Math · Unit 3 · Weeks 13–18 · 30–40 min

Scoring Guide: Properties, Patterns & Two-Step Problems

47 points total

Part 1: Properties of Multiplication

13 points

Solve. Show how you used a property.

1.
9 × 4 = 36. (a) What is 4 × 9? (b) Name the property that tells you.
(2 pts)
Answer: (a) 36 (b) commutative property
2.
Solve 9 × 2 × 5 the easy way. Put in parentheses to show which two factors you multiply first.
(2 pts)
Answer: 90; for example, 9 × (2 × 5) = 9 × 10 = 90.
3.
Fill in the blanks. 7 × 9 = (5 × 9) + (2 × 9) = ____ + ____ = ____
(2 pts)
Answer: 45 + 18 = 63
4.
A garden has 9 rows of 6 plants. Split it into 5 rows and 4 rows. Find the plants in each part. How many plants in all?
(2 pts)
Answer: 5 × 6 = 30 and 4 × 6 = 24; 30 + 24 = 54 plants
5.
(a) 0 × 7 = ____ (b) 9 × 1 = ____ (c) 0 ÷ 8 = ____ (d) 15 ÷ 1 = ____
(2 pts)
Answer: (a) 0 (b) 9 (c) 0 (d) 15
6.
Leo says 4 × 2 × 3 and 3 × 4 × 2 have different answers because the numbers are in a different order. Is Leo right? Solve both and explain.
(3 pts)
Answer: No. Both are 24. Look for: you can change the order or the grouping of factors and the product stays the same (commutative and associative properties).

Scoring: Items 1 and 3: 1 point for each part (item 3: 1 point for 45 and 18, 1 point for 63). Item 2: 1 point for a helpful grouping and 1 point for 90. Item 4: 1 point for both parts and 1 point for 54. Item 5: 2 points if all four are right; 1 point if two or three are right. Item 6: 3 points for "no," 24 for both and a property reason; 2 points for both products right with a weak reason; 1 point for "no" only.

Reteach if needed: Week 13, Week 17, Week 18. Week 13 Days 1–4 (commutative, associative, break apart, rules for 0 and 1), Week 17 Day 4 and Week 18 Day 3 (naming and using the properties).

Part 2: Two-Step Problems & Unknowns

15 points

Solve. Show each step. Use a letter for the unknown when the item asks.

7.
Solve for the letter. (a) n × 7 = 56 (b) 45 ÷ m = 9
(2 pts)
Answer: (a) n = 8 (b) m = 5
8.
Solve for the letter. (a) k − 18 = 27 (b) 34 + p = 61
(2 pts)
Answer: (a) k = 45 (b) p = 27
9.
(a) 5 + 3 × 7 = ____ (b) (5 + 3) × 7 = ____
(2 pts)
Answer: (a) 26 (b) 56
10.
A coach has 7 boxes with 6 balls in each box. 9 balls are flat. How many balls are not flat? Write an equation for each step, using a letter for the unknown.
(3 pts)
Answer: 33 balls. For example, 7 × 6 = b, b = 42; 42 − 9 = f, f = 33.
11.
Ana has 28 stickers. Her aunt gives her 20 more. She puts all of them equally on 6 pages. How many stickers are on each page?
(3 pts)
Answer: 8 stickers (28 + 20 = 48; 48 ÷ 6 = 8)
12.
Juan added 487 + 326 and got 713. (a) Round each number to the nearest 100 and estimate the sum. (b) Is 713 reasonable? (c) What is the exact sum?
(3 pts)
Answer: (a) 500 + 300 = 800 (b) No, 713 is too far from 800. (c) 813

Scoring: Items 1–3: 1 point for each part. Items 4–5: 1 point for the first step, 1 point for the second step and 1 point for the answer with a word. In item 4, if your child writes the steps with ? instead of a letter, take off 1 point. Item 6: 1 point for each part.

Reteach if needed: Week 14, Week 15. Week 15 Days 1–2 (finding the hidden question; letters for unknowns), Week 15 Day 3 (multiply or divide first), Week 15 Day 4 (estimating by rounding) and Week 14 Day 4 (two-step party problems).

Part 3: Patterns & Multiples of 10

12 points

Use patterns and place value to answer.

13.
(a) 3 × 50 = ____ (b) 7 × 60 = ____ (c) 9 × 20 = ____
(3 pts)
Answer: (a) 150 (b) 420 (c) 180
14.
Explain how to find 6 × 70 using tens. What is 6 × 70?
(2 pts)
Answer: 420. Look for: 70 is 7 tens, so 6 × 7 tens = 42 tens, and 42 tens is 420.
15.
Find the rule. Then fill in the missing OUT number. IN 3 → OUT 24 IN 5 → OUT 40 IN 7 → OUT ____
(2 pts)
Answer: Rule: multiply by 8 (× 8). OUT = 56
16.
Without multiplying, tell whether each product is even or odd. (a) 5 × 9 (b) 6 × 7
(2 pts)
Answer: (a) odd (both factors are odd; 5 × 9 = 45) (b) even (one factor is even; 6 × 7 = 42)
17.
Look at the ×4 products: 4, 8, 12, 16, 20, 24. Are all ×4 products even? Explain why.
(3 pts)
Answer: Yes. Look for: 4 × a number is double (2 ×) the number and then doubled again, so it can always be split into 2 equal groups; or 4 is even, and even × any number is even.

Scoring: Item 1: 1 point for each product. Item 2: 1 point for 420 and 1 point for the tens explanation. Item 3: 1 point for the rule and 1 point for 56. Item 4: 1 point for each part. Item 5: 3 points for "yes" and a clear doubling or even-factor reason; 2 points for "yes" with a reason that only lists examples; 1 point for "yes" only.

Reteach if needed: Week 16. Week 16 Days 1–2 (chart patterns; even and odd products), Week 16 Day 3 (multiplying by multiples of 10) and Week 16 Day 4 (in/out tables).

Part 4: Mixed × and ÷

7 points

Solve. Write the answer with a word when there is one.

18.
(a) 72 ÷ 9 = ____ (b) 7 × 7 = ____ (c) 36 ÷ 6 = ____ (d) 8 × 3 = ____
(2 pts)
Answer: (a) 8 (b) 49 (c) 6 (d) 24
19.
Write an equation for this problem, then solve it. 63 crayons are shared equally by 7 friends. How many crayons does each friend get?
(2 pts)
Answer: 63 ÷ 7 = c (or 7 × c = 63); c = 9 crayons
20.
A store has 6 shelves with 9 hats on each shelf. It sells 15 hats. How many hats are left?
(3 pts)
Answer: 39 hats (6 × 9 = 54; 54 − 15 = 39)

Scoring: Item 1: 2 points if all four are right; 1 point if two or three are right. Item 2: 1 point for the equation and 1 point for 9. Item 3: 1 point for each step and 1 point for 39 hats.

Reteach if needed: Week 17, Week 18. Week 17 Days 1–3 (sharing and grouping; dividing with a related fact; choosing × or ÷) and Week 18 Days 1–2 (fact strategies and fact families).

Score box

Part	Points earned	Possible
1. Properties of Multiplication		13
2. Two-Step Problems & Unknowns		15
3. Patterns & Multiples of 10		12
4. Mixed × and ÷		7
Total		47

Level: Enter points to see the level.

D · Developing: 0–23
A · Approaching: 24–32
P · Proficient: 33–42
E · Exceeding: 43–47