachers used only one or two representations.
Concrete Pictorial Abstract (CPA) Instructional Approach
The CPA approach suggests that there are three steps necessary for pupils to develop understanding of a mathematical concept.
Concrete: “Doing Stage”: Physical manipulation of objects to solve math problems.
Pictorial: “Seeing Stage”: Use of imaged to represent objects when solving math problems.
Abstract: “Symbolic Stage”: Use of only numbers and symbols to solve math problems.
CPA is a gradual systematic approach. Each stage builds on to the previous stage. Reinforcement of concepts are achieved by going back and forth between these representations
Mathematical Discourse and Strategic Questioning
Discourse involves asking strategic questions that elicit from students both how a problem was solved and why a particular method was chosen. Students learn to critique their own and others' ideas and seek out efficient mathematical solutions.
While classroom discussions are nothing new, the theory behind classroom discourse stems from constructivist views of learning where knowledge is created internally through interaction with the environment. It also fits in with socio-cultural views on learning where students working together are able to reach new understandings that could not be achieved if they were working alone.
Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions.
Asking better questions can open new doors for students, promoting mathematical thinking and classroom discourse. Can the questions you're asking in the mathematics classroom be answered with a simple “yes” or “no,” or do they invite students to deepen their understanding?
To help you encourage deeper discussions, here are 100 questions to incorporate into your instruction by Dr. Gladis Kersaint, mathematics expert and advisor for Ready Mathematics.
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Conceptual Understanding
Students demonstrate conceptual understanding in mathematics when they provide evidence that they can:
• recognize, label, and generate examples of concepts;
• use and interrelate models, diagrams, manipulatives, and varied representations of concepts;
• identify and apply principles; know and apply facts and definitions;
• compare, contrast, and integrate related concepts and principles; and
• recognize, interpret, and apply the signs, symbols, and terms used to represent concepts.
Conceptual understanding reflects a student's ability to reason in settings involving the careful application of concept definitions, relations, or representations of either.
Procedural Fluency
Procedural fluency is the ability to:
• apply procedures accurately, efficiently, and flexibly;
• to transfer procedures to different problems and contexts;
• to build or modify procedures from other procedures; and
• to recognize when one strategy or procedure is more appropriate to apply than another.
Procedural fluency is more than memorizing facts or procedures, and it is more than understanding and being able to use one procedure for a given situation. Procedural fluency builds on a foundation of conceptual understanding, strategic reasoning, and problem solving (NGA Center & CCSSO, 2010; NCTM, 2000, 2014). Research suggests that once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them (Hiebert, 1999). Therefore, the development of students’ conceptual understanding of procedures should precede and coincide with instruction on procedures.
Math Fact Fluency: Automaticity
Students who possess math fact fluency can recall math facts with automaticity. Automaticity is the ability to do things without occupying the mind with the low-level details required, allowing it to become an automatic response pattern or habit. It is usually the result of learning, repetition, and practice.
K-2 Math Fact Fluency Expectation
K.OA.5 Add and Subtract within 5.
1.OA.6 Add and Subtract within 10.
2.OA.2 Add and Subtract within 20.
Math Fact Fluency: Fluent Use of Mathematical Strategies
First and second grade students are expected to solve addition and subtraction facts using a variety of strategies fluently.
1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
Use strategies such as:
• counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);
• decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9);
• using the relationship between addition and subtraction; and
• creating equivalent but easier or known sums.
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on:
o place value,
o properties of operations, and/or
o the relationship between addition and subtraction;
Evidence of Student Thinking
Effective classroom instruction and more importantly, improving student performance, can be accomplished when educators know how to elicit evidence of students’ understanding on a daily basis. Informal and formal methods of collecting evidence of student understanding enable educators to make positive instructional changes. An educators’ ability to understand the processes that students use helps them to adapt instruction allowing for student exposure to a multitude of instructional approaches, resulting in higher achievement. By highlighting student thinking and misconceptions, and eliciting information from more students, all teachers can collect more representative evidence and can therefore better plan instruction based on the current understanding of the entire class.
Mathematical Proficiency
To be mathematically proficient, a student must have:
• Conceptual understanding: comprehension of mathematical concepts, operations, and relations;
• Procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently, and appropriately;
• Strategic competence: ability to formulate, represent, and solve mathematical problems;
• Adaptive reasoning: capacity for logical thought, reflection, explanation, and justification;
• Productive disposition: habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy.
Evidence should:
• Provide a window in student thinking;
• Help teachers to determine the extent to which students are reaching the math learning goals; and
• Be used to make instructional decisions during the lesson and to prepare for subsequent lessons.
English Language Learners (ELL) and Special Education (SPED) Considerations
In order to develop proficiency in the Standard for Mathematical Practice 3 (Construct Viable Arguments and Critique the Reasoning of Others) and Standard for Mathematical Practice 4 (Model with Mathematics), it is important to provide English Language Learners (ELLs) and Special Education Students with two levels of access to the tasks: language access and content access.
Language Access
In the tasks presented, we can distinguish between the vocabulary and the language functions needed to provide entry points to the math content. These vocabulary words and language functions must be explicitly taught to ensure comprehension of the tasks. Some ways this can be done are by using the following approaches:
1. Introduce the most essential vocabulary/language functions before beginning the tasks. Select words and concepts that are essential in each task.
Vocabulary Words:
• Tier I (Nonacademic language) Mostly social language; terms used regularly in everyday situations (e.g., small, orange, clock)
• Tier II (General academic language) Mostly academic language used regularly in school but not directly associated with mathematics (e.g., combine, describe, consequently), and academic language broadly associated with mathematics (e.g., number, angle, equation, average, product)
• Tier III (Math technical language) Academic language associated with specific math topics (e.g., perfect numbers, supplementary angles, quadratic equations, mode, median)
Language Functions:
• Pronounce each word for students and have them repeat after you.
• Introduce the vocabulary in a familiar and meaningful context and then again in a contentspecific setting.
• Math-specific examples include but are not limited to the following: explain, describe, inform, order, classify, analyze, infer, solve problems, define, generalize, interpret, hypothesize.
2. Use visuals when introducing new words and concepts.
• Provide experiences that help demonstrate the meaning of the vocabulary words (e.g., realia, pictures, photographs, and graphic organizers).
• Write key words on the board, and add gestures to help students interpret meaning.
• Have students create their own visuals to aid in their learning. For example, assign a few content-specific vocabulary words to each student, and ask them to write student-friendly definitions and draw pictures to show what the words mean.
3. Build background knowledge.
• Explicit links to previously taught lessons, tasks, or texts should be emphasized to activate prior knowledge.
• Review relevant vocabulary that has already been introduced, and highlight familiar words that have a new meaning.
• Access the knowledge that students bring from their native cultures.
4. Promote oral language development through cooperative learning groups.
• ELLs need ample opportunities to speak English and authentic reasons to use academic language.
• Working in small groups is especially beneficial because ELLs learn to negotiate the meanings of vocabulary words with their classmates.
5. Native Language Support
• Full proficiency in the native language leads to higher academic gains in English. Because general structural and functional characteristics of languages transfer, allowing second language learners to access content in the native language provides them with a way to construct meaning in English.
• In order to assist ELLs, the strategic use of the native language can be incorporated into English instruction as a support structure in order to clarify, build prior knowledge, extend comprehension, and bridge experiences. This can be integrated into a teacher’s instructional practices through technology, human resources (e.g., paraprofessionals, peers, and parents), native language materials, and flexible grouping.
6. Possible Sentences
Moore, D.W., & Moore, S.A. (1986). "Possible sentences." In Reading in the content areas: Improving classroom instruction. Dubuque, IA: Kendall/Hunt.
