6th Grade Mathematics - Orange Board of Education



2nd Grade Mathematics

Sums and Differences to 100

Unit 1 Curriculum Map: September 6th – November 14th, 2017

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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. |Second Grade Unit I NJSLS |p. 16 |

|X. |Eight Mathematical Practices |p. 23 |

|XI. |Ideal Math Block |p. 26 |

|XII. |Math Workstations |p. 27 |

|XIII. |Math In Focus Lesson Structure |p.30 |

|XIX. |Ideal Math Block Planning Template |p. 33 |

|XX. |Planning Calendar |p. 36 |

|XXI. |Instructional and Assessment Framework |p. 38 |

|XXII. |Performance Tasks |p. 41 |

|XXIII. |PLD Rubric |p. 47 |

|XXIV. |Data Driven Instruction |p. 48 |

|XXV. |Math Portfolio Expectations |p. 51 |

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:

2.OA.1

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2.NBT.5

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

2.NBT.9

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Learning Goal(s):

Students will use multiple representations to solve multi-step addition and/or subtraction situations (2.OA.1) and explain the connection between various solution paths (2.NBT.5, 2.NBT.9).

Student Friendly Version:

We are learning to represent and solve word problems and explain how different representations match the story situation and the math operations.

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.

K-2 CONCEPT MAP

|Second Grade Unit I |

|In this Unit Students will: |

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|2.OA.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of: |

|Adding to, |

|Taking from, |

|Putting Together, |

|Taking Apart, and |

|Comparing with unknowns in all positions |

| |

|2.O.A.2: Fluently add and subtract within 20 using mental strategies: |

|Count On/ Count Back |

|Making Ten/Decomposing (Ten) |

|Addition and Subtraction Relationship |

|Doubles +/- |

|Know from memory all sums of two one digit numbers. |

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|2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. |

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|2.MD.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two |

|measurements relate to the size of the unit chosen. |

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|2.MD.3: Estimate lengths using units of inches, feet, centimeters, and meters. |

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|2.MD.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. |

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|2.MD.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using |

|drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. |

|Embedded Standards: 2.OA.1 and 2.OA.2 |

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|2.MD.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., |

|and represent whole-number sums and differences within 100 on a number line diagram. |

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|Mathematical Practices |

|Make sense of 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: Operations and Algebraic Thinking |

|2.OA.1 |Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, |

| |with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. |

|Second Grade students extend their work with addition and subtraction word problems in two major ways. First, they represent and solve word problems within 100, building upon their previous work to 20. In addition, |

|they represent and solve one and two-step word problems of all three types (Result Unknown, Change Unknown, Start Unknown). Please see Table 1 at end of document for examples of all problem types. |

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|One-step word problems use one operation. Two-step word problems use two operations which may include the same operation or opposite operations. |

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|Two-Step Problems: Because Second Graders are still developing proficiency with the most difficult subtypes (shaded in white in Table 1 at end of the glossary): Add To/Start Unknown; Take From/Start Unknown; |

|Compare/Bigger Unknown; and Compare/Smaller Unknown, two-step problems do not involve these sub-types (Common Core Standards Writing Team, May 2011). Furthermore, most two-step problems should focus on single-digit |

|addends since the primary focus of the standard is the problem-type. |

|New Jersey Student Learning Standards: Operations and Algebraic Thinking |

|2.OA.2 |Fluently add and subtract within 20 using mental strategies. |

| |By end of Grade 2, know from memory all sums of two one-digit numbers. |

| |See standard 1.OA.6 for a list of mental strategies. |

| |

|Building upon their work in First Grade, Second Graders use various addition and subtraction strategies in order to fluently add and subtract within 20: |

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|1.OA.6 Mental Strategies |

|Counting On/Counting Back |

|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 (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4) |

|Creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12, 12 + 1 = 13 |

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|Second Graders internalize facts and develop fluency by repeatedly using strategies that make sense to them. When students are able to demonstrate fluency they are accurate, efficient, and flexible. Students must have|

|efficient strategies in order to know sums from memory. |

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|Research indicates that teachers can best support students’ memory of the sums of two one-digit numbers through varied experiences including making 10, breaking numbers apart, and working on mental strategies. These |

|strategies replace the use of repetitive timed tests in which students try to memorize operations as if there were not any relationships among the various facts. When teachers teach facts for automaticity, rather than|

|memorization, they encourage students to think about the relationships among the facts. (Fosnot & Dolk, 2001) |

