Chapter 11: Representing Numbers
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Representing Numbers with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Using counters (a Grade 1 idea used in this chapter)
- Using drawings (a Grade 1 idea used in this chapter)
- Using dots (a Grade 1 idea used in this chapter)
- Using tally marks (a Grade 1 idea used in this chapter)
- Using ten frames (a Grade 1 idea used in this chapter)
- Using fingers (a Grade 1 idea used in this chapter)
- Using number words (a Grade 1 idea used in this chapter)
- Using numerals (a Grade 1 idea used in this chapter)
- Showing a number in two ways (a Grade 1 idea used in this chapter)
- Choosing a useful representation (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.
11.1 Using counters
Using counters 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 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 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using counters 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.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using counters 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.
Worked Example 3
Problem: Which tool could help with Using counters?
- 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 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?
- 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 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 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 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using counters 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. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.2 Using drawings
Using drawings 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 Using drawings 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 is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using drawings 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 Using drawings.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using drawings 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 Using drawings.
Worked Example 3
Problem: Which tool could help with Using drawings?
- 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 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 Using drawings?
- 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 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 Using drawings 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 is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using drawings can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using drawings 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 Using drawings best through concrete examples and clear words.
Answer: A correct simple example of Using drawings.
Worked Example 7
Problem: Show Using drawings 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 Using drawings best through concrete examples and clear words.
Answer: A correct simple example of Using drawings.
Worked Example 8
Problem: Show Using drawings 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 Using drawings best through concrete examples and clear words.
Answer: A correct simple example of Using drawings.
Worked Example 9
Problem: Show Using drawings 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 Using drawings best through concrete examples and clear words.
Answer: A correct simple example of Using drawings.
Worked Example 10
Problem: Show Using drawings 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 Using drawings best through concrete examples and clear words.
Answer: A correct simple example of Using drawings.
Practice Exercise
Create one small question about Using drawings. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.3 Using dots
Using dots 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 Using dots mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using dots is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using dots 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 Using dots.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using dots 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 Using dots.
Worked Example 3
Problem: Which tool could help with Using dots?
- 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 dots 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 Using dots?
- 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 dots 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 Using dots 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 dots is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using dots can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using dots 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 Using dots best through concrete examples and clear words.
Answer: A correct simple example of Using dots.
Worked Example 7
Problem: Show Using dots 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 Using dots best through concrete examples and clear words.
Answer: A correct simple example of Using dots.
Worked Example 8
Problem: Show Using dots 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 Using dots best through concrete examples and clear words.
Answer: A correct simple example of Using dots.
Worked Example 9
Problem: Show Using dots 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 Using dots best through concrete examples and clear words.
Answer: A correct simple example of Using dots.
Worked Example 10
Problem: Show Using dots 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 Using dots best through concrete examples and clear words.
Answer: A correct simple example of Using dots.
Practice Exercise
Create one small question about Using dots. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.4 Using tally marks
Using tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 tally marks mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Using tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Using tally marks.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Using tally marks.
Worked Example 3
Problem: Which tool could help with Using tally marks?
- 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 tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 tally marks?
- 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 tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using tally marks 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 tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Using tally marks can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Using tally marks. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.5 Using ten frames
Using ten frames 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 Using ten frames mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using ten frames is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using ten frames 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 Using ten frames.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using ten frames 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 Using ten frames.
Worked Example 3
Problem: Which tool could help with Using ten frames?
- 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 ten frames 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 Using ten frames?
- 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 ten frames 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 Using ten frames 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 ten frames is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using ten frames can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using ten frames 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 Using ten frames best through concrete examples and clear words.
Answer: A correct simple example of Using ten frames.
Worked Example 7
Problem: Show Using ten frames 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 Using ten frames best through concrete examples and clear words.
Answer: A correct simple example of Using ten frames.
Worked Example 8
Problem: Show Using ten frames 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 Using ten frames best through concrete examples and clear words.
Answer: A correct simple example of Using ten frames.
Worked Example 9
Problem: Show Using ten frames 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 Using ten frames best through concrete examples and clear words.
