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Distributive Property GridFREEWorksheet Generator(Grade 3)

Distributive Property Grid worksheets (Grade 3) with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems.

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Set A โ€ข 10 Qs
PanMaths.comDistributive Property Grid Worksheets โ€ข Set A (Medium)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.9 ร— 3 = (6 + ___) ร— 3 = 18 + 9 = 27
Answer:
________________
2.9 ร— 8 = (6 ร— 8) + (3 ร— 8) = ___ + 24 = 72
Answer:
________________
3.9 ร— 6 = (5 ร— 6) + (4 ร— 6) = 30 + ___ = 54
Answer:
________________
4.9 ร— 4 = (5 ร— 4) + (4 ร— 4) = 20 + 16 = ___
Answer:
________________
5.8 ร— 3 = (5 + ___) ร— 3 = 15 + 9 = 24
Answer:
________________
6.6 ร— 7 = (3 ร— 7) + (3 ร— 7) = ___ + 21 = 42
Answer:
________________
7.7 ร— 8 = (4 ร— 8) + (3 ร— 8) = 32 + ___ = 56
Answer:
________________
8.9 ร— 5 = (5 ร— 5) + (4 ร— 5) = 25 + 20 = ___
Answer:
________________
9.7 ร— 5 = (4 + ___) ร— 5 = 20 + 15 = 35
Answer:
________________
10.8 ร— 7 = (4 ร— 7) + (4 ร— 7) = ___ + 28 = 56
Answer:
________________
PanMaths.com โ€ข Free Math Worksheet Generator โ€ข Set A (Medium)Page 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Set A (Medium)
Answer Key
Total Problems: 10
1.9 ร— 3 = (6 + ___) ร— 3 = 18 + 9 = 27
Answer:
3
1. Decompose Factor: Split 9 into friendly addends: (6 + 3).
2. Apply Distributive Law: (6 + 3) ร— 3 = (6 ร— 3) + (3 ร— 3).
3. Compute Partial Products: 6 ร— 3 = 18 and 3 ร— 3 = 9.
4. Sum Partial Products: 18 + 9 = 27 โœ…
2.9 ร— 8 = (6 ร— 8) + (3 ร— 8) = ___ + 24 = 72
Answer:
48
1. Decompose Factor: Split 9 into friendly addends: (6 + 3).
2. Apply Distributive Law: (6 + 3) ร— 8 = (6 ร— 8) + (3 ร— 8).
3. Compute Partial Products: 6 ร— 8 = 48 and 3 ร— 8 = 24.
4. Sum Partial Products: 48 + 24 = 72 โœ…
3.9 ร— 6 = (5 ร— 6) + (4 ร— 6) = 30 + ___ = 54
Answer:
24
1. Decompose Factor: Split 9 into friendly addends: (5 + 4).
2. Apply Distributive Law: (5 + 4) ร— 6 = (5 ร— 6) + (4 ร— 6).
3. Compute Partial Products: 5 ร— 6 = 30 and 4 ร— 6 = 24.
4. Sum Partial Products: 30 + 24 = 54 โœ…
4.9 ร— 4 = (5 ร— 4) + (4 ร— 4) = 20 + 16 = ___
Answer:
36
1. Decompose Factor: Split 9 into friendly addends: (5 + 4).
2. Apply Distributive Law: (5 + 4) ร— 4 = (5 ร— 4) + (4 ร— 4).
3. Compute Partial Products: 5 ร— 4 = 20 and 4 ร— 4 = 16.
4. Sum Partial Products: 20 + 16 = 36 โœ…
5.8 ร— 3 = (5 + ___) ร— 3 = 15 + 9 = 24
Answer:
3
1. Decompose Factor: Split 8 into friendly addends: (5 + 3).
2. Apply Distributive Law: (5 + 3) ร— 3 = (5 ร— 3) + (3 ร— 3).
3. Compute Partial Products: 5 ร— 3 = 15 and 3 ร— 3 = 9.
4. Sum Partial Products: 15 + 9 = 24 โœ…
6.6 ร— 7 = (3 ร— 7) + (3 ร— 7) = ___ + 21 = 42
Answer:
21
1. Decompose Factor: Split 6 into friendly addends: (3 + 3).
2. Apply Distributive Law: (3 + 3) ร— 7 = (3 ร— 7) + (3 ร— 7).
3. Compute Partial Products: 3 ร— 7 = 21 and 3 ร— 7 = 21.
4. Sum Partial Products: 21 + 21 = 42 โœ…
7.7 ร— 8 = (4 ร— 8) + (3 ร— 8) = 32 + ___ = 56
Answer:
24
1. Decompose Factor: Split 7 into friendly addends: (4 + 3).
2. Apply Distributive Law: (4 + 3) ร— 8 = (4 ร— 8) + (3 ร— 8).
3. Compute Partial Products: 4 ร— 8 = 32 and 3 ร— 8 = 24.
4. Sum Partial Products: 32 + 24 = 56 โœ…
8.9 ร— 5 = (5 ร— 5) + (4 ร— 5) = 25 + 20 = ___
Answer:
45
1. Decompose Factor: Split 9 into friendly addends: (5 + 4).
2. Apply Distributive Law: (5 + 4) ร— 5 = (5 ร— 5) + (4 ร— 5).
3. Compute Partial Products: 5 ร— 5 = 25 and 4 ร— 5 = 20.
4. Sum Partial Products: 25 + 20 = 45 โœ…
9.7 ร— 5 = (4 + ___) ร— 5 = 20 + 15 = 35
Answer:
3
1. Decompose Factor: Split 7 into friendly addends: (4 + 3).
2. Apply Distributive Law: (4 + 3) ร— 5 = (4 ร— 5) + (3 ร— 5).
3. Compute Partial Products: 4 ร— 5 = 20 and 3 ร— 5 = 15.
4. Sum Partial Products: 20 + 15 = 35 โœ…
10.8 ร— 7 = (4 ร— 7) + (4 ร— 7) = ___ + 28 = 56
Answer:
28
1. Decompose Factor: Split 8 into friendly addends: (4 + 4).
2. Apply Distributive Law: (4 + 4) ร— 7 = (4 ร— 7) + (4 ร— 7).
3. Compute Partial Products: 4 ร— 7 = 28 and 4 ร— 7 = 28.
4. Sum Partial Products: 28 + 28 = 56 โœ…
PanMaths.com โ€ข Answer Key & Worked SolutionsPage 2 of 2
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Worksheet Info

