This question tests 3rd grade area: finding the area of a rectangle by tiling it with unit squares, and showing that the area equals the product of the side lengths (CCSS.3.MD.7.a). When we tile a rectangle with unit squares, we create rows and columns. For example, a 3-by-5 rectangle has 3 rows with 5 squares in each row, giving 3×5=15 total squares. Multiplying the side lengths (length × width) gives the same answer as counting all the tiles because multiplication counts equal groups efficiently. The rectangle has dimensions 3 by 5. When tiled with unit squares, it has 3 rows of 5 squares each (or 5 columns of 3 squares each). Choice C is correct because 3 rows of 5 squares = 3×5 = 15 square units, which can be verified by counting all tiles OR multiplying length times width: 3×5=15. This shows understanding that tiling and multiplication give the same area. Choice B represents adding instead of multiplying, wrong calculation, perimeter confusion, missing units. This typically happens because students confuse addition with multiplication, miscalculate or miscount, confuse area (inside space) with perimeter (distance around), or forget area is measured in square units. To help students: Use physical tiles or graph paper to build rectangles, then count AND multiply to see they match. Show that '3 rows of 5' means 5+5+5 (repeated addition) which equals 3×5 (multiplication). Practice with various rectangle sizes: 2×4, 3×5, 4×6. Help students see the connection: rows × squares per row = total squares. Watch for: Students who add dimensions instead of multiply (3+5 instead of 3×5), students who confuse area with perimeter, students who multiply but forget to say 'square units,' and students who don't connect the visual tiling to the multiplication. Use the language 'rows of' to bridge to multiplication: 'I see 4 rows of 7 squares, so 4 times 7 equals 28.' This develops fluency with multiplication as counting equal groups while building area understanding.

This question tests 3rd grade area: finding the area of a rectangle by tiling it with unit squares, and showing that the area equals the product of the side lengths (CCSS.3.MD.7.a). When we tile a rectangle with unit squares, we create rows and columns. For example, a 3-by-5 rectangle has 3 rows with 5 squares in each row, giving 3×5=15 total squares. Multiplying the side lengths (length × width) gives the same answer as counting all the tiles because multiplication counts equal groups efficiently. The rectangle has dimensions 5 meters by 4 meters. When tiled with unit squares, it has 5 rows of 4 squares each (or 4 columns of 5 squares each). Choice C is correct because 5 rows of 4 squares = 5×4 = 20 square meters, which can be verified by counting all tiles OR multiplying length times width: 5×4=20. This shows understanding that tiling and multiplication give the same area. Choice B represents adding instead of multiplying, wrong calculation, perimeter confusion, missing units. This typically happens because students confuse addition with multiplication, miscalculate or miscount, confuse area (inside space) with perimeter (distance around), or forget area is measured in square units. To help students: Use physical tiles or graph paper to build rectangles, then count AND multiply to see they match. Show that '3 rows of 5' means 5+5+5 (repeated addition) which equals 3×5 (multiplication). Practice with various rectangle sizes: 2×4, 3×5, 4×6. Help students see the connection: rows × squares per row = total squares. Watch for: Students who add dimensions instead of multiply (3+5 instead of 3×5), students who confuse area with perimeter, students who multiply but forget to say 'square units,' and students who don't connect the visual tiling to the multiplication. Use the language 'rows of' to bridge to multiplication: 'I see 4 rows of 7 squares, so 4 times 7 equals 28.' This develops fluency with multiplication as counting equal groups while building area understanding.

This question tests 3rd grade area: finding the area of a rectangle by tiling it with unit squares, and showing that the area equals the product of the side lengths (CCSS.3.MD.7.a). When we tile a rectangle with unit squares, we create rows and columns. For example, a 3-by-5 rectangle has 3 rows with 5 squares in each row, giving 3×5=15 total squares. Multiplying the side lengths (length × width) gives the same answer as counting all the tiles because multiplication counts equal groups efficiently. The rectangle has dimensions 5 by 8. When tiled with unit squares, it has 5 rows of 8 squares each (or 8 columns of 5 squares each). Choice C is correct because 5 rows of 8 squares = 5×8 = 40 square units, which can be verified by counting all tiles OR multiplying length times width: 5×8=40. This shows understanding that tiling and multiplication give the same area. Choice A represents adding instead of multiplying, wrong calculation, perimeter confusion, missing units. This typically happens because students confuse addition with multiplication, miscalculate or miscount, confuse area (inside space) with perimeter (distance around), or forget area is measured in square units. To help students: Use physical tiles or graph paper to build rectangles, then count AND multiply to see they match. Show that '3 rows of 5' means 5+5+5 (repeated addition) which equals 3×5 (multiplication). Practice with various rectangle sizes: 2×4, 3×5, 4×6. Help students see the connection: rows × squares per row = total squares. Watch for: Students who add dimensions instead of multiply (3+5 instead of 3×5), students who confuse area with perimeter, students who multiply but forget to say 'square units,' and students who don't connect the visual tiling to the multiplication. Use the language 'rows of' to bridge to multiplication: 'I see 4 rows of 7 squares, so 4 times 7 equals 28.' This develops fluency with multiplication as counting equal groups while building area understanding.

