# Student Work Examples

Grade 6 | Grade 7 | Grade 8 | For all Grades

Student Work from various CMP Units is provided to stimulate conversations about the mathematical teaching and learning embedded in individual Problems. To add more examples of student work on CMP problems, please email connectedmath@msu.edu. For more information about current research on student work carried out by the CMP Staff, visit the Student Work in Curriculum Materials Research Project.

## Grade 6

*Let's Be Rational*

#### problem 3.3

These student strategies (from Let’s Be Rational Problem 3.3) are a teacher’s documentation of student thinking over many years using CMP. Knowing the ways that students may approach the problems can be helpful to teachers in a few ways

*Decimal Ops*

#### Problem 4.1

These student strategies (from Decimal Ops Problem 4.1) are a teacher’s documentation of student thinking. Knowing the ways that students may approach the problems can be helpful.

*Variables and Patterns*

#### Problem 1.3: From Lewes to Chincoteague Island: Stories, Tables, Graphs

Problem 1.3 in Variables and Patterns challenges students to create a table and graph representation that match some written information expressed in words. There is no one single correct answer. The challenge in the problem requires students to analyze how information is shown on a table and graph. Sample student work is shown.

#### Problem 2.4: What's the Story?

Three CMP teachers offer strategies for how to engage students in thinking about Problem 2.4 in Variables and Patterns. The problem requires students to identify the variables, decide how they are related in “stories”, and then choose the graph that best represents the relationship. Sample student work is shown.

## Grade 7

*Shapes and Designs*

#### Problem 2.2

Shapes and Designs Problem 2.2 asks students to make an important generalization about the angle sum property for any polygon. Students are introduced to the strategies of three students and asked to make sense of the strategies for finding the angle sums of polygons.

#### Problem 2.3

The photos show students working during the Explore (from *Shapes and Designs* Problem 2.3) to create posters that show regular polygons that do and do not tessellate.

*Comparing and Scaling*

#### Problem 1.2: Making Juice

The “Orange Juice” Problem in the Grade 7 Unit: *Comparing and Scaling* has become a classic CMP problem. Iterations of the problem have been in all three versions of CMP. While working with the problem, students generate many interesting strategies for determining the “most orangey” tasting juice from four different recipes.

#### Problem 2.1: Sharing Pizza

Students use many strategies to decide if the amount of pizza a camper would eat differs by which table the camper selects. This student work represents some of strategies that students use.

*Moving Straight Ahead*

#### Problem 2.1: Henri and Emile' Race

Students use many strategies to decide how long to make the race between the two brothers. Some strategies are more efficient and effective than others. This student work represents a variety of strategies that students use. The work does not show students’ answers to the question.

## Grade 8

*Growing, Growing, Growing*

#### Problem 2.1: Killer Plant Strikes Lake Victoria

Students use various representations to show the growth of a water plant. This is the first time that students must make sense of a y-intercept that is not equal to 1. This student work represents some of strategies that students use.

*Frogs, Fleas, and, Painted Cubes*

#### Check Up Preparation for Frogs, Fleas, and, Painted Cubes

*Frogs, Fleas, and, Painted Cubes* is designated as an Algebra I unit in CMP3. Many CMP2 districts taught this unit to all 8th Graders and continue to use the unit with all Grade 8 students for CMP3. The unit develops students’ proficiency with the distributive property and quadratic functions.

## For All Grades

*Examples from Grade 7*

#### Unit Posters Help Students Summarize Their Learning

At the end of each Unit, a teacher in Michigan has students summarize the Investigations on posters. Throughout the year students improved their ability to document and articulate their mathematical thinking.