Chapter 16: Composing and Decomposing Numbers
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Composing and Decomposing Numbers with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Making 5 in different ways (a Grade 1 idea used in this chapter)
- Making 10 in different ways (a Grade 1 idea used in this chapter)
- Making teen numbers in different ways (a Grade 1 idea used in this chapter)
- Breaking a number into two parts (a Grade 1 idea used in this chapter)
- Part-part-whole models (a Grade 1 idea used in this chapter)
- Using counters to split numbers (a Grade 1 idea used in this chapter)
- Using drawings to split numbers (a Grade 1 idea used in this chapter)
- Writing two parts for a whole (a Grade 1 idea used in this chapter)
- Finding a missing part (a Grade 1 idea used in this chapter)
- Composing and decomposing 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.
16.1 Making 5 in different ways
Making 5 in different ways 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 Making 5 in different ways mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making 5 in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Making 5 in different ways 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 Making 5 in different ways.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making 5 in different ways 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 Making 5 in different ways.
Worked Example 3
Problem: Which tool could help with Making 5 in different ways?
- 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 5 in different ways 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 Making 5 in different ways?
- 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 5 in different ways 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 Making 5 in different ways 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 5 in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Making 5 in different ways can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Making 5 in different ways 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 Making 5 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 5 in different ways.
Worked Example 7
Problem: Show Making 5 in different ways 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 Making 5 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 5 in different ways.
Worked Example 8
Problem: Show Making 5 in different ways 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 Making 5 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 5 in different ways.
Worked Example 9
Problem: Show Making 5 in different ways 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 Making 5 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 5 in different ways.
Worked Example 10
Problem: Show Making 5 in different ways 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 Making 5 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 5 in different ways.
Practice Exercise
Create one small question about Making 5 in different ways. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.2 Making 10 in different ways
Making 10 in different ways 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 Making 10 in different ways mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making 10 in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Making 10 in different ways 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 Making 10 in different ways.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making 10 in different ways 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 Making 10 in different ways.
Worked Example 3
Problem: Which tool could help with Making 10 in different ways?
- 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 10 in different ways 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 Making 10 in different ways?
- 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 10 in different ways 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 Making 10 in different ways 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 10 in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Making 10 in different ways can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Making 10 in different ways 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 Making 10 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 10 in different ways.
Worked Example 7
Problem: Show Making 10 in different ways 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 Making 10 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 10 in different ways.
Worked Example 8
Problem: Show Making 10 in different ways 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 Making 10 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 10 in different ways.
Worked Example 9
Problem: Show Making 10 in different ways 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 Making 10 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 10 in different ways.
Worked Example 10
Problem: Show Making 10 in different ways 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 Making 10 in different ways best through concrete examples and clear words.
Answer: A correct simple example of Making 10 in different ways.
Practice Exercise
Create one small question about Making 10 in different ways. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.3 Making teen numbers in different ways
Making teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 teen numbers in different ways mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Making teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Worked Example 2
Problem: Show one small example of Making teen numbers in different ways.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: A correct small model or drawing can show the meaning of Making teen numbers in different ways.
Worked Example 3
Problem: Which tool could help with Making teen numbers in different ways?
- 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 teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 teen numbers in different ways?
- 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 teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Making teen numbers in different ways 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 teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Making teen numbers in different ways can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Count to 6. What number comes just before 6?
- Count forward until 6.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 5
Worked Example 7
Problem: Count to 12. What number comes just before 12?
- Count forward until 12.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 11
Worked Example 8
Problem: Count to 19. What number comes just before 19?
- Count forward until 19.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 18
Worked Example 9
Problem: Count to 27. What number comes just before 27?
- Count forward until 27.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 26
Worked Example 10
Problem: Count to 44. What number comes just before 44?
- Count forward until 44.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 43
Practice Exercise
Create one small question about Making teen numbers in different ways. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.4 Breaking a number into two parts
Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 Breaking a number into two parts mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Worked Example 2
Problem: Show one small example of Breaking a number into two parts.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: A correct small model or drawing can show the meaning of Breaking a number into two parts.
Worked Example 3
Problem: Which tool could help with Breaking a number into two parts?
- 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: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 Breaking a number into two parts?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Breaking a number into two parts 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: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Breaking a number into two parts can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Count to 6. What number comes just before 6?
- Count forward until 6.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 5
Worked Example 7
Problem: Count to 12. What number comes just before 12?