Categorygrade-3
Grade LevelGrade 3
DifficultyEasy, Medium, Hard, Sprint
Time5-10 min
CCSS CodeCCSS.MATH.CONTENT.3.OA.B.5

Skills Practiced

  • โœ“ Distributive Property Grid

Key Strategies

  • ๐Ÿงฑ Area Model Grid Split: Split a large rectangle into two smaller rectangles sharing the same height. E.g. A 7 ร— 8 rectangle splits into a 5 ร— 8 rectangle (area 40) and a 2 ร— 8 rectangle (area 16); Total Area = 40 + 16 = 56.
  • ๐Ÿ–๏ธ The Break-Apart 5s Strategy: Because multiplying by 5 is easy, decompose numbers from 6 to 9 into 5 + n. For 7 ร— 6: (5 + 2) ร— 6 = (5 ร— 6) + (2 ร— 6) = 30 + 12 = 42.
  • ๐Ÿ”Ÿ Decade / Tens Partitioning: When multiplying teen numbers, break apart into 10 + ones: 12 ร— 6 = (10 + 2) ร— 6 = 60 + 12 = 72.
  • โž• Sum of Partial Products: Multiply each smaller part first, then add the partial products to find the final total: (pโ‚ ร— n) + (pโ‚‚ ร— n) = Total Product.

