DUE 6-13: Facilitators Guide Template - CC 6-12.docxmc-14193-39844713.us-east-1.elb.amazonaws.com/...201… · Web viewHere we are starting to move from the concrete to the pictorial

Module Focus: Grade 3 – Module 4 Sequence of Sessions

Overarching Objectives of this November 2013 Network Team Institute Module Focus sessions for K-5 will follow the sequence of the Concept Development component of the specified modules, using this narrative as a tool

for achieving deep understanding of mathematical concepts. Relevant examples of Fluency, Application, and Student Debrief will be highlighted in order to examine the ways in which these elements contribute to and enhance conceptual understanding.

High-Level Purpose of this Session Focus. Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for

teaching these modules. Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that

develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same . (Specific progression document to be determined as appropriate for each grade level and module being presented.)

Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade in order to fully implement the curriculum.

Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while maintaining the balance of rigor that is built into the curriculum. Instructional supports. Participants will be prepared to utilize models appropriately in promoting conceptual understanding throughout A Story of Units.

Related Learning Experiences● This session is part of a sequence of Module Focus sessions examining the Grade 3 curriculum, A Story of Units.

Session Outcomes

What do we want participants to be able to do as a result of this session?

How will we know that they are able to do this?

Focus. Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for teaching these modules.

Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same . (Specific progression

Participants will be able to articulate the key points listed above.

document to be determined as appropriate for each grade level and module being presented.)

Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module addresses the major work of the grade in order to fully implement the curriculum.

Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while maintaining the balance of rigor that is built into the curriculum.

Instructional supports. Participants will be prepared to utilize models appropriately in promoting conceptual understanding throughout A Story of Units.

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Grade 3 Module 4 Concept Development

135 minutes

Examine of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.

Grade 3 Module 4 Grade 3 Module 4 PPT

Session Roadmap

Section: Grade 3 Module 4 Concept Development Time: 135 Minutes

[135 minutes] In this section, you will… Examine of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.

Materials used include: PPT and Participant handouts

Time Slide

#Slide #/ Pic of Slide Script/ Activity directions GROU

P

1 1 NOTE THAT THIS SESSION IS DESIGNED TO BE 135 MINUTES IN LENGTH.Welcome! In this module focus session, we will examine Grade 3 – Module 4. This is an exciting and interesting unit because it provides a nice application of Modules 1 and 3 as students learn about area concepts.

1 2 The objective for this session is to help you prepare to implement Module 4 by examining the mathematical models and instructional strategies in the lessons.To achieve this objective, we’ll be looking at the specific models used within each Topic to see how it moves the learning forward.

1 3 The fourth module in Grade 3 is Multiplication and Area. The module includes 16 lessons and is allotted 20 instructional days.This module builds on understandings established in Modules 1 and 3 with multiplication and division and creates authentic contexts for relating these prior understandings. It seeks to build a conceptual understanding of area through the lens of multiplication instead of merely establishing the “formula” for area.

7 4 In Module 4, students explore area and relate it to their prior understanding of multiplication. As you read the module overview, hopefully you will see how the concepts from Modules 1 and 3 are used to support the students’ understanding of area.Take a few minutes to read the Module Overview. As you read, highlight key phrases that help build a picture of what the learning in this Module will look like. After you finish reading, gather your thoughts by jotting down 1-2 sentences that summarize the major learning of the module. (Allow 1 minute for jotting.)Turn and talk with others at your table. Share observations about what is new or different to you about the way these concepts are presented. (Allow 2 minutes for discussion.)

1 5 This model shows how students will progress from using arrays in Modules 1 and 3 to using the area model in Module 4. Turn and talk to a partner about how this model shows the progression from arrays to the area model.

6 6 Now that you know the focus of the module, let’s see how students are assessed on their mastery. Take a look at the problems on the end-of-module assessment. Talk to your neighbor, what concepts will students need to master by the end of the module? What do you find interesting or surprising?Keep these problems in mind as we look at the models in the module and see how it builds up to the students’ level of mastery.

5 7 Topic A provides foundations for understanding area. Students use a variety of manipulatives to concretely support their understanding of area as the amount of space that a two-dimensional figure takes up.Note to presenter: Use the document camera and Problem 1 from Lesson 1’s Problem Set to show how the concept of area is established. Use triangle pattern blocks to cover Shapes A and B and discuss how each shape is covered by the same number of green triangles. Then use Problem 5 from Lesson 1’s Problem Set to show how square units are established as a unit to measure area. Use square pattern blocks to cover the rectangle and discuss how we say the area of the rectangle is 6 square units. Why do we call them square units? Why do we use square units?

