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 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 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.

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 2-by-9 rectangle can be thought of as 2 by (5+4). We can calculate the area as $2 \times 9 = 18$, OR as $(2 \times 5) + (2 \times 4) = 10 + 8 = 18$. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The area model is 2 units wide and divided into sections of 5 units and 4 units long, making the total length 5+4=9 units. Choice B is correct because the first section area is $2 \times 5 = 10$ square units, the second section area is $2 \times 4 = 8$ square units, total is 10+8=18 square units, which matches $2 \times(5+4) = 2 \times 9 = 18$ and shows the distributive property using an area model. Choice A represents a common error of adding instead of multiplying, such as 5+4=9, which happens because students forget to multiply by the width or misapply the distributive property. 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 5 is 10, plus 2 times 4 is 8, and 10 plus 8 equals 18—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like posters or hallways. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 2×5+4 instead of 2×5+2×4), students who multiply all three numbers together (2×5×4), 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-5 rectangle can be thought of as 4 by (3+2). We can calculate the area as 4×5=20, OR as (4×3)+(4×2)=12+8=20. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The garden is 4 meters wide and split into sections of 3 m and 2 m lengths, making the total length 3+2=5 m. Choice B is correct because the first section area is 4×3=12 square meters, the second section area is 4×2=8 square meters, total is 12+8=20 square meters, which matches 4×(3+2)=4×5=20 and shows the distributive property using an area model. Choice A represents a common error of calculating only one section, such as 4×3=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: '4 times 5 equals 20' AND '4 times 3 is 12, plus 4 times 2 is 8, and 12 plus 8 equals 20—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like gardens or rooms. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 4×3+2 instead of 4×3+4×2), students who multiply all three numbers together (4×3×2), 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 (2+5). We can calculate the area as 6×7=42, OR as (6×2)+(6×5)=12+30=42. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The rectangle is 6 units wide and divided into sections of 2 units and 5 units long, making the total length 2+5=7 units. Choice C is correct because the first section area is 6×2=12 square units, the second section area is 6×5=30 square units, total is 12+30=42 square units, which matches 6×(2+5)=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 6×5=30, 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 2 is 12, plus 6 times 5 is 30, and 12 plus 30 equals 42—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like hallways or decks. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 6×2+5 instead of 6×2+6×5), students who multiply all three numbers together (6×2×5), 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 3-by-7 rectangle can be thought of as 3 by $(5 + 2)$. We can calculate the area as $3 \times 7 = 21$, OR as $(3 \times 5) + (3 \times 2) = 15 + 6 = 21$. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The poster is 3 inches wide and divided into two sections: one $3 \times 5$ and one $3 \times 2$, with total height $5 + 2 = 7$ inches. Choice A is correct because the first section area is $3 \times 5 = 15$ square inches, second section area is $3 \times 2 = 6$ square inches, total is $15 + 6 = 21$ square inches, which matches $3 \times(5 + 2) = 3 \times 7 = 21$ and shows the distributive property through area addition. Choice B represents a common error of calculating only one section ($3 \times 5 = 15$), 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: '3 times 7 equals 21' AND '3 times 5 is 15, plus 3 times 2 is 6, and 15 plus 6 equals 21—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like posters or signs. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating $3 \times 5 + 2$ instead of $3 \times 5 + 3 \times 2$), students who multiply all three numbers together ($3 \times 5 \times 2$), 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-6 rectangle can be thought of as 6 by (2+4). We can calculate the area as 6×6=36, OR as (6×2)+(6×4)=12+24=36. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The rectangle is 6 units wide and divided into two sections: one 6×2 and one 6×4, with total length 2+4=6 units. Choice B is correct because the first section area is 6×2=12 square units, second section area is 6×4=24 square units, total is 12+24=36 square units, which matches 6×(2+4)=6×6=36 and shows the distributive property through area addition. Choice A represents a common error of calculating only one section (6×4=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 6 equals 36' AND '6 times 2 is 12, plus 6 times 4 is 24, and 12 plus 24 equals 36—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like rectangular areas. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 6×2+4 instead of 6×2+6×4), students who multiply all three numbers together (6×2×4), 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 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 4-by-5 rectangle can be thought of as 4 by (3+2). We can calculate the area as 4×5=20, OR as (4×3)+(4×2)=12+8=20. This demonstrates the distributive property: multiplying by a sum equals the sum of the products. The garden is 4 meters wide and divided into two sections: one 4×3 and one 4×2, with total length 3+2=5 meters. Choice B is correct because the first section area is 4×3=12 square meters, second section area is 4×2=8 square meters, total is 12+8=20 square meters, which matches 4×(3+2)=4×5=20 and shows the distributive property through area addition. Choice A represents a common error of calculating only one section (4×3=12), which happens because students forget to add both parts or misapply the distributive property by not multiplying the second length. To help students: Use two-color tiles or shaded areas to physically show the two sections. Calculate both ways: '4 times 5 equals 20' AND '4 times 3 is 12, plus 4 times 2 is 8, and 12 plus 8 equals 20—same answer!' Practice with multiple examples to see the pattern. Connect to real scenarios like gardens or rooms. Watch for: Students who forget to multiply the constant dimension by BOTH parts (calculating 4×3+2 instead of 4×3+4×2), students who multiply all three numbers together (4×3×2), 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.