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|It is no accident that the standard says “know from memory” rather than “memorize”. The first describes an outcome, whereas the second might be seen as describing a method of achieving that outcome. So no, the |

|standards are not dictating timed tests. (McCallum, October 2011) |

|New Jersey Student Learning Standards: Measurement and Data |

|2.MD.1 |Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. |

|Second Graders build upon their non-standard measurement experiences in First Grade by measuring in standard units for the first time. Using both customary (inches and feet) and metric (centimeters and meters) units, |

|Second Graders select an attribute to be measured (e.g., length of classroom), choose an appropriate unit of measurement (e.g., yardstick), and determine the number of units (e.g., yards). As teachers provide rich |

|tasks that ask students to perform real measurements, these foundational understandings of measurement are developed: |

|Understand that larger units (e.g., yard) can be subdivided into equivalent units (e.g., inches) (partition). |

|Understand that the same object or many objects of the same size such as paper clips can be repeatedly used to determine the length of an object (iteration). |

|Understand the relationship between the size of a unit and the number of units needed (compensatory principal). Thus, the smaller the unit, the more units it will take to measure the selected attribute. |

|When Second Grade students are provided with opportunities to create and use a variety of rulers, they can connect their understanding of non-standard units from First Grade to standard units in second grade. |

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|For example: |

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|2.MD.2 |Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.|

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|Second Grade students measure an object using two units of different lengths. |

|This experience helps students realize that the unit used is as important as the attribute being measured. |

|This is a difficult concept for young children and will require numerous experiences for students to predict, measure, and discuss outcomes. |

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|Example: A student measured the length of a desk in both feet and centimeters. She found that the desk was 3 feet long. |

|She also found out that it was 36 inches long. |

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|Teacher: Why do you think you have two different measurements for the same desk? |

|Student: It only took 3 feet because the feet are so big. It took 36 inches because an inch is a whole lot smaller than a foot. |

|2.MD.3 |Estimate lengths using units of inches, feet, centimeters, and meters. |

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|Second Grade students estimate the lengths of objects using inches, feet, centimeters, and meters prior to measuring. |

|Estimation helps the students focus on the attribute being measured and the measuring process. |

|As students estimate, the student has to consider the size of the unit- helping them to become more familiar with the unit size. |

|In addition, estimation also creates a problem to be solved rather than a task to be completed. |

|Once a student has made an estimate, the student then measures the object and reflects on the accuracy of the estimate made and considers this information for the next measurement. |

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|Example: |

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|Teacher: How many inches do you think this string is if you measured it with a ruler? |

|Student: An inch is pretty small. I’m thinking it will be somewhere between 8 and 9 inches. |

|Teacher: Measure it and see. |

|Student: It is 9 inches. I thought that it would be somewhere around there. |

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|2.MD.4 |Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. |

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|Second Grade students determine the difference in length between two objects by using the same tool and unit to measure both objects. Students choose two objects to measure, identify an appropriate tool and unit, |

|measure both objects, and then determine the differences in lengths. |

|2.MD.5 |Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and |

| |equations with a symbol for the unknown number to represent the problem. |

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|Second Grade students apply the concept of length to solve addition and subtraction word problems with numbers within 100. Students should use the same unit of measurement in these problems. |

|Equations may vary depending on students’ interpretation of the task. |

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|Example: In P.E. class Kate jumped 14 inches. Mary jumped 23 inches. How much farther did Mary jump than Kate? |

|Write an equation and then solve the problem. |

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|2.MD.6 |Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and |

| |differences within 100 on a number line diagram. |

|Building upon their experiences with open number lines, Second Grade students create number lines with evenly spaced points corresponding to the numbers to solve addition and subtraction problems to 100. They |

|recognize the similarities between a number line and a ruler. |

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|Example: There were 27 students on the bus. 19 got off the bus. How many students are on the bus? |

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|Student A: I used a number line. I started at 27. I broke up 19 into 10 and 9. That way, I could take a jump of 10. I landed on 17. Then I broke the 9 up into 7 and 2. I took a jump of 7. That got me to 10. Then I |

|took a jump of 2. That’s 8. So, there are 8 students now on the bus. |

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|Student B: I used a number line. I saw that 19 is really close to 20. Since 20 is a lot easier to work with, I took a jump of 20. But, that was one too many. So, I took a jump of 1 to make up for the extra. I landed |

|on 8. So, there are 8 students on the bus. |

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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 |