Answer: A correct simple example of Using ten frames.
Worked Example 10
Problem: Show Using ten frames 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 Using ten frames best through concrete examples and clear words.
Answer: A correct simple example of Using ten frames.
Practice Exercise
Create one small question about Using ten frames. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.6 Using fingers
Using fingers 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 Using fingers mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using fingers is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using fingers 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 Using fingers.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using fingers 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 Using fingers.
Worked Example 3
Problem: Which tool could help with Using fingers?
- 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 fingers 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 Using fingers?
- 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 fingers 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 Using fingers 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 fingers is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using fingers can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using fingers 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 Using fingers best through concrete examples and clear words.
Answer: A correct simple example of Using fingers.
Worked Example 7
Problem: Show Using fingers 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 Using fingers best through concrete examples and clear words.
Answer: A correct simple example of Using fingers.
Worked Example 8
Problem: Show Using fingers 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 Using fingers best through concrete examples and clear words.
Answer: A correct simple example of Using fingers.
Worked Example 9
Problem: Show Using fingers 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 Using fingers best through concrete examples and clear words.
Answer: A correct simple example of Using fingers.
Worked Example 10
Problem: Show Using fingers 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 Using fingers best through concrete examples and clear words.
Answer: A correct simple example of Using fingers.
Practice Exercise
Create one small question about Using fingers. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.7 Using number words
Using number words 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 number words mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using number words helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using number words 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 number words.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using number words 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 number words.
Worked Example 3
Problem: Which tool could help with Using number words?
- 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 number words 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 number words?
- 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 number words 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 number words 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 number words helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using number words 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 number words. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.8 Using numerals
Using numerals 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 numerals mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using numerals helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using numerals 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 numerals.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using numerals 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 numerals.
Worked Example 3
Problem: Which tool could help with Using numerals?
- 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 numerals 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 numerals?
- 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 numerals 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 numerals 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 numerals helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Using numerals 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 numerals. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.9 Showing a number in two ways
Showing a number in two 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 Showing a number in two ways mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Showing a number in two ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Showing a number in two 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 Showing a number in two ways.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Showing a number in two 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 Showing a number in two ways.
Worked Example 3
Problem: Which tool could help with Showing a number in two 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: Showing a number in two 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 Showing a number in two 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: Showing a number in two 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 Showing a number in two 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: Showing a number in two ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Showing a number in two 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 Showing a number in two ways. Show it with objects, a picture, or numbers, then check by counting or comparing again.
11.10 Choosing a useful representation
Choosing a useful representation 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 Choosing a useful representation mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Choosing a useful representation helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Choosing a useful representation 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 Choosing a useful representation.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Choosing a useful representation 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 Choosing a useful representation.
Worked Example 3
Problem: Which tool could help with Choosing a useful representation?
- 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: Choosing a useful representation 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 Choosing a useful representation?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Choosing a useful representation 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 Choosing a useful representation 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: Choosing a useful representation helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Choosing a useful representation 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 Choosing a useful representation. 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 Using counters.
- Create and solve one original problem about Using drawings.
- Create and solve one original problem about Using dots.
- Create and solve one original problem about Using tally marks.
- Create and solve one original problem about Using ten frames.
- Create and solve one original problem about Using fingers.
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 Using counters?
Answer: Using counters helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q2. What is the main idea in Using drawings?
Answer: Using drawings 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 Using dots?
Answer: Using dots is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q4. What is the main idea in Using tally marks?
Answer: Using tally marks helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q5. What is the main idea in Using ten frames?
Answer: Using ten frames is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q6. What is the main idea in Using fingers?
Answer: Using fingers is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q7. What is the main idea in Using number words?
Answer: Using number words helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q8. What is the main idea in Using numerals?
Answer: Using numerals helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q9. What is the main idea in Showing a number in two ways?
Answer: Showing a number in two ways helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q10. What is the main idea in Choosing a useful representation?
Answer: Choosing a useful representation helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
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.