Possible Sentences is a pre-reading strategy that focuses on vocabulary building and student prediction prior to reading. In this strategy, teachers write the key words and phrases of a selected text on the chalkboard. Students are asked to:
• Define all of the terms
• Group the terms into related pairs
• Write sentences using these word pairs
Steps to Possible Sentences
1) Prior to the reading assignment, list all essential vocabulary words in the task on the board.
2) Working in pairs, ask students to define the words and select pairs of related words from the list.
3) Ask students to write sentences using each of the word pairs that they might expect to appear in the task, given its title and topic.
4) Select several students to write their possible sentences on the board.
5) Engage the students in a discussion of the appropriateness of the word pairing and the plausibility of each sentence as a possible sentence in the selection.
6) Have students read the task and test the accuracy of their predictions. Sentences that are not accurate should be revised.
7) Poll the class for common accurate and inaccurate predictions. Discuss possible explanations for the success or failure of these predictions.
8) Introduce students to sentence frames which reinforce sentence structure while enabling ELLs to participate in classroom and/or group discussion.
7. The Frayer Model
Frayer, D., Frederick, W. C., and Klausmeier, H. J. (1969). A Schema for testing the level of cognitive mastery. Madison, WI: Wisconsin Center for Education Research.
The Frayer Model is a graphic organizer used for word analysis and vocabulary building. It assists students in thinking about and describing the meaning of a word or concept by:
• Defining the term
• Describing its essential characteristics
• Providing examples of the idea
• Offering non-examples of the idea
Steps to the Frayer Model
1) Explain the Frayer Model graphic organizer to the class. Use a common word to demonstrate the various components of the form. Model the type and quality of desired answers when giving this example.
2) Select a list of key concepts from the task. Write this list on the chalkboard and review it with the class before students read the task.
3) Divide the class into student pairs. Assign each pair one of the key concepts and have them read the task carefully to define this concept. Have these groups complete the four-square organizer for this concept.
4) Ask the student pairs to share their conclusions with the entire class. Use these presentations to review the entire list of key concepts.
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8. Semantic Webbing
Maddux, C. D., Johnson, D. L., & Willis, J. W. (1997). Educational computing: Learning with tomorrow's technologies. Boston: Allyn & Bacon.
Semantic Webbing builds a graphical representation of students' knowledge and perspectives about the key themes of a task before and after the learning experience. Semantic Webbing achieves three goals:
• Activating students' prior knowledge and experience
• Helping students organize both their prior knowledge and new information
• Allowing students to discover relationships between their prior and new knowledge
Steps to Semantic Webbing
1) Write a key word or phrase from the task on the board.
2) Have students think of as many words as they know that relate to this key idea. Write these words on the side on the chalkboard.
3) Ask students to group these words into logical categories and label each category with a descriptive title.
4) Encourage students to discuss/debate the choice of the category for each word.
5) Write the students' conclusions (the categories and their component words) on the chalkboard.
6) Have the students read the task in pairs and repeat the process above.
7) When they finish reading, have students add new words and categories related to the key idea.
Native Language Support:
Full proficiency in the native language leads to higher academic gains in English. Because general structural and functional characteristics of language transfer, allowing second language learners to access content in the native language provides them with a way to construct meaning in English. In order to assist ELLs, the strategic use of the native language can be incorporated into English instruction as a support structure to clarify, to build prior knowledge, to extend comprehension, and to bridge experiences. This can be integrated into a teacher’s instructional practice through the following: technology, human resources (e.g., paraprofessionals, peers, and parents), native language materials, and flexible grouping.
Content Access
When engaging ELL/SPED students in cognitively demanding tasks, teachers should consider which concepts the ELLs/SPEDs are likely to encounter when accessing mathematics and which of these pose the most challenges.
Teachers should consider what the student is required to know as well as be able to do.
What is the mathematics in the task?
What prior knowledge is required in order for ELL/SPED students to proceed?
In order to activate prior knowledge and prepare ELL/SPED for the demands of the tasks in the lesson, we suggest that they engage in a different but similar task prior to working on the selected performance assessment tasks, such as the following:
1. Use of Manipulatives
Provide ELL/SPED students with manipulatives when appropriate. While there are different types of manipulatives available commercially, teacher-made materials are recommended and encouraged. Manipulatives are always appropriate when introducing a concept regardless of the grade.
2. Graphic Organizers
Graphic organizers, such as Venn diagrams, Frayer Models, charts and/or tables, help ELLs/SPEDs understand relationships, recognize common attributes, and make associations with the concepts being discussed.
3. Use of Technology
Technology must be integrated whenever possible. Various software and internet-based programs can also be very beneficial, many of which are available in the ELLs’ native languages. Use of technology develops and reinforces basic skills.
4. Differentiated Instruction
While all students can benefit from differentiated instruction, it is crucial for teachers to identify the different learning modalities of their ELLs/SPEDs. Teachers and ELLs/SPEDs are collaborators in the learning process. Teachers must adjust content, process, and product in response to the readiness, interests, and learning profiles of their students. In order to create and promote the appropriate climate for ELLs/SPEDs to succeed, teachers need to know, engage, and assess the learner.
5. Assessment for Learning (AfL)
Whenever ELL/SPED students are engaged in tasks for the purpose of formative assessments, the strategies of Assessment for Learning (AfL) are highly recommended. AfL consists of five key strategies for effective formative assessment:
1) Clarifying, sharing and understanding goals for learning and criteria for success with learners
2) Engineer effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning
3) Providing feedback that moves learning forward
4) Activating students as owners of their own learning
5) Activating students as learning resources for one another
Scaffolding: A Tool to Accessibility
In order to be successful members of a rigorous academic environment, ELLs/SPED need scaffolds to help them access curriculum. These scaffolds are temporary, and the process of constructing them and then removing them when they are no longer needed is what makes them a valuable tool in the education of ELLs/SPEDs. The original definition of scaffolding comes from Jerome Bruner (1983), who defines scaffolding as “a process of setting up the situation to make the child’s entry easy and successful, and then gradually pulling back and handing the role to the child as he becomes skilled enough to manage it.” The scaffolds are placed purposefully to teach specific skills and language. Once students learn these skills and gain the needed linguistic and content knowledge, these scaffolds are no longer needed. Nevertheless, each child moves along his/her own continuum, and while one child may no longer need the scaffolds, some students may still depend on them. Thus, constant evaluation of the process is an inevitable
step in assuring that scaffolds are ujsed successfully.
The scaffolding types necessary for ELLs/SPEDs are modeling, activating and bridging prior knowledge and/or experiences, text representation, metacognitive development, contextualization, and building schema:
• Modeling: finished products of prior students’ work, teacher-created samples, sentence starters, writing frameworks, shared writing, etc.
• Activating and bridging prior knowledge and/or experiences: using graphic organizers, such as anticipatory guides, extended anticipatory guide, semantic maps, interviews, picture walk discussion protocols, think-pair-share, KWL, etc.
• Text representation: transforming a piece of writing into a pictorial representation, changing one genre into another, etc.
• Metacognitive development: self-assessment, think-aloud, asking clarifying questions, using a rubric for self evaluation, etc.
• Contextualization: metaphors, realia, pictures, audio and video clips, newspapers, magazines, etc.
• Building schema: bridging prior knowledge and experience to new concepts and ideas, etc.
