Module Focus: Grade 2 – Module 7 Sequence of Sessions

Overarching Objectives of this February 2014 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.  

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.   

Related Learning Experiences● This session is part of a sequence of Module Focus sessions examining the Grade 2 curriculum, A Story of Units.

Key Points Students gain mastery of addition and subtraction strategies within 100 and problem solving strategies while working with

various contexts of length, money, and data. Students apply knowledge of composition and decomposition of numbers to units of money. A solid conceptual understanding of length allows students to apply their knowledge to multiple contexts.

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 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.

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

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Introduction to the Module

10 mins Establish the instructional focus of Grade 2 Module 7

Grade 2 Module 7 PPT Facilitators Guide

Review Grade 2 Module 7

Topic A Lessons 20 mins Examine the lessons of Topic A. G2 M7 Lesson Excerpts G2 M7 Problem Set Excerpts

Review Topic A.

Topic B Lessons 35 mins Examine the lessons of Topic B. G2 M7 Lesson Excerpts G2 M7 Problem Set Excerpts

Review Topic B.

Topic C/D Lessons 20 minsExamine the lessons of Topics C and D.

G2 M7 Lesson Excerpts G2 M7 Problem Set Excerpts

Review Topics C and D.

Topic E/F Lessons 20 minsExamine the lessons of Topics E and F.

G2 M7 Lesson Excerpts G2 M7 Problem Set Excerpts

Review Topics E and F.

Summary 5 minsReiterate the key points of Grade 2 Module 7 and facilitate discussion.

Grade 2 Module 7 PPT Facilitators Guide

Session Roadmap

Section: Grade 2, Module 7 Time: 110 minutes

[110 minutes] In this section, you will… Materials used include:

TimeSlide #

Slide #/ Pic of Slide Script/ Activity directions GROUP

30 sec

1. Welcome! In this module focus session, we will examine Grade 2 – Module 7.

1 min 2. The ultimate objective is to prepare you to implement Module 7. To do this we will:•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.

30 sec

3. We will begin by exploring the module overview to understand the purpose of this module. Then we will dig in to the math of the module.We’ll lead you through the teaching sequence, one concept at a time. Along the way, we’ll also examine the other lesson components and how they function in collaboration with the concept development. Finally, we’ll take a look back at the module, reflecting on all the parts as one cohesive whole.

Let’s get started with the module overview.

30 sec

4. Grade 2 Module 7 is Problem Solving with Length, Money, and Data. The module includes 26 lessons and is allotted 30 instructional days.

10 min

5. Take 8 minutes to read the descriptive narrative of the Module 7 Overview. As you read, highlight language that shows the progression of learning in this module.Summarize the sequence of the major learning in Module 7.

(After 8 minutes)Share with others at your table: What is new and different about the way these concepts are presented? (See below.)

30 sec

6. Now that you have a broad view of the module, we will examine the sequence of learning, topic by topic.

1 min 7. In Module 7, students collect, represent, and interpret categorical data. They record this data in tables with either tally marks or numbers, and then draw both picture and bar graphs to represent the data. Students use the information to solve put-together, take-apart, and compare problems.

5 min 8. In Lesson 1, working within a science context, students categorize animals into classes (mammals, birds, fish, and reptiles), organize them in the form of a table, and then use the category counts to solve word problems. Students repeat the process with animal habitats, and they transition from recording the data with tally marks to using numbers.

**Guide participants through the lesson excerpt.**

5 min 9. Students learn that a picture graph can be oriented horizontally or vertically and that each picture represents one object. In this lesson students use a template for their graphs, but in later lessons, grid paper provides support as students construct graphs.

(In Grade 3 students learn that each object can represent more than one object.) Students ask and answer questions based on the information displayed in the graph.

**Guide participants through the lesson excerpt.**

5 min 10. Following the same procedure and using the same data as in Lesson 2, students learn to draw and label a bar graph in Lesson 3. They learn that one axis names the category while the other shows a single-unit count scale. They work with both vertical and horizontal orientations. As students ask and answer questions based on the data in the graphs, they relate the count scale to finding sums and differences on a number line diagram.

Allow 2 minutes for participants to complete page 1 of the Problem Set.

2 min 11. In Lesson 4, students gain more practice with bar graphs, as they generate data, graph it, and ask and answer questions. In Lesson 5, they design a survey to create data for a table and bar graph, which they use to ask and answer questions. The Problem Set and Homework in Lesson 5 involve coins, which leads into Topic B.

2 min 12. Topic B begins with a brief review of coin names and values (In Grade 1, students learned to recognize coin names and values).

Students begin by ordering coins and counting the total value. Then they find the total value of a group of coins and bills in the context of simple addition and subtraction word problems. They see how different combinations of coins can be manipulated to make the same total value.

