This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using distributive property as a strategy. The distributive property of multiplication states you can break apart one factor and distribute the multiplication. 8×7 = 8×(5+2) = (8×5)+(8×2) = 40+16 = 56. In this problem, we can solve 7×8 by breaking 8 into 5+3. The distributive property helps by using known facts like 7×5 and adding 7×3. Choice A is correct because it breaks 7×8 into 7×5 + 7×3 = 35+21 = 56 using distributive property. This demonstrates proper use of the distributive as a strategy. Choice C is incorrect because it shows 35+3 instead of 35+21, forgetting to distribute to both terms. This error occurs when students apply property incorrectly. To help students apply properties: Explicitly teach and name properties with examples. Distributive: Use area models (split rectangle) or break-apart strategies. Teach: "Use facts you know to figure out facts you don't." Practice as strategies, not just as abstract properties: "How can distributive property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using distributive property as a strategy. The distributive property of multiplication states you can break apart one factor and distribute the multiplication. 8×7 = 8×(5+2) = (8×5)+(8×2) = 40+16 = 56. In this problem, we need to identify which strategy uses distributive to solve 7×9. The distributive property helps by breaking 9 into 10-1 and distributing. Choice B is correct because it breaks 7×9 into 7×(10-1) = 70-7=63 using distributive property. This demonstrates proper use of the distributive as a strategy. Choice C is incorrect because it shows (7+9)×1=16, confusing with addition and not distributing multiplication. This error occurs when students confuse properties or don't understand the property. To help students apply properties: Explicitly teach and name properties with examples. Distributive: Use area models (split rectangle) or break-apart strategies. Teach: "Use facts you know to figure out facts you don't." Practice as strategies, not just as abstract properties: "How can distributive property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using associative property as a strategy. The associative property of multiplication states that the way factors are grouped doesn't change the product. In this problem, we can solve 2×3×7 by regrouping to make easier calculations. The associative property helps by allowing strategic grouping of factors. Choice A is correct because it regroups (2×3)×7 = 6×7 = 42, calculating 2×3 first, then multiplying by 7. This demonstrates proper use of the associative property as a strategy. Choice C is incorrect because it shows 2×(3×7) = 2×10 = 20, containing a calculation error (3×7=21, not 10). This error occurs when students apply the property correctly but make computational mistakes within the regrouping. To help students apply properties: Model different groupings with manipulatives. Practice mental math strategies: "Which grouping makes this easier?" Show that all valid groupings give the same answer.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using commutative property as a strategy. The commutative property of multiplication states the order of factors doesn't change the product. 6×4 = 4×6 = 24. Helpful when you know one fact (like 4×6) and need the reverse (6×4)—it's the same! In this problem, we need to identify which equation shows order doesn’t change the product. The commutative property helps by switching factors without altering the result. Choice B is correct because it recognizes 8×5 = 5×8 by commutative property, so both equal 40. This demonstrates proper use of the commutative as a strategy. Choice A is incorrect because it claims 6×7=6+7, confusing multiplication with addition. This error occurs when students confuse properties or don't understand the property. To help students apply properties: Explicitly teach and name properties with examples. Commutative: Use arrays that can be rotated (6 rows of 4 = 4 rows of 6). Teach: "If you know one fact, you know its reverse!" Practice as strategies, not just as abstract properties: "How can commutative property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using commutative property as a strategy. The commutative property of multiplication states the order of factors doesn't change the product. 6×4 = 4×6 = 24. Helpful when you know one fact (like 4×6) and need the reverse (6×4)—it's the same! In this problem, we need to find 8×6 given that 6×8=48. The commutative property helps by recognizing that switching the order gives the same product. Choice C is correct because it recognizes 8×6 = 6×8 by commutative property, so both equal 48. This demonstrates proper use of the commutative as a strategy. Choice B is incorrect because it claims 46, perhaps confusing with addition or another operation. This error occurs when students don't understand the property or make computational mistakes. To help students apply properties: Explicitly teach and name properties with examples. Commutative: Use arrays that can be rotated (6 rows of 4 = 4 rows of 6). Teach: "If you know one fact, you know its reverse!" Practice as strategies, not just as abstract properties: "How can commutative