Chapter 54: Composing and Decomposing Shapes
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Composing and Decomposing Shapes with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Putting shapes together (a Grade 1 idea used in this chapter)
- Taking shapes apart (a Grade 1 idea used in this chapter)
- Making a rectangle from smaller shapes (a Grade 1 idea used in this chapter)
- Making a picture from shapes (a Grade 1 idea used in this chapter)
- Finding shapes inside a larger shape (a Grade 1 idea used in this chapter)
- Using two triangles to make a new shape (a Grade 1 idea used in this chapter)
- Rearranging shape pieces (a Grade 1 idea used in this chapter)
- Explaining how a shape was built (a Grade 1 idea used in this chapter)
- Shape puzzles (a Grade 1 idea used in this chapter)
- Compose-and-decompose review (a Grade 1 idea used in this chapter)
How to Learn This Chapter
Read or listen to the explanation, use objects or pictures when helpful, follow one step at a time, and try the example again before checking the answer.
54.1 Putting shapes together
Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Putting shapes together mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Putting shapes together.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Putting shapes together.
Worked Example 3
Problem: Which tool could help with Putting shapes together?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Putting shapes together?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Putting shapes together in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Putting shapes together can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Putting shapes together. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.2 Taking shapes apart
Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Taking shapes apart mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Taking shapes apart.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Taking shapes apart.
Worked Example 3
Problem: Which tool could help with Taking shapes apart?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Taking shapes apart?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Taking shapes apart in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Taking shapes apart can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Taking shapes apart. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.3 Making a rectangle from smaller shapes
Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Making a rectangle from smaller shapes mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Making a rectangle from smaller shapes.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Making a rectangle from smaller shapes.
Worked Example 3
Problem: Which tool could help with Making a rectangle from smaller shapes?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Making a rectangle from smaller shapes?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Making a rectangle from smaller shapes in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Making a rectangle from smaller shapes can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Making a rectangle from smaller shapes. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.4 Making a picture from shapes
Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Making a picture from shapes mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Making a picture from shapes.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Making a picture from shapes.
Worked Example 3
Problem: Which tool could help with Making a picture from shapes?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Making a picture from shapes?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Making a picture from shapes in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Making a picture from shapes can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Making a picture from shapes. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.5 Finding shapes inside a larger shape
Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Finding shapes inside a larger shape mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Finding shapes inside a larger shape.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Finding shapes inside a larger shape.
Worked Example 3
Problem: Which tool could help with Finding shapes inside a larger shape?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Finding shapes inside a larger shape?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Finding shapes inside a larger shape in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Finding shapes inside a larger shape can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Finding shapes inside a larger shape. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.6 Using two triangles to make a new shape
Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Using two triangles to make a new shape mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Using two triangles to make a new shape.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Using two triangles to make a new shape.
Worked Example 3
Problem: Which tool could help with Using two triangles to make a new shape?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Using two triangles to make a new shape?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using two triangles to make a new shape in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Using two triangles to make a new shape can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Using two triangles to make a new shape. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.7 Rearranging shape pieces
Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Rearranging shape pieces mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Rearranging shape pieces.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Rearranging shape pieces.
Worked Example 3
Problem: Which tool could help with Rearranging shape pieces?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Rearranging shape pieces?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Rearranging shape pieces in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Rearranging shape pieces can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Rearranging shape pieces. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.8 Explaining how a shape was built
Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Explaining how a shape was built mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Explaining how a shape was built.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Explaining how a shape was built.
Worked Example 3
Problem: Which tool could help with Explaining how a shape was built?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Explaining how a shape was built?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Explaining how a shape was built in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Explaining how a shape was built can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Explaining how a shape was built. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.9 Shape puzzles
Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Shape puzzles mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Worked Example 2
Problem: Show one small example of Shape puzzles.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: A correct small model or drawing can show the meaning of Shape puzzles.
Worked Example 3
Problem: Which tool could help with Shape puzzles?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Shape puzzles?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Shape puzzles in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Answer: Shape puzzles can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Name a shape or object with this clue: 0 straight sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: circle
Worked Example 7
Problem: Name a shape or object with this clue: 3 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: triangle
Worked Example 8
Problem: Name a shape or object with this clue: 4 equal sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: square
Worked Example 9
Problem: Name a shape or object with this clue: 4 sides.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: rectangle
Worked Example 10
Problem: Name a shape or object with this clue: round 3D object.
- Think about the clue.
- Match it to a familiar shape or object.
Very beginner explanation: Shape attributes help us identify and describe shapes.
Answer: sphere
Practice Exercise
Create one small question about Shape puzzles. Show it with objects, a picture, or numbers, then check by counting or comparing again.
54.10 Compose-and-decompose review
Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Compose-and-decompose review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Worked Example 2
Problem: Show one small example of Compose-and-decompose review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: A correct small model or drawing can show the meaning of Compose-and-decompose review.
