3rd Grade Properties of Multiplication Test Solutions and Scoring (PDF)
This properties multiplication test answers for 3rd Grade covers properties of multiplication (Common Core 3.OA.B.5), with a free PDF to print.
Grade 3 · Common Core State Standards: 3.OA.B.5
Properties multiplication test answers: worked solutions
Question 1 – Read an array [2 pts]
- 5 rows of 9 dots: \(5 \times 9 = 45\).
- Turn the array: \(9 \times 5 = 45\). The product is 45.
Scoring: 1 point for a correct sentence with product in (a); 1 point for the turned sentence in (b).
Question 2 – Missing factors [2 pts]
- \(8 \times 3 = 3 \times 8\), so \(n = 3\).
- \(9 \times 6 = 6 \times 9 = 54\).
Scoring: 1 point for each correct answer.
Question 3 – Regroup the factors [2 pts]
- \(2 \times 4 = 8\), then \(8 \times 5 = 40\).
- \(4 \times 5 = 20\), then \(2 \times 20 = 40\).
Both products are 40.
Scoring: 1 point for each correct product.
Question 4 – Split the array [2 pts]
- \(6 \times 8 = 6 \times 5 + 6 \times 3\).
- \(6 \times 5 = 30\) and \(6 \times 3 = 18\), and \(30 + 18 = 48\).
Scoring: 1 point for each part.
Question 5 – Complete the sentence [2 pts]
- \(9 = 5 + 4\), so \(n = 4\).
- \(7 \times 5 = 35\) and \(7 \times 4 = 28\). \(35 + 28 = 63\).
Scoring: 1 point for each correct answer.
Question 6 – Friendly products [2 pts]
- \(5 \times 2 = 10\), then \(10 \times 8 = 80\).
- \(4 \times 5 = 20\), then \(20 \times 3 = 60\).
Scoring: 1 point for each correct product.
Question 7 – Card binders [3 pts]
- \(3 \times 4 = 12\) pages. \(12 \times 6 = 72\) cards.
- \(3 \times (4 \times 6) = 3 \times 24 = 72\).
Scoring: In (a), 1 point for 12 pages and 1 point for 72 cards. In (b), 1 point for a valid regrouping that gives 72.
Question 8 – Library shelves [3 pts]
- \(7 \times 6 = 42\) red books and \(7 \times 4 = 28\) blue books. \(42 + 28 = 70\).
- Each shelf holds \(6 + 4 = 10\): \(7 \times 10 = 70\).
Scoring: In (a), 1 point for the two correct products and 1 point for the sum 70. In (b), 1 point for 7 × 10.
Question 9 – Find the mistake [2 pts]
- Ben split 7 into \(5 + 2\) but multiplied the 2 by 7 instead of by 6. Each part must be multiplied by the other factor, 6.
- \(6 \times 7 = 6 \times 5 + 6 \times 2 = 30 + 12 = 42\).
Scoring: 1 point for a clear explanation; 1 point for the correct sentence and product 42.
Total score
20 points
Key facts behind this properties multiplication test answers
- Commutative: \(3 \times 6 = 6 \times 3\). The order of two factors does not change the product.
- Associative: \((2 \times 3) \times 4 = 2 \times (3 \times 4)\). Regrouping three factors does not change the product.
- Distributive: \(6 \times 7 = 6 \times 5 + 6 \times 2\). Split a factor, multiply the parts, then add.
- An array turned on its side shows the commutative property.
- Known facts help you find unknown facts, such as 5s and 2s for 7s and 8s.
How to use this properties multiplication test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
All Grade 3 chapters: Grade 3 math.