NYC Department of Eduction, ELL Considerations for Common Core-Aligned Tasks in Mathematics
Retrieved on December 5, 2016
K-2 CONCEPT MAP
|Kindergarten Unit IV |
|In this Unit Students will: |
| |
|Counting and Cardinality |
|Count to 100 by ones and by tens |
|Count forward beginning from a given number within the known sequence. |
|Write numbers from 0 to 20. |
|Represent a number of objects with a written numeral 0-20. |
|Understand the relationship between numbers and quantities; |
|Count to answer "how many |
|Given a number from 1-20, count out that many objects. |
|Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. |
|Compare two numbers between 1 and 10 presented as written numerals. |
|Decompose numbers less than or equal to 10 into pairs in more than one way. |
| |
|Operation and Algebraic Thinking |
|Fluently add and subtract within 5. |
| |
|Numbers and Operations in Base Ten |
|Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition |
|or decomposition by a drawing or equation (e.g., 18 = 10 + 8). |
|Understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. |
| |
| |
|Mathematical Practices |
| |
|Make sense of problems and persevere in solving them. |
|Reason abstractly and quantitatively. |
|Construct viable arguments and critique the reasoning of others. |
|Model with mathematics. |
|Use appropriate mathematical tools. |
|Attend to precision. |
|Look for and make use of structure. |
|Look for and express regularity in repeated reasoning. |
| |
|New Jersey Student Learning Standards: Counting and Cardinality |
|.1 | |
| |Count to 100 by ones and by tens |
| |
|Students’ rote count by starting at one and counting to 100. When students count by tens they are only expected to master counting on the decade (0, 10, 20, 30, 40 …). This objective does not require recognition of |
|numerals. It is focused on the rote number sequence. |
|.2 |Count forward beginning from a given number within the known sequence (instead of having to begin at 1). |
| |
|Students begin a rote forward counting sequence from a number other than 1. Thus, given the number 4, the student would count, “4, 5, 6, 7 …” This objective does not require recognition of numerals. It is focused on|
|the rote number sequence 0-100. |
|.3 | |
| |Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). |
| |
|Students write the numerals 0-20 and use the written numerals 0-20 to represent the amount within a set. |
|For example, if the student has counted 9 objects, then the written numeral “9” is recorded. |
|Students can record the quantity of a set by selecting a number card/tile (numeral recognition) or writing the numeral. |
| |
|Students can also create a set of objects based on the numeral presented. |
|For example, if a student picks up the number card “13”, the student then creates a pile of 13 counters. While children may experiment with writing numbers beyond 20, this standard places emphasis on numbers 0-20. |
| |
|Due to varied development of fine motor and visual development, reversal of numerals is anticipated. |
|While reversals should be pointed out to students and correct formation modeled in instruction, the emphasis of this standard is on the use of numerals to represent quantities rather than the correct handwriting |
|formation of the actual numeral itself. |
|.4 |Understand the relationship between numbers and quantities; connect counting to cardinality. |
| |When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. |
| |Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were|
| |counted. |
| |Understand that each successive number name refers to a quantity that is one larger. |
|Students count a set of objects and see sets and numerals in relationship to one another. These connections are higher-level skills that require students to analyze, reason about, and explain relationships between |
|numbers and sets of objects. The expectation is that students are comfortable with these skills with the numbers 1-20 by the end of Kindergarten. |
| |
|Students implement correct counting procedures by pointing to one object at a time (one-to-one correspondence), using one counting word for every object (synchrony/ one-to-one tagging), while keeping track of |
|objects that have and have not been counted. This is the foundation of counting. |
| |
|Students answer the question “How many are there?” by counting objects in a set and understanding that the last number stated when counting a set (…8, 9, 10) represents the total amount of objects: “There are 10 |
|bears in this pile.” (cardinality). Since an important goal for children is to count with meaning, it is important to have children answer the question, “How many do you have?” after they count. Often times, |
|children who have not developed cardinality will count the amount again, not realizing that the 10 they stated means 10 objects in all. |
| |
|Young children believe what they see. Therefore, they may believe that a pile of cubes that they counted may be more if spread apart in a line. As children move towards the developmental milestone of conservation of|
|number, they develop the understanding that the number of objects does not change when the objects are moved, rearranged, or hidden. Children need many different experiences with counting objects, as well as |
|maturation, before they can reach this developmental milestone. |
|.5 | |
| |Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; |
| |given a number from 1-20, count out that many objects. |
| |
|In order to answer “how many?” students need to keep track of objects when counting. Keeping track is a method of counting that is used to count each item once and only once when determining how many. After numerous|
|experiences with counting objects, along with the developmental understanding that a group of objects counted multiple times will remain the same amount, students recognize the need for keeping track in order to |
|accurately determine “how many”. Depending on the amount of objects to be counted, and the students’ confidence with counting a set of objects, students may move the objects as they count each, point to each object |
|as counted, look without touching when counting, or use a combination of these strategies. It is important that children develop a strategy that makes sense to them based on the realization that keeping track is |
|important in order to get an accurate count, as opposed to following a rule, such as “Line them all up before you count”, in order to get the right answer. |
| |
| |
|As children learn to count accurately, they may count a set correctly one time, but not another. Other times they may be able to keep track up to a certain amount, but then lose track from then on. Some |
|arrangements, such as a line or rectangular array, are easier for them to get the correct answer but may limit their flexibility with developing meaningful tracking strategies, so providing multiple arrangements |
|help children learn how to keep track. Since scattered arrangements are the most challenging for students, this standard specifies that students only count up to 10 objects in a scattered arrangement and count up to|
|20 objects in a line, rectangular array, or circle. |
|New Jersey Student Learning Standards: Operations and Algebraic Thinking |
|K.OA.3 | |
| |Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5|
| |= 2 + 3 and 5 = 4 + 1). |
| |
|Students develop an understanding of part-whole relationships as they recognize that a set of objects (5) can be broken into smaller sub-sets (3 and 2) and still remain the total amount (5). In addition, this |
|objective asks students to realize that a set of objects (5) can be broken in multiple ways (3 and 2; 4 and 1). Thus, when breaking apart a set (decompose), students use the understanding that a smaller set of |
|objects exists within that larger set (inclusion). |
| |
|Example: |
|“Bobby Bear is missing 5 buttons on his jacket. How many ways can you use blue and red buttons to finish his jacket? |
|Draw a picture of all your ideas. |
|Students could draw pictures of: 4 blue and 1 red button 3 blue and 2 red buttons 2 blue and 3 red buttons 1 blue and 4 red buttons |
| |
|In Kindergarten, students need ample experiences breaking apart numbers and using the vocabulary “and” & “same amount as” before symbols (+, =) and equations (5= 3 + 2) are introduced. If equations are used, a |
|mathematical representation (picture, objects) needs to be present as well. |
|K.OA.5 |Fluently add and subtract within 5. |
| |
|Students are fluent when they display accuracy (correct answer), efficiency (a reasonable amount of steps in about 3-5 seconds* without resorting to counting), and flexibility (using strategies such as the |
|distributive property). |
|Students develop fluency by understanding and internalizing the relationships that exist between and among numbers. Oftentimes, when children think of each “fact” as an individual item that does not relate to any |
|other “fact”, they are attempting to memorize separate bits of information that can be easily forgotten. Instead, in order to fluently add and subtract, children must first be able to see sub-parts within a number |
|(inclusion, .4.c). |
|New Jersey Student Learning Standards: Numbers and Operations in Base Ten |
|K.NBT.1 |Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing |
