This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. The rectangle has dimensions: length 7 feet, width 6 feet. Choice B is correct because area = 7×6 = 42 square feet, showing understanding of area calculation. Choice A represents a common error of confusing area with perimeter by adding 7+6+7+6=26 instead of multiplying. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). Practice both: 'This garden is 8 by 5. Perimeter for fence: 8+5+8+5=26 feet. Area for planting: 8×5=40 square feet.' For unknown sides: 'Perimeter 30, one side 8. Draw rectangle, label known sides 8 and 8, subtract from 30: 30-16=14 left for other two sides, so each is 7.' To show same perimeter/different areas: Build multiple rectangles with 20 unit-long border—1×9 (area 9), 2×8 (area 16), 3×7 (area 21), 4×6 (area 24), 5×5 (area 25)—shapes closer to square have more area. Watch for: Students who confuse perimeter and area, students who forget units (feet vs square feet), students who add only two sides for perimeter, students who add instead of multiply for area, and students who don't recognize perimeter and area are independent (same perimeter ≠ same area). Use real contexts and physical models.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. Two rectangles both have area 24 square feet: A is 1×24 (perimeter 50) and B is 4×6 (perimeter 20). Choice A is correct because Rectangle A has longer perimeter (50 > 20), showing understanding that same area can have different perimeters, with longer thinner shapes having larger perimeters. Choice C represents assuming same area means same perimeter, which typically happens because students don't recognize that perimeter and area are independent. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). To show same area/different perimeters: For area 24—1×24 (perimeter 50), 2×12 (perimeter 28), 3×8 (perimeter 22), 4×6 (perimeter 20)—shapes closer to square have smaller perimeters. Watch for: Students who confuse perimeter and area, students who forget units (feet vs square feet), students who add only two sides for perimeter, students who add instead of multiply for area, and students who don't recognize perimeter and area are independent (same perimeter ≠ same area). Use real contexts and physical models.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. Two rectangles: A is 1×9 (perimeter 20 feet), B is 5×5 (perimeter 20 feet), asking which has more area. Choice B is correct because A area=1×9=9 square feet, B area=5×5=25 square feet, so B has greater area, showing same perimeter can have different areas with squarer shapes having more area. Choice C represents assuming same perimeter means same area, which fails because area depends on dimensions, not just perimeter; this happens when students don't recognize perimeter and area are independent. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). To show same perimeter/different areas: Build multiple rectangles with 20 unit-long border—1×9 (area 9), 2×8 (area 16), 3×7 (area 21), 4×6 (area 24), 5×5 (area 25)—shapes closer to square have more area. Watch for: Assuming same perimeter equals same area, or calculation errors in area.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. The problem states the rectangular garden is 8 feet by 5 feet, asking for fence needed, which is perimeter. Choice B is correct because perimeter = 8+5+8+5 = 26 feet or 2×(8+5)=26 feet, showing understanding of perimeter calculation for fencing around the garden. Choice C represents a calculation error, like multiplying 8×5=40 instead of adding sides, which typically happens because students confuse distance around (perimeter) with space inside (area). To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). Practice both: 'This garden is 8 by 5. Perimeter for fence: 8+5+8+5=26 feet. Area for planting: 8×5=40 square feet.' Watch for: Students who confuse perimeter and area, students who forget units (feet vs square feet), students who add only two sides for perimeter, students who add instead of multiply for area, and students who don't recognize perimeter and area are independent (same perimeter ≠ same area). Use real contexts and physical models.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. The problem states the rectangle is 10 yards by 2 yards, asking for perimeter. Choice C is correct because perimeter = 10+2+10+2 = 24 yards or 2×(10+2)=24 yards, showing understanding of perimeter calculation. Choice B represents confusing with area, calculating 10×2=20 square yards, which typically happens because students mix up adding for perimeter versus multiplying for area. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). Practice both: 'This rectangle is 10 by 2. Perimeter: 10+2+10+2=24 yards. Area: 10×2=20 square yards.' Watch for: Students who confuse perimeter and area, students who forget units (feet vs square feet), students who add only two sides for perimeter, students who add instead of multiply for area, and students who don't recognize perimeter and area are independent (same perimeter ≠ same area). Use real contexts and physical models.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. The garden is a rectangle with dimensions 8 feet by 5 feet, and the question asks for the fence needed, which is the perimeter. Choice B is correct because perimeter = 8+5+8+5 = 26 feet or 2×(8+5)=26 feet, showing understanding of perimeter calculation for fencing around the garden. Choice C represents a common error of multiplying instead of adding, like confusing area (8×5=40) with perimeter, which happens because students mix up the operations for inside space versus border distance. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). Practice both: 'This garden is 8 by 5. Perimeter for fence: 8+5+8+5=26 feet. Area for planting: 8×5=40 square feet.' Watch for: Students who confuse perimeter and area, forget units (feet vs square feet), or add only two sides for perimeter.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. The problem states: perimeter 30 meters with one side 9 meters, asking for the other side. Choice A is correct because opposite sides are equal, so 2×9 + 2×other = 30, other = (30-18)/2 = 6 meters, showing understanding of finding unknown side lengths from perimeter. Choice B represents a common error of halving the perimeter without subtracting, like 30/2=15 then subtracting only one side (15-9=6, but misplaced), but actually it's correct here—no, B is 12, which might be doubling 6 or halving 24 incorrectly; this happens when students forget to account for both pairs of sides. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). For unknown sides: 'Perimeter 30, one side 9. Draw rectangle, label known sides 9 and 9, subtract from 30: 30-18=12 left for other two sides, so each is 6.' Watch for: Students who don't recognize opposite sides equal or subtract incorrectly.

