Chapter 18: Introduction to Addition
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Introduction to Addition with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Addition means putting together (a Grade 1 idea used in this chapter)
- Joining two groups (a Grade 1 idea used in this chapter)
- Using the plus sign (a Grade 1 idea used in this chapter)
- Using the equals sign (a Grade 1 idea used in this chapter)
- Writing addition sentences (a Grade 1 idea used in this chapter)
- Adding with counters (a Grade 1 idea used in this chapter)
- Adding with drawings (a Grade 1 idea used in this chapter)
- Adding by counting on (a Grade 1 idea used in this chapter)
- Addition stories (a Grade 1 idea used in this chapter)
- Checking an addition model (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.
18.1 Addition means putting together
Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Addition means putting together mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Worked Example 2
Problem: Show one small example of Addition means putting together.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: A correct small model or drawing can show the meaning of Addition means putting together.
Worked Example 3
Problem: Which tool could help with Addition means putting together?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Addition means putting together?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Addition means putting together in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Addition means putting together can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Addition means putting together. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.2 Joining two groups
Joining two groups 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 Joining two groups mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Joining two groups is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Joining two groups 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 Joining two groups.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Joining two groups 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 Joining two groups.
Worked Example 3
Problem: Which tool could help with Joining two groups?
- 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: Joining two groups 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 Joining two groups?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Joining two groups 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 Joining two groups 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: Joining two groups is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Joining two groups can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Joining two groups. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.3 Using the plus sign
Using the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 the plus sign mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Using the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Worked Example 2
Problem: Show one small example of Using the plus sign.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: A correct small model or drawing can show the meaning of Using the plus sign.
Worked Example 3
Problem: Which tool could help with Using the plus sign?
- 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 the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 the plus sign?
- 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 the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using the plus sign 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 the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Using the plus sign can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Using the plus sign. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.4 Using the equals sign
Using the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
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 the equals sign mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Worked Example 2
Problem: Show one small example of Using the equals sign.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: A correct small model or drawing can show the meaning of Using the equals sign.
Worked Example 3
Problem: Which tool could help with Using the equals sign?
- 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 the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
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 the equals sign?
- 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 the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using the equals sign 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 the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using the equals sign can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Fill the box: 2 + □ = 5.
- Ask what must be added to the first number.
- Count on until you reach the total.
Very beginner explanation: The missing number keeps both sides equal.
Answer: 3
Worked Example 7
Problem: Fill the box: 4 + □ = 5.
- Ask what must be added to the first number.
- Count on until you reach the total.
Very beginner explanation: The missing number keeps both sides equal.
Answer: 1
Worked Example 8
Problem: Fill the box: 5 + □ = 7.
- Ask what must be added to the first number.
- Count on until you reach the total.
Very beginner explanation: The missing number keeps both sides equal.
Answer: 2
Worked Example 9
Problem: Fill the box: 6 + □ = 8.
- Ask what must be added to the first number.
- Count on until you reach the total.
Very beginner explanation: The missing number keeps both sides equal.
Answer: 2
Worked Example 10
Problem: Fill the box: 7 + □ = 10.
- Ask what must be added to the first number.
- Count on until you reach the total.
Very beginner explanation: The missing number keeps both sides equal.
Answer: 3
Practice Exercise
Create one small question about Using the equals sign. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.5 Writing addition sentences
Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Writing addition sentences mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Worked Example 2
Problem: Show one small example of Writing addition sentences.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: A correct small model or drawing can show the meaning of Writing addition sentences.
Worked Example 3
Problem: Which tool could help with Writing addition sentences?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Writing addition sentences?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Writing addition sentences in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Writing addition sentences can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Writing addition sentences. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.6 Adding with counters
Adding with 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 Adding with counters mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Adding with counters helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Adding with 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 Adding with counters.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Adding with 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 Adding with counters.
Worked Example 3
Problem: Which tool could help with Adding with 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: Adding with 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 Adding with 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: Adding with 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 Adding with 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: Adding with counters helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Adding with 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 Adding with counters. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.7 Adding with drawings
Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Adding with drawings mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Worked Example 2
Problem: Show one small example of Adding with drawings.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: A correct small model or drawing can show the meaning of Adding with drawings.
Worked Example 3
Problem: Which tool could help with Adding with 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: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Adding with 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: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Adding with 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: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Adding with drawings can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Adding with drawings. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.8 Adding by counting on
Adding by counting on 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 Adding by counting on mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Adding by counting on helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Adding by counting on 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 Adding by counting on.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Adding by counting on 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 Adding by counting on.
Worked Example 3
Problem: Which tool could help with Adding by counting on?
- 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: Adding by counting on 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 Adding by counting on?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Adding by counting on 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 Adding by counting on 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: Adding by counting on helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Adding by counting on 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 Adding by counting on. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.9 Addition stories
Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Addition stories mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Worked Example 2
Problem: Show one small example of Addition stories.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: A correct small model or drawing can show the meaning of Addition stories.
Worked Example 3
Problem: Which tool could help with Addition stories?
- 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: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Addition stories?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Addition stories 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: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Addition stories can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Addition stories. Show it with objects, a picture, or numbers, then check by counting or comparing again.
18.10 Checking an addition model
Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Checking an addition model mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Worked Example 2
Problem: Show one small example of Checking an addition model.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: A correct small model or drawing can show the meaning of Checking an addition model.
Worked Example 3
Problem: Which tool could help with Checking an addition model?
- 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: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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 Checking an addition model?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Checking an addition model 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: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Answer: Checking an addition model can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Find 2 + 3.
- Make a group of 2.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 7
Problem: Find 4 + 1.
- Make a group of 4.
- Add 1 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 5
Worked Example 8
Problem: Find 5 + 2.
- Make a group of 5.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 7
Worked Example 9
Problem: Find 6 + 3.
- Make a group of 6.
- Add 3 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 9
Worked Example 10
Problem: Find 8 + 2.
- Make a group of 8.
- Add 2 more.
- Count all the objects.
Very beginner explanation: Addition puts quantities together.
Answer: 10
Practice Exercise
Create one small question about Checking an addition model. 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 Addition means putting together.
- Create and solve one original problem about Joining two groups.
- Create and solve one original problem about Using the plus sign.
- Create and solve one original problem about Using the equals sign.
- Create and solve one original problem about Writing addition sentences.
- Create and solve one original problem about Adding with counters.
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 Addition means putting together?
Answer: Addition means putting together teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Q2. What is the main idea in Joining two groups?
Answer: Joining two groups 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 the plus sign?
Answer: Using the plus sign teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Q4. What is the main idea in Using the equals sign?
Answer: Using the equals sign builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q5. What is the main idea in Writing addition sentences?
Answer: Writing addition sentences teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Q6. What is the main idea in Adding with counters?
Answer: Adding with counters helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q7. What is the main idea in Adding with drawings?
Answer: Adding with drawings teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Q8. What is the main idea in Adding by counting on?
Answer: Adding by counting on helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q9. What is the main idea in Addition stories?
Answer: Addition stories teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
Q10. What is the main idea in Checking an addition model?
Answer: Checking an addition model teaches how to put quantities together. Learners use objects, drawings, ten frames, and counting-on strategies before writing number sentences.
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.