| |or equation (e.g., 18 = 10 + 8)*; understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. |
|Students explore numbers 11-19 using representations, such as manipulatives or drawings. Keeping each count as a single unit, kindergarteners use 10 objects to represent “10” rather than creating a unit called a ten |
|(unitizing) as indicated in the First Grade CCSS standard 1.NBT.1a: 10 can be thought of as a bundle of ten ones — called a “ten.” |
| |
|Example: |
|Teacher: “I have some chips here. Do you think they will fit on our ten frame? Why? Why Not?” |
|Students: Share thoughts with one another. |
|Teacher: “Use your ten frame to investigate.” |
|Students: “Look. There’s too many to fit on the ten frame. Only ten chips will fit on it.” |
|Teacher: “So you have some leftovers?” |
|Students: “Yes. I’ll put them over here next to the ten frame.” |
|Teacher: “So, how many do you have in all?” |
|Student A: “One, two, three, four, five… ten, eleven, twelve, thirteen, fourteen. I have fourteen. Ten fit on and four didn’t.” |
|Student B: Pointing to the ten frame, “See them- that’s 10… 11, 12, 13, 14. There’s fourteen.” |
|Teacher: Use your recording sheet (or number sentence cards) to show what you found out. |
| |
|Student Recording Sheets Example: |
| |
| |
|[pic] |
Eight Mathematical Practices
|The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. |
|1 |Make sense of problems and persevere in solving them |
| | |
| |In Kindergarten, students learn that doing math involves solving problems and discussing how they solved them. Students will begin to explain the meaning of a |
| |problem, and look for ways to solve it. Kindergarteners will learn how to use objects and pictures to help them understand and solve problems. They will begin to |
| |check their thinking when the teacher asks them how they got their answer, and if the answer makes sense. When working in small groups or with a partner they will |
| |listen to the strategies of the group and will try different approaches. |
|2 |Reason abstractly and quantitatively |
| | |
| |Mathematically proficient students in Kindergarten make sense of quantities and the relationships while solving tasks. This involves two processes- |
| |decontextualizing and contextualizing. |
| |In Kindergarten, students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 7 children on the |
| |playground and some children go line up. If there are 4 children still playing, how many children lined up?” Kindergarten students are expected to translate that |
| |situation into the equation: 7-4 = ___, and then solve the task. |
| |Students also contextualize situations during the problem solving process. For example, while solving the task above, students refer to the context of the task to |
| |determine that they need to subtract 4 since the number of children on the playground is the total number of students except for the 4 that are still playing. |
| |Abstract reasoning also occurs when students measure and compare the lengths of objects. |
|3 |Construct viable arguments and critique the reasoning of others |
| | |
| |Mathematically proficient students in Kindergarten accurately use mathematical terms to construct arguments and engage in discussions about problem solving |
| |strategies. For example, while solving the task, “There are 8 books on the shelf. If you take some books off the shelf and there are now 3 left, how many books did |
| |you take off the shelf?” students will solve the task, and then be able to construct an accurate argument about why they subtracted 3 form 8 rather than adding 8 |
| |and 3. Further, Kindergarten students are expected to examine a variety of problem solving strategies and begin to recognize the reasonableness of them, as well as |
| |similarities and differences among them. |
|4 |Model with mathematics |
| | |
| |Mathematically proficient students in Kindergarten model real-life mathematical situations with a number sentence or an equation, and check to make sure that their |
| |equation accurately matches the problem context. |
| |Kindergarten students rely on concrete manipulatives and pictorial representations while solving tasks, but the expectation is that they will also write an equation|
| |to model problem situations. |
| |For example, while solving the task “there are 7 bananas on the counter. If you eat 3 bananas, how many are left?” Kindergarten students are expected to write the |
| |equation 7-3 = 4. |
| |Likewise, Kindergarten students are expected to create an appropriate problem situation from an equation. |
| |For example, students are expected to orally tell a story problem for the equation 4+5 = 9. |
|5 |Use appropriate tools strategically |
| | |
| |Mathematically proficient students in Kindergarten have access to and use tools appropriately. These tools may include counters, place value (base ten) blocks, |
| |hundreds number boards, number lines, and concrete geometric shapes (e.g., pattern blocks, 3-d solids). Students should also have experiences with educational |
| |technologies, such as calculators, virtual manipulatives, and mathematical games that support conceptual understanding. |
| |During classroom instruction, students should have access to various mathematical tools as well as paper, and determine which tools are the most appropriate to use.|
| |For example, while solving the task “There are 4 dogs in the park. If 3 more dogs show up, how many dogs are they?” |
| |Kindergarten students are expected to explain why they used specific mathematical tools.” |
|6 |Attend to precision |
| | |
| |Mathematically proficient students in Kindergarten are precise in their communication, calculations, and measurements. In all mathematical tasks, students in |
| |Kindergarten describe their actions and strategies clearly, using grade-level appropriate vocabulary accurately as well as giving precise explanations and reasoning|
| |regarding their process of finding solutions. |
| |For example, while measuring objects iteratively (repetitively), students check to make sure that there are no gaps or overlaps. During tasks involving number |
| |sense, students check their work to ensure the accuracy and reasonableness of solutions. |
|7 |Look for and make use of structure |
| | |
| |Mathematically proficient students in Kindergarten carefully look for patterns and structures in the number system and other areas of mathematics. While solving |
| |addition problems, students begin to recognize the commutative property, in that 1+4 = 5, and 4+1 = 5. |
| |While decomposing teen numbers, students realize that every number between 11 and 19, can be decomposed into 10 and some leftovers, such as 12 = 10+2, 13 = 10+3, |
| |etc. |
| |Further, Kindergarten students make use of structures of mathematical tasks when they begin to work with subtraction as missing addend problems, such as 5- 1 = __ |
| |can be written as 1+ __ = 5 and can be thought of as how much more do I need to add to 1 to get to 5? |
|8 |Look for and express regularity in repeated reasoning |
| | |
| |Mathematically proficient students in Kindergarten begin to look for regularity in problem structures when solving mathematical tasks. |
| |Likewise, students begin composing and decomposing numbers in different ways. |
| |For example, in the task “There are 8 crayons in the box. Some are red and some are blue. How many of each could there be?” |
| |Kindergarten students are expected to realize that the 8 crayons could include 4 of each color (4+4 = 8), 5 of one color and 3 of another (5+3 = 8), etc. |
| |For each solution, students repeated engage in the process of finding two numbers that can be joined to equal 8. |
MATH WORKSTATIONS
Math workstations allow students to engage in authentic and meaningful hands-on learning. They often last for several weeks, giving students time to reinforce or extend their prior instruction. Before students have an opportunity to use the materials in a station, introduce them to the whole class, several times. Once they have an understanding of the concept, the materials are then added to the work stations.
Station Organization and Management Sample
Teacher A has 12 containers labeled 1 to 12. The numbers correspond to the numbers on the rotation chart. She pairs students who can work well together, who have similar skills, and who need more practice on the same concepts or skills. Each day during math work stations, students use the center chart to see which box they will be using and who their partner will be. Everything they need for their station will be in their box. Each station is differentiated. If students need more practice and experience working on numbers 0 to 10, those will be the only numbers in their box. If they are ready to move on into the teens, then she will place higher number activities into the box for them to work with.
[pic][pic]
In the beginning there is a lot of prepping involved in gathering, creating, and organizing the work stations. However, once all of the initial work is complete, the stations are easy to manage. Many of her stations stay in rotation for three or four weeks to give students ample opportunity to master the skills and concepts.
Read Math Work Stations by Debbie Diller.
In her book, she leads you step-by-step through the process of implementing work stations.