2 8 Students start Lesson 2 with a 1” by 12” strip of paper. They use their ruler to mark each inch along the top and bottom of the strip. Then they connect the marks as shown. Finally, they cut the strip along the lines they’ve drawn. These tiles are used to establish the square inch as a unit to measure area. Students discuss the difference between square units and square inches. They repeat this process with a 1 cm by 12 cm paper strip.T: Since the sides of the squares each measure 1 inch, we call one of these squares a square inch. What is the area of your paper strip in square

inches?S: 12 square inches!T: Did the number of squares change?S: No.T: Talk to a partner. What changed about the way we talked about the area of the paper strip?S: The units changed. Before we called them square units, but now we can call them square inches because all 4 sides measure 1 inch. We

named this square unit. A square unit could have sides of any length. A square inch is always the same thing.

4 9 Work with a partner to use the square inch tiles to create 3 rectangles (as outlined in script below). Estimate to draw each rectangle in the chart on your Problem Set.Bags of the square inch units (for each pair) on tables after lunch. T: Now arrange all 12 squares into 2 equal rows. Remember, the squares have to touch but can’t overlap.T: Draw your rectangle in the chart for Problem 1. What is the area of the rectangle?S: 12 square inches.T: Record the area. You can record it by writing 12 square inches, or you can write 12 sq in.T: Rearrange all 12 squares into 3 equal rows to make a new rectangle. Draw it in the chart and record the area. At my signal, whisper the area of your rectangle to a partner. (Signal.)S: 12 square inches.T: Rearrange all 12 squares into 4 equal rows to make a new rectangle. Draw it in the chart and record the area. At my signal, whisper the area of your rectangle to a partner. (Signal.)S: 12 square inches.

1 10 You just completed this activity with square inch tiles, in the Concept Development, students repeat the process using square centimeter tiles. This activity does a couple of things. First of all, it helps establish square inches and square centimeters as units to measure area. Secondly, it allows the students to see that different rectangles can have the same area.T: How is it possible that these three different rectangles and our paper strip all have the same area?S: We used the same squares for each one, so they all have the same area. We rearranged 12 square inches each time. Just rearranging them doesn’t change the area.

2 11 Use the inch grid paper on the Problem Set to shade in Rectangle B. Here we are starting to move from the concrete to the pictorial. T: Slip the grid paper into your personal board. Each side of the square in the grid measures 1 inch. How is this grid paper like the tiles we used? S: They’re both square inches.T: Shade the grid paper to represent the rectangle you made with tiles.

1 12 Let’s do a fluency from Lesson 4.Products in an Array (3 minutes)Materials: (S) Personal white boardsNote: This fluency anticipates relating multiplication with area in G3–M4–Topic B.T: (Project an array with 5 rows of 3 stars.) How many rows of stars do you see?S: 5 rows.T: How many stars are in each row?S: 3 stars.T: On your boards, write two multiplication sentences that can be used to find the total number of stars.S: (Write 5 × 3 = 15 and 3 × 5 = 15.)Continue with the following possible sequence: 4 by 6, 7 by 3, 8 by 5, and 9 by 7.

1 13 (Lesson 4)Products in an Array (3 minutes)Materials: (S) Personal white boardsNote: This fluency anticipates relating multiplication with area in G3–M4–Topic B.T: (Project an array with 5 rows of 3 stars.) How many rows of stars do you see?S: 5 rows.T: How many stars are in each row?S: 3 stars.T: On your boards, write two multiplication sentences that can be used to find the total number of stars.S: (Write 5 × 3 = 15 and 3 × 5 = 15.)Continue with the following possible sequence: 4 by 6, 7 by 3, 8 by 5, and 9 by 7.




3 17 Turn and talk to a partner about how this fluency relates to the learning in Module 4.Possible answers:

• This fluency relates to the area model progression diagram, which shows students progressing from arrays to the area model.

• Students will be multiplying the side lengths of an area model to find the area,

2 18 Compare Rectangles1 and 2 to the rectangle that you shaded in on your inch grid paper. Do all 3 rectangles have the same area? This helps students see the importance of avoiding gaps and overlaps when measuring area.T: Why is it important to avoid gaps or overlaps when we measure area?S: If there are gaps or overlaps the amount of space the rectangle takes up changes. The square unit would be wrong since some area is taken away if there are overlaps or some is added if there are gaps.

8 19 Take a few minutes to read the Lesson 4 Concept Development and try some practice problems from the Problem Set. I invite you to place question marks next to parts of the script and models that you would like more clarification on. Possible Answers:

• Pattern blocks were used to establish the concept of area.• Students used tiles to create/tile rectangles and measure about

area.• Students created rectangles and then shaded these rectangles in on

grid paper.

