Chapter 6: Counting Forward and Backward
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Counting Forward and Backward with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Counting forward by ones (a Grade 1 idea used in this chapter)
- Counting backward by ones (a Grade 1 idea used in this chapter)
- Starting at a number other than zero (a Grade 1 idea used in this chapter)
- Counting to 50 (a Grade 1 idea used in this chapter)
- Counting backward from 20 (a Grade 1 idea used in this chapter)
- Counting backward from 50 (a Grade 1 idea used in this chapter)
- Finding the next number (a Grade 1 idea used in this chapter)
- Finding the previous number (a Grade 1 idea used in this chapter)
- Filling number-sequence gaps (a Grade 1 idea used in this chapter)
- Counting games and routines (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.
6.1 Counting forward by ones
Counting forward by ones 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 Counting forward by ones mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting forward by ones helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting forward by ones 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 Counting forward by ones.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting forward by ones 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 Counting forward by ones.
Worked Example 3
Problem: Which tool could help with Counting forward by ones?
- 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: Counting forward by ones 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 Counting forward by ones?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting forward by ones 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 Counting forward by ones 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: Counting forward by ones helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting forward by ones can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: How many tens and ones are in 10?
- 10 has 1 full group(s) of ten.
- 0 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 1 tens and 0 ones
Worked Example 7
Problem: How many tens and ones are in 12?
- 12 has 1 full group(s) of ten.
- 2 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 1 tens and 2 ones
Worked Example 8
Problem: How many tens and ones are in 19?
- 19 has 1 full group(s) of ten.
- 9 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 1 tens and 9 ones
Worked Example 9
Problem: How many tens and ones are in 27?
- 27 has 2 full group(s) of ten.
- 7 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 2 tens and 7 ones
Worked Example 10
Problem: How many tens and ones are in 44?
- 44 has 4 full group(s) of ten.
- 4 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 4 tens and 4 ones
Practice Exercise
Create one small question about Counting forward by ones. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.2 Counting backward by ones
Counting backward by ones 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 Counting backward by ones mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting backward by ones helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting backward by ones 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 Counting backward by ones.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting backward by ones 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 Counting backward by ones.
Worked Example 3
Problem: Which tool could help with Counting backward by ones?
- 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: Counting backward by ones 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 Counting backward by ones?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting backward by ones 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 Counting backward by ones 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: Counting backward by ones helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting backward by ones can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: How many tens and ones are in 10?
- 10 has 1 full group(s) of ten.
- 0 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 1 tens and 0 ones
Worked Example 7
Problem: How many tens and ones are in 12?
- 12 has 1 full group(s) of ten.
- 2 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 1 tens and 2 ones
Worked Example 8
Problem: How many tens and ones are in 19?
- 19 has 1 full group(s) of ten.
- 9 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 1 tens and 9 ones
Worked Example 9
Problem: How many tens and ones are in 27?
- 27 has 2 full group(s) of ten.
- 7 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 2 tens and 7 ones
Worked Example 10
Problem: How many tens and ones are in 44?
- 44 has 4 full group(s) of ten.
- 4 object(s) are left as ones.
Very beginner explanation: Groups of ten and leftover ones show place value.
Answer: 4 tens and 4 ones
Practice Exercise
Create one small question about Counting backward by ones. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.3 Starting at a number other than zero
Starting at a number other than zero 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 Starting at a number other than zero mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Starting at a number other than zero helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Starting at a number other than zero 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 Starting at a number other than zero.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Starting at a number other than zero 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 Starting at a number other than zero.
Worked Example 3
Problem: Which tool could help with Starting at a number other than zero?
- 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: Starting at a number other than zero 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 Starting at a number other than zero?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Starting at a number other than zero 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 Starting at a number other than zero 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: Starting at a number other than zero helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Starting at a number other than zero 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 Starting at a number other than zero. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.4 Counting to 50
Counting to 50 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 Counting to 50 mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting to 50 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting to 50 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 Counting to 50.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting to 50 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 Counting to 50.
Worked Example 3
Problem: Which tool could help with Counting to 50?