Students also learn how to make change from a dollar, using counting on, simplifying strategies, and the relationship between addition and subtraction.

5 min 13. Students count the total value of a group of coins. They apply their knowledge of addition strategies and skip counting by 5s and 10s when there are multiple nickels and dimes.

Take a moment to complete the Problem Set. Then analyze and discuss with a partner how the Problem Set builds from simple to complex. The Concept Development is scaffolded in the same way.

2 min 14. In this fluency activity, students are introduced to the Decomposition Tree as a whole class, with the teacher recording as students decompose a given amount. Then, they are given their own decomposition tree and 90 seconds to decompose a specified amount in as many ways as they can.This fluency allows students to work at their own skill level, providing differentiation, as well as supporting their understanding of the part-whole relationship in the context of money.

5 min 15. Students find the total value of a group of coins in the context of simple addition and subtraction word problems with the result unknown.

To solve add to or take from problem types, students use the RDW process to draw, write the corresponding number sentence, and write a statement with the solution.

**Participants work with a partner and alternate the roles of teacher and student. For this lesson, Partner A is the teacher and Partner B is the student. In the following lesson, they will switch roles.**

1 min 16. Lesson 8 continues work with word problems involving money. Students apply their understanding of place value strategies and skip-counting to find the total value of a group of bills.

Students arrange bills from greatest to least, count on to find the total, and write a number sentence to represent the total value of a group of bills. Sometimes, they add up to four 2-digit numbers.

Students may write number sentences in any number of ways. One student might skip count mentally; another might look to make a ten. Students are encouraged to think flexibly and to apply solution strategies.

1 min 17. This is an example of how students might use place value strategies to solve this problem.

6 min 18. Students manipulate different combinations of coins within the context of word problems.

Students work cooperatively to explain their reasoning and solution strategies.

**Guide participants through the lesson excerpt. Then allow 1-2 minutes to complete the Problem Set excerpts.**

3 min 19. Lesson 10 adds the complexity of using the fewest number of coins.

Students see that just as they changed 10 ones for 1 ten in Modules 3, 4, and 5, they can also change coins of a lesser value for coins of a greater value (e.g., 2 nickels for 1 dime).

Allow 1-2 minutes to complete the Problem Set excerpt.

5 min 20. In Lesson 11, students learn how to make change from one dollar using counting on, simplifying strategies (e.g., the arrow way), and the relationship between addition and subtraction. They represent the part–whole relationship using a number bond and by writing a number sentence, often using the related addition to solve.

**Guide participants through the lesson excerpt.**

3 min 21. In Lesson 12, students use play money to act out scenarios with a partner, and they apply the strategies learned in Lesson 11 to solve word problems.

Students focus on making a ten, counting up, and skip-counting with fives and tens to solve. While efficiency is noted, students can make change in a variety of ways.

Solve this problem on your personal white board and share your solution with a partner.

*Note: Lesson 13 is solving two-step word problems involving dollars or cents.

1 min 22. In Lesson 13, students solve two-step word problems using the same strategies from Lessons 11 and 12.

3 min 23. Topic C reinforces the measurement concepts and skills learned in Module 2, but now with a focus on customary units.

In Lesson 14, students use an inch tile to measure various objects using iteration. By connecting to prior learning, students deepen their understanding of a length unit, seeing again that just as it was with the centimeter cube, the length unit is the distance from one end of the tile (or cube) to the other or from one hash mark to the next.

In Lesson 15, students create inch rulers using the same process as they did in Module 2 to create centimeter rulers, using the mark and advance technique with inch tiles to record each length unit with a hash mark. They now relate 12 inches to a new unit, the foot (supporting their work with arrays by recognizing that a new unit can be made with any value).

1 min 24. Topic D builds upon the work students completed in Module 2 with centimeter measures, as students now explore measurement using both customary and metric units.

Students continue to see examples of how the larger the length unit, the fewer number of units are needed to measure; likewise, the smaller the length unit, the more units are needed.

8 min 25. In Lesson 16, students rotate through various centers and measure a variety of objects with inch rulers and yardsticks.

They must strategically choose the appropriate measurement tool and units for measuring a given object. In doing so, they develop mental images of customary benchmark lengths.

Assign each table one center to perform and complete the corresponding recording sheet. Have a short share-out when participants finish. Allow approximately 7 minutes for this activity.

1 min 26. Students apply their experiences in Lesson 16 to estimating the lengths of different objects and then checking their estimates by measuring.

For example, a student might estimate that a desk is three feet tall and then measure to discover that it is actually three feet, six inches tall.

3 min 27. In Lesson 18, students measure the same objects twice, using both metric and customary units.