MATH WORKSTATION INFORMATION CARD
MATH WORKSTATION SCHEDULE Week of: _________________
|DAY |Technology |Problem Solving Lab |Fluency |Math |Small Group Instruction |
| |Lab | |Lab |Journal | |
|Mon. |Group ____ |Group ____ |Group ____ |Group ____ | |
| | | | | |BASED |
| | | | | |ON CURRENT OBSERVATIONAL DATA |
|Tues. |Group ____ |Group ____ |Group ____ |Group ____ | |
|Wed. |Group ____ |Group ____ |Group ____ |Group ____ | |
|Thurs. |Group ____ |Group ____ |Group ____ |Group ____ | |
|Fri. |Group ____ |Group ____ |Group ____ |Group ____ | |
INSTRUCTIONAL GROUPING
| |GROUP A | |GROUP B |
|1 | |1 | |
|2 | |2 | |
|3 | |3 | |
|4 | |4 | |
|5 | |5 | |
|6 | |6 | |
| |
| |GROUP C | |GROUP D |
|1 | |1 | |
|2 | |2 | |
|3 | |3 | |
|4 | |4 | |
|5 | |5 | |
|6 | |6 | |
Math In Focus Lesson Structure
|LESSON STRUCTURE |RESOURCES |COMMENTS |
|Chapter Opener |Teacher Materials |Recall Prior Knowledge (RPK) can take place just before the |
|Assessing Prior Knowledge |Quick Check |pre-tests are given and can take 1-2 days to front load |
| |Pre-Test (Assessment Book) |prerequisite understanding |
| |Recall Prior Knowledge | |
|The Pre Test serves as a diagnostic test of| |Quick Check can be done in concert with the RPK and used to |
|readiness of the upcoming chapter |Student Materials |repair student misunderstandings and vocabulary prior to the |
| |Student Book (Quick Check); Copy of |pre-test ; Students write Quick Check answers on a separate sheet |
| |the Pre Test; Recall prior Knowledge |of paper |
| | | |
| | |Quick Check and the Pre Test can be done in the same block (See |
| | |Anecdotal Checklist; Transition Guide) |
| | | |
| | |Recall Prior Knowledge – Quick Check – Pre Test |
|Direct Involvement/Engagement |Teacher Edition |The Warm Up activates prior knowledge for each new lesson |
|Teach/Learn |5-minute warm up |Student Books are CLOSED; Big Book is used in Gr. K |
| |Teach; Anchor Task |Teacher led; Whole group |
|Students are directly involved in making | |Students use concrete manipulatives to explore concepts |
|sense, themselves, of the concepts – by |Technology |A few select parts of the task are explicitly shown, but the |
|interacting the tools, manipulatives, each |Digi |majority is addressed through the hands-on, constructivist |
|other, and the questions | |approach and questioning |
| |Other |Teacher facilitates; Students find the solution |
| |Fluency Practice | |
|Guided Learning and Practice |Teacher Edition |Students-already in pairs /small, homogenous ability groups; |
|Guided Learning |Learn |Teacher circulates between groups; Teacher, anecdotally, captures |
| | |student thinking |
| |Technology | |
| |Digi | |
| | |Small Group w/Teacher circulating among groups |
| |Student Book |Revisit Concrete and Model Drawing; Reteach |
| |Guided Learning Pages |Teacher spends majority of time with struggling learners; some |
| |Hands-on Activity |time with on level, and less time with advanced groups |
| | |Games and Activities can be done at this time |
| Independent Practice |Teacher Edition |Let’s Practice determines readiness for Workbook and small |
| |Let’s Practice |group work and is used as formative assessment; Students not |
|A formal formative | |ready for the Workbook will use Reteach. The Workbook is |
|…assessment |Student Book |continued as Independent Practice. |
| |Let’s Practice |Manipulatives CAN be used as a communications tool as needed. |
| | |Completely Independent |
| |Differentiation Options |On level/advance learners should finish all workbook pages. |
| |All: Workbook | |
| |Extra Support: Reteach | |
| |On Level: Extra Practice | |
| |Advanced: Enrichment | |
| Extending the Lesson |Math Journal | |
| |Problem of the Lesson | |
| |Interactivities | |
| |Games | |
| Lesson Wrap Up |Problem of the Lesson |Workbook or Extra Practice Homework is only assigned when |
| |Homework (Workbook , Reteach, or |students fully understand the concepts (as additional |
| |Extra Practice) |practice) |
| | |Reteach Homework (issued to struggling learners) should be |
| | |checked the next day |
| End of Chapter Wrap Up |Teacher Edition |Use Chapter Review/Test as “review” for the End of Chapter |
|and Post Test |Chapter Review/Test |Test Prep. Put on your Thinking Cap prepares students for |
| |Put on Your Thinking Cap |novel questions on the Test Prep; Test Prep is graded/scored. |
| | |The Chapter Review/Test can be completed |
| |Student Workbook |Individually (e.g. for homework) then reviewed in class |
| |Put on Your Thinking Cap |As a ‘mock test’ done in class and doesn’t count |
| | |As a formal, in class review where teacher walks students |
| |Assessment Book |through the questions |
| |Test Prep | |
| | |Test Prep is completely independent; scored/graded |
| | |Put on Your Thinking Cap (green border) serve as a capstone |
| | |problem and are done just before the Test Prep and should be |
| | |treated as Direct Engagement. By February, students should be|
| | |doing the Put on Your Thinking Cap problems on their own |
TRANSITION LESSON STRUCTURE (No more than 2 days)
• Driven by Pre-test results, Transition Guide
• Looks different from the typical daily lesson
|Transition Lesson – Day 1 |
| |
|Objective: |
|CPA Strategy/Materials |Ability Groupings/Pairs (by Name) |
| | |
| | |
| | |
| | |
| | |
|Task(s)/Text Resources |Activity/Description |
| | |
| | |
| | |
| | |
| | |
IDEAL MATH BLOCK LESSON PLANNING TEMPLATE
|CCSS &| |
|OBJ:(s| |
|) | |
| | |
| | |
| | |
| | |
| |Fluency: | |
| |K.OA.5 | |
| |Strategy: | |
| | | |
| |Tool(s): | |
|Math |Getting Ready | |
|In | | |
|Focus/| | |
|EnGage| | |
|NY | | |
| |Investigate | |
| | | |
| | | |
| |Discover | |
| |Explore | |
| |Apply | |
| | | |
|Differ|Small Group Instruction | |
|entiat| | |
|ion: | | |
|Math | | |
|Workst| | |
|ations| | |
| |Tech. Lab | |
| | | |
| | | |
| |Problem Solving Lab | |
| |CCSS: | |
| |K.OA.1 | |
| |K.OA.2 | |
| | | |
| | | |
| |Fluency Lab | |
| |K.OA.5 | |
| | | |
| |Strategy: | |
| | | |
| |Tool(s): | |
| |Math Journal | |
| | | |
| |MP3: Construct viable | |
| |arguments and critique | |
| |the reasoning of others | |
| |Summary/ Lesson Closure | |
Danielson Framework for Teaching: Domain 1: Planning Preparation
Lesson Planning Support Tool
______________________________________________________________________________________________________
Component 1A: Knowledge of Content and Pedagogy
Content
(Fluency Practice and Anchor Problem clearly outlined in lesson plans provide reinforcement of prerequisite knowledge/skills needed;
(Essentials question(s) and lesson objective(s) support learning of New Jersey Student Learning Standards grade level expectations;
Pedagogy
(Daily fluency practice is clearly outlined in lesson plans;
(Multiple strategies are evident within lesson plans;