Worked Example 3
Problem: Which tool could help with Compose-and-decompose review?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Compose-and-decompose review?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Compose-and-decompose review in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Compose-and-decompose review can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Compose-and-decompose review with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Compose-and-decompose review best through concrete examples and clear words.
Answer: A correct simple example of Compose-and-decompose review.
Worked Example 7
Problem: Show Compose-and-decompose review with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Compose-and-decompose review best through concrete examples and clear words.
Answer: A correct simple example of Compose-and-decompose review.
Worked Example 8
Problem: Show Compose-and-decompose review with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Compose-and-decompose review best through concrete examples and clear words.
Answer: A correct simple example of Compose-and-decompose review.
Worked Example 9
Problem: Show Compose-and-decompose review with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Compose-and-decompose review best through concrete examples and clear words.
Answer: A correct simple example of Compose-and-decompose review.
Worked Example 10
Problem: Show Compose-and-decompose review with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Compose-and-decompose review best through concrete examples and clear words.
Answer: A correct simple example of Compose-and-decompose review.
Practice Exercise
Create one small question about Compose-and-decompose review. Show it with objects, a picture, or numbers, then check by counting or comparing again.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read or listen to the question before solving.
- Use objects, a drawing, ten frame, number line, table, graph, or simple number sentence when useful.
- Explain your thinking and check by counting, comparing, or using another simple model.
Extra Practice
- Create and solve one original problem about Putting shapes together.
- Create and solve one original problem about Taking shapes apart.
- Create and solve one original problem about Making a rectangle from smaller shapes.
- Create and solve one original problem about Making a picture from shapes.
- Create and solve one original problem about Finding shapes inside a larger shape.
- Create and solve one original problem about Using two triangles to make a new shape.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the main idea in Putting shapes together?
Answer: Putting shapes together develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q2. What is the main idea in Taking shapes apart?
Answer: Taking shapes apart develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q3. What is the main idea in Making a rectangle from smaller shapes?
Answer: Making a rectangle from smaller shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q4. What is the main idea in Making a picture from shapes?
Answer: Making a picture from shapes develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q5. What is the main idea in Finding shapes inside a larger shape?
Answer: Finding shapes inside a larger shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q6. What is the main idea in Using two triangles to make a new shape?
Answer: Using two triangles to make a new shape develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q7. What is the main idea in Rearranging shape pieces?
Answer: Rearranging shape pieces develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q8. What is the main idea in Explaining how a shape was built?
Answer: Explaining how a shape was built develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q9. What is the main idea in Shape puzzles?
Answer: Shape puzzles develops spatial sense by describing shapes, objects, positions, and how parts fit together.
Q10. What is the main idea in Compose-and-decompose review?
Answer: Compose-and-decompose review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q11. Why is it useful to use counters or drawings?
Answer: They make the quantities visible and help you understand before using only numbers.
Q12. Why should you count carefully?
Answer: Careful counting means each object is counted once and no object is missed.
Q13. What can you do if a problem feels hard?
Answer: Use smaller numbers, draw a picture, use objects, and solve one small step at a time.
Q14. Why should both sides of an equals sign match?
Answer: The equals sign means the two sides have the same value.
Q15. How can a number line help?
Answer: It shows number order and can help you count forward or backward.
Q16. How can a ten frame help?
Answer: It organizes objects into groups that make numbers and addition easier to see.
Q17. Why are equal shares important?
Answer: Equal shares make fair groups or equal parts.
Q18. How do patterns help us predict?
Answer: A pattern rule tells us what should come next.
Q19. Why do we label a graph or table?
Answer: Labels tell us what the information represents.
Q20. How can you describe a shape?
Answer: Talk about its sides, corners, flat or curved surfaces, and other visible attributes.
Q21. How can you compare two objects?
Answer: Choose one attribute, such as length, mass, or capacity, and compare that same attribute.
Q22. Why is a calendar useful?
Answer: It organizes days, weeks, months, dates, and events.
Q23. Why does money have different values?
Answer: Different coins and bills represent different amounts of money.
Q24. Why should you explain your answer?
Answer: Explaining shows how you thought about the problem and helps you check your reasoning.
Q25. What should you do after a mistake?
Answer: Look at the step again, fix it, and try a similar example.
Q26. How can you be a confident math learner?
Answer: Use positive self-talk, try a strategy, ask questions, and remember that mistakes help you learn.
Q27. When should you use a picture?
Answer: Use a picture when it helps you see quantities, shapes, positions, or a story problem.
Q28. When should you use objects?
Answer: Use objects when you want to count, join, take away, share, sort, or compare in a hands-on way.
Q29. How can you check addition?
Answer: Recount the combined objects or use another model.
Q30. How can you check subtraction?
Answer: Put the taken-away part and the part left back together to see if they make the starting amount.