They learn that centimeters are smaller than inches, but meters are larger than both feet and yards. This reinforces the understanding that when measuring with a smaller unit, more iterations of that unit are needed to measure the same object than when measuring with a larger unit.

Allow 2 minutes to read the lesson excerpt. Then discuss the Debrief questions.

1 min 28. In Lesson 19, students compare different lengths using addition and subtraction. They determine how much longer one object is than another, subtracting the smaller length from the larger one.

Problems are solved in a variety of ways using the relationship between addition and subtraction (e.g., 25 in – 18 in = ____ in, or 18 in + _____ = 25 in), and the differences are expressed using standard length units (e.g., 7 in).

The work with measurement tools and various length units in Topic D lays the groundwork for problem solving in Topic E, as students use the more abstract tape diagrams to relate addition and subtraction to length.

Take a minute to solve the Application Problem from Lesson 19 using the RDW process.

1 min 29. In Topic E, students using drawings to compare lengths and write equations with an unknown to represent problems, just as they did in Module 2.

They also build upon their understanding of length by representing whole numbers as lengths on a number line, then representing two-digit sums and differences on a number line.

1 min 30. Students use drawings to compare lengths and write equations with an unknown to represent problems, just as they did in Module 2. In this lesson, however, students solve two-digit addition and subtraction measurement problems using customary or metric units, composing or decomposing a ten if necessary.

Just as they made comparisons and found differences using bar graphs in Topic A, students now compare lengths using the tape diagram, essentially a horizontal bar, to solve two-step problems.

Take a minute to solve this problem (on slide) from the Problem Set using the RDW process.

5 min 31. Students represent whole numbers as lengths on a number line in Lesson 21. Students identify unknown numbers by using mental benchmarks or reference points (e.g., 5, 10, 25, 50) and intervals of 1, 5, or 10.

Problems increase in complexity as students use their understanding of place value and the distance between positions to label points. For example, they label 340 as one endpoint when 350 is the midpoint and 360 is the other endpoint.

2 min 32. In Lesson 22, students represent two-digit sums and differences on a number line and write a number sentence to represent the addition or subtraction situation. For example, they solve the following problems using a number line marked with endpoints 0 and 50, marked intervals of 10, and unmarked intervals of 5.

“On a football field, Pepe starts running at the 10 yard line. He runs 25 yards, pauses, and runs 11 more yards. Which yard line is Pepe on now? How far has he run?”

In comparison, “Marcel starts running at the 5 yard line. He runs 15 yards, pauses, runs 15 more yards, stumbles, and runs 6 more yards. Which yard line is Marcel on now? How far has he run?”

1 min 33. Building on the work in Topic E, students now connect the process of measuring to displaying data in line plots.The purpose of the line plot is to display measurement data.

This topic follows the development of students’ understanding of measurement and graphing, and the ruler’s relation to the number line, and it speaks to the intentionality of the curriculum design.

5 min 34. In Lesson 23, students measure their own handspan (i.e., the distance from the tip of the thumb to the tip of the pinky with hand fully extended) as well as those of five friends, rounding the lengths to the nearest whole inch.

They then share the data as a class. Using tally marks, students create a table to record and organize the data.

**Guide participants through the lesson excerpt.**

5 min 35. In Lesson 24, students display the data from the previous lesson’s table as a line plot, relating the horizontal measurement scale in whole centimeters and inches to the number line diagram.

Students observe and comment on the patterns they observe in the line plot. They discover that while a table is useful for organizing data, a line plot allows for the visual comparisons of the different quantities.

**Guide participants through the lesson excerpt.**

1 min 36. In Lessons 25 and 26, students are presented with different data sets, which they represent using line plots. They then discuss the results and learn how to interpret the data.

30 sec

37. Now that you’ve had the chance to see and practice the concepts, skills, and models of Module 7, let’s take a moment to reflect back on the module overall.

4-6 min

38. Take 2-3 minutes to turn and talk with others at your table.

Share out for 2-3 minutes.

2 min 39. Let’s review some key points of this session:

• Students gain mastery of addition and subtraction strategies within 100 and problem solving strategies while working with various contexts of length, money, and data.

• Students apply knowledge of composition and decomposition of numbers to units of money.

• A solid conceptual understanding of length allows students to apply their knowledge to multiple contexts.

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 Grade 2 Module 7 PPT Grade 2 Module 7 Facilitators Guide Grade 2 Module 7 Lesson Excerpts Grade 2 Module 7 Problem Set Excerpts Picture Cards, Templates, and Recording Sheets

Additional Suggested Resources● How to Implement A Story of Units● A Story of Units Year Long Curriculum Overview● A Story of Units CCLS Checklist