© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Grade 2 – Module 6

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives Examine the development of mathematical understanding across the module using a focus on Concept Development within the lessons. Introduce mathematical models and instructional strategies to support implementation of A Story of Units.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Overview of A Story of Units

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Overview Read the narrative. *key concepts models and tools Important vocabulary What is new and different about the way these concepts are presented?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic A Formation of Equal Groups How does addition provide a foundation for understanding multiplication? How can equal groups be represented mathematically?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson Objective: Use manipulatives to create equal groups. Are these groups equal or unequal? How do you know? Lesson 1

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 1 Problem Set Lesson 1, Student Debrief For Problem 5, how did you go about making the three groups equal? Make a prediction: How are these equal groups related to addition?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lessons 2 and 3 Lesson Objective: Use math drawings to represent equal groups, and relate to repeated addition.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 3 Lesson Objective: Use math drawings to represent equal groups, and relate to repeated addition.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 4 Lesson Objective: Represent equal groups with tape diagrams, and relate to repeated addition.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 4 Application Problem

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic B Arrays and Equal Groups Why is the array a useful model for representing equal groups?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Spatial Relationships and Structuring Another type of composition and decomposition is essential to students mathematical development – spatial structuring. Students need to conceptually structure an array to understand two-dimensional regions as truly two-dimensional. … Spatial structuring is thus the mental operation of constructing an organization or form for an object or set of objects in space, a form of abstraction. … As the mental structuring process helps them organize their counting, they become more systematic, using the array structure to guide the quantification. Eventually, they begin to use repeated addition of the number in each row or each column. Such spatial structuring precedes meaningful mathematical use of the structures, including multiplication and, later, area, volume, and the coordinated plane. Geometry Progression, pages 10-11

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 5 Lesson Objective: Compose arrays from rows and columns, and count to find the total using objects.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 6 Lesson Objective: Decompose arrays into rows and columns, and relate to repeated addition.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 6 Problem Set How is decomposing arrays similar to decomposing numbers? For Problem 3(a), did you write the repeated addition number sentence in terms of rows or columns? Why didnt it matter? How does adding or removing rows or columns change the repeated addition number sentence? Lesson 6, Student Debrief

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 7 Lesson Objective: Represent arrays and distinguish rows and columns using math drawings. Concrete to Pictorial

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 8 Lesson Objective: Create arrays using square tiles with gaps.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 8 Application Problem

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 9 Problem Set Draw a tape diagram and array. Then write an addition number sentence to match. In a card game, 3 players get 4 cards each. One more player joins the game. How many total cards should be dealt now?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic C Rectangular Arrays as a Foundation for Multiplication and Division How does the composition of arrays build a foundation for multiplication? How does the decomposition of arrays build a foundation for division?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lessons 10 and 11 Lesson Objective: Use square tiles to compose a rectangle, and relate to the array model. Can we make a square array with 10 tiles? Lesson 10, Concept Development

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 12 Lesson Objective: Use math drawings to compose a rectangle with square tiles. Explain to your partner how to draw a rectangle with one square tile. Why was precision important today? How is this different from drawing an array with Xs? How does drawing a rectangle support the idea of composing a larger unit from smaller units? Use the terms square, rows, and columns in your response. Lesson 12, Student Debrief

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 13 Lesson Objective: Use square tiles to decompose a rectangle.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 14 Lesson Objective: Use scissors to partition a rectangle into same-size squares, and compose arrays with the squares.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 15 Lesson Objective: Use math drawings to partition a rectangle with square tiles, and relate to repeated addition. For Problem 4, if you were to continue adding columns of 2, would your array look more like a train or a tower? If you wanted to increase the total number of tiles quickly, would you suggest adding more rows or columns? Why? Explain why you couldnt draw another column of 2 in Problem 5 Lesson 15, Student Debrief

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 16 Lesson Objective: Use grid paper to create designs to develop spatial structuring. Why do you think we spent time creating designs and learning about tessellations today? Lesson 16, Student Debrief

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic D The Meaning of Even and Odd Numbers What strategies can be used to determine if a number is even or odd?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 17 Lesson Objective: Relate doubles to even numbers, and write number sentences to express the sum. What connections do you see between even numbers and skip counting? Lesson 17, Student Debrief

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 18 Lesson Objective: Pair objects and skip-count to relate to even numbers. What connections can you make between pairing objects and equal groups? If a number is even, can you make equal groups? If it is not even? How can you prove whether 52 is even? How about 73? Lesson 18, Student Debrief and UDL Box

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 19 Lesson Objective: Investigate the pattern of even numbers: 0, 2, 4, 6, and 8 in the ones place, and relate to odd numbers.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 19 Homework

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 20 Lesson Objective: Use rectangular arrays to investigate odd and even numbers.

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Biggest Takeaway Turn and Talk: What insights have you gained about the importance of establishing a strong foundation in equal groups, repeated addition, and arrays in relation to multiplication and division? How will this benefit student understanding of multiplication and division in Grade 3? What connections do you see between the composition and decomposition in Module 6 and the composition and decomposition in previous modules?

© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points Module 6 focuses on using repeated addition to find the total number of objects arranged in rectangular arrays (2.OA.4), partitioning rectangles into rows and columns of same-size squares (2.G.2), and determining numbers as even and odd (2.OA.3). This foundational understanding is crucial, since multiplication and division is the major work of Grade 3. Module 6 also supports the required fluency of Grade 3: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.