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

Associative Property of Multiplication ยท Free Worksheets (Grade 3)

Practice associative property of multiplication (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.comAssociative Property of Multiplication Worksheets โ€ข Set A (Standard)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.
(2ร—3)ร—4=2ร—(___ร—4)
Workspace:
2.
(4ร—2)ร—5=4ร—(2ร—5)=___
Workspace:
3.
(3ร—3)ร—2=3ร—(3ร—___)
Workspace:
4.
5ร—(2ร—6)=(___ร—2)ร—6
Workspace:
5.
(2ร—4)ร—3=2ร—(4ร—3)=___
Workspace:
6.
(3ร—2)ร—7=3ร—(___ร—7)
Workspace:
7.
(2ร—2)ร—8=2ร—(2ร—___)
Workspace:
8.
(5ร—2)ร—7=5ร—(2ร—7)=___
Workspace:
9.
3ร—(2ร—9)=(___ร—2)ร—9
Workspace:
10.
(2ร—5)ร—8=2ร—(5ร—8)=___
Workspace:
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.
(2ร—3)ร—4=2ร—(___ร—4)Ans: 3
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (2 ร— 3) ร— 4 = 6 ร— 4 = 24.
3. Grouping 2 (Right First): 2 ร— (3 ร— 4) = 2 ร— 12 = 24.
4. Factor Matching: The missing factor is 3 โœ…
2.
(4ร—2)ร—5=4ร—(2ร—5)=___Ans: 40
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (4 ร— 2) ร— 5 = 8 ร— 5 = 40.
3. Grouping 2 (Right First): 4 ร— (2 ร— 5) = 4 ร— 10 = 40.
4. Final Calculation: Both groupings yield the identical product of 40 โœ…
3.
(3ร—3)ร—2=3ร—(3ร—___)Ans: 2
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (3 ร— 3) ร— 2 = 9 ร— 2 = 18.
3. Grouping 2 (Right First): 3 ร— (3 ร— 2) = 3 ร— 6 = 18.
4. Factor Matching: The missing factor is 2 โœ…
4.
5ร—(2ร—6)=(___ร—2)ร—6Ans: 5
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (5 ร— 2) ร— 6 = 10 ร— 6 = 60.
3. Grouping 2 (Right First): 5 ร— (2 ร— 6) = 5 ร— 12 = 60.
4. Factor Matching: The missing factor is 5 โœ…
5.
(2ร—4)ร—3=2ร—(4ร—3)=___Ans: 24
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (2 ร— 4) ร— 3 = 8 ร— 3 = 24.
3. Grouping 2 (Right First): 2 ร— (4 ร— 3) = 2 ร— 12 = 24.
4. Final Calculation: Both groupings yield the identical product of 24 โœ…
6.
(3ร—2)ร—7=3ร—(___ร—7)Ans: 2
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (3 ร— 2) ร— 7 = 6 ร— 7 = 42.
3. Grouping 2 (Right First): 3 ร— (2 ร— 7) = 3 ร— 14 = 42.
4. Factor Matching: The missing factor is 2 โœ…
7.
(2ร—2)ร—8=2ร—(2ร—___)Ans: 8
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (2 ร— 2) ร— 8 = 4 ร— 8 = 32.
3. Grouping 2 (Right First): 2 ร— (2 ร— 8) = 2 ร— 16 = 32.
4. Factor Matching: The missing factor is 8 โœ…
8.
(5ร—2)ร—7=5ร—(2ร—7)=___Ans: 70
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (5 ร— 2) ร— 7 = 10 ร— 7 = 70.
3. Grouping 2 (Right First): 5 ร— (2 ร— 7) = 5 ร— 14 = 70.
4. Final Calculation: Both groupings yield the identical product of 70 โœ…
9.
3ร—(2ร—9)=(___ร—2)ร—9Ans: 3
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (3 ร— 2) ร— 9 = 6 ร— 9 = 54.
3. Grouping 2 (Right First): 3 ร— (2 ร— 9) = 3 ร— 18 = 54.
4. Factor Matching: The missing factor is 3 โœ…
10.
(2ร—5)ร—8=2ร—(5ร—8)=___Ans: 80
1. Associative Property Law: (a ร— b) ร— c = a ร— (b ร— c). Changing grouping does not change the product.
2. Grouping 1 (Left First): (2 ร— 5) ร— 8 = 10 ร— 8 = 80.
3. Grouping 2 (Right First): 2 ร— (5 ร— 8) = 2 ร— 40 = 80.
4. Final Calculation: Both groupings yield the identical product of 80 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“ Associative Property of Multiplication

