standard_description: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
problem_activity: Narrative
The purpose of this activity is for students to relate drawings of equal groups to arrays. Specifically, students look for arrays that have the same number of objects in each row or column as each drawing has in each group. In some arrays, the equal groups in the drawing are represented as rows, and in some, they are represented in columns. Students have the opportunity to explain the connections they see between the drawings and arrays, receive feedback from their peers, and revise their explanation for precision and clarity (MP3, MP6). This will be useful in future lessons when students record multiplication expressions and equations to represent arrays.
This activity uses
MLR1 Stronger and Clearer Each Time
. Advances: reading, writing.
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Attention, Organization
Required Materials
Materials to Copy
Card Sort Arrays
Required Preparation
Create a set of cards from the blackline master for each group of 2 or 4 students.
Launch
Groups of 2 or 4
Distribute one set of pre-cut cards to each group of students.
Activity
“This set of cards includes drawings of equal groups and arrays. Match each drawing to an array. Work with your partner to justify your choices.”
8 minutes: partner work time
“Independently choose a match you and your partner made. Write down how you know that the drawing matches the array.”
2 minutes: independent work time
MLR1 Stronger and Clearer Each Time
“Share your response to why your cards match with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: structured partner discussion
Repeat with 2–3 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2–3 minutes: independent work time
Student Facing
Match the drawings of equal groups and arrays that are alike. Be prepared to explain your reasoning.
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Choose a match you and your partner made. Write down how you know the drawing matches the array.
Student Response
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Activity Synthesis
Have 2-3 students share the matches they made and describe how they know those cards go together.
“Did your group agree on the matches? What did you look for to decide two cards were matches?” (Yes, we looked for equal groups that had the same number of dots in a group as one of the rows in the array.)
Listen for language students use to describe their matches and the structure of the arrays. As needed, ask:
“What do you mean by _____?”
“What else could we call _____?”
“How could you use ‘equal groups’ to explain your match?”
Highlight the use of terms like row, column, and equal groups.


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