property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using associative property as a strategy. The associative property of multiplication states the way factors are grouped doesn't change the product. (3×5)×2 = 3×(5×2). Both equal 30. Helpful for three or more factors: regroup to make easier calculations (2×5=10, then 10×3=30 is easier than 2×3=6, then 6×5=30). In this problem, we need to find a regrouping that helps solve 2×3×7. The associative property helps by grouping to make multiplication easier, like (2×3)×7. Choice B is correct because it regroups (2×3)×7 as 6×7 = 42. This demonstrates proper use of the associative as a strategy. Choice D is incorrect because it groups incorrectly as 2×37, leading to a wrong product. This error occurs when students apply property incorrectly. To help students apply properties: Explicitly teach and name properties with examples. Associative: Model with nested containers (boxes/bags/items). Show both groupings equal same total. Practice as strategies, not just as abstract properties: "How can associative property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using associative property as a strategy. The associative property of multiplication states that the way factors are grouped doesn't change the product: (a×b)×c = a×(b×c). In this problem, we can solve 3×5×2 by regrouping to make easier calculations. The associative property helps by allowing us to group factors in the most convenient way. Choice A is correct because it regroups (3×5)×2 = 15×2 = 30, calculating 3×5 first, then multiplying by 2. This demonstrates proper use of the associative property as a strategy. Choice D is incorrect because it shows 3×(5×2) = 3×7 = 21, which contains a calculation error (5×2=10, not 7). This error occurs when students apply the property correctly but make computational mistakes within the regrouping. To help students apply properties: Model with nested containers (boxes/bags/items) to show both groupings equal the same total. Practice choosing strategic groupings like pairing factors that make 10.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using distributive property as a strategy. The distributive property of multiplication states that you can break apart one factor and distribute the multiplication. In this problem, we need to find 7×6 using the known fact 7×5=35, which means breaking 6 into 5+1. The distributive property helps by allowing us to use known facts to find new ones. Choice A is correct because it breaks 6 into 5+1 and distributes: 7×6 = 7×(5+1) = 7×5+7×1 = 35+7 = 42. This demonstrates proper use of the distributive property as a strategy. Choice B is incorrect because it shows 7×5+1 instead of 7×5+7×1, forgetting to multiply 7 by the second part. This error occurs when students don't understand that multiplication must be distributed to both terms. To help students apply properties: Use area models to show how breaking apart one dimension still gives the same total area. Emphasize: "Multiply by ALL parts when you break apart."

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using distributive property as a strategy. The distributive property of multiplication states you can break apart one factor and distribute the multiplication. 8×7 = 8×(5+2) = (8×5)+(8×2) = 40+16 = 56. In this problem, we can solve 7×8 by breaking 8 into 5+3. The distributive property helps by using known facts like 7×5 and adding 7×3. Choice B is correct because it breaks 7×8 into 7×5 + 7×3 = 35+21=56 using distributive property. This demonstrates proper use of the distributive as a strategy. Choice D is incorrect because it shows 48, perhaps from miscalculating 7×5+7×3 as 35+13 or similar error. This error occurs when students don't understand the property or make computational mistakes. To help students apply properties: Explicitly teach and name properties with examples. Distributive: Use area models (split rectangle) or break-apart strategies. Teach: "Use facts you know to figure out facts you don't." Practice as strategies, not just as abstract properties: "How can distributive property help you?" Connect to real situations. Watch for students who memorize property names but don't apply them strategically, or who make errors within the property application.

This question tests applying properties of operations to multiply and divide (CCSS.3.OA.5), specifically using distributive property as a strategy. The distributive property of multiplication states that you can break apart one factor and distribute the multiplication. In this problem, we need to find 7×8 by breaking 8 into 5+3, allowing us to use known facts (7×5=35 and 7×3=21). The distributive property helps by breaking difficult facts into easier ones. Choice A is correct because it properly distributes: 7×8 = 7×(5+3) = 7×5+7×3 = 35+21 = 56. This demonstrates proper use of the distributive property as a strategy. Choice B is incorrect because it shows 35+3 instead of 35+21, forgetting to multiply 7×3 and just adding 3. This error occurs when students don't fully distribute the multiplication to all parts. To help students apply properties: Use area models to show how a 7×8 rectangle can be split into 7×5 and 7×3 sections. Practice identifying which decompositions use known facts effectively.