- Count forward until 12.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 11
Worked Example 8
Problem: Count to 19. What number comes just before 19?
- Count forward until 19.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 18
Worked Example 9
Problem: Count to 27. What number comes just before 27?
- Count forward until 27.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 26
Worked Example 10
Problem: Count to 44. What number comes just before 44?
- Count forward until 44.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 43
Practice Exercise
Create one small question about Breaking a number into two parts. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.5 Part-part-whole models
Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
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 Part-part-whole models mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Worked Example 2
Problem: Show one small example of Part-part-whole models.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: A correct small model or drawing can show the meaning of Part-part-whole models.
Worked Example 3
Problem: Which tool could help with Part-part-whole models?
- 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: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
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 Part-part-whole models?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Part-part-whole models 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: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Part-part-whole models can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Part-part-whole models 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 Part-part-whole models best through concrete examples and clear words.
Answer: A correct simple example of Part-part-whole models.
Worked Example 7
Problem: Show Part-part-whole models 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 Part-part-whole models best through concrete examples and clear words.
Answer: A correct simple example of Part-part-whole models.
Worked Example 8
Problem: Show Part-part-whole models 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 Part-part-whole models best through concrete examples and clear words.
Answer: A correct simple example of Part-part-whole models.
Worked Example 9
Problem: Show Part-part-whole models 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 Part-part-whole models best through concrete examples and clear words.
Answer: A correct simple example of Part-part-whole models.
Worked Example 10
Problem: Show Part-part-whole models 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 Part-part-whole models best through concrete examples and clear words.
Answer: A correct simple example of Part-part-whole models.
Practice Exercise
Create one small question about Part-part-whole models. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.6 Using counters to split numbers
Using counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 counters to split numbers mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Worked Example 2
Problem: Show one small example of Using counters to split numbers.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: A correct small model or drawing can show the meaning of Using counters to split numbers.
Worked Example 3
Problem: Which tool could help with Using counters to split numbers?
- 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 counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 counters to split numbers?
- 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 counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using counters to split numbers 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 counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using counters to split numbers can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Count to 6. What number comes just before 6?
- Count forward until 6.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 5
Worked Example 7
Problem: Count to 12. What number comes just before 12?
- Count forward until 12.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 11
Worked Example 8
Problem: Count to 19. What number comes just before 19?
- Count forward until 19.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 18
Worked Example 9
Problem: Count to 27. What number comes just before 27?
- Count forward until 27.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 26
Worked Example 10
Problem: Count to 44. What number comes just before 44?
- Count forward until 44.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 43
Practice Exercise
Create one small question about Using counters to split numbers. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.7 Using drawings to split numbers
Using drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 drawings to split numbers mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Worked Example 2
Problem: Show one small example of Using drawings to split numbers.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: A correct small model or drawing can show the meaning of Using drawings to split numbers.
Worked Example 3
Problem: Which tool could help with Using drawings to split numbers?
- 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 drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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 drawings to split numbers?
- 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 drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using drawings to split numbers 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 drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using drawings to split numbers can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Count to 6. What number comes just before 6?
- Count forward until 6.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 5
Worked Example 7
Problem: Count to 12. What number comes just before 12?
- Count forward until 12.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 11
Worked Example 8
Problem: Count to 19. What number comes just before 19?
- Count forward until 19.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 18
Worked Example 9
Problem: Count to 27. What number comes just before 27?
- Count forward until 27.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 26
Worked Example 10
Problem: Count to 44. What number comes just before 44?
- Count forward until 44.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 43
Practice Exercise
Create one small question about Using drawings to split numbers. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.8 Writing two parts for a whole
Writing two parts for a whole 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 Writing two parts for a whole mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Writing two parts for a whole is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Writing two parts for a whole 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 Writing two parts for a whole.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Writing two parts for a whole 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 Writing two parts for a whole.
Worked Example 3
Problem: Which tool could help with Writing two parts for a whole?
- 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: Writing two parts for a whole 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 Writing two parts for a whole?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Writing two parts for a whole 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 Writing two parts for a whole 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: Writing two parts for a whole is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Writing two parts for a whole can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Writing two parts for a whole 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 Writing two parts for a whole best through concrete examples and clear words.
Answer: A correct simple example of Writing two parts for a whole.
Worked Example 7
Problem: Show Writing two parts for a whole 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 Writing two parts for a whole best through concrete examples and clear words.
Answer: A correct simple example of Writing two parts for a whole.