3 20 In Topic B, students progress from using square tile manipulatives to drawing their own area model. Let’s take a look at how this transition starts to happen in Lesson 5.Note to presenter: Use the document camera and Problem 1(c) from Lesson 5’s Problem Set to show how students use a ruler to complete the grid.

3 21 Now that you’ve seen how students are starting to use drawings to find area, try this word problem on your Problem Set.

1 22 Answer to Problem 4 from Lesson 5’s Problem Set.

1 23 Students can use this experience of drawing rectangular arrays to draw the missing square units to complete this array.

1 24 Students can use the square units in the second row to complete the top row.T: Look at the second row. Can you use those square units to help you know how many square units make the top row? S: The second row has 1 more square unit than the top row. You can just follow the line it makes to divide the rectangle into 2 square units.T: Use your straight edge to draw that line now.

1 25 Once the top row is complete, students can use a ruler to complete the rest of the rows and columns.T: Talk to your partner: Use the top row to figure out how many square units will fit in each of the rows below. How do you know?S: Each row should have 6 square units, because rows in an array are equal!T: Use the lines that are already there as guides, and with your straight edge, draw lines to complete the array.

1 26 Students move toward finding the area of an incomplete array by completing 1 column and 1 row.T: Can we estimate to draw unit squares inside the rectangle?S: Yes.T: It might take us longer, because fewer units are given. A quicker way to find the area is to figure out the number of rows and the number of

columns.

1 27 Students complete the first row and column, label the side lengths, and then find the area.T: Label the side lengths of the rectangle, including units.S: (Draw and label side lengths 5 units and 6 units.)T: What number sentence can be used to find the area?S: 5 × 6 = 30.

1 28 This problem from the Problem Set demonstrates the usefulness of being able to find the area of an incomplete array.

1 29 The students are presented with this model and asked if they have to complete the array to find the area. Students realize that they can find the area by multiplying the side lengths.T: Talk to your partner: Do we need to complete the array to find the area of the rectangle? Why or why not?S: Yes, then we can skip-count each row to find the total. No, we already know the side lengths!T: How are the side lengths related to the area?S: If you multiply the side lengths together, the product is the same as the area.T: Talk to a partner: Can you multiply any two side lengths to find the area?S: No, you have to multiply the side length that shows the number of rows times the side length that shows the number of squares in each row.T: What multiplication equation can be used to find the area of this rectangle?S: 4 × 7 = 28.

1 30 Once they realize that the area of a rectangle can be found by multiplying the side lengths, students use the area model to find the area of a rectangle. They can also find an unknown side length, given the area and one side length.

3 31 Turn and talk to a partner to answer this debrief question from Lesson 8.Possible answer:

• The side lengths show the number of rows and the number of columns, to find the total unit squares, or area, you can multiply the number of rows times the number of columns.

8 32 Take a few minutes to read the Lesson 7 Concept Development and try some practice problems from the Problem Set. I invite you to place question marks next to parts of the script and models that you would like more clarification on. Possible Answers:

• In Lesson 6, students complete rectangular arrays.• In Lesson 7, the area model is established.• Lesson 8 shows how the area model is used to multiply the side

lengths to find the area.

1 33 In Topic C, students manipulate rectangular arrays to concretely demonstrate arithmetic properties as they apply to area. As we work through this topic, try to see how the concepts in Modules 1 and 3 are applied with respect to area.

1 34 Students start by cutting a rectangular grid in half and finding the area of one of the rectangles. Since the rectangles are equal, finding the area of one rectangle gives the area of the other rectangle.T: How can you find the area of one of the rectangles?S: Multiply the side lengths. Multiply 5 times 10.T: Answer Problem 1(b). (Allow students time to work.) What is the area of one of the rectangles?S: 50 square centimeters!T: What is the area of the other rectangle? How do you know?S: 50 square centimeters because the rectangles are equal.T: How can you find the total area of the rectangles?S: Add 50 square centimeters plus 50 square centimeters.

8 35 Students place the 2 smaller rectangles side by side to create a new, larger rectangle. This helps students see that area is additive, which is an important property that the students will need in the next lesson, when they apply the distributive property.T: What did you notice about the sum of the areas of the 2 small rectangles and the area of the longer rectangle?S: They’re the same!T: How can we use the areas of 2 small rectangles that form a longer rectangle to find the area of the longer rectangle?S: Add the areas of the smaller rectangles!Note to presenter: Use the document camera and the problem from Lesson 10’s Concept Development to show how the distributive property can be used to find the area of a large rectangle. Invite participants to try the example problems on their Problem Set.

