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Module Focus: Grade 2 – Module 8 Sequence of Sessions

Overarching Objectives of this May 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● In Grade 2 Module 8, students continue to develop their understanding of units within units as they describe and analyze 2-

dimensional shapes and then combine polygons to build composite shapes.● Grade 2 Module 8 develops fraction concepts, extending student understanding of part/whole relationships to unit fractions as equal

parts of a whole.● Students partition and describe equal shares of a whole as halves, thirds, and fourths, but they do not write, add, or subtract fractions;

that is the domain of Grade 3.● Students apply fraction concepts to telling time. They relate 30 minutes to a half hour and 15 minutes to a quarter hour.● Scaffolding Focused: Amplify Language● Scaffolding Focused: Move from Concrete to Representation to Abstract● Scaffolding Focused: Give Specific Guidelines for Speaking, Reading, Writing, or Listening

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 and demonstrate the key points above.

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Introduction 14 min Introduces Grade 2 Module 8• Grade 2 Module 8 PPT• Facilitator Guide

Review Grade 2 Module 8

Topic A: Attributes of Geometric Shapes

99 minExplores the attributes of geometric shapes.

• Grade 2 Module 8 PPT• Facilitator Guide

Review Topic A

Topic B: Composite Shapes and Fraction Concepts

56 minExplores fraction concepts to build and partition shapes using tangrams and pattern blocks.


Review Topic B

Topic C: Halves, Thirds, and Fourths

73 min Explores partitioning circles and rectangles into equal fractional


Review Topic C

of Circles and Rectangles

parts

Topic D: Application of Fractions to Tell Time and Review

64 min

Explores applying fraction and skip-counting skills to telling time and reviews the key points of Grade 2 Module 8.


Review Topic D

Session Roadmap

Section: Introduction Time: 14 minutes

In this section, you will be introduced to the Grade 2 Module 8 focus session.

Materials used include:• Grade 2 Module 8 PPT• Grade 2 Module 8 Facilitator Guide• Grade 2 Module 8 Module Overview

Time Slide # Slide #/ Pic of Slide Script/ Activity directions GROUP

0 min 1. NOTE THAT THIS SESSION IS DESIGNED TO BE 300 MINUTES IN LENGTH.

Welcome! In this module focus session, we will examine Grade 2 – Module 8.

30 sec 2. The ultimate objective is to prepare you to implement Module 8. 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.

• As an overall theme of this NTI, we’ve been asked to pay special attention to the ways in which we can provide scaffolds to support specific student needs. Before we begin our examination of the mathematics in this module, let’s take a few minutes to review some of the principles we can use to support learning.

1 min 3. The mathematics modules were created based on the premise that scaffolding must be folded into the curriculum in such a way that it is part of its very DNA. The instruction in these modules is intentionally designed to provide multiple entry points for students at all levels.

Teachers are encouraged to pay particular attention to the manner in which knowledge is sequenced in the curriculum and to capitalize on that sequence when working with special student populations. Most lessons move from simple to complex allowing teachers to locate specific steps where students are struggling or need a challenge.

That said, there are specific resources to highlight and enhance strategies that can provide critical access for all students.

In developing the scaffolds already contained in the curriculum, Universal Design for Learning (UDL) has provided a structure for thinking about how to meet the needs of diverse learners. Broadly speaking, that structure asks teachers to consider multiple means of representation; multiple means of action and expression; and multiple means of engagement. These dimensions promote engagement of students and provide multiple approaches to the same content.

Individual lessons contain marginal notes to teachers (in text boxes)

highlighting specific UDL information about scaffolds that might be employed with particular intentionality when working with students. These tips are strategically placed in the lesson where the teacher might use the strategy to the best advantage.

Let’s now examine additional strategies that can be considered.In this module study, we will focus on three key ideas for developing scaffolds that can be adapted for your classroom to meet the needs of your students.

Explicit focus on the language of mathematics, using the development from concrete to representation to abstract in the building of concepts, and communicating clear expectations in instructions are areas that can provide multiple entry points for students and can be used to promote student learning.

1 min 4. Much of what we share in the mathematics classroom with students is embedded in language that is specific. Students learn casual language before academic language. This means they may sound comfortable and fluent, but may need additional support in their writing and speaking in an academic environment.

Presenters should stress that academic language is an essential component of closing the achievement gap and providing access to grade level content and beyond.