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| |Mathematically proficient students in Second Grade examine problems and tasks, can make sense of the meaning of the task and find an entry point or a way to start the task. Second Grade students also develop a |

| |foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Second Grade, students’ work continues to use concrete manipulatives and pictorial |

| |representations as well as mental mathematics. Second Grade students also are expected to persevere while solving tasks; that is, if students reach a point in which they are stuck, they can reexamine the task in a |

| |different way and continue to solve the task. Lastly, mathematically proficient students complete a task by asking themselves the question, “Does my answer make sense?” |

|2 |Reason abstractly and quantitatively |

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| |Mathematically proficient students in Second Grade make sense of quantities and relationships while solving tasks. This involves two processes- decontextualizing and contextualizing. In Second Grade, students represent |

| |situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 25 children in the cafeteria and they are joined by 17 more children. How many students are in the cafeteria? ” Second|

| |Grade students translate that situation into an equation, such as: 25 + 17 = __ and then solve the problem. Students also contextualize situations during the problem solving process. For example, while solving the task |

| |above, students can refer to the context of the task to determine that they need to subtract 19 since 19 children leave. The processes of reasoning also other areas of mathematics such as determining the length of |

| |quantities when measuring with standard units. |

|3 |Construct viable arguments and critique the reasoning of others |

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| |Mathematically proficient students in Second Grade accurately use definitions and previously established solutions to construct viable arguments about mathematics. During discussions about problem solving strategies, |

| |students constructively critique the strategies and reasoning of their classmates. For example, while solving 74 - 18, students may use a variety of strategies, and after working on the task, can discuss and critique |

| |each other’s reasoning and strategies, citing similarities and differences between strategies. |

|4 |Model with mathematics |

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| |Mathematically proficient students in Second Grade 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. Second|

| |Grade students use concrete manipulatives and pictorial representations to provide further explanation of the equation. Likewise, Second Grade students are able to create an appropriate problem situation from an |

| |equation. For example, students are expected to create a story problem for the equation 43 + 17 = ___ such as “There were 43 gumballs in the machine. Tom poured in 17 more gumballs. How many gumballs are now in the |

| |machine?” |

|5 |Use appropriate tools strategically |

| |Mathematically proficient students in Second Grade have access to and use tools appropriately. These tools may include snap cubes, place value (base ten) blocks, hundreds number boards, number lines, rulers, and |

| |concrete geometric shapes (e.g., pattern blocks, 3-d solids). |

| |Students also have experiences with educational technologies, such as calculators and virtual manipulatives, which support conceptual understanding and higher-order thinking skills. |

| |During classroom instruction, students have access to various mathematical tools as well as paper, and determine which tools are the most appropriate to use. For example, while measuring the length of the hallway, |

| |students can explain why a yardstick is more appropriate to use than a ruler. |

|6 |Attend to precision |

| |Mathematically proficient students in Second Grade are precise in their communication, calculations, and measurements. |

| |In all mathematical tasks, students in Second Grade communicate 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 an object, care is taken to line up the tool correctly in order to get an accurate measurement. During tasks involving number sense, students consider if their answer is reasonable and check|

| |their work to ensure the accuracy of solutions. |

|7 |Look for and make use of structure |

| |Mathematically proficient students in Second Grade carefully look for patterns and structures in the number system and other areas of mathematics. For example, students notice number patterns within the tens place as |

| |they connect skip count by 10s off the decade to the corresponding numbers on a 100s chart. While working in the Numbers in Base Ten domain, students work with the idea that 10 ones equal a ten, and 10 tens equals 1 |

| |hundred. |

| |In addition, Second Grade students also make use of structure when they work with subtraction as missing addend problems, such as 50- 33 = __ can be written as 33+ __ = 50 and can be thought of as,” How much more do I |

| |need to add to 33 to get to 50?” |

|8 |Look for and express regularity in repeated reasoning |

| |Mathematically proficient students in Second Grade begin to look for regularity in problem structures when solving mathematical tasks. For example, after solving two digit addition problems by decomposing numbers (33+ |

| |25 = 30 + 20 + 3 +5), students may begin to generalize and frequently apply that strategy independently on future tasks. |

| |Further, students begin to look for strategies to be more efficient in computations, including doubles strategies and making a ten. |

| |Lastly, while solving all tasks, Second Grade students accurately check for the reasonableness of their solutions during and after completing the task. |

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MATH WORKSTATIONS

Math work stations 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.

