This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. Keisha's garden is a 3-by-6 rectangle that can be thought of as 3 by (4+2). We can calculate the area as 3×6=18, OR as (3×4)+(3×2)=12+6=18. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The garden is 3 units wide. It's divided into two sections: one 3×4 and one 3×2. The total length is 4+2=6. Choice A is correct because the first section area is 3×4=12 square units, the second section area is 3×2=6 square units, and the total is 12+6=18 square units, which matches 3×(4+2)=3×6=18. This shows understanding of area as additive and the distributive property. Choice B (12) represents calculating only one section (3×4), forgetting to add the 3×2 section. This typically happens because students forget to find both section areas or stop after the first calculation. To help students: Use two-color tiles or shaded areas to physically show the two sections of the garden. Calculate both ways: '3 times 6 equals 18' AND '3 times 4 is 12, plus 3 times 2 is 6, and 12 plus 6 equals 18—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios: 'Keisha's garden has a vegetable section (3×4) and an herb section (3×2).' Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 3×4+2 instead of 3×4+3×2), students who multiply all three numbers together (3×4×2), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 4-by-8 rectangle can be thought of as 4 by (5+3). We can calculate the area as 4×8=32, OR as (4×5)+(4×3)=20+12=32. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The area model is 4 units wide and divided into two sections: one 4×5 and one 4×3, with total length 5+3=8 units. Choice B is correct because the first section area is 4×5=20 square units, second section area is 4×3=12 square units, total is 20+12=32 square units, which matches 4×(5+3)=4×8=32 and shows the distributive property through area addition. Choice A represents a common error of misadding or partial calculation (like 4×5+3=23), which happens because students forget to multiply both parts or make addition errors. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '4 times 8 equals 32' AND '4 times 5 is 20, plus 4 times 3 is 12, and 20 plus 12 equals 32—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like divided spaces. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 4×5+3 instead of 4×5+4×3), students who multiply all three numbers together (4×5×3), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 2-by-9 rectangle can be thought of as 2 by (6+3). We can calculate the area as 2×9=18, OR as (2×6)+(2×3)=12+6=18. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The divided rectangle is 2 units wide and split into two sections: one 2×6 and one 2×3, with total length 6+3=9 units. Choice A is correct because it shows 2×(6+3)=(2×6)+(2×3)=12+6=18 square units, matching the total area calculated as 2×9=18 and explicitly demonstrating the distributive property through area decomposition. Choice B represents a common error of distributing incorrectly (2×6+3=15 instead of 2×6+2×3), which typically happens because students forget to multiply the added number by the common factor. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '2 times 9 equals 18' AND '2 times 6 is 12, plus 2 times 3 is 6, and 12 plus 6 equals 18—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like split rectangles. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 2×6+3), students who multiply all three numbers together (2×6×3), and students who subtract instead of add. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that $a \times(b + c) = (a \times b) + (a \times c)$ (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. Maya's floor is a 5-by-8 rectangle that can be thought of as 5 by $(4+4)$. We can calculate the area as $5 \times 8 = 40$, OR as $(5 \times 4) + (5 \times 4) = 20 + 20 = 40$. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The floor is 5 units wide. It's divided into two equal sections: one $5 \times 4$ and another $5 \times 4$. The total length is $4+4=8$. Choice C is correct because the first section area is $5 \times 4 = 20$ square units, the second section area is $5 \times 4 = 20$ square units, and the total is $20 + 20 = 40$ square units, which matches $5 \times(4+4) = 5 \times 8 = 40$. This shows understanding of area as additive and the distributive property. Choice D (20) represents calculating only one section ($5 \times 4$), forgetting that there are two equal sections. This typically happens because students see the repeated 4 and think they only need to calculate once. To help students: Use two-color tiles or shaded areas to physically show the two equal sections of the floor. Calculate both ways: '5 times 8 equals 40' AND '5 times 4 is 20, plus 5 times 4 is 20, and 20 plus 20 equals 40—same answer!' Emphasize that even when sections are equal size, we still add both. Connect to real scenarios: 'Maya's floor has two equal rugs, each 5 by 4.' Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating $5 \times 4$ once), students who add the dimensions instead of areas, and students who don't recognize that equal sections still need to be added. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 5-by-6 rectangle can be thought of as 5 by (2+4). We can calculate the area as 5×6=30, OR as (5×2)+(5×4)=10+20=30. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The hallway is 5 feet wide and split into sections of 2 ft and 4 ft lengths, making the total length 2+4=6 ft. Choice A is correct because the first section area is 5×2=10 square feet, the second section area is 5×4=20 square feet, total is 10+20=30 square feet, which matches 5×(2+4)=5×6=30 and shows the distributive property using an area model. Choice B represents a common error of calculating only one section, such as 5×4=20, which happens because students forget to add both section areas or misapply the distributive property. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '5 times 6 equals 30' AND '5 times 2 is 10, plus 5 times 4 is 20, and 10 plus 20 equals 30—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like hallways or gardens. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 5×2+4 instead of 5×2+5×4), students who multiply all three numbers together (5×2×4), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 4-by-8 rectangle can be thought of as 4 by (5+3). We can calculate the area as 4×8=32, OR as (4×5)+(4×3)=20+12=32. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The rectangle is 4 units wide and divided into sections of 5 units and 3 units long, making the total length 5+3=8 units. Choice A is correct because the first section area is 4×5=20 square units, the second section area is 4×3=12 square units, total is 20+12=32 square units, which matches 4×(5+3)=4×8=32 and shows the distributive property using an area model. Choice D represents a common error of multiplying all three numbers, such as 4×5×3=60, which happens because students incorrectly apply multiplication instead of the distributive property. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '4 times 8 equals 32' AND '4 times 5 is 20, plus 4 times 3 is 12, and 20 plus 12 equals 32—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like rooms or fields. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 4×5+3 instead of 4×5+4×3), students who multiply all three numbers together (4×5×3), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 5-by-8 rectangle can be thought of as 5 by (2+6). We can calculate the area as 5×8=40, OR as (5×2)+(5×6)=10+30=40. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The deck is 5 feet wide and divided into two sections: one 5×2 and one 5×6, with total length 2+6=8 feet. Choice A is correct because the first section area is 5×2=10 square feet, second section area is 5×6=30 square feet, total is 10+30=40 square feet, which matches 5×(2+6)=5×8=40 and shows the distributive property through area addition. Choice B represents a common error of calculating only one section (5× something partial, like 4×4=16 miscalculation), which happens because students forget to add both parts or make multiplication errors. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '5 times 8 equals 40' AND '5 times 2 is 10, plus 5 times 6 is 30, and 10 plus 30 equals 40—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like decks or patios. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 5×2+6 instead of 5×2+5×6), students who multiply all three numbers together (5×2×6), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that $a \times(b + c) = (a \times b) + (a \times c)$ (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 6-by-7 rectangle can be thought of as 6 by (4+3). We can calculate the area as $6 \times 7 = 42$, OR as $(6 \times 4) + (6 \times 3) = 24 + 18 = 42$. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The hallway is 6 feet wide and divided into two sections: one $6 \times 4$ and one $6 \times 3$, with total length $4 + 3 = 7$ feet. Choice A is correct because the first section area is $6 \times 4 = 24$ square feet, second section area is $6 \times 3 = 18$ square feet, total is $24 + 18 = 42$ square feet, which matches $6 \times(4 + 3) = 6 \times 7 = 42$ and shows the distributive property through area addition. Choice B represents a common error of calculating only one section ($6 \times 4 = 24$), which happens because students forget to add both parts or misapply the distributive property. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '6 times 7 equals 42' AND '6 times 4 is 24, plus 6 times 3 is 18, and 24 plus 18 equals 42—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like hallways or corridors. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating $6 \times 4 + 3$ instead of $6 \times 4 + 6 \times 3$), students who multiply all three numbers together ($6 \times 4 \times 3$), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 3-by-6 rectangle can be thought of as 3 by (4+2). We can calculate the area as 3×6=18, OR as (3×4)+(3×2)=12+6=18. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The area model is 3 units wide and divided into sections of 4 units and 2 units long, making the total length 4+2=6 units. Choice A is correct because the first section area is 3×4=12 square units, the second section area is 3×2=6 square units, total is 12+6=18 square units, which matches 3×(4+2)=3×6=18 and shows the distributive property using an area model. Choice B represents a common error of calculating only one section, such as 3×4=12, which happens because students forget to add both section areas or misapply the distributive property. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '3 times 6 equals 18' AND '3 times 4 is 12, plus 3 times 2 is 6, and 12 plus 6 equals 18—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like posters or fields. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 3×4+2 instead of 3×4+3×2), students who multiply all three numbers together (3×4×2), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.

This question tests 3rd grade area and distributive property: using tiling/area models to show that a×(b+c)=(a×b)+(a×c) (CCSS.3.MD.7.c). When a rectangle is divided into two parts, the total area equals the sum of the two section areas. For example, a 6-by-7 rectangle can be thought of as 6 by (4+3). We can calculate the area as 6×7=42, OR as (6×4)+(6×3)=24+18=42. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The deck is 6 feet wide and split into sections of 4 ft and 3 ft lengths, making the total length 4+3=7 ft. Choice A is correct because the first section area is 6×4=24 square feet, the second section area is 6×3=18 square feet, total is 24+18=42 square feet, which matches 6×(4+3)=6×7=42 and shows the distributive property using an area model. Choice B represents a common error of calculating only one section, such as 6×4=24, which happens because students forget to add both section areas or misapply the distributive property. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '6 times 7 equals 42' AND '6 times 4 is 24, plus 6 times 3 is 18, and 24 plus 18 equals 42—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like decks or gardens. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 6×4+3 instead of 6×4+6×3), students who multiply all three numbers together (6×4×3), and students who don't recognize that the two methods give the same total. This builds foundation for algebraic thinking and shows that area can be decomposed and recombined.