standard_description: Use the structure of an expression to identify ways to rewrite it. For example, see x^(4) – y^(4 )as (x^(2))^(2 )– (y^(2))^(2), thus recognizing it as a difference of squares that can be factored as (x^(2 )– y^(2))(x^(2 )+ y^(2)).
problem_activity: Narrative
The purpose of this activity is for students to decompose 6 into 2 parts. Students see that the total number of cubes remains the same when it is decomposed into 2 parts. Although students may notice that they can do this in different ways, that idea is not the focus until the next activity.
MLR8 Discussion Supports.
Display and encourage students to use the following sentence frames: “I have _____ cubes in my hand”, “I have _____ cubes on my desk,” and “I have _____ cubes altogether.”
Advances: Speaking, Reading, Representing
Required Materials
Materials to Gather
Connecting cubes
Required Preparation
Each student needs 6 connecting cubes.
Launch
Groups of 2
Give each student 6 connecting cubes.
Activity
“You have 6 cubes. Put some of the cubes in your hand and some on your desk.”
30 seconds: independent work time
“Tell your partner how many cubes are in your hand. Show them the cubes.”
“Tell your partner how many cubes are on your desk. Show them the cubes.”
“Tell your partner how many cubes you have altogether.”
Student Response
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Activity Synthesis
Invite a student to share.
“How many cubes did you have in your hand? How many cubes were on your desk?”
Write an expression to represent the parts.
“How many cubes did you have in all?” (6)
“The total number of cubes stays the same when we break them up into 2 parts.”


aligns: no