Students may have a preconceived or informal idea of the meaning of a mathematical term. Be specific in the definition or meaning that will be used.

Be cautions of words with multiple meanings that might be confusing• a garden plot and the request to plot points on a coordinate plane

Words with multiple meaning must be anticipated and then addressed, and teachers must also be prepared to pause and provide explanations when students identify words the teacher has not anticipated. Whenever possible, words with multiple means should be avoided on assessments, particularly when the meanings may be close enough to be confusing.

Make sure that Language is internally consistent (if practice problems ask students to solve, the assessments should use the same term). If language is not internally consistent, then different terms are highlighted and taught.• add, plus, sum, combine, all mean the same thing• prism, a rectangular prism, box, package all reference the same figure

in G6M5_L11

1 min 5. The more concrete and visual these ideas can be in foundational stages, the better!• Use contexts that are familiar to students in your classroom.• Use graphic organizers or other means for students to visually

organize thinking.

Note: Teachers should be thoughtful and purposeful about which graphic organizers they select. Are teachers introducing a new concept with a need to organize notes or are they connecting ideas comparing and contrasting? The goal is always to help students make those connections and not use a graphic organizer just for the novelty of it.

• Consider using non-verbal displays of mathematical relationships in your scaffolding.

• Use multiple representations and multiple approaches in explaining problems and allowing students to express solutions.

• Use pictures/ visuals/ illustrations are used to make content clearer.

1 min 6. Each day needs structured opportunities for students to speak and write in English.• Students can chorally repeat key vocabulary or phrases• Have them “turn to a neighbor and explain”

Clearly set expectations by the explicit instructions in student-friendly language.

Use visuals in your instructions.

Be direct about language.

• Pause to discuss a vocabulary term and discuss how it may be used in the lesson. Have students repeat the word chorally so that they can all hear and practice.

Provide sentence frames for anyone who may benefit.• “The volume of my prism is ___units cubed. I found this by ______.• “My idea is similar to _____’s because ____.”

Generic/ universal sentence frames may remain posted in the classroom throughout the year. These might include:• “I agree with ____ because ___” or “I think the answer is _____

because...”

2 min 7. Let’s review some key points of scaffolding instruction.

As we study the module for this session, be thinking about specific scaffolds that might be most helpful for your classroom. We will pause at various points in the session to intentionally examine and discuss suggestions for scaffolds.

30 sec 8. We will begin by exploring the module overview to understand the purpose of this module. Then we will dig into 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.

0 sec 9. Advance for animation.

The eighth and last module in Grade 2 is Time, Shapes, and Fractions as Equal Parts of Shapes. The module includes 16 lessons and is allotted 20 instructional days.

7 min 10. Take 6 minutes to read the descriptive narrative of the Module 8 Overview. As you read, highlight language that shows the progression of learning in this module.

(After 6 minutes)

Share with others at your table: How do composition and decomposition relate to time, shapes, and fractions? (All year long, students have been learning that smaller units can be put together to compose a larger unit, and a larger unit can be decomposed into smaller units. They’ve done it with numbers, with measurement, with units of ones, tens, and hundreds, with arrays, with money. Now they’re applying that same part/whole thinking to units of minutes and hours, to halves, thirds, and fourths as 1 whole, and to triangles becoming squares.)

Note that fluency in this final module focuses on 2.NBT.5, addition and subtraction strategies within 100, as students end the year practicing this required fluency. In G3, there is limited work with the addition and subtraction algorithm, so students need to solidify their understanding before moving on to multiplication and division.

0 sec 11. Now that you have a broad view of the module, we will examine the sequence of learning, topic by topic.

Section: Topic A: Attributes of Geometric Shapes Time: 99 minutes

In this section, you will focus on the attributes of geometric shapes. Materials used include:• Grade 2 Module 8 PPT• Grade 2 Module 8 Facilitator Guide• Grade 2 Module 8 Topic Opener A• Grade 2 Module 8 Lesson 1 Problem Set• Grade 2 Module 8 Lesson 2 Excerpt


5 min 12. Take 2-3 minutes to read the Topic Opener. Then take 1 or 2 minutes to think about this question and discuss it at your table.

Why is the use of exemplars and variants important to students as they develop concepts about shapes? (2.G.1 calls for students to recognize and draw shapes having specified attributes. We don’t want students limited by a belief that, for example, only isosceles triangles that are standing on the horizontal base are triangles. We want to broaden rather than limit their ideas about shapes.)