- 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: Counting to 50 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 Counting to 50?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting to 50 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 Counting to 50 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: Counting to 50 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting to 50 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 Counting to 50. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.5 Counting backward from 20
Counting backward from 20 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 Counting backward from 20 mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting backward from 20 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting backward from 20 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 Counting backward from 20.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting backward from 20 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 Counting backward from 20.
Worked Example 3
Problem: Which tool could help with Counting backward from 20?
- 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: Counting backward from 20 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 Counting backward from 20?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting backward from 20 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 Counting backward from 20 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: Counting backward from 20 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting backward from 20 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 Counting backward from 20. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.6 Counting backward from 50
Counting backward from 50 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 Counting backward from 50 mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting backward from 50 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting backward from 50 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 Counting backward from 50.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting backward from 50 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 Counting backward from 50.
Worked Example 3
Problem: Which tool could help with Counting backward from 50?
- 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: Counting backward from 50 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 Counting backward from 50?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting backward from 50 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 Counting backward from 50 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: Counting backward from 50 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting backward from 50 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 Counting backward from 50. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.7 Finding the next number
Finding the next number 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 Finding the next number mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding the next number helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Finding the next number 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 Finding the next number.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding the next number 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 Finding the next number.
Worked Example 3
Problem: Which tool could help with Finding the next number?
- 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 the next number 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 Finding the next number?
- 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 the next number 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 Finding the next number 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 the next number helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Finding the next number 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 Finding the next number. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.8 Finding the previous number
Finding the previous number 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 Finding the previous number mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding the previous number helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Finding the previous number 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 Finding the previous number.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding the previous number 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 Finding the previous number.
Worked Example 3
Problem: Which tool could help with Finding the previous number?
- 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 the previous number 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 Finding the previous number?
- 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 the previous number 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 Finding the previous number 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 the previous number helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Finding the previous number 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 Finding the previous number. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.9 Filling number-sequence gaps
Filling number-sequence gaps 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 Filling number-sequence gaps mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Filling number-sequence gaps helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Filling number-sequence gaps 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 Filling number-sequence gaps.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Filling number-sequence gaps 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 Filling number-sequence gaps.
Worked Example 3
Problem: Which tool could help with Filling number-sequence gaps?
- 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: Filling number-sequence gaps 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 Filling number-sequence gaps?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Filling number-sequence gaps 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 Filling number-sequence gaps 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: Filling number-sequence gaps helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Filling number-sequence gaps 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 Filling number-sequence gaps. Show it with objects, a picture, or numbers, then check by counting or comparing again.
6.10 Counting games and routines
Counting games and routines 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 Counting games and routines mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting games and routines helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting games and routines 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 Counting games and routines.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting games and routines 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 Counting games and routines.
Worked Example 3
Problem: Which tool could help with Counting games and routines?
- 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: Counting games and routines 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 Counting games and routines?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting games and routines 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 Counting games and routines 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: Counting games and routines helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting games and routines 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 Counting games and routines. 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 Counting forward by ones.
- Create and solve one original problem about Counting backward by ones.
- Create and solve one original problem about Starting at a number other than zero.
- Create and solve one original problem about Counting to 50.
- Create and solve one original problem about Counting backward from 20.
- Create and solve one original problem about Counting backward from 50.
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 Counting forward by ones?
Answer: Counting forward by ones helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q2. What is the main idea in Counting backward by ones?
Answer: Counting backward by ones helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q3. What is the main idea in Starting at a number other than zero?
Answer: Starting at a number other than zero helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q4. What is the main idea in Counting to 50?
Answer: Counting to 50 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q5. What is the main idea in Counting backward from 20?
Answer: Counting backward from 20 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q6. What is the main idea in Counting backward from 50?
Answer: Counting backward from 50 helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q7. What is the main idea in Finding the next number?
Answer: Finding the next number helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q8. What is the main idea in Finding the previous number?
Answer: Finding the previous number helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q9. What is the main idea in Filling number-sequence gaps?
Answer: Filling number-sequence gaps helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q10. What is the main idea in Counting games and routines?
Answer: Counting games and routines 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.