(Mathematical tools outlined within lesson plans;
___________________________________________________________________________________________________________________________
Component 1B: Knowledge of Students
Intentional Student Grouping is evident within lesson plans:
Independent Practice: Which students will work on:
(MIF Re-Teach
(MIF Practice
(MIF Extra Practice
(MIF Enrichment
Math Workstations: Which students will work in:
(Fluency Lab
(Technology Lab
(Math Journal
(Problem Solving Lab
Component 1C: Setting Instructional Outcomes
(Lesson plan objectives are aligned to one or more New Jersey Student Standards for Learning
(Connections made to previous learning
(Outcomes: student artifacts are differentiated
Component 1D: Demonstrating Knowledge of Resources
District Approved Programs: (Use Math In Focus/EnGageNY/Go Math resources are evident
Technology: ( Technology used to help students understand the lesson objective is evident
( Students use technology to gain an understanding of the lesson objective
Supplemental Resources: ( Integration of additional materials evident (Math Workstations)
________________________________________________________________________________________________________________________
Component 1E: Designing Coherent Instruction
(Lesson Plans support CONCEPTUAL UNDERSTANDING
(Lesson Plans show evidences of CONCRETE, PICTORIAL, and ABSTRACT representation
(Alignment between OBJECTIVES, APPLICATION, and ASSESSMENT evident
___________________________________________________________________________________________________________________________
Component 1F: Assessing Student Learning
Lesson Plans include: ( Focus Question/Essential Understanding
( Anchor Problem
( Checks for Understanding
( Demonstration of Learning (Exit Ticket)
Planning Calendar January 2017
|Monday |Tuesday |Wednesday |Thursday |Friday |
|2 |3 |4 |5 |6 |
|9 |10 |11 |12 |13 |
|16 |17 |18 |19 |20 |
|23 |24 |25 |26 |27 |
|30 |31 | | | |
February 2017
|Monday |Tuesday |Wednesday |Thursday |Friday |
| | |1 |2 |3 |
| | | | |MIF CH. 8 |
| | | | |TEST PREP |
| | | | |MIF CH. 8 PERFORMANCE TASK |
|6 |7 |8 |9 |10 |
|13 |14 |15 |16 |17 |
| | | | |MIF CH. 9 |
| | | | |TEST |
| | | | |MIF CH. 9 PERFORMANCE TASK |
|20 |21 |22 |23 |24 |
|27 |28 | | | |
Planning Calendar April 2017
|Monday |Tuesday |Wednesday |Thursday |Friday |
|3 |4 |5 |6 END OF MP 3 |7 |
| | | | | |
|10 |11 |12 |13 |14 |
|17 |18 |19 |20 |21 |
|24 |25 |26 |27 |28 |
| | | |MIF CH. 18 | |
| | | |TEST | |
| | | |MIF CH. 18 PERFORMANCE TASK | |
May 2017
|Monday |Tuesday |Wednesday |Thursday |Friday |
|1 |2 |3 |4 |5 |
|8 |9 |10 |11 |12 |
|15 |16 |17 |18 |19 |
| | | |ENGAGENY |ENGAGENY |
| | | |MODULE 5 |MODULE 5 |
| | | |MID-MODULE ASSESSMENT |MID-MODULE ASSESSMENT |
|22 |23 |24 |25 |26 |
|ENGAGENY | | | | |
|MODULE 5 | | | | |
|MID-MODULE ASSESSMENT | | | | |
|29 |30 |31 | | |
June 2017
|Monday |Tuesday |Wednesday |Thursday |Friday |
| | | |1 |2 |
|5 |6 |7 |8 |9 |
| |ENGAGENY |ENGAGENY |ENGAGENY | |
| |MODULE 5 |MODULE 5 |MODULE 5 | |
| |END OF MODULE ASSESSMENT |END OF MODULE ASSESSMENT |END OF MODULE ASSESSMENT | |
|12 |13 |14 |15 |16 |
|19 |20 |21 |22 |23 |
|MIF CH. 15 TEST | | | | |
|MIF CH. 15 PERFORMANCE TASK | | | | |
|26 |27 |28 |29 |30 |
Kindergarten Math Unit IV Instructional and Assessment Framework
|Recommended |Activities |CCSS |Notes |
|April 10th- , 2017 |Math In Focus Ch. 18 Lesson 1 | | |
| |Writing Subtraction and Representing Subtraction Stories | | |
| | | | |
| | |.3 | |
| | |.4 | |
| | |.5 | |
| | | | |
| | | | |
| | | | |
|April 11th- , 2017 |Math In Focus Ch. 18 Lesson 1 | | |
| |Writing Subtraction and Representing Subtraction Stories | | |
|April 12th- , 2017 |Math In Focus Ch. 18 Lesson 1 | | |
| |Writing Subtraction and Representing Subtraction Stories | | |
|April 13th- , 2017 |Math In Focus Ch. 18 Lesson 2 | | |
| |Comparing Sets | | |
|April 14th – 21st, 2017 |Spring Recess | | |
|April 24th , 2017 |Math In Focus Ch. 18 Lesson 2 | | |
| |Comparing Sets | | |
|April 25th , 2017 |Math In Focus Ch. 18 Lesson 3 | | |
| |Subtraction Facts to 5 | | |
|April 26th , 2017 |Math In Focus Ch. 18 Lesson 3 | | |
| |Subtraction Facts to 5 | | |
|April 27th , 2017 |MIF Ch. 18 Assessment | | |
| |MIF Ch. 18 Performance Task | | |
|April 28th , 2017 |EnGageNY Module 5: Topic A: Lesson 1 | | |
| |Count straws into piles of ten; count the piles as 10 ones. |.1 | |
| | |.2 | |
| | |.4a .4b | |
| | |.4c | |
| | |.5 | |
| | | | |
| | |K.NBT.1 | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
|May 1st , 2017 |EnGageNY Module 5: Topic A: Lesson 2 | | |
| |Count 10 objects within counts of 10 to 20 objects, and describe | | |
| |as 10 ones and ___ ones. | | |
|May 2nd, 2017 |EnGageNY Module 5: Topic A: Lesson 3 | | |
| |Count and circle 10 objects within images of 10 to 20 objects, | | |
| |and describe as 10 ones and ___ ones. | | |
|May 3rd, 2017 |EnGageNY Module 5: Topic A: Lesson 4 | | |
| |Count straws the Say Ten way to 19; make a pile for each ten. | | |
|May 4th , 2017 |EnGageNY Module 5: Topic A: Lesson 5 | | |
| |Count straws the Say Ten way to 20; make a pile for each ten. | | |
|May 5th , 2017 |EnGageNY Module 5: Topic B: Lesson 6 Model with objects and |.3 K.NBT.1 | |
| |represent numbers 10 to 20 with place value or Hide Zero cards. |.1 | |
| | |.2 | |
| | |.4a .4b | |
| | |.4c | |
| | |.5 | |
| |EnGageNY Module 5: Topic B: Lesson 7 Model and write numbers 10 | | |
|May 8th, 2017 |to 20 as number bonds. | | |
|May 9th, 2017 |EnGageNY Module 5: Topic B: Lesson 8 Model teen numbers with | | |
| |materials from abstract to concrete. | | |
|May 10th, 2017 |EnGageNY Module 5: Topic B: Lesson 9 | | |
| |Draw teen numbers from abstract to pictorial. | | |
|May 11th, 2017 |EnGageNY Module 5: Topic C: Lesson 10 | | |
| |Build a Rekenrek to 20. | | |
| | |.4b .4c | |
| | |.5 K.NBT.1 | |
| | |.3 .4a | |
|May 12th, 2017 |EnGageNY Module 5: Topic C: Lesson 11 | | |
| |Show, count, and write numbers 11 to 20 in tower configurations | | |
| |increasing by 1—a pattern of 1 larger. | | |
|May 15th, 2017 |EnGageNY Module 5: Topic C: Lesson 12 | | |
| |Represent numbers 20 to 11 in tower configurations decreasing by | | |
| |1—a pattern of 1 smaller. | | |
|May 16th, 2017 |EnGageNY Module 5: Topic C: Lesson 13 | | |
| |Show, count, and write to answer how many questions in linear and| | |
| |array configurations. | | |
|May 17th, 2017 |EnGageNY Module 5: Topic C: Lesson 14 | | |
| |Show, count, and write to answer how many questions with up to 20| | |
| |objects in circular configurations. | | |
|May 18th, 2017 |Mid-Module Assessment: Topics A–C (Interview-style assessment) | | |
| | | | |
| | |.1-5 | |
| | | | |
| | |K.NBT.1 | |
|May 19th, 2017 |Mid-Module Assessment: Topics A–C (Interview-style assessment) | | |
|May 22nd, 2017 |Mid-Module Assessment: Topics A–C (Interview-style assessment) | | |