4 min 13. This Application Problem presents students with a fun and engaging way to remember what they learned about shapes in Kinder and G1.

Take a moment to make shapes using all 12 toothpicks, then draw 3 of those shapes on your whiteboards.

Toothpicks make this problem highly engaging, but they are optional, depending on whether students need to work at the concrete level.

Have participants use toothpicks to create and draw shapes using 12 toothpicks.

16 min 14. In Lesson 1, students discuss two-dimensional shapes, focusing on the attributes of number of sides and number of corners. Then students use those attributes to create two-dimensional shapes on geoboards. The shapes are intentionally not named.

**Guide participants through the lesson excerpt.**

2 min 15. Complete these problems from the Problem Set, then discuss the questions with a partner.

The Problem Set reinforces the day’s concept development, as students independently form equal groups. Working with a static image moves them a step beyond their work with objects. The debrief questions are designed to encourage the articulation of their understanding. Note that the second question sets the stage for Lesson 2, in which students will relate equal groups to repeated addition.

16. Note to presenter:If applicable, insert this slide at an appropriate point in the module study for an in-depth examination of a problem or task for multiple entry points through the principles of the Universal Design for Learning (UDL).

Delete this slide from this current sequence after you’ve used it elsewhere as needed.

REPRESENTATION: The “what” of learning.How does the task present information and content in different ways?How students gather facts and categorize what they see, hear, and read.How are they identifying letters, words, or an author's style?

In this task, teachers can ...Pre-teach vocabulary and symbols, especially in ways that build a connection to the learners’ experience and prior knowledge by providing text based examples and illustrations of fields. Integrate numbers and symbols into word problems.

ACTION/EXPRESSION: The “how” of learning.How does the task differentiate the ways that students can express what they know?How do they plan and perform tasks?How do students organize and express their ideas?

In this task, teachers can...Anchor instruction by pre-teaching critical prerequisite concepts through demonstration or models (i.e. use of two dimensional representations of space and geometric models).

ENGAGEMENT: The “why” of learning.How does the task stimulate interest and motivation for learning?How do students get engaged?How are they challenged, excited, or interested?

In this task, teachers can...Optimize relevance, value and authenticity by designing activities so that

learning outcomes are authentic, communicate to real audiences, and reflect a purpose that is clear to the participants.

If available, reviewing student work would provide participants with the opportunity to deeply understand the benefits of students sharing their thinking in working the problem. Assessments in the module have rubrics that clearly outline expectations and could be used in the discussion.

4 min 17. Use the template to solve this Application Problem. This brainteaser challenges students to search for a familiar shape, the triangle, in a different way. It encourages students to recognize triangles of different sizes and orientations.

Hint: There are five of each variation of triangle as students track them around the pentagon.

16 min 18. In Lesson 2, students learn the definitions of polygon, triangle, quadrilateral, pentagon, and hexagon, as they work in groups and use uncooked spaghetti to create these shapes. Then they play a game called Complete that Shape in which they see part of a shape on the board and are told the name of the shape. They must use their understanding of the attributes of shapes to build the entire shape.

**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.**

16 min 19. In Lesson 3, students use a ruler to draw straight lines as they draw triangles, quadrilaterals, pentagons, and hexagons. They name and describe their shapes to a partner, circle all angles, and count all sides. They see that the defining attributes of shapes don’t change, even though the length of the sides varies.


16 min 20. In Lesson 4, students use attributes such as side length, parallel lines, and right angles to identify quadrilaterals. Students are introduced to trapezoids, rhombuses and parallelograms. While students learn the names of these shapes, the emphasis remains on analyzing shapes based on their varied attributes. In doing so, they begin to notice the similarities and differences between various quadrilaterals.


20 min 21. In Lesson 5, students create a square using toothpicks and sticky tack, then they describe the square’s attributes to a partner. Then, after looking at a cube and discussing the number of edges, students are challenged to create a cube. Once the cube is constructed, students analyze the number of faces and right angles. The lesson ends with students following step-by-step directions to practice drawing cubes. From this lesson, students see a square as a face of the cube.


Section: Topic B: Composite Shapes and Fraction Concepts

Time: 56 minutes

In this section, you will focus on exploring fraction concepts to build and partition shapes using tangrams and pattern blocks.

