Mixing Bowls

What You’ll Need: A small mixing bowl A large mixing bowl Various objects What objects can you find so that about 10 of those objects just about fill each of your mixing bowls? Sample answer: I could fill the small mixing bowl with about 10 toy cars. I could fill the large mixing bowl with a whole bag of potatoes.

Closest to 7

What You’ll Need:
Closest to 7 printout

Print and cut out the number cards from the Closest to 7 printout. Shuffle and place the cards face down in a pile. Then give students these instructions:
Play in pairs or in a small group. Each player picks up 3 cards without revealing them to the other players. Players choose 2 of their cards so that the total when they add them together is as close to 7 as they can get. The player closest to 7 gets a point. If more than one player is equally close to 7, each of those players gets a point. The first player with 10 points wins.

Example:
Shirley picked 2, 3, and 2. She chose 2 and 3 because she knows 2 + 3 equals 5, which is only 2 away from 7.
Troy picked 4, 4, and 1. He chose 4 and 4 because he knows 4 + 4 equals 8, which is only 1 away from 7.
Troy gets 1 point because his number is closest to 7.

Sea Legs

What You’ll Need: Counters (optional) A group of crabs and starfish has 30 legs altogether. How many are crabs and how many are starfish? Crabs have 10 legs and starfish have 5 legs. Sample answer: There could be 2 crabs and 2 starfish. There could also be 1 crab and 4 starfish.

Two-Digit Takeaway

What You’ll Need:
Two-Digit Takeaway printout

Print and cut out the number cards from the Two-Digit Takeaway printout. Separate and shuffle the one-digit number cards, and place them in a pile. Shuffle the two-digit number cards, and place them in a different pile. Then give students these instructions:
Play in pairs. Each player picks up one card from each pile and subtracts one number from the other number. The player with the greater difference gets 1 point. Return the cards to their piles, shuffle, and repeat. The first player with 10 points wins.

Example:
Alon picked up an 8 and an 11. He makes the equation 11 − 8. The difference is 3.
Matt picked up a 4 and a 19. He makes the equation 19 − 4. The difference is 15.
Matt gets a point because he has the greater difference.

Three-Digit Dig

What You’ll Need:
No materials necessary

How many three-digit numbers less than 500 are there where the hundreds digit is greater than the tens digit and the tens digit is greater than the ones digit? For example, 421 would work, but 412 would not since 2 is greater, not less, than 1. 422 would also not work since the digits go down only once.

Answer:
I realized that numbers below 200 do not fit since the digits can go down only once and not twice.
Then I went to the 200s. 210 fits because 1 and 0 are the only numbers less than 2.
Then I went to the 300s. 321, 320, and 310 all fit because 2, 1, and 0 are less than 3.
Then I went to the 400s. 432, 431, 430, 421, 420, and 410 all fit because 3, 2, 1, and 0 are less than 4.
In total, there are 10 numbers.

What’s the Rule?

What You’ll Need:
No materials necessary

Suppose there is a rule that you apply to two numbers. The rule can involve a combination of addition, subtraction, multiplication, or division. It turns out that if you use the rule, this is what happens:
2 and 3 turn into 13.
2 and 10 turn into 34.
4 and 5 turn into 23.
6 and 8 turn into 36.
What do you think 4 and 9 turn into?

Sample answer:
I noticed that 13 is 2 less than 15 and 15 is 3 groups of 2 + 3.
I noticed that 34 is 2 less than 36 and 36 is 3 groups of 2 + 10.
But it did not work for 4 and 5 since 23 is not 2 less than 3 groups of 4 + 5.
But then I noticed that 23 is 4 less than 3 groups of 9, and 4 is the first number just as 2 was the first number in the first two facts. That means that when I use 6 and 8, it should be 6 less than 3 groups of 6 + 8, and that works.
I predict that 4 and 9 turn into 4 less than 3 groups of 13, so it would be 35.

