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๐ŸŽ“ Grade 3๐Ÿ“„ Free PDFโœ… Answer Keys๐ŸŽฏ 4 Classroom Sets

Distributive Property Grid ยท Free Worksheets (Grade 3)

Practice distributive property grid (Grade 3) with free printable PDF worksheets. 4 pre-packaged classroom sets with 100% verified step-by-step answer keys, plus an unlimited live customizer for teachers and homeschoolers.

๐Ÿ“Aligned to Common Core (CCSS.MATH.CONTENT.3.OA.B.5)ยท5-10 min per sheet
Format:
Count:
PanMaths.comDistributive Property Grid Worksheets โ€ข Set A (Standard)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.7 ร— 6 = (5 + ___) ร— 6 = 30 + 12 = 42
Answer:
________________
2.8 ร— 4 = (5 ร— 4) + (3 ร— 4) = ___ + 12 = 32
Answer:
________________
3.6 ร— 7 = (5 ร— 7) + (1 ร— 7) = 35 + 7 = ___
Answer:
________________
4.9 ร— 5 = (5 ร— 5) + (4 ร— 5) = 25 + ___ = 45
Answer:
________________
5.7 ร— 8 = (5 ร— 8) + (2 ร— 8) = 40 + 16 = ___
Answer:
________________
6.8 ร— 6 = (4 + ___) ร— 6 = 24 + 24 = 48
Answer:
________________
7.9 ร— 6 = (5 ร— 6) + (4 ร— 6) = ___ + 24 = 54
Answer:
________________
8.6 ร— 8 = (3 ร— 8) + (3 ร— 8) = 24 + 24 = ___
Answer:
________________
9.8 ร— 7 = (5 ร— 7) + (3 ร— 7) = 35 + ___ = 56
Answer:
________________
10.9 ร— 7 = (5 ร— 7) + (4 ร— 7) = 35 + 28 = ___
Answer:
________________
PanMaths.com โ€ข Free Printable Math WorksheetsPage 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Set A (Standard)
Answer Key
Total Problems: 10
1.7 ร— 6 = (5 + ___) ร— 6 = 30 + 12 = 42
Answer:
2
1. Decompose Factor: Split 7 into friendly addends: (5 + 2).
2. Apply Distributive Law: (5 + 2) ร— 6 = (5 ร— 6) + (2 ร— 6).
3. Compute Partial Products: 5 ร— 6 = 30 and 2 ร— 6 = 12.
4. Sum Partial Products: 30 + 12 = 42 โœ…
2.8 ร— 4 = (5 ร— 4) + (3 ร— 4) = ___ + 12 = 32
Answer:
20
1. Decompose Factor: Split 8 into friendly addends: (5 + 3).
2. Apply Distributive Law: (5 + 3) ร— 4 = (5 ร— 4) + (3 ร— 4).
3. Compute Partial Products: 5 ร— 4 = 20 and 3 ร— 4 = 12.
4. Sum Partial Products: 20 + 12 = 32 โœ…
3.6 ร— 7 = (5 ร— 7) + (1 ร— 7) = 35 + 7 = ___
Answer:
42
1. Decompose Factor: Split 6 into friendly addends: (5 + 1).
2. Apply Distributive Law: (5 + 1) ร— 7 = (5 ร— 7) + (1 ร— 7).
3. Compute Partial Products: 5 ร— 7 = 35 and 1 ร— 7 = 7.
4. Sum Partial Products: 35 + 7 = 42 โœ…
4.9 ร— 5 = (5 ร— 5) + (4 ร— 5) = 25 + ___ = 45
Answer:
20
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…
5.7 ร— 8 = (5 ร— 8) + (2 ร— 8) = 40 + 16 = ___
Answer:
56
1. Decompose Factor: Split 7 into friendly addends: (5 + 2).
2. Apply Distributive Law: (5 + 2) ร— 8 = (5 ร— 8) + (2 ร— 8).
3. Compute Partial Products: 5 ร— 8 = 40 and 2 ร— 8 = 16.
4. Sum Partial Products: 40 + 16 = 56 โœ…
6.8 ร— 6 = (4 + ___) ร— 6 = 24 + 24 = 48
Answer:
4
1. Decompose Factor: Split 8 into friendly addends: (4 + 4).
2. Apply Distributive Law: (4 + 4) ร— 6 = (4 ร— 6) + (4 ร— 6).
3. Compute Partial Products: 4 ร— 6 = 24 and 4 ร— 6 = 24.
4. Sum Partial Products: 24 + 24 = 48 โœ…
7.9 ร— 6 = (5 ร— 6) + (4 ร— 6) = ___ + 24 = 54
Answer:
30
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…
8.6 ร— 8 = (3 ร— 8) + (3 ร— 8) = 24 + 24 = ___
Answer:
48
1. Decompose Factor: Split 6 into friendly addends: (3 + 3).
2. Apply Distributive Law: (3 + 3) ร— 8 = (3 ร— 8) + (3 ร— 8).
3. Compute Partial Products: 3 ร— 8 = 24 and 3 ร— 8 = 24.
4. Sum Partial Products: 24 + 24 = 48 โœ…
9.8 ร— 7 = (5 ร— 7) + (3 ร— 7) = 35 + ___ = 56
Answer:
21
1. Decompose Factor: Split 8 into friendly addends: (5 + 3).
2. Apply Distributive Law: (5 + 3) ร— 7 = (5 ร— 7) + (3 ร— 7).
3. Compute Partial Products: 5 ร— 7 = 35 and 3 ร— 7 = 21.
4. Sum Partial Products: 35 + 21 = 56 โœ…
10.9 ร— 7 = (5 ร— 7) + (4 ร— 7) = 35 + 28 = ___
Answer:
63
1. Decompose Factor: Split 9 into friendly addends: (5 + 4).
2. Apply Distributive Law: (5 + 4) ร— 7 = (5 ร— 7) + (4 ร— 7).
3. Compute Partial Products: 5 ร— 7 = 35 and 4 ร— 7 = 28.
4. Sum Partial Products: 35 + 28 = 63 โœ…
PanMaths.com โ€ข Answer Key & 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.

๐ŸŽฏ 4 Differentiated Classroom Sets Included

Standard 10Version A

Set A: Core Distributive Break-Apart (10 Problems)

Balanced equations decomposing factors 6 to 9 into friendly 5s and smaller parts.

Anti-CheatVersion B

Set B: Alternate Numbers (10 Problems)

Identical curriculum structure with alternate factor pairs to prevent classroom copying.

ChallengingVersion C

Set C: Missing Partial Products & Addends (8 Problems)

Solve for missing decomposed addends, partial products, and final sums.

Speed SprintVersion D

Set D: 3-Minute Fluency Sprint (15 Problems)

Fast-paced drill computing total products from distributive partial product expressions.

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.

What is included in the 4 differentiated worksheet sets?

Set A covers standard core practice (Balanced equations decomposing factors 6 to 9 into friendly 5s and smaller parts.). Set B is an Anti-Cheat version with alternate numbers to prevent copying. Set C features challenging problems, and Set D is a timed sprint.

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.