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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: | |

| |2.OA.2 | |

| | | |

| |Strategy: | |

| | | |

| |Tool(s): | |

|Math |Launch | |

|In | | |

|Focus/| | |

|EnGage| | |

|NY | | |

| |Exploration | |

| | | |

| | | |

| | | |

| |Independent Practice | |

| | | |

| | | |

| | | |

| | | |

| | | |

|Differ|Small Group Instruction | |

|entiat| | |

|ion: | | |

|Math | | |

|Workst| | |

|ations| | |

| |Tech. Lab | |

| |Problem Solving Lab | |

| |CCSS: | |

| |2.OA.1 | |

| |2.NBT.6 | |

| |2.NBT.7 | |

| |Fluency Lab | |

| |2.OA.2 | |

| |2.NBT.5 | |

| |2.NBT.8 | |

| | | |

| |Strategy: | |

| |Tool(s): | |

| |Math Journal | |

| | | |

| |MP3: Construct viable | |

| |arguments and critique | |

| |the reasoning of others | |

| |Summary | |

| |Exit Ticket | |

| | | |

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 September 2016

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | | |1 |2 |

|5 |6 |7 |8 |9 |

|12 |13 |14 |15 |16 |

|19 |20 |21 |22 |23 |

| | | |EnGageNY | |

| | | |End of Module 1 | |

| | | |Assessment | |

|26 |27 |28 |29 |30 |

| |SGO | |SGO | |

| |Diagnostic (BOY) |SGO |Diagnostic (BOY) | |

| |Assessment |Diagnostic (BOY) |Assessment | |

| | |Assessment | | |

October 2016

|Monday |Tuesday |Wednesday |Thursday |Friday |

|3 |4 |5 |6 |7 |

| |MIF Ch. 7 Test Prep | | | |

| |& | | | |

| |Performance Task | | | |

|10 |11 |12 |13 |14 |

| |Math Workstations: |Math Workstations: |Math Workstations: | |

| |SGO |SGO |SGO | |

| |Performance Tasks |Performance Tasks |Performance Tasks | |

|17 |18 |19 |20 |21 |

| | |EnGageNY | | |

| | |End of Module 2 | | |

| | |Assessment | | |

|24 |25 |26 |27 |28 |

|Math Workstations: |Math Workstations: |Math Workstations: | | |

|SGO |SGO |SGO | | |

|Fluency Assessments |Fluency Assessments |Fluency Assessments | | |

|31 | | | | |

|MIF Ch. 13 Test Prep | | | | |

|& | | | | |

|Performance Task | | | | |

Planning Calendar November 2016

|Monday |Tuesday |Wednesday |Thursday |Friday |

| |1 |2 |3 |4 |

|7 |8 |9 |10 |11 |

| | |Performance Tasks | | |

| | |Fluency Benchmark I END OF MP | | |

|14 |15 |16 |17 |18 |

|21 |22 |23 |24 |25 |

|28 |29 |30 | | |

December 2016

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | | |1 |2 |

|5 |6 |7 |8 |9 |

|12 |13 |14 |15 |16 |

|19 |20 |21 |22 |23 |

|26 |27 |28 |29 |30 |

Grade 2 Unit 1 Instructional and Assessment Framework

|Recommended Pacing |Activities |CCSS |Notes |

|September 8-9, 2016 |Setting Up Classroom Routines/Procedures | |Routines/Procedures: |

| |Introduction to Math Workstations | |Ask 3 Then Me |

| | | |Math Talk Moves |

| | | |Math Notebooks |

| | | |Math Workstations |

|September 12, 2016 |EnGageNY Module A Lesson 1 |2.OA.1 | |

| |Practice Making Ten and adding to ten | | |

|September 13, 2016 |EnGageNY Module A Lesson 2 | | |

| |Practice making the next ten and adding to a multiple of ten | | |

|September 14, 2016 |EnGageNY Module B Lesson 3 |2.OA.1 | |

| |Add and subtract like units |2.OA.2 | |

| | |2.NBT.5 | |

|September 15, 2016 |EnGageNY Module B Lesson 4 | |EnGageNY Modules provided by Math |

