Math Is Playful

Play with numbers, solve equation riddles, and use strategy to crack math puzzles.

6.AT
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
Number Riddle: I am a number. When you multiply me by 4, then add 3, you get 31. What number am I?
Strategy: Work backward! Start with 31, subtract 3, then divide by 4. Or set up an equation: 4n + 3 = 31.
The number is
✓Correct! 4 × 7 + 3 = 28 + 3 = 31.
✗Work backward: 31 − 3 = 28, then 28 ÷ 4 = 7.
Warm-Up 2
Which expression equals 20 when x = 4?
Hint: Substitute 4 for x in each choice and see which one gives 20.
✓Correct! 5 × 4 = 20.
✗Substitute x = 4: A = 17, B = 20, C = 20, D = 21. The simplest match is B: 5x = 20.
P

Practice

5 questions
Practice 1
Equation Puzzle: Solve for m.
2m + 6 = 18
Steps: 1) Subtract 6 from both sides. 2) Divide both sides by 2.
m =
Show your steps:

Sentence frame: "First I subtracted ___ from both sides to get 2m = ___. Then I divided by ___ to get m = ___."

✓Correct! 2m + 6 = 18 → 2m = 12 → m = 6.
✗Subtract 6: 2m = 12. Divide by 2: m = 6.
Practice 2
Magic Number Box: A number goes in and the rule is "multiply by 3, then subtract 5." If the output is 13, what was the input?
Strategy: Write the equation: 3n − 5 = 13. Solve by adding 5 to both sides, then dividing by 3.
Show your equation work:

Sentence frame: "The equation is 3n − 5 = 13. Adding 5 gives 3n = ___. Dividing by 3 gives n = ___."

✓Correct! 3n − 5 = 13 → 3n = 18 → n = 6.
✗3n − 5 = 13 → 3n = 18 → n = 6 (C).
Practice 3
Sort each item: is it an equation or an expression?
Key difference: An equation has an equal sign (=). An expression does not.
7x = 42
3a + 9
y ÷ 2 = 10
5(n − 1)
15 = 3 + 4k
2² + 8
Equations
Expressions
✓All correct! Equations have an equal sign. Expressions are math phrases without one.
✗Some items are in the wrong group. Look for the = sign to identify equations!
Practice 4
Fill-in Puzzle: Find the value that makes each equation true.
Hint: Use inverse operations. Addition undoes subtraction. Multiplication undoes division.
a. − 4 = 5
b. 3 × = 24
c. ÷ 2 = 5

Sentence frame: "I know ___ is the answer because ___ and ___ equals ___."

✓All correct! 9 − 4 = 5, 3 × 8 = 24, and 10 ÷ 2 = 5.
✗Check each: 9 − 4 = 5, 3 × 8 = 24, 10 ÷ 2 = 5.
Practice 5
Game Strategy: In a number game, you score points equal to 2n + 1, where n is your roll. If you need exactly 15 points to win, what must you roll?
Strategy: Set up the equation 2n + 1 = 15 and solve for n.
Explain your solution:

Sentence frame: "I solved 2n + 1 = 15. Subtracting 1 gives 2n = ___. Dividing by 2 gives n = ___."

✓Correct! 2n + 1 = 15 → 2n = 14 → n = 7. You need to roll a 7!
✗2n + 1 = 15 → 2n = 14 → n = 7 (C).
★

Challenge

1 question
Challenge
Double Puzzle: I am thinking of two consecutive whole numbers. The sum of the smaller number and twice the larger number is 17. What are the two numbers?
Strategy: Let the smaller number be n. The larger is n + 1. Write the equation: n + 2(n + 1) = 17.
Smaller number:
Larger number:
Show your algebraic reasoning:

Sentence frame: "I let the smaller number be n. The equation is n + 2(n + 1) = 17. Simplifying: ___ = 17, so n = ___. The numbers are ___ and ___."

✓Correct! n + 2(n + 1) = 17 → 3n + 2 = 17 → 3n = 15 → n = 5. The numbers are 5 and 6.
✗n + 2(n+1) = 17 → 3n + 2 = 17 → n = 5. The numbers are 5 and 6.