|May 23rd, 2017 |EnGageNY Module 5: Topic D: Lesson 15 | | |
| |Count up and down by tens to 100 with Say Ten and regular | | |
| |counting. | | |
| | | | |
| | | | |
| | | | |
| | |.1 | |
| | |.2 | |
| | |.3 .4c | |
| | |.5 | |
| | | | |
| | |K.NBT.1 | |
|May 24th, 2017 |EnGageNY Module 5: Topic D: Lesson 16 | | |
| |Count within tens by ones. | | |
|May 25th, 2017 |EnGageNY Module 5: Topic D: Lesson 17 | | |
| |Count across tens when counting by ones through 40. | | |
|May 26th, 2017 |EnGageNY Module 5: Topic D: Lesson 18 | | |
| |Count across tens by ones to 100 with and without objects. | | |
|May 29th, 2017 |EnGageNY Module 5: Topic D: Lesson 19 | | |
| |Explore numbers on the Rekenrek. | | |
|May 30th, 2017 |EnGageNY Module 5: Topic E: Lesson 20 | | |
| |Represent teen number compositions and decompositions as addition| | |
| |sentences. |.5 | |
| | | | |
| | |K.NBT.1 | |
| | | | |
| | |.1 | |
| | |.2 | |
| | |.3 .4c | |
| | |.6 | |
| | | | |
| | |1.OA.8 1.NBT.3 | |
|May 31st, 2017 |EnGageNY Module 5: Topic E: Lesson 21 | | |
| |Represent teen number decompositions as 10 ones and some ones, | | |
| |and find a hidden part. | | |
|June 1st, 2017 |EnGageNY Module 5: Topic E: Lesson 22 | | |
| |Decompose teen numbers as 10 ones and some ones; compare some | | |
| |ones to compare the teen numbers. | | |
|June 2nd, 2017 |EnGageNY Module 5: Topic E: Lesson 23 | | |
| |Reason about and represent situations, decomposing teen numbers | | |
| |into 10 ones and some ones and composing 10 ones and some ones | | |
| |into a teen number. | | |
|June 5th, 2017 |EnGageNY Module 5: Topic E: Lesson 24 | | |
| |Culminating Task—Represent teen number decompositions in various | | |
| |ways. | | |
|June 6th, 2017 |End-of-Module Assessment: Topics D–E (Interview-style assessment)| | |
| | | | |
| | |.1-5 | |
| | | | |
| | |K.NBT.1 | |
|June 7th, 2017 |End-of-Module Assessment: Topics D–E (Interview-style assessment)| | |
|June 8th , 2017 |End-of-Module Assessment: Topics D–E (Interview-style assessment)| | |
|June 9th , 2017 |Spiral Review | | |
| |Math Workstations | | |
| | | | |
| | | | |
| | |K.OA | |
| | |K.NBT | |
| | |K.MD | |
| | |K.G | |
|June 12th, 2017 |KINDERGARTEN END OF YEAR ASSESSMENT | | |
| |Math Workstations | | |
|June 13th, 2017 |KINDERGARTEN END OF YEAR ASSESSMENT | | |
| |Math Workstations | | |
|June 14th, 2017 |KINDERGARTEN END OF YEAR ASSESSMENT | | |
| |Math Workstations | | |
|June 15th, 2017 |KINDERGARTEN END OF YEAR ASSESSMENT | | |
| |Math Workstations | | |
|June 16th, 2017 |KINDERGARTEN END OF YEAR ASSESSMENT | | |
| |Math Workstations | | |
|June 19th, 2017 |KINDERGARTEN END OF YEAR ASSESSMENT |END OF MP | |
| |Math Workstations | | |
New Jersey Student Learning Standards
Kindergarten Mathematics
Student Fluency Progress Monitoring Tool
NJSLS: K.OA.5: Add and subtract within 5.
Student Name: _________________________________________ School: ___________________ Teacher: ___________________
Student Conference Note:
Student: Shade in each box upon mastery of fact.
Teacher: Enter the date mastery was achieved for each fact in the upper left corner.
AUTOMATICITY
Addition Facts within 5
|5 |4 |
|PLD Level 5: 100% |PLD Level 4: 89% |PLD Level 3: 79% |PLD Level 2: 69% |PLD Level 1: 59% |
|Distinguished command |Strong Command |Moderate Command |Partial Command |Little Command |
|Student work shows distinguished levels |Student work shows strong levels of |Student work shows moderate levels of |Student work shows partial understanding |Student work shows little understanding |
|of understanding of the mathematics. |understanding of the mathematics. |understanding of the mathematics. |of the mathematics. |of the mathematics. |
| | | | | |
|Student constructs and communicates a |Student constructs and communicates a |Student constructs and communicates a |Student constructs and communicates an |Student attempts to constructs and |
|complete response based on |complete response based on |complete response based on |incomplete response based on student’s |communicates a response using the: |
|explanations/reasoning using the: |explanations/reasoning using the: |explanations/reasoning using the: |attempts of explanations/ reasoning using|Tools: |
|Tools: |Tools: |Tools: |the: |Manipulatives |
|Manipulatives |Manipulatives |Manipulatives |Tools: |Five Frame |
|Five Frame |Five Frame |Five Frame |Manipulatives |Ten Frame |
|Ten Frame |Ten Frame |Ten Frame |Five Frame |Number Line |
|Number Line |Number Line |Number Line |Ten Frame |Part-Part-Whole Model |
|Part-Part-Whole Model |Part-Part-Whole Model |Part-Part-Whole Model |Number Line |Strategies: |
|Strategies: |Strategies: |Strategies: |Part-Part-Whole Model |Drawings |
|Drawings |Drawings |Drawings |Strategies: |Counting All |
|Counting All |Counting All |Counting All |Drawings |Count On/Back |
|Count On/Back |Count On/Back |Count On/Back |Counting All |Skip Counting |
|Skip Counting |Skip Counting |Skip Counting |Count On/Back |Making Ten |
|Making Ten |Making Ten |Making Ten |Skip Counting |Decomposing Number |
|Decomposing Number |Decomposing Number |Decomposing Number |Making Ten |Precise use of math vocabulary |
|Precise use of math vocabulary |Precise use of math vocabulary |Precise use of math vocabulary |Decomposing Number | |
|Response includes an efficient and | | |Precise use of math vocabulary |Response includes limited evidence of the|
|logical progression of mathematical |Response includes a logical progression |Response includes a logical but incomplete| |progression of mathematical reasoning and|
|reasoning and understanding. |of mathematical reasoning and |progression of mathematical reasoning and |Response includes an incomplete or |understanding. |
| |understanding. |understanding. |illogical progression of mathematical | |
| | |Contains minor errors. |reasoning and understanding. | |
|5 points |4 points |3 points |2 points |1 point |
DATA DRIVEN INSTRUCTION
Formative assessments inform instructional decisions. Taking inventories and assessments, observing reading and writing behaviors, studying work samples and listening to student talk are essential components of gathering data. When we take notes, ask questions in a student conference, lean in while a student is working or utilize a more formal assessment we are gathering data. Learning how to take the data and record it in a meaningful way is the beginning of the cycle.
Analysis of the data is an important step in the process. What is this data telling us? We must look for patterns, as well as compare the notes we have taken with work samples and other assessments. We need to decide what are the strengths and needs of individuals, small groups of students and the entire class. Sometimes it helps to work with others at your grade level to analyze the data.