| |Make a ten to add within 20 | |Department: |

| | | |Lesson Implementation: |

| | | |50-60 minutes |

| | | | |

| | | |Continue to reinforce mental strategies: |

| | | |Count on/Count back; |

| | | |Making ten/Decomposing ten; |

| | | |Addition and subtraction relationships; |

| | | |Doubles +/- |

| | | | |

| | | |Demonstration of Learning: |

| | | |Exit tickets: (5 min.) |

| | | |Students complete independently. |

| | | |Analyze and utilize the results of exit |

| | | |tickets to drive instructional decision |

| | | |making. |

| | | |Place exit tickets in Student Portfolios |

|September 16, 2016 |EnGageNY Module B Lesson 5 | | |

| |Make a ten to add within 100 | | |

|September 19, 2016 |EnGageNY Module B Lesson 6 | | |

| |Subtract single-digit numbers from multiples of 10 within 100 | | |

|September 20, 2016 |EnGageNY Module B Lesson 7 | | |

| |Take from ten within 20 | | |

|September 21, 2016 |EnGageNY Module B Lesson 8 | | |

| |Take from ten within 100 | | |

|September 22, 2016 |EnGageNY End of Module 1 Assessment | | |

|September 23, 2016 |Math In Focus Ch. 7 |2.NBT.5 | |

| |Chapter Opener & Recall Prior Knowledge | | |

| |Quick Check & Pre-Test | | |

|September 26, 2016 |Math In Focus Ch. 7 Lesson 1 |2.MD.1 | |

| |Measuring in Meters |2.MD.3 | |

|September 27, 2016 |Math In Focus Ch. 7 Lesson 2 |2.MD.4 | |

| |Comparing Lengths in Meters | | |

| |Math Workstation: SGO Diagnostic (BOY) Assessment | | |

|September 28, 2016 |Math In Focus Ch. 7 Lesson 3 |2.MD.1 | 9/27 -9/30 |

| |Measuring in Centimeters |2.MD.3 |Administer |

| |Math Workstation: SGO Diagnostic (BOY) Assessment | |SGO Assessments |

| | | |during the last 20 minutes of the math |

| | | |block. |

|September 29, 2016 |Math In Focus Ch. 7 Lesson 4 |2.MD.1 | |

| |Comparing Lengths in Centimeters |2.MD.4 | |

| |Math Workstation: SGO Diagnostic (BOY) Assessment | | |

|September 30, 2016 | Math In Focus Ch. 7 Lesson 5 |2.MD.5 | |

| |Real World Problems: Metric Length |2.MD.6 | |

| |Math In Focus Ch. 7 |2.MD.1-6 |EnGageNY Modules provided by Math |

|October 3, 2016 |Problem Solving & Chapter Wrap-Up | |Department: |

| | | |Lesson Implementation: |

| | | |50-60 minutes |

| | | | |

| | | |Demonstration of Learning: |

| | | |Exit tickets: (5 min.) |

| | | |Students complete independently. |

| | | |Analyze and utilize the results of exit |

| | | |tickets to drive instructional decision |

| | | |making. |

| | | |Place exit tickets in Student Portfolios |

| | | | |

| | | | for MIF materials |

|October 4, 2016 |Math In Focus Ch. 7 Test Prep | | |

| |MIF Ch. 7 Performance Task | | |

| |EnGageNY Module 2 A Lesson 1 |2.MD.1 | |

|October 5, 2016 |Connect measurement with physical units by using multiple copies of | | |

| |the same physical unit to measure | | |

|October 6, 2016 |EnGageNY Module 2 A Lesson 2 | | |

| |Use iteration with one physical unit to measure | | |

|October 7, 2016 |EnGageNY Module 2 A Lesson 3 | | |

| |Apply concepts to create unit rulers and measure lengths using unit | | |

| |rulers | | |

| |EnGageNY Module 2 B Lesson 4 |2.MD.1 | |

|October 10, 2016 |Measure various objects using centimeter rulers and meter sticks |2.MD.3 | |

| |EnGageNY Module 2 B Lesson 5 | | |

|October 11, 2016 |Develop estimation strategies by applying prior knowledge of length | | |

| |and using mental benchmarks | | |

| |EnGageNY Module 2 C Lesson 6 |2.MD.1 | |

|October 12, 2016 |Measure and compare lengths using centimeters and meters |2.MD.2 | |

| | |2.MD.4 | |

| |EnGageNY Module 2 C Lesson 7 | | |

|October 13, 2016 |Measure and compare lengths using metric length units and non-standard| | |

| |length units; | | |

| |EnGageNY Module 2 D Lesson 8 |2.MD.1 | |

|October 14, 2016 |Solve addition and subtraction word problems using the ruler as a |2.MD.2 | |

| |number line |2.MD.3 | |

| | |2.MD.4 | |

| | |2.MD.5 | |

| | |2.MD.6 | |

| |EngageNY Module 2 D Lesson 9 | | |

|October 17, 2016 |Measure lengths of string using measurement tools; and use tape | | |

