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

Properties, Patterns & Two-Step Problems

47 points total · Name: ____________________ Date: __________

For the adult

Give this test on a calm day, after the unit's last lesson. Sit with your child and read the directions for each part aloud. Read any item aloud if your child asks. Reading is not what this test checks. Do not time the test. The time given is only a guide, so you can plan. Take a short break between parts if your child is tired. Do not teach or hint during the test. If your child is stuck, say "Do your best, then we can move on." When you score, use the answer and the partial-credit notes for each part. Then add the points and find the level at the end. Your child may use grid paper and two colors of crayon to break apart arrays, counters, and the property reference card from Week 13. Keep the multiplication chart put away. For two-step problems, remind your child to find the hidden first question, to do multiplying or dividing before adding or subtracting when there are no parentheses, and to round to check whether an answer makes sense.

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)
2.
Solve 9 × 2 × 5 the easy way. Put in parentheses to show which two factors you multiply first.
(2 pts)
3.
Fill in the blanks. 7 × 9 = (5 × 9) + (2 × 9) = ____ + ____ = ____
(2 pts)
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)
5.
(a) 0 × 7 = ____ (b) 9 × 1 = ____ (c) 0 ÷ 8 = ____ (d) 15 ÷ 1 = ____
(2 pts)
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)

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)
8.
Solve for the letter. (a) k − 18 = 27 (b) 34 + p = 61
(2 pts)
9.
(a) 5 + 3 × 7 = ____ (b) (5 + 3) × 7 = ____
(2 pts)
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)
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)
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)

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)
14.
Explain how to find 6 × 70 using tens. What is 6 × 70?
(2 pts)
15.
Find the rule. Then fill in the missing OUT number. IN 3 → OUT 24 IN 5 → OUT 40 IN 7 → OUT ____
(2 pts)
16.
Without multiplying, tell whether each product is even or odd. (a) 5 × 9 (b) 6 × 7
(2 pts)
17.
Look at the ×4 products: 4, 8, 12, 16, 20, 24. Are all ×4 products even? Explain why.
(3 pts)

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)
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)
20.
A store has 6 shelves with 9 hats on each shelf. It sells 15 hats. How many hats are left?
(3 pts)