Worked Example 8
Problem: Show Writing two parts for a whole 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 Writing two parts for a whole best through concrete examples and clear words.
Answer: A correct simple example of Writing two parts for a whole.
Worked Example 9
Problem: Show Writing two parts for a whole 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 Writing two parts for a whole best through concrete examples and clear words.
Answer: A correct simple example of Writing two parts for a whole.
Worked Example 10
Problem: Show Writing two parts for a whole 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 Writing two parts for a whole best through concrete examples and clear words.
Answer: A correct simple example of Writing two parts for a whole.
Practice Exercise
Create one small question about Writing two parts for a whole. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.9 Finding a missing part
Finding a missing part 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 Finding a missing part mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding a missing part is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding a missing part 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 Finding a missing part.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding a missing part 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 Finding a missing part.
Worked Example 3
Problem: Which tool could help with Finding a missing part?
- 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 a missing part 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 Finding a missing part?
- 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 a missing part 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 Finding a missing part 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 a missing part is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding a missing part can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Finding a missing part 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 Finding a missing part best through concrete examples and clear words.
Answer: A correct simple example of Finding a missing part.
Worked Example 7
Problem: Show Finding a missing part 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 Finding a missing part best through concrete examples and clear words.
Answer: A correct simple example of Finding a missing part.
Worked Example 8
Problem: Show Finding a missing part 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 Finding a missing part best through concrete examples and clear words.
Answer: A correct simple example of Finding a missing part.
Worked Example 9
Problem: Show Finding a missing part 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 Finding a missing part best through concrete examples and clear words.
Answer: A correct simple example of Finding a missing part.
Worked Example 10
Problem: Show Finding a missing part 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 Finding a missing part best through concrete examples and clear words.
Answer: A correct simple example of Finding a missing part.
Practice Exercise
Create one small question about Finding a missing part. Show it with objects, a picture, or numbers, then check by counting or comparing again.
16.10 Composing and decomposing review
Composing and decomposing 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 Composing and decomposing review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Composing and decomposing review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Composing and decomposing 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 Composing and decomposing review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Composing and decomposing 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 Composing and decomposing review.
Worked Example 3
Problem: Which tool could help with Composing and decomposing 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: Composing and decomposing 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 Composing and decomposing 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: Composing and decomposing 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 Composing and decomposing 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: Composing and decomposing review is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Composing and decomposing review can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Composing and decomposing 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 Composing and decomposing review best through concrete examples and clear words.
Answer: A correct simple example of Composing and decomposing review.
Worked Example 7
Problem: Show Composing and decomposing 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 Composing and decomposing review best through concrete examples and clear words.
Answer: A correct simple example of Composing and decomposing review.
Worked Example 8
Problem: Show Composing and decomposing 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 Composing and decomposing review best through concrete examples and clear words.
Answer: A correct simple example of Composing and decomposing review.
Worked Example 9
Problem: Show Composing and decomposing 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 Composing and decomposing review best through concrete examples and clear words.
Answer: A correct simple example of Composing and decomposing review.
Worked Example 10
Problem: Show Composing and decomposing 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 Composing and decomposing review best through concrete examples and clear words.
Answer: A correct simple example of Composing and decomposing review.
Practice Exercise
Create one small question about Composing and decomposing 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 Making 5 in different ways.
- Create and solve one original problem about Making 10 in different ways.
- Create and solve one original problem about Making teen numbers in different ways.
- Create and solve one original problem about Breaking a number into two parts.
- Create and solve one original problem about Part-part-whole models.
- Create and solve one original problem about Using counters to split numbers.
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 Making 5 in different ways?
Answer: Making 5 in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q2. What is the main idea in Making 10 in different ways?
Answer: Making 10 in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q3. What is the main idea in Making teen numbers in different ways?
Answer: Making teen numbers in different ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q4. What is the main idea in Breaking a number into two parts?
Answer: Breaking a number into two parts helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q5. What is the main idea in Part-part-whole models?
Answer: Part-part-whole models uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Q6. What is the main idea in Using counters to split numbers?
Answer: Using counters to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q7. What is the main idea in Using drawings to split numbers?
Answer: Using drawings to split numbers helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q8. What is the main idea in Writing two parts for a whole?
Answer: Writing two parts for a whole is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q9. What is the main idea in Finding a missing part?
Answer: Finding a missing part is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q10. What is the main idea in Composing and decomposing review?
Answer: Composing and decomposing 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.