| |diagrams to represent and compare the lengths | | |

| |EngageNY Module 2 D Lesson 10 | | |

|October 18, 2016 |Apply conceptual understanding of measurement by solving two-step word| | |

| |problems | | |

|Recommended |Activities |CCSS |Notes |

|October 19, 2016 |EnGageNY End of Module 2 Assessment |2.MD.1-6 |10/24 -10/26 |

| | | |Administer |

| | | |SGO Assessments |

| | | |during the last 20 minutes of |

| | | |the math block. |

|October 20, 2016 |Math In Focus Chapter 13 |2.NBT.7 | |

| |Chapter Opener; Recall Prior Knowledge; |2.MD.1 | |

| |Quick Check; Pre-Test | | |

|October 21, 2016 |Math In Focus Chapter 13 Lesson 1 |2.MD.1 | |

| |Measuring in Feet |2.MD.3 | |

|October 24, 2016 |Math In Focus Chapter 13 Lesson 2 |2.MD.1 | |

| |Comparing Lengths in Feet |2.MD.4 | |

| |Math Workstations: SGO Fluency Assessments | | |

|October 25, 2016 |Math In Focus Chapter 13 Lesson 3 |2.MD.1 | |

| |Measuring in Inches |2.MD.3 | |

| |Math Workstations: SGO Fluency Assessments | | |

|October 26, 2016 |Math In Focus Chapter 13 Lesson 4 |2.MD.1 | |

| |Comparing Lengths in Inches and Feet |2.MD.2 | |

| |Math Workstations: SGO Fluency Assessments |2.MD.4 | |

|October 27, 2016 |Math In Focus Chapter 13 Lesson 5 |2.MD.5-6 | |

| |Real World Problems: Customary Length |2.OA.1 | |

|October 28, 2016 |Math In Focus Ch. 13 |2.MD.1-6 | |

| |Problem Solving & Chapter Wrap-Up | | |

|October 31, 2016 |Math In Focus Ch. 13 Test Prep | | |

| |MIF Ch. 13 Performance Task | | |

|November 1, 2016 |EngageNY Module 3 Lesson 1 |2.NBT.1 | |

| |Bundle and count ones, tens, and hundreds to 1,000. | | |

|November 2, 2016 |EngageNY Module 3 Lesson 2 |2.NBT.1 | |

| |Count up and down between 100 and 220 using ones and tens |2.NBT.2 | |

|November 3, 2016 |EngageNY Module 3 Lesson 3 | | |

| |Count up and down between 90 and 1,000 using ones, tens, and hundreds. | | |

|November 4, 2016 |EngageNY Module 3 Lesson 4 |2.NBT.1 | |

| |Count up to 1,000 on the place value chart. |2.NBT.2 | |

| | |2.NBT.3 | |

|November 7, 2016 |EngageNY Module 3 Lesson 5 | | |

| |Write base ten three-digit numbers in unit form; show the value of each digit. | | |

|November 8, 2016 |EngageNY Module 3 Lesson 6 | | |

| |Write base ten numbers in expanded form. | | |

|November 9, 2016 |Performance Tasks: Blocks, Yards, Jumping Contest | | |

2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Blocks

Performance Task (2.OA.1)

Name: ___________________________________________ Teacher: ________________ Date: ________

I have some blocks. Dan has some blocks. Together we have 100 blocks.

How many blocks do we each have?

Use word, pictures, and numbers to explain your thinking.

Solution: _________________________________________________________________________

2.OA.1 Compare-Bigger Unknown: Fewer; One-Step

2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Yards

Performance Task (2.MD.5)

Name: ___________________________________________ Teacher: ________________ Date: ________

Dan ran 9 fewer yards than Sam. Sam ran for 21 yards. How many yards did Dan run?

Solution: ___________

2.OA.1 Compare – Difference Unknown: More; One-Step

2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Jumping Contest

Performance Task (2.MD.6)

Name: ___________________________________________ Teacher: ________________ Date: ________

The class had a jumping contest. Sam jumped 38 inches. Tom jumped 55 inches. How much farther did Tom jump than Sam?

Use a number line to solve.

Solution: ___________

2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

(SAMPLE)

Express Yourself

Math Journal (2.MD.4)

Name: ___________________________________________ Teacher: ________________ Date: ________

What can you say about the objects below?

Use words, pictures and numbers to express your thinking.