Closest to Thirty

What You’ll Need: Closest to Thirty printout Print and cut out the number cards from the Closest to Thirty printout. Shuffle and place the cards face down in a pile. Then give students these instructions: Play in pairs or in a small group. Each player picks up three cards without revealing them to the other players. Players choose two of their cards to multiply and then add the value of the third card. The player closest to 30 wins a point. If more than one player is equally close to 30, each of those players gets a point. The first player with 10 points wins the game. Example: Abed picked 9, 6, and 4. He chose 6 and 4 because he knows that 6 times 4 equals 24. He then added the 9, which gave him 33, so he’s only 3 away from 30. Annie picked 4, 7, and 3. She chose 4 and 7 because she knows that 4 times 7 equals 28. She then added the 3, which gave her 31, so she’s only 1 away from 30. Annie gets 1 point because her number is closest to 30.

Curious Clues

What You’ll Need: No materials necessary Play in pairs. Think of a number between 1000 and 100 000. Give your partner three clues that will help them figure out the number without giving them the number. One clue should involve place-value ideas. One clue should involve division. One clue should involve addition. You should need all three clues to guess the number. Take turns guessing each other’s numbers. Example: I chose the number 4285. These were my clues: The number has 4 in the thousands place. The number has the same hundreds and tens digits as 195 + 92. The number has the same ones digit as 10 ÷ 2.

Repeating Rolls

What You’ll Need: Two number cubes (1–6) What is the experimental probability that if you roll two number cubes six times, you will repeat one of the sums you get? Sample answer: I figured out the experimental probability. I rolled a pair of number cubes 60 times. I separated the information into 10 groups of 6 rolls and figured out whether I repeated a sum in each group. These were the sums I rolled: 5, 6, 3, 8, 4, 7 10, 8, 6, 8, 8, 6 4, 2, 8, 10, 7, 6 9, 9, 6, 12, 3, 10 4, 5, 3, 5, 8, 8 7, 10, 3, 8, 5, 5, 9, 6, 7, 2, 12, 7 7, 5, 10, 4, 8, 11 7, 6, 7, 10, 10, 4 9, 9, 6, 8, 4, 10 I got a repeat 7 times out of 10 groups, so the experimental probability is 70%.

Adjustable Algebra

What You’ll Need:
No materials necessary

Choose a number. Use ten different algebraic expressions that describe that number in terms of other numbers. For example, if my number was 25, I could think of 25 as 2x + 1 if x = 12.
Make sure that some expressions involve addition, some involve subtraction, some involve multiplication, and some involve division. The expressions can involve several operations.

Sample answers:
I picked the number 40.
I know that 40 is 2x if x = 20.
I know that 40 is x + 5 if x = 35.
I know that 40 is 2x + 8 if x = 16.
I know that 40 is 2x – 10 if x = 25.
I know that 40 is 3x ÷ 3 if x = 40.
I know that 40 is 4x – 12 if x = 13.
I know that 40 is 100 – 3x if x = 20.
I know that 40 is 2x ÷ 3 if x = 60.
I know that 40 is 5x ÷ 2 if x = 16.
I know that 40 is 17x + 6 if x = 2.

Division Decisions

What You’ll Need: No materials necessary Fill in the blanks to make the equation below true. Make sure you do not use any of the same digits on the left side of the equation as on the right side. ☐☐.☐ ÷ 0.☐= ☐☐.☐÷ 0.☐ Sample answer: 44.2 ÷ 0.2 = 66.3 ÷ 0.3

Twenty Touchdown

What You’ll Need: Twenty Touchdown printout Print and cut out the number cards from the Twenty Touchdown printout. Shuffle and place the cards face down in a pile. Then give students these instructions: Play in pairs or in small groups. Choose four cards without looking at the values. Then look at them and try to arrange them in the boxes below to get as close to 20 as possible. ☐☐% of ☐☐ The person closest to 20 gets a point. The first person with 10 points wins the game. Example: Gosia picked 4, 2, 7, and 0. She knows that 24% of 70 is about (frac{1}{4}) of 70, which is close to 18. Alexi picked 3, 5, 1, and 2. He knows that 51% of 32 is about (frac{1}{2}) of 32, which is close to 16. Gosia gets 1 point because her number is closest to 20.