Materials used include:• Grade 2 Module 8 PPT

• Grade 2 Module 8 Facilitator Guide• Grade 2 Module 8 Topic Opener B• Grade 2 Module 8 Lesson 6 Excerpt• Grade 2 Module 8 Lesson 7 Excerpt• Grade 2 Module 8 Lesson 8 Excerpt



In Topic B, students explore fraction concepts as they build and partition composite shapes using tangrams and pattern blocks. The tangram enables students to see shapes within shapes. After cutting out the pieces, students explore the various new shapes they can compose by repositioning the pieces.

Next, students work with the tangram pieces and pattern blocks to explore the fraction concept of equal shares as they compose shapes, e.g., using 2 triangles (halves) to form a square or 3 triangles (thirds) to compose a trapezoid. (In response to the question.)

1 min 23. Take a moment to read this passage from the Progressions document.

This means that students will not be writing fractions using numerator and denominator. In Grade 2 we are developing the concept of fractions as equal shares and describing those shares using fraction language of halves, thirds, and fourths. Students also learn to relate the equal parts to a whole, e.g., 2 halves, 3 thirds, 4 fourths.

Notice how the part/whole relationship runs throughout the curriculum, with the emphasis on units continually developed and built upon. Students have worked with units of frogs, apples, ones, tens, centimeters, dimes, row, columns, and now halves, thirds, and fourths.

16 min 24. In Lesson 6, students decompose a tangram and use the shapes to compose other shapes. As they explore, students are encouraged to flip, slide, and turn pieces; the new shapes do not have to be shapes the students can name.

Then, students are challenged to use specific pieces to create certain shapes, e.g., use the square and the two smallest triangles to create a larger triangle, then join that triangle with a partner’s to make a square.

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

16 min 25. In Lesson 7, students use the two smallest triangles from the tangram to create various shapes composed of two equals parts or shares, called halves. Next, they use pattern blocks to create composite shapes described as thirds and fourths.


16 min 26. In Lesson 8, students work together using pattern blocks and the Problem Set to explore equal shares. They use one pattern block to cover a half, a third, or a fourth of a given shape, and then draw a picture of the composite shape formed by halves, thirds, or fourths. Then, they shade the smaller polygon within the composite shape. Once again, students see units within units.

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


Section: Topic C: Halves, Thirds, and Fourths of Circles and Rectangles

Time: 73 minutes

In this section, you will focus on partitioning circles and rectangles into equal fractional parts.

Materials used include:• Grade 2 Module 8 PPT• Grade 2 Module 8 Facilitator Guide• Grade 2 Module 8 Topic Opener C• Grade 2 Module 8 Lesson 10 Excerpt• Grade 2 Module 8 Lesson 11 Problem Set• Grade 2 Module 8 Lesson 12 Problem Set



Topic C focuses on partitioning circles and rectangles into equal fractional parts. Students begin by partitioning shapes into two equal shares, or halves, and then progress to creating fourths by halving the halves. They also decompose a whole into thirds.

In the latter half of the topic, students assemble a whole out of fractional parts. They also partition a square paper into differently shaped fourths and conclude that equal shares of identical wholes do not need to have the same shape. (In response to the question.)

This topic provides a foundation for Topic D, in which students apply what they have learned about fractional parts of a circle to telling time on an analog clock.

16 min 29. In Lesson 9, students work first with a rectangle, then with a circle to partition the shapes into two equal shares, or halves. Then, they work with images of shaded shapes, examining them and explaining whether a partitioned circle or rectangle is or is not two equal shares.


16 min 30. Lesson 10 is a continuation of Lesson 9. Here, students partition circles and rectangles into thirds and fourths and examine shaded shapes to determine how many thirds or fourths are represented by the shaded or unshaded portion.

They then apply their understanding of partitioning to imagine their rectangles and circles as sheet cakes and pizzas as they divide them into equal shares of halves, thirds, and fourths.


16 min 31. In Lesson 11, students move from concrete to pictorial as they first compose a whole out of halves, thirds, and fourths by matching parts with their classmates. Then, they are given one part of a whole which they glue to a piece of paper and then they draw to complete the whole.



16 min 33. Topic C ends with Lesson 12, in which students recognize that equal shares of identical wholes do not need to have the same shape. To accomplish this students use geoboards to partition shapes into differently shaped halves, thirds, and fourths.



Section: Topic D: Application of Fractions to Tell Time and Review

Time: 64 minutes

In this section, you will focus on applying fraction and skip-counting skills to telling time and review the key points of Grade 2 Module 8.