2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

(SAMPLE)

Measurements

Math Journal (2.MD.4)

Name: ___________________________________________ Teacher: ________________ Date: ________

What can you say about the objects below?

Use words, pictures and numbers to express your thinking.

|Got It |Not There Yet |

|Evidence shows that the student essentially has the target concept or big math idea.|Student shows evidence of a major misunderstanding, incorrect concepts or procedure, or a failure to engage in the task. |

|PLD Level 5: 100% |PLD Level 4: 89% |PLD Level 3: 79% |

|Distinguished command |Strong Command |Moderate Command |

|MASTERED (86% - 100%): | | |

|DEVELOPING (67% - 85%): | | |

|INSECURE (51%-65%): | | |

|BEGINNING (0%-50%): | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

Student Conference Form SCHOOL: ______________________________________ TEACHER: __________________________

Student Name: __________________________________________________________________________ Date: ____________________________

|NJSLS: |ACTIVITY OBSERVED: |

|OBSERVATION NOTES: |

| |

| |

|FEEDBACK GIVEN: |

| |

| |

|GOAL SET: |

| |

| |

|NEXT STEPS: |

| |

| |

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.

• 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.

MATHEMATICIAN: ____________________________________________________ SCHOOL: _______________________________ TEACHER: _________________________________ DATE: __________

MATH PORTFOLIO REFLECTION FORM

PORTFOLIO ARTIFACT: _________________________________________________________________________________________________

THIS IS AN EXAMPLE OF THE WORK THAT I AM MOST PROUD OF BECAUSE…..

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

THIS WORK ALSO SHOWS THAT I NEED TO WORK ON…

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ADDITION FACTS WITHIN 20

20 |19 |18 |17 |16 |15 |14 |13 |12 |11 |10 |9 |8 |7 |6 |5 |4 |3 |2 |1 |0 | |0+20

20+0 |0+19

19+0 |0+18

18+0 |0+17

17+0 |0+16

16+0 |0+15

15+0 |0+14

14+0 |0+13

13+0 |0+12

12+0 |0+11

11+0 |0+10

10 +0 |0+9

9+0 |0+8

8+0 |0+7

7+0 |0+6

6+0 |0+5

5+0 |0+4

4+0 |0+3

3+0 |0+2

2+0 |0+1

1+0 |0+0 | |1+19

19+1 |1+18

18+1 |1+17

17+1 |1+16

16+1 |1+15

15+1 |1+1414+1 |1+1313+1 |1+12

12+1 |1+11

11+1 |1+10

10+1 |1+9

9+1 |1+8

8+1 |1+7

7+1 |1+6

6+1 |1+5

5+1 |1+4

4+1 |1+3

3+1 |1+2

2+1 |1+1 | | | |2+18

18+2 |2+17

17+2 |2+16

16+2 |2+15

15+2 |2+14

14+2 |2+13

13+2 |2+1212+2 |2+11

11+2 |2+10

10+2 |2+9

9+2 |2+8

8+2 |2+7

7+2 |2+6

6+2 |2+5

5+2 |2+4

4+2 |2+3

3+2 |2+2 | | | | | |3+17

17+3 |3+16

16+3 |3+15

15+3 |3+14

14+3 |3+13

13+3 |3+12

12+3 |3+11

11+3 |3+10

10+3 |3+9

9+3 |3+8

8+3 |3+7

7+3 |3+6

6+3 |3+5

5+3 |3+4

4+3 |3+3 | | | | | | | |4+16

16+4 |4+15

15+4 |4+14

14+4 |4+13

13+4 |4+1212+4 |4+11

11+4 |4+10

10+4 |4+9

9+4 |4+8

8+4 |4+7

7+4 |4+6

6+4 |4+5

5+4 |4+4 | | | | | | | | | |5+15

15+5 |5+1414+5 |5+13

13+5 |5+12

12+5 |5+11

11+5 |5+10

10+5 |5+9

9+5 |5+8

8+5 |5+7

7+5 |5+6

6+5 |5+5 | | | | | | | | | | | |6+14

14+6 |6+13

13+6 |6+12

12+6 |6+11

11+6 |6+10

10+6 |6+9

9+6 |6+8

8+6 |6+7

7+6 |6+6 | | | | | | | | | | | | | |7+13

13+7 |7+12

12+7 |7+11

11+7 |7+10

10+7 |7+9

9+7 |7+8

8+7 |7+7 | | | | | | | | | | | | | | | |8+12

12+8 |8+11

11+8 |8+10

10+8 |8+9

9+8 |8+8 | | | | | | | | | | | | | | | | | |9+11

11+9 |9+10

10+9 |9+9 | | | | | | | | | | | | | | | | | | | |10+10 | | | | | | | | | | | | | | | | | | | | | |