Key Strategies

  • ๐Ÿ“ฆ Grouping with Parentheses: Always calculate the numbers inside parentheses first: (2 ร— 3) ร— 4 = 6 ร— 4 = 24.
  • ๐ŸŽฏ Make-a-Ten Shortcut: Look for factors that multiply to 10 (e.g. 5 ร— 2). In 4 ร— (5 ร— 2), multiply 5 ร— 2 = 10 first, then 4 ร— 10 = 40.
  • โš–๏ธ Balancing Grouped Equations: Match the three factors on both sides of the equal sign: (3 ร— 4) ร— 2 = 3 ร— (___ ร— 2). The missing factor must be 4.
  • ๐Ÿงฑ 3D Unit Cube Layer Model: A block of 2 ร— 3 ร— 4 cubes has 2 layers of (3 ร— 4) or 4 layers of (2 ร— 3); both arrangements contain 24 total cubes.
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Related Worksheets

๐Ÿ“œ Standard: CCSS.MATH.CONTENT.3.OA.B.5๐Ÿ”— CCSS.MATH.CONTENT.3.OA.A.1๐Ÿ”— CCSS.MATH.CONTENT.3.OA.C.7

Mastering Associative Property of Multiplication: Core Concepts & Mental Models

The Associative Property of Multiplication states that when multiplying three or more numbers, the grouping of factors (indicated by parentheses) does not change the product: (a ร— b) ร— c = a ร— (b ร— c). This empowers students to strategically pair friendly numbers firstโ€”such as multiplying 2 and 5 to create an easy 10.

Worked Example & SolutionTeacher Step-by-Step Method
๐Ÿ“ Problem: Find the product of (4 ร— 2) ร— 5 using two different groupings.
Worked Solution: Grouping 1: (4 ร— 2) ร— 5 = 8 ร— 5 = 40. Grouping 2: 4 ร— (2 ร— 5) = 4 ร— 10 = 40. Both groupings produce the identical product of 40.

๐Ÿ’ก Essential Strategies for Associative Property of Multiplication

๐Ÿ“ฆ Grouping with Parentheses

Always calculate the numbers inside parentheses first: (2 ร— 3) ร— 4 = 6 ร— 4 = 24.

๐ŸŽฏ Make-a-Ten Shortcut

Look for factors that multiply to 10 (e.g. 5 ร— 2). In 4 ร— (5 ร— 2), multiply 5 ร— 2 = 10 first, then 4 ร— 10 = 40.

โš–๏ธ Balancing Grouped Equations

Match the three factors on both sides of the equal sign: (3 ร— 4) ร— 2 = 3 ร— (___ ร— 2). The missing factor must be 4.

๐Ÿงฑ 3D Unit Cube Layer Model

A block of 2 ร— 3 ร— 4 cubes has 2 layers of (3 ร— 4) or 4 layers of (2 ร— 3); both arrangements contain 24 total cubes.

๐Ÿ“– Key Mathematical Vocabulary

Associative Property

The mathematical rule stating that changing how factors are grouped does not change their product: (a ร— b) ร— c = a ร— (b ร— c).

Grouping

Using parentheses ( ) to show which two numbers should be multiplied together first.

Factor

Any of the numbers being multiplied together.

Product

The final result or answer of multiplication.

Intermediate Product

The product of the two numbers inside parentheses before multiplying by the third factor.

Friendly Numbers

Numbers like 10 or 20 that are easy to multiply mentally.

๐ŸŽฏ 4 Differentiated Classroom Sets Included

Standard 10Version A

Set A: Core 3-Factor Groupings (10 Problems)

Balanced 3-factor multiplication equations demonstrating the associative property.

Anti-CheatVersion B

Set B: Alternate Numbers (10 Problems)

Identical structure with alternate factor trios to prevent copying in classroom settings.

ChallengingVersion C

Set C: Missing Factor Grouping Equations (8 Problems)

Solve for missing factors across equivalent grouped equations and verify products.

Speed SprintVersion D

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

Timed drill multiplying three single-digit factors with parentheses.

โ“ Frequently Asked Questions

How do you solve a associative property of multiplication problem step by step?

Here is a worked example: "Find the product of (4 ร— 2) ร— 5 using two different groupings.". Solution: Grouping 1: (4 ร— 2) ร— 5 = 8 ร— 5 = 40. Grouping 2: 4 ร— (2 ร— 5) = 4 ร— 10 = 40. Both groupings produce the identical product of 40.

What is the core learning objective for associative property of multiplication?

Apply the associative property of multiplication to group three factors in different ways: (a ร— b) ร— c = a ร— (b ร— c), creating friendly intermediate products to simplify mental computation within 100. 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 3-factor multiplication equations demonstrating the associative property.). 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 associative property of multiplication 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.