Materials used include:• Grade 2 Module 8 PPT• Grade 2 Module 8 Facilitator Guide• Grade 2 Module 8 Topic Opener D• Grade 2 Module 8 Partitioned Circle Template• Grade 2 Module 8 Lesson 14 Excerpt• Grade 2 Module 8 Lesson Story Template• Grade 2 Module 8 Lesson 16 Excerpt• Grade 2 Module 8 Mid-Module Assessment



In Topic D, students apply fraction and skip-counting skills to telling time. They use their understanding of partitioning shapes into equal shares to make paper clocks, which they then use to practice telling time to the nearest half and quarter hour. (In response to the question.)

They relate 30 minutes to a half hour and 15 minutes to a quarter hour, gaining an understanding of the language “half past,” “a quarter after,” and “a quarter to.” They also relate everyday activities to a.m. and p.m.

Topic D ends with a lesson in which students apply their subtraction skills to solve problems involving time intervals, including the final challenge of determining how many days before they become third-graders.

36. Note to presenter:Insert this slide at appropriate points in the module study for an in-depth look at scaffolds. You may highlight a scaffold that already exists and discuss it or locate a point where a student might encounter difficulty and explore options.

Delete the slide from this current sequence after you’ve inserted it in appropriate places throughout your session.

Note to presenter: When you have inserted the slide, list several suggestions for scaffolds that would address the situation.

16 min 37. In Lesson 13, following a review using a geared clock, students construct a paper clock. They then use this clock and relate their understanding of fourths and halves to a quarter and a fourth of an hour.


16 min 38. In Lesson 14, students relate each of the 12 numbers on the clock face with intervals of 5 minutes. They use skip-counting to count up and down from 60 by fives in preparation for telling time to the nearest 5 minutes. Fluency work with skip-counting by fives prepares students for this work.

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

1 min 39. In Lesson 15, students develop an understanding of a.m. and p.m., using pictures of everyday activities in a booklet that they can color, assemble, and take home.

**Share the pictures from the book.**

16 min 40. In Lesson 16, students work with a partner to solve word problems involving time intervals. The last problem is a group challenge: Find out how many days there are until they become third-graders.

**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. **

6 min 41. Take 3-4 minutes to complete the mid-module assessment and then take 2-3 minutes to match each assessment item to the lesson in which the content was taught.

0 sec 42. Now that you’ve had the chance to see and practice the concepts, skills, and models of Module 8, let’s take a moment to reflect back on the module overall.

3 min 43. Take 2 minutes to turn and talk with others at your table.Let’s take a minute to share out.• How do composition and decomposition relate to time, shapes, and

fractions? (Students learn they can decompose hours into minutes, compose and decompose shapes into other shapes, and partition 1 whole into equal shares and compose equal shares into 1 whole.)

• What is the importance of sequencing fractions prior to time? (Students are able to understand the quarter and half hour through the partitioning of circles.)

• What units are students working with in Module 8? (minutes, hours, halves, thirds, fourths)

• How does thinking of fractions as units prepare students to add and subtract fractions in G3? (Just as students added 2 frogs and 3 frogs in Kindergarten, seeing fractions as units will help them apply all of the addition and subtraction skills and strategies they have learned to add and subtract, for example, 2 fourths + 3 fourths = 5 fourths, or 1 whole

and 1 fourth.)

1 min 44. Let’s review some key points of this session.

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 8 PPT● Grade 2 Module 8 Facilitator Guide● Grade 2 Module 8 Module Overview● Grade 2 Module 8 Topic Opener A● Grade 2 Module 8 Topic Opener B● Grade 2 Module 8 Topic Opener C● Grade 2 Module 8 Topic Opener D Grade 2 Module 8 Lesson 1 Problem Set Grade 2 Module 8 Lesson 2 Excerpt Grade 2 Module 8 Lesson 6 Excerpt Grade 2 Module 8 Lesson 7 Excerpt Grade 2 Module 8 Lesson 8 Excerpt Grade 2 Module 8 Lesson 10 Excerpt Grade 2 Module 8 Lesson 11 Problem Set Grade 2 Module 8 Lesson 12 Problem Set Grade 2 Module 8 Partitioned Circle Template

Grade 2 Module 8 Lesson 14 Excerpt Grade 2 Module 8 Lesson Story Template Grade 2 Module 8 Lesson 16 Excerpt Grade 2 Module 8 Mid-Module Assessment

Additional Suggested Resources

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

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