Related Worksheets

๐Ÿ“œ Standard: CCSS.MATH.CONTENT.3.OA.B.5๐Ÿ”— CCSS.MATH.CONTENT.3.MD.C.7.C๐Ÿ”— CCSS.MATH.CONTENT.3.OA.C.7

Mastering Distributive Property Grid: Core Concepts & Mental Models

The Distributive Property of Multiplication states that multiplying a sum by a number gives the same result as multiplying each addend separately and adding the products together: a ร— (b + c) = (a ร— b) + (a ร— c). By visually splitting a large array or area grid into two smaller, friendlier rectangles (like 5s and 2s), students make difficult multiplication facts effortless.

Worked Example & SolutionTeacher Step-by-Step Method
๐Ÿ“ Problem: Find 7 ร— 8 using the Break-Apart (5 + 2) Distributive Property strategy.
Worked Solution: Step 1: Decompose 7 into friendly parts (5 + 2). Step 2: Write the distributive expression: (5 + 2) ร— 8 = (5 ร— 8) + (2 ร— 8). Step 3: Compute partial products: 5 ร— 8 = 40 and 2 ร— 8 = 16. Step 4: Add partial products: 40 + 16 = 56. Therefore, 7 ร— 8 = 56.

๐Ÿ’ก Essential Strategies for Distributive Property Grid

๐Ÿงฑ Area Model Grid Split

Split a large rectangle into two smaller rectangles sharing the same height. E.g. A 7 ร— 8 rectangle splits into a 5 ร— 8 rectangle (area 40) and a 2 ร— 8 rectangle (area 16); Total Area = 40 + 16 = 56.

๐Ÿ–๏ธ The Break-Apart 5s Strategy

Because multiplying by 5 is easy, decompose numbers from 6 to 9 into 5 + n. For 7 ร— 6: (5 + 2) ร— 6 = (5 ร— 6) + (2 ร— 6) = 30 + 12 = 42.

๐Ÿ”Ÿ Decade / Tens Partitioning

When multiplying teen numbers, break apart into 10 + ones: 12 ร— 6 = (10 + 2) ร— 6 = 60 + 12 = 72.

โž• Sum of Partial Products

Multiply each smaller part first, then add the partial products to find the final total: (pโ‚ ร— n) + (pโ‚‚ ร— n) = Total Product.

๐Ÿ“– Key Mathematical Vocabulary

Distributive Property

The property stating that multiplying a number by a sum equals the sum of the individual products: a ร— (b + c) = (a ร— b) + (a ร— c).

Decompose

To break a number apart into two or more smaller, friendlier addends (e.g. breaking 7 into 5 + 2).

Partial Product

The result of multiplying one part of a decomposed factor by the other factor before finding the total sum.

Area Model

A visual rectangle whose total area represents the product of its length and width, partitioned into sections.

Addend

Any of the numbers being added together inside parentheses.

โ“ Frequently Asked Questions

How do you solve a distributive property grid problem step by step?

Here is a worked example: "Find 7 ร— 8 using the Break-Apart (5 + 2) Distributive Property strategy.". Solution: Step 1: Decompose 7 into friendly parts (5 + 2). Step 2: Write the distributive expression: (5 + 2) ร— 8 = (5 ร— 8) + (2 ร— 8). Step 3: Compute partial products: 5 ร— 8 = 40 and 2 ร— 8 = 16. Step 4: Add partial products: 40 + 16 = 56. Therefore, 7 ร— 8 = 56.

What is the core learning objective for distributive property grid?

Use grid and area models to represent the distributive property by decomposing a challenging factor into friendly addends (such as 5 + n or 10 + n), finding partial products, and summing them to find the total product. This directly aligns with Common Core Standard CCSS.MATH.CONTENT.3.OA.B.5.

How does the unlimited distributive property grid worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of distributive property grid problems with unique numbers. No two worksheets are ever the same โ€” perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

Are these distributive property grid worksheets free to print with answer keys?

Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.