Compose Shapes

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Answer Key & Explanations

Compose Shapes · Grade 1 · Worksheet 3

1. Sophia is making a picture with pattern blocks. She wants to create a large rectangle by putting smaller rectangles together. If she uses 8 small rectangles, and she puts them in a row with 4 rectangles in the top row and 4 rectangles in the bottom row, what shape does she make? Answer: a larger rectangle Solution: Sophia puts 4 rectangles in a row across the top. Then she puts 4 more rectangles directly below them in a second row. Each small rectangle has straight sides and square corners.
   Full step-by-step solution

   Sophia puts 4 rectangles in a row across the top. Then she puts 4 more rectangles directly below them in a second row. Each small rectangle has straight sides and square corners. When you put two rows of rectangles together, the top edges line up and the sides line up, making one big shape that still has straight sides and square corners. So the shape she makes is a larger rectangle.

2. Mere has 12 square tiles. She wants to put them together to make one big rectangle. She puts 4 tiles in the first row. How many tiles will be in each of the other rows if all rows have the same number of tiles? Answer: 4 tiles in each row, or 3 rows total (3 rows of 4) Solution: Mere has 12 square tiles total. She puts 4 tiles in the first row. Since all rows must have the same number of tiles, each row will also have 4 tiles.
   Full step-by-step solution

   Step 1: Mere has 12 square tiles total. Step 2: She puts 4 tiles in the first row. Step 3: Since all rows must have the same number of tiles, each row will also have 4 tiles. Step 4: To find how many rows, divide the total tiles by the number per row: 12 divided by 4 = 3 rows. Step 5: So the rectangle is 3 rows tall and 4 tiles wide. The answer is 4 tiles per row, making 3 rows.

3. Charlotte is making a picture with shape tiles. She puts together 8 small triangles to make a larger shape. If she arranges all 8 triangles so their points meet in the center, what larger shape can she make? Answer: an octagon Solution: Understand that when you arrange triangles around a center point, the base of each triangle forms one side of the new shape. Count the number of triangles being used: 8.
   Full step-by-step solution

   Step 1: Understand that when you arrange triangles around a center point, the base of each triangle forms one side of the new shape. Step 2: Count the number of triangles being used: 8. Step 3: Each triangle contributes one side to the outer shape. Step 4: Therefore, the new shape will have 8 sides. Step 5: A shape with 8 sides is called an octagon. Answer: an octagon.

4. Noah is making a design on the floor using pattern blocks. He puts 8 small triangles together around a center point, and they form a larger shape. What is the name of the shape that Noah made? Answer: octagon Solution: Noah arranges 8 triangles so that their points all meet at one center point. The outer edges of the triangles form the boundary of a new larger shape. Count the sides of the outer shape.
   Full step-by-step solution

   Step 1: Noah arranges 8 triangles so that their points all meet at one center point. Step 2: The outer edges of the triangles form the boundary of a new larger shape. Step 3: Count the sides of the outer shape. Each triangle contributes one outer side, so there are 8 sides. Step 4: A shape with 8 sides is called an octagon. The prefix 'oct-' means eight. The answer is octagon.

5. Emma is making a new shape by putting together smaller shapes. She puts 3 small triangles together, point to point, in a row. If each triangle has 3 sides, and she puts them together so that they share sides, what is the name of the new shape she makes? Answer: trapezoid Solution: Draw one triangle. It has 3 sides. Place a second triangle next to the first, sharing one side.
   Full step-by-step solution

   Step 1: Draw one triangle. It has 3 sides. Step 2: Place a second triangle next to the first, sharing one side. Now the combined shape has 4 sides (a quadrilateral). Step 3: Place a third triangle next to the second, sharing another side. The new combined shape has 4 sides: one top side (long), one bottom side (long), and two slanted sides on the ends. Step 4: A shape with 4 sides where the top and bottom are parallel but different lengths is called a trapezoid. The answer is trapezoid.

6. Sarah has 5 square tiles. She uses all of them to make a larger rectangle. If she puts the tiles in one row, how many sides does the larger rectangle have? Answer: 4 Solution: Sarah has 5 square tiles. She uses all of them to make a larger rectangle. She puts the tiles in one row.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the problem** Sarah has 5 square tiles. She uses all of them to make a larger rectangle. She puts the tiles in **one row**. We are asked: how many sides does the **larger rectangle** have? --- **Step 2: Visualize the arrangement** If she puts all 5 square tiles in one row, they form a longer rectangle made of 5 equal squares joined edge-to-edge. Each square tile has 4 sides, but when they are joined, some sides are no longer outer sides of the larger rectangle. --- **Step 3: Count the sides of the larger rectangle** Think of the larger rectangle as a single shape. It is a rectangle, so it has **4 sides** in total: top, bottom, left, right. But let's verify carefully: - Top side: one long continuous side (length of 5 tiles) - Bottom side: one long continuous side (length of 5 tiles) - Left side: one side (height of 1 tile) - Right side: one side (height of 1 tile) So the larger rectangle has exactly **4 sides**. --- **Step 4: Address possible confusion** Sometimes people might think: each tile has 4 sides, so 5 tiles have 20 sides, then subtract shared edges. But the question asks: "how many sides does the larger rectangle have?" — not the total exposed perimeter segments, but the number of sides of the rectangle as a single shape. A rectangle always has 4 sides. --- **Step 5: Conclusion** The answer is **4**. --- **Final Answer:** 4

7. Mere has 6 identical square tiles. If she puts them together in a row, side by side, what new 2D shape does she make? Answer: a rectangle Solution: Start with 6 square tiles. Each square has 4 equal sides. When you place them side by side in a row, the top and bottom edges line up to form one long top edge and one long bottom edge.
   Full step-by-step solution

   Step 1: Start with 6 square tiles. Each square has 4 equal sides. Step 2: When you place them side by side in a row, the top and bottom edges line up to form one long top edge and one long bottom edge. Step 3: The left and right ends are still the sides of the first and last square. Step 4: The new shape has 2 long sides and 2 short sides. Opposite sides are equal. Step 5: A shape with 4 sides and opposite sides equal is a rectangle. The answer is a rectangle.

8. Noah is making a picture with shapes. He puts 2 small squares together side by side to make a new shape. What shape did Noah make? Answer: rectangle Solution: Start with 2 small squares. Each square has 4 equal sides. Put them together side by side so they share one side.
   Full step-by-step solution

   Step 1: Start with 2 small squares. Each square has 4 equal sides. Step 2: Put them together side by side so they share one side. Step 3: The new shape has 2 long sides (made from two square sides) and 2 short sides (the top and bottom of one square). Step 4: A shape with 4 sides, where two sides are longer and two sides are shorter, is called a rectangle. The answer is a rectangle.

9. Sophia is making a picture with shapes. She puts 6 small triangles together around a center point, with their points touching. What shape do the 6 triangles make when they are arranged this way? Answer: hexagon Solution: Sophia places 6 triangles so their points meet at one spot in the middle. Step 2: The outer edges of the triangles form a shape with 6 straight sides. Step 3: A shape with 6 sides is called a hexagon.
   Full step-by-step solution

   Step 1: Sophia places 6 triangles so their points meet at one spot in the middle. Step 2: The outer edges of the triangles form a shape with 6 straight sides. Step 3: A shape with 6 sides is called a hexagon. The answer is hexagon.