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 practice division within 100 by playing a game called Race to 1. The goal of the game is to repeatedly divide numbers until they reach one.
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community.
Supports accessibility for: Social-Emotional Functioning, Organization
Required Materials
Materials to Gather
Number cubes
Launch
Groups of 2
“Take a minute to read the directions for Race to 1.”
1 minute: quiet think time
“Let’s look at a sample game. Jada rolled a 3 on her first turn, then rolled 2 a few times afterwards. Talk with your partner about what her next move should be if she rolls 2 on her next turn.” (She should divide 4 or 6 by 2 because those moves get her really close to one.)
1 minute: partner discussion
Share responses.
Give each group a number cube.
Activity
“Play Race to 1 with your partner.”
10–15 minutes: partner work time
If students finish early, have them play again. Students can fill in the same numbers from the first game at the top of the columns of the second game or use the numbers 24, 36, 48, and 72 for a challenge.
Student Facing
Directions for Race to 1
On your first turn:
Roll a number cube. The number you roll is your divisor. (If you roll a 5, roll again.)
Choose one number from the top row of your table. Divide it by your divisor.
Write a division expression and record the quotient in the table. Your turn is done.
On all your other turns:
Roll a number cube. The number you roll is your divisor. (If you roll a 5, roll again.)
Choose either a quotient from one of your past turns or a new number from the top row of the table. Divide it by your divisor.
Write a division expression and record the quotient in the table.
The first player to get a quotient of 1 wins.
Sample Game
Jada rolled 3 on her first turn, then rolled 2 a few times afterwards.
|    start number     |     12      |     16      | 18 |     24      |
|---------------------|-------------|-------------|----|-------------|
| division expression | \(12\div3\) | \(16\div2\) |    | \(24\div2\) |
|      quotient       |      4      |      8      |    |     12      |
| division expression |             |             |    | \(12\div2\) |
|      quotient       |             |             |    |      6      |
| division expression |             |             |    |             |
|      quotient       |             |             |    |             |
Game 1
|    start number     | 12 | 16 | 18 | 24 |
|---------------------|----|----|----|----|
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
| division expression |    |    |    |    |
|      quotient       |    |    |    |    |
Game 2
|    start number     |   |   |   |   |
|---------------------|---|---|---|---|
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
| division expression |   |   |   |   |
|      quotient       |   |   |   |   |
Activity Synthesis
“How was having an efficient way to divide helpful as you played Race to 1?” (I had to decide which number I was going to divide, so it was helpful to be able to do it quickly. I had to divide a few times on each turn.)
“What was a helpful strategy as you played Race to 1?” (I had to think about which number I could divide by the number I rolled. I divided the smallest number by the largest divisor to try to get to the quotient to be as small as possible so I could get to 1 first.)


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