This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. Two rectangles both have perimeter 20 feet: A is 1×9 (area 9) and B is 5×5 (area 25). Choice B is correct because Rectangle B has greater area (25 > 9), showing understanding that same perimeter can have different areas, with squarer shapes having more area. Choice C represents assuming same perimeter means same area, which typically happens because students don't recognize that perimeter and area are independent. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). To show same perimeter/different areas: Build multiple rectangles with 20 unit-long border—1×9 (area 9), 2×8 (area 16), 3×7 (area 21), 4×6 (area 24), 5×5 (area 25)—shapes closer to square have more area. Watch for: Students who confuse perimeter and area, students who forget units (feet vs square feet), students who add only two sides for perimeter, students who add instead of multiply for area, and students who don't recognize perimeter and area are independent (same perimeter ≠ same area). Use real contexts and physical models.

Perimeter $$= 2(9) + 2(7) = 18 + 14 = 32$$ meters. Cost $$= 32 \times \2 = \64$$. Choice A gives the perimeter in meters, not the cost. Choice B results from calculating area ($$9 \times 7 = 63$$) times cost per meter. Choice D results from doubling the correct cost.

When you see a problem about extending or changing the size of a shape, focus carefully on what's being asked. This question wants to know how much additional fencing Tommy needs - not the total perimeter of the new pen.

Let's visualize what's happening. Tommy's original pen is 4 feet by 6 feet. When he extends the length from 6 feet to 8 feet, he's adding 2 feet to the length while keeping the width at 4 feet. Picture this: he's essentially adding a rectangular section that is 2 feet by 4 feet to one end of his pen.

To fence in this new section, Tommy needs fencing for three sides of this added rectangle (the fourth side is already connected to his existing pen). So he needs: one piece that's 2 feet long, one piece that's 4 feet long, and another piece that's 2 feet long. That's $$2 + 4 + 2 = 8$$ feet of additional fencing.

Choice A (4 feet) only accounts for the width of the addition. Choice B (16 feet) calculates the difference between the full perimeters of the old and new pens, but includes fencing Tommy already has. Choice C (12 feet) might come from incorrectly adding all four sides of the 2×4 addition ($$2 + 4 + 2 + 4 = 12$$), forgetting that one side connects to existing fencing.

Remember: when a shape is extended, you only need new fencing for the exposed edges of the addition, not for the side that connects to what's already there.