SUBTRACTION FACTS WITHIN 20

20 |19 |18 |17 |16 |15 |14 |13 |12 |11 |10 |9 |8 |7 |6 |5 |4 |3 |2 |1 |0 | |20-0 |20-1 |20-2 |20-3 |20-4 |20-5 |20-6 |20-7 |20-8 |20-9 |20-10 |20-11 |20-12 |20-13 |20-14 |20-15 |20-16 |20-17 |20-18 |20-19 |20-20 | | |19-0 |19-1 |19-2 |19-3 |19-4 |19-5 |19-6 |19-7 |19-8 |19-9 |19-10 |19-11 |19-12 |19-13 |19-14 |19-15 |19-16 |19-17 |19-18 |19-19 | | | |18-0 |18-1 |18-2 |18-3 |18-4 |18-5 |18-6 |18-7 |18-8 |18-9 |18-10 |18-11 |18-12 |18-13 |18-14 |18-15 |18-1 6 |18-17 |18-18 | | | | |17-0 |17-1 |17-2 |17-3 |17-4 |17-5 |17-6 |17-7 |17-8 |17-9 |17-10 |17-11 |17-12 |17-13 |17-4 |17-15 |17-16 |17-17 | | | | | |16-0 |16-1 |16-2 |16-3 |16-4 |16-5 |16-6 |16-7 |16-8 |16-9 |16-10 |16-11 |15-12 |15-13 |16-14 |16-15 |16-16 | | | | | | |15-0 |15-1 |15-2 |15-3 |15-4 |15-5 |15-6 |15-7 |15-8 |15-9 |15-10 |15-11 |15-12 |15-13 |15-14 |15-15 | | | | | | | |14-0 |14-1 |14-2 |14-3 |14-4 |14-5 |14-6 |14-7 |14-8 |14-9 |14-10 |14-11 |14-12 |14-13 |14-14 | | | | | | | | |13-0 |13-1 |13-2 |13-3 |13-4 |13-5 |13-6 |13-7 |13-8 |13-9 |13-10 |13-11 |13-12 |13-13 | | | | | | | | | |12-0 |12-1 |12-2 |12-3 |12-4 |12-5 |12-6 |12-7 |12-8 |12-9 |12-10 |12-11 |12-12 | | | | | | | | | | |11-0 |11-1 |11-2 |11-3 |11-4 |11-5 |11-6 |11-7 |11-8 |11-9 |11-10 |11-11 | | | | | | | | | | | |10-0 |10-1 |10-2 |10-3 |10-4 |10-5 |10-6 |10-7 |10-8 |10-9 |10-10 | | | | | | | | | | | | |9-0 |9-1 |9-2 |9-3 |9-4 |9-5 |9-6 |9-7 |9-8 |9-9 | | | | | | | | | | | | | |8-0 |8-1 |8-2 |8-3 |8-4 |8-5 |8-6 |8-7 |8-8 | | | | | | | | | | | | | | |7-0 |7-1 |7-2 |7-3 |7-4 |7-5 |7-6 |7-7 | | | | | | | | | | | | | | | |6-0 |6-1 |6-2 |6-3 |6-4 |6-5 |6-6 | | | | | | | | | | | | | | | | |5-0 |5-1 |5-2 |5-3 |5-4 |5-5 | | | | | | | | | | | | | | | | | |4-0 |4-1 |4-2 |4-3 |4-4 | | | | | | | | | | | | | | | | | | |3-0 |3-1 |3-2 |3-3 | | | | | | | | | | | | | | | | | | | |2-0 |2-1 |2-2 | | | | | | | | | | | | | | | | | | | | |1-0 |1-1 | | | | | | | | | | | | | | | | | | | | | |0-0 | |

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:

:

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[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.

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ORANGE PUBLIC SCHOOLS

OFFICE OF CURRICULUM AND INSTRUCTION

OFFICE OF MATHEMATICS

(Pictures)

(Manipulatives)

(Written)

(Real Life Situations)

(Communication)

1st & 2nd Grade Ideal Math Block

Essential Components

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.

15-2

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

POST TEST

POST TEST

ADDITIONAL PRACTICE

INDEPENDENT PRACTICE

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