This question tests 3rd grade area: finding the area of a rectangle by tiling it with unit squares, and showing that the area equals the product of the side lengths (CCSS.3.MD.7.a). When we tile a rectangle with unit squares, we create rows and columns. For example, a 3-by-5 rectangle has 3 rows with 5 squares in each row, giving 3×5=15 total squares. Multiplying the side lengths (length × width) gives the same answer as counting all the tiles because multiplication counts equal groups efficiently. The rectangle has dimensions 4 by 7. When tiled with unit squares, it has 4 rows of 7 squares each (or 7 columns of 4 squares each). Choice B is correct because 4 rows of 7 squares = 4×7 = 28 square units, which can be verified by counting all tiles OR multiplying length times width: 4×7=28. This shows understanding that tiling and multiplication give the same area. Choice A represents adding instead of multiplying, wrong calculation, perimeter confusion, missing units. This typically happens because students confuse addition with multiplication, miscalculate or miscount, confuse area (inside space) with perimeter (distance around), or forget area is measured in square units. To help students: Use physical tiles or graph paper to build rectangles, then count AND multiply to see they match. Show that '3 rows of 5' means 5+5+5 (repeated addition) which equals 3×5 (multiplication). Practice with various rectangle sizes: 2×4, 3×5, 4×6. Help students see the connection: rows × squares per row = total squares. Watch for: Students who add dimensions instead of multiply (3+5 instead of 3×5), students who confuse area with perimeter, students who multiply but forget to say 'square units,' and students who don't connect the visual tiling to the multiplication. Use the language 'rows of' to bridge to multiplication: 'I see 4 rows of 7 squares, so 4 times 7 equals 28.' This develops fluency with multiplication as counting equal groups while building area understanding.

This question tests 3rd grade area: finding the area of a rectangle by tiling it with unit squares, and showing that the area equals the product of the side lengths (CCSS.3.MD.7.a). When we tile a rectangle with unit squares, we create rows and columns. For example, a 3-by-5 rectangle has 3 rows with 5 squares in each row, giving 3×5=15 total squares. Multiplying the side lengths (length × width) gives the same answer as counting all the tiles because multiplication counts equal groups efficiently. The rectangle has dimensions 3 by 4, with Jamal counting 12 tiles and Sofia multiplying 3×4=12. Choice A is correct because counting gives 12 and multiplying gives 12 square units, which can be verified by both methods matching for 3 rows of 4 squares = 3×4=12. This shows understanding that tiling and multiplication give the same area. Choice B represents adding instead of multiplying, wrong calculation, perimeter confusion, missing units. This typically happens because students confuse addition with multiplication, miscalculate or miscount, confuse area (inside space) with perimeter (distance around), or forget area is measured in square units. To help students: Use physical tiles or graph paper to build rectangles, then count AND multiply to see they match. Show that '3 rows of 5' means 5+5+5 (repeated addition) which equals 3×5 (multiplication). Practice with various rectangle sizes: 2×4, 3×5, 4×6. Help students see the connection: rows × squares per row = total squares. Watch for: Students who add dimensions instead of multiply (3+5 instead of 3×5), students who confuse area with perimeter, students who multiply but forget to say 'square units,' and students who don't connect the visual tiling to the multiplication. Use the language 'rows of' to bridge to multiplication: 'I see 4 rows of 7 squares, so 4 times 7 equals 28.' This develops fluency with multiplication as counting equal groups while building area understanding.