1 36 Problem Set answers.

1 37Problem Set possible answer.

8 38 Take a few minutes to read the Lesson 11 Concept Development. We are going to do a practice problem together after you read the Concept Development. I invite you to place question marks next to parts of the script and models that you would like more clarification on. Possible Answer:

• Students use the associative property to find all possible whole number side lengths of a rectangle with a given area.

Note to the presenter: After discussing the answer to this problem, use the document camera to demonstrate how to find all possible whole number side lengths for a rectangle with an area of 36 square units. In the Application Problem for this lesson, students see that 3 x 12 = 36. Use this equation and apply the associative property as outlined in the Concept Development to model how this strategy is used. Now that you have seen how the associative property can be used to find all possible while number side lengths of a rectangle with a given area, try the problems in your Problem Set.

1 39 Answers to Problem Set.

3 40 Now that you’ve had a chance to explore the lessons in Topic C, I’d like you to turn and talk to a partner to answer this question.Possible answer:The major theme for Topic C is utilizing the properties the students learned in Module 3, such as the associative and distributive properties, but now it is done in area models

1 41 Topic D provides students with opportunities to solve problems involving area and to see how their learning in Module 4 can be applied to real world contexts.

5 42 Solve these word problems on your Problem Set. After you solve, share your strategy with a partner.

1 43 Possible solutions to word problems.

1 44 Students are now ready to tackle finding the area of a composite figure, such as this one. The beauty of these composite figures is that they allow for creativity when finding the area. Visualize how you would break this figure up in to rectangles to find the area. T: Talk to your partner: Can we find the area of the shaded figure by multiplying side lengths? How do you know?S: No, because it isn’t a rectangle. We can count the unit squares inside, though.T: In the Application Problem, we used the break apart and distribute strategy to find the area of a larger rectangle by breaking it into smaller rectangles. Turn and talk to your partner: How might we use a strategy like that to find the area of the shaded figure?

1 45 Students can break the figure up in to these 3 rectangles.

1 46 Or these 3 rectangles. Then they can find the area of each rectangle and add to find the area of the figure. Can you see another way to break up this composite figure into rectangles?

1 47 Students can also find the area of the large rectangle and the subtract the area of the small rectangle to find the area of the shaded figure.Try the problems involving finding the area of composite figures on your Problem Set.

2 48 Let’s do a fluency activity from Lesson 14.Find the Area (5 minutes) Materials: (S) Personal white boardsNote: This fluency reviews the relationship between side lengths and area and supports the perception of the composite shapes by moving from part to whole using a grid.T: (Project the first figure on the right.) On your boards, write a number sentence to show the area of the shaded rectangle.S: (Write 5 × 2 = 10 square units or 2 × 5 = 10 square units.)T: Write a number sentence to show the area of the unshaded rectangle. S: (Write 3 × 2 = 6 square units or 2 × 3 = 6 square units.)T: (Write __ sq units + __ sq units = __ sq units.) Using the areas of the shaded and unshaded rectangle, write an addition sentence to show the area of the entire figure. S: (Write 10 sq units + 6 sq units = 16 sq units or 6 sq units + 10 sq units = 16 sq units.) Continue with the other figures (slides 38-40).

1 49

1 50

1 51

4 52 Try this word Application Problem from Lesson 14. You will find it on your Problem Set.

1 53 Possible solution to word problem.

8 54 Take a few minutes to read the Lesson 15 Concept Development. I invite you to place question marks next to parts of the script and models that you would like more clarification on. Possible Answers:

• Students have to be able to measure to find the side lengths of each room.

• They have to know how to find the area of composite figures.• Students need to use a strategy to find the area of a large rectangle.

3 55 Now that you’ve seen the development of the concepts in Module 4, take a few minutes to discuss your thoughts on this question with a partner. Share out up to three ideas as a whole group.

3 56 Take two minutes to turn and talk with others at your table. During this session, what information was particularly helpful and/or insightful? What new questions do you have?Allow 2 minutes for participants to turn and talk. Bring the group to order and advance to the next slide.

1 57 Review session objective and the steps to help teachers prepare to implement Module 4.

Use the following icons in the script to indicate different learning modes.

Video Reflect on a prompt Active learning Turn and talk

Turnkey Materials Provided

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Additional Suggested Resources

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Documents

DUE 6-13: Facilitators Guide Template - CC 6-12.docxmc-14193-39844713.us-east-1.elb.amazonaws.com/...201… · Web viewHere we are starting to move from the concrete to the pictorial