Once we have analyzed our data and created our findings, it is time to make informed instructional decisions. These decisions are guided by the following questions:
• What mathematical practice(s) and strategies will I utilize to teach to these needs?
• What sort of grouping will allow for the best opportunity for the students to learn what it is I see as a need?
• Will I teach these strategies to the whole class, in a small guided group or in an individual conference?
• Which method and grouping will be the most effective and efficient? What specific objective(s) will I be teaching?
Answering these questions will help inform instructional decisions and will influence lesson planning.
Then we create our instructional plan for the unit/month/week/day and specific lessons.
It’s important now to reflect on what you have taught.
Did you observe evidence of student learning through your checks for understanding, and through direct application in student work?
What did you hear and see students doing in their reading and writing?
Data Analysis Form School: __________________ Teacher: __________________________ Date: _______________
Assessment: ____________________________________________ NJSLS: _____________________________________________________
|GROUPS (STUDENT INITIALS) |SUPPORT PLAN |PROGRESS |
|MASTERED (86% - 100%) (PLD 4/5): | | |
|DEVELOPING (67% - 85%) (PLD 3): | | |
|INSECURE (51%-65%) (PLD 2): | | |
|BEGINNING (0%-50%) (PLD 1): | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
MATH PORTFOLIO EXPECTATIONS
The Student Assessment Portfolios for Mathematics are used as a means of documenting and evaluating students’ academic growth and development over time and in relation to the CCSS-M. Student Assessment Portfolios differ from student work folders in that they will contain tasks aligned specifically to the SGO focus. The September task entry(-ies) will reflect the prior year content and can serve as an additional baseline measure.
All tasks contained within the Student Assessment Portfolios are “practice forward” (closely aligned to the Standards for Mathematical Practice).
Four (4) or more additional tasks will be included in the Student Assessment Portfolios for Student Reflection and will be labeled as such.
In March – June, the months extending beyond the SGO window, tasks will shift from the SGO focus to a focus on the In-depth Opportunities for each grade.
K-2 General portfolio requirements
• As a part of last year’s end of year close-out process, we asked that student portfolios be ‘purged’; retaining a few artifacts and self-reflection documents that would transition with them to the next grade. In this current year, have students select 2-3 pieces of prior year’s work to file in the Student Assessment Portfolio.
• Tasks contained within the Student Assessment Portfolios are “practice forward” and denoted as “Individual”, “Partner/Group”, and “Individual w/Opportunity for Student Interviews[1].
• Each Student Assessment Portfolio should contain a “Task Log” that documents all tasks, standards, and rubric scores aligned to the performance level descriptors (PLDs).
• Student work should be attached to a completed rubric; teacher feedback on student work is expected.
• Students will have multiple opportunities to revisit certain standards. Teachers will capture each additional opportunity “as a new and separate score” in the task log and in Genesis.
• A 2-pocket folder for each Student Assessment Portfolio is recommended.
• All Student Assessment Portfolio entries should be scored and recorded in Genesis as an Authentic Assessment grade (25%)[2].
• All Student Assessment Portfolios must be clearly labeled, maintained for all students, inclusive of constructive teacher and student feedback and accessible for administrator review
MATHEMATICS PORTFOLIO: END OF YEAR REQUIREMENTS
At the start of the school year, you were provided with guidelines for helping students maintain their Mathematics Portfolios whereby students added artifacts that documented their growth and development over time. Included in the portfolio process was the opportunity for students to reflect on their thinking and evaluate what they feel constitutes “quality work.” As a part of the end of year closeout process, we are asking that you work with your students to help them ‘purge’ their current portfolios and retain the artifacts and self-reflection documents that will transition with them to the next grade.
Grades K-2
Purging and Next-Grade Transitioning
During the third (3rd) week of June, give students the opportunity to review and evaluate their portfolio to date; celebrating their progress and possibly setting goals for future growth. During this process, students will retain ALL of their current artifacts in their Mathematics Portfolios. The Student Profile Sheet from the end of year assessment should also be included in the student math portfolio. In the upcoming school year, after the new teacher has reviewed the portfolios, students will select 1-2 pieces to remain in the portfolio and take the rest home.
NAME: ____________________________________________________ DATE: ____________________
[pic]
NAME: ____________________________________________________ DATE: ____________________
[pic]
[pic]
[pic]
Resources
Engage NY
[0]=im_field_subject%3A19
Common Core Tools
Achieve the Core
Manipulatives
Illustrative Math Project :
Inside Mathematics:
Sample Balance Math Tasks:
Georgia Department of Education:
Gates Foundations Tasks:
Minnesota STEM Teachers’ Center:
Singapore Math Tests K-12:
:
-----------------------
[1] The Mathematics Department will provide guidance on task selection, thereby standardizing the process across the district and across grades/courses.
[2] The Mathematics Department has propagated gradebooks with appropriate weights.
-----------------------
ORANGE PUBLIC SCHOOLS
OFFICE OF CURRICULUM AND INSTRUCTION
OFFICE OF MATHEMATICS
(Pictures)
(Manipulatives)
(Written)
(Real Life Situations)
(Communication)
Kindergarten Ideal Math Block
Essential Components
15-20 min.
50-60 min.
SUMMARY: Whole Group
Lesson Closure: Student Reflection; Real Life Connections to Concept
Problem
Solving
Lab
CENTERS/STATIONS:
Pairs / Small Group/ Individual
DIFFERENTIATED activities designed to RETEACH, REMEDIATE, ENRICH student’s understanding of concepts.
Small Group
Instruction
Technology Lab
Fluency Lab
Math
Journal
Lab
FLUENCY: Partner/Small Group
CONCRETE, PICTORIAL, and ABSTRACT approaches to support ARITHMETIC FLUENCY and FLUENT USE OF STRATEGIES.
5 min.
Getting Ready: Whole Group
Anchor Task: Math In Focus Learn
INVESTIGATE: Whole Group
Children are invited to sing, clap, rhyme, and discuss colorful, playful scenes presented in the BIG BOOK while the teacher SYSTEMATICALLY EMPLOYS and ELICITS related MATH TALK.
Note:
• Place emphasis on the flow of the lesson in order to ensure the development of students’ conceptual understanding.
• Outline each essential component within lesson plans.
• Math Workstations may be conducted in the beginning of the block in order to utilize additional support staff.
• Recommended: 5-10 technology devices for use within TECHNOLOGY and FLUENCY workstations.
APPLY: INDEPENDENT PRACTICE
Math In Focus Let’s Practice, Workbook, Reteach, Extra Practice, Enrichment
DISCOVER: Whole Group
Provides HANDS-ON work to allow children to ACT OUT or ENGAGE ACTIVELY with the new MATH IDEA
EXPLORE: Partner / Small Group
Math In Focus Hands-On, Guided Practice, Let’s Explore
Math Workstation: _____________________________________________________________________ Time: _________________
NJSLS.:
_____________________________________________________________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________________________________________________________
Objective(s): By the end of this task, I will be able to:
• ________________________________________________________________________________________________________________________________________________
• ________________________________________________________________________________________________________________________________________________
• ________________________________________________________________________________________________________________________________________________
Task(s):
• _______________________________________________________________________________________________________________________________________________
• _______________________________________________________________________________________________________________________________________________
• _______________________________________________________________________________________________________________________________________________
• ______________________________________________________________________________________________________________________________________________
Exit Ticket:
• ______________________________________________________________________________________________________________________________________________
• ______________________________________________________________________________________________________________________________________________
• ______________________________________________________________________________________________________________________________________________
PRE TEST
DIRECT ENGAGEMENT
GUIDED LEARNING
ADDITIONAL PRACTICE
INDEPENDENT PRACTICE
POST TEST
WINTER RECESS
DISTRICT UNIT III ASSESSMENT
SPRING RECESS
................
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