standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Narrative
The purpose of this activity is for students to create stories and relate the action in the stories to the action of adding or taking away counters. While in the first activity, the story was provided, in this activity students create the action in the story, which is an opportunity to hear what language students associate with addition and subtraction (MP6). Mats with pictures of each setting are provided to help students make connections between what they do with their cubes and what is happening in the story. The goal of the activity synthesis is to relate the action in the story to the action with counters and show students expressions that represent these actions (MP2).
MLR8 Discussion Supports.
Synthesis: Provide all students with an opportunity to produce these words and numbers by inviting students to chorally repeat the expression in unison 1-2 times. For example: “7 take away 3” and “
\(7 - 3\)
”.
Advances: Listening, Speaking
Representation: Internalize Comprehension.
Synthesis: First demonstrate, then invite students to name each action they take as they tell their stories. For example, “Four ducks are swimming in a lake. Two ducks fly away. When the ducks fly away, I take away 2 counters.”
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
Two-color counters
Launch
Groups of 2
“We have heard and acted out some stories about students playing at school. Where else in your community do you see people playing outside? Describe it to your partner.”
30 seconds: quiet think time
1 minute: partner discussion
Share and record responses.
Display images from the student book.
“Some of the places where we play and walk around outside are parks and playgrounds. These stories all take place in different parks and playgrounds. How are these pictures the same as parks and playground that you have been to? How are they different?”
Give each student a bag of 10 two-color counters.
“We’re going to use our counters to show what is happening in our stories, but this time, the stories aren’t finished yet.”
Activity
Display the student workbook page of a field and read the first question. Count out 7 counters and place them on the field.
“I’ve got 7 kids playing tag in the field. What do you think happens next in the story?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Choose one student response and demonstrate the action with the counters.
“Now it’s your turn. I’m going to read you the first part of the story. Your job is to think about what happens next in the story. Then tell the story to your partner and show them what happens with your counters.”
Read each question. Give students quiet think time and partner discussion time for each question.
Student Facing
There were 7 kids playing tag on the field.
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There were 2 kids eating at the picnic table.
[IMG]
There were 4 ducks swimming in the lake.
[IMG]
There were 5 kids playing hopscotch.
[IMG]
Student Response
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Advancing Student Thinking
If students represent the given sentence with counters but need encouragement to make up the rest of the story, consider asking:
“Can you use your counters to show me what happened first in the story?”
“What do you think happened next? Do you think more kids came to play tag or do you think some kids went home?”
Activity Synthesis
For each question, choose a student to share their story and demonstrate what happens with their counters. Record the action with words and numbers and an expression. For example: “7 take away 3” and “
\(7 - 3\)
”.
As each student shares, ask: “What do the counters represent?”


aligns: no