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

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Background

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. 

The school that shared this student work offers two courses in Grade 8. The advanced course, called “High School Algebra I”, uses all 8 of the CMP3 units. The course for all other students, called “Grade 8 Algebra”, uses all of the CMP3 units except for the last part of It’s in the System and all of Function Junction

The shared student work is from the non-advanced course.

Description

The students in this classroom were concerned about taking Check Up 2 after Investigation 2 in the Grade 8 unit: Frogs, Fleas, and Painted Cubes. The teacher told them that the Check Up was primarily about the quadratic expressions and the distributive property. The students asked if they could review the ideas before taking the Check Up the next day. 

The teacher gave the following instructions to students.

  • Get into groups of two or three.
  • On a piece of chart paper, write what you know about the forms of quadratic expressions and the distributive property that we have been discussing.
  • After charts are posted in the room, you will choose classmates to explain their paper. You can pick people who have different ideas or ways of showing the thinking.
  • You can ask questions and take notes on any of the ideas that you find helpful and that add to what you already know.

The teacher has found this strategy helpful as a way to summarize and refine learning.

Three Artifacts are provided:

  • Pictures of the chart papers that represent examples of students summarizing the distributive property.
  • A copy of Check Up 2
  • A document with analysis of the student strategies

Purpose

This student work represents a strategy employed by a teacher to help students reflect and summarize what they knew about the distributive property. This strategy proved to be a beneficial formative assessment that helped both the teacher and the students determine and refine mathematical understandings.

This student work can serve as a guide for planning, teaching, assessing, and reflecting on the mathematics of this Investigation. The work can be downloaded for teachers to examine during planning time, for use in a collaborative meeting, for use with students, or for use in professional development activities.

Question to Consider

Planning for the Summary of the Task
  • What strategies do you anticipate students using to accomplish the task?
  • How do these pieces of student work reflect the mathematical goals of the Investigation?
Formative Assessment
  • What mathematical strengths do the students have? Weaknesses?
  • What types of questions might you ask to help these students clarify or extend their thinking?
  • Could these students successfully answer the questions on Check Up 2?
  • If your students produce work like this, what impact will it have on how you would teach the next few problems?
Planning for the Discussion
  • What opportunities could be provided for students to compare and contrast the thinking?
  • How might you orchestrate a discussion of the ideas if your students produce work like these samples?
Teacher Reflections
  • Have the students demonstrated sufficient understanding?
  • How will this set of student work affect your planning for the next lesson?