This question tests 3rd grade area: finding the area of a rectangle by tiling it with unit squares, and showing that the area equals the product of the side lengths (CCSS.3.MD.7.a). When we tile a rectangle with unit squares, we create rows and columns. For example, a 3-by-5 rectangle has 3 rows with 5 squares in each row, giving 3×5=15 total squares. Multiplying the side lengths (length × width) gives the same answer as counting all the tiles because multiplication counts equal groups efficiently. The rectangle has dimensions 5 by 8. When tiled with unit squares, it has 5 rows of 8 squares each (or 8 columns of 5 squares each). Choice C is correct because 5 rows of 8 squares = 5×8 = 40 square units, which can be verified by counting all tiles OR multiplying length times width: 5×8=40. This shows understanding that tiling and multiplication give the same area. Choice A represents adding instead of multiplying, wrong calculation, perimeter confusion, missing units. This typically happens because students confuse addition with multiplication, miscalculate or miscount, confuse area (inside space) with perimeter (distance around), or forget area is measured in square units. To help students: Use physical tiles or graph paper to build rectangles, then count AND multiply to see they match. Show that '3 rows of 5' means 5+5+5 (repeated addition) which equals 3×5 (multiplication). Practice with various rectangle sizes: 2×4, 3×5, 4×6. Help students see the connection: rows × squares per row = total squares. Watch for: Students who add dimensions instead of multiply (3+5 instead of 3×5), students who confuse area with perimeter, students who multiply but forget to say 'square units,' and students who don't connect the visual tiling to the multiplication. Use the language 'rows of' to bridge to multiplication: 'I see 4 rows of 7 squares, so 4 times 7 equals 28.' This develops fluency with multiplication as counting equal groups while building area understanding.

The original rectangle has 4 × 7 = 28 tiles total. When rearranged into 2 rows, each row must have 28 ÷ 2 = 14 tiles. The area remains 28 square units because the same tiles are used.

When you see a problem about rearranging rectangular areas, remember that the total area must stay the same no matter how you change the dimensions. This is a key principle in geometry problems.

Let's work through this step by step. First, we need to find the total area of the original bulletin board. We know they used 42 square tiles total, so the area is 42 square tiles. We can verify this makes sense: if the rectangle is 6 tiles wide, then $$42 \div 6 = 7$$ rows, giving us $$6 \times 7 = 42$$ tiles.

Now, for the new rectangle that's 7 tiles wide, we need to find how many rows will give us the same area of 42 square tiles. We divide: $$42 \div 7 = 6$$ rows. Let's check: $$7 \times 6 = 42$$. Perfect! This matches our original area exactly.

Looking at the wrong answers: Choice A gives us $$7 \times 5 = 35$$ tiles, which is 7 tiles short of our needed 42. Choice B gives us $$7 \times 8 = 56$$ tiles, which is 14 tiles too many. Choice D gives us $$7 \times 7 = 49$$ tiles, which is 7 tiles too many. These answers all use the phrase "close to 42," but in mathematics, we need exact answers, not approximations.

The correct answer is C because $$7 \times 6 = 42$$ matches the original area exactly.

Strategy tip: In area problems, always check that your new dimensions give you exactly the same total area as the original—close isn't good enough!

When you see a problem about finding the area of rectangles made from tiles, you need to count all the tiles, not just focus on one dimension. Area means the total space inside a shape, which equals the number of rows times the number of tiles in each row.

Let's calculate each rectangle's area correctly. Rectangle A has 3 rows with 6 tiles each, so its area is $$3 \times 6 = 18$$ tiles. Rectangle B has 2 rows with 9 tiles each, so its area is $$2 \times 9 = 18$$ tiles. Both rectangles have exactly the same area of 18 tiles, so Jake is wrong. The fact that 9 is greater than 6 doesn't matter because Rectangle B has fewer rows.

Looking at the wrong answers: Choice A incorrectly calculates both areas (17 and 19 don't match our multiplication), but concludes Jake is right. Choice B also gets wrong areas (18 and 20) and agrees with Jake. Choice C gets Rectangle A's area wrong as 21, though it correctly identifies that Rectangle A would be larger if that were true. Only choice D correctly calculates both areas as 18 and recognizes they're equal.

Remember this key strategy: when comparing areas of tiled rectangles, always multiply rows times tiles per row for each rectangle. Don't just compare the bigger numbers you see - a rectangle with more tiles per row but fewer rows might actually have the same or smaller total area.

The original rectangle had 6 rows with 4 tiles each, so the area was 6 × 4 = 24 square inches. The changes Maya made afterward (removing and adding tiles) don't affect the area of the original rectangle.