Chapter 35: Equality and the Equals Sign
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Equality and the Equals Sign with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Equals means the same amount (a Grade 1 idea used in this chapter)
- Balancing two sides (a Grade 1 idea used in this chapter)
- True number sentences (a Grade 1 idea used in this chapter)
- False number sentences (a Grade 1 idea used in this chapter)
- Same total in different ways (a Grade 1 idea used in this chapter)
- Using objects to show equality (a Grade 1 idea used in this chapter)
- Using drawings to show equality (a Grade 1 idea used in this chapter)
- Comparing both sides (a Grade 1 idea used in this chapter)
- Fixing an unequal sentence (a Grade 1 idea used in this chapter)
- Equality review (a Grade 1 idea used in this chapter)
How to Learn This Chapter
Read or listen to the explanation, use objects or pictures when helpful, follow one step at a time, and try the example again before checking the answer.
35.1 Equals means the same amount
Equals means the same amount 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 Equals means the same amount mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Equals means the same amount builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Equals means the same amount 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 Equals means the same amount.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Equals means the same amount 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 Equals means the same amount.
Worked Example 3
Problem: Which tool could help with Equals means the same amount?
- 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: Equals means the same amount 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 Equals means the same amount?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Equals means the same amount 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 Equals means the same amount 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: Equals means the same amount builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Equals means the same amount 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 Equals means the same amount. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.2 Balancing two sides
Balancing two sides 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 Balancing two sides mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Balancing two sides is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Balancing two sides 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 Balancing two sides.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Balancing two sides 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 Balancing two sides.
Worked Example 3
Problem: Which tool could help with Balancing two sides?
- 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: Balancing two sides 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 Balancing two sides?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Balancing two sides 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 Balancing two sides 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: Balancing two sides is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Balancing two sides can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Balancing two sides 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 Balancing two sides best through concrete examples and clear words.
Answer: A correct simple example of Balancing two sides.
Worked Example 7
Problem: Show Balancing two sides 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 Balancing two sides best through concrete examples and clear words.
Answer: A correct simple example of Balancing two sides.
Worked Example 8
Problem: Show Balancing two sides 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 Balancing two sides best through concrete examples and clear words.
Answer: A correct simple example of Balancing two sides.
Worked Example 9
Problem: Show Balancing two sides 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 Balancing two sides best through concrete examples and clear words.
Answer: A correct simple example of Balancing two sides.
Worked Example 10
Problem: Show Balancing two sides 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 Balancing two sides best through concrete examples and clear words.
Answer: A correct simple example of Balancing two sides.
Practice Exercise
Create one small question about Balancing two sides. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.3 True number sentences
True number sentences 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 True number sentences mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: True number sentences helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: True number sentences 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 True number sentences.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: True number sentences 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 True number sentences.
Worked Example 3
Problem: Which tool could help with True number 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: True number sentences 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 True number 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: True number sentences 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 True number 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: True number sentences helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: True number sentences 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 True number sentences. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.4 False number sentences
False number sentences 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 False number sentences mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: False number sentences helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: False number sentences 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 False number sentences.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: False number sentences 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 False number sentences.
Worked Example 3
Problem: Which tool could help with False number 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: False number sentences 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 False number 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: False number sentences 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 False number 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: False number sentences helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: False number sentences 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 False number sentences. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.5 Same total in different ways
Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Same total in different ways mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Worked Example 2
Problem: Show one small example of Same total in different ways.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: A correct small model or drawing can show the meaning of Same total in different ways.
Worked Example 3
Problem: Which tool could help with Same total in different ways?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Same total in different ways?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Same total in different ways in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Same total in different ways is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Same total in different ways can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Same total in different ways with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Same total in different ways best through concrete examples and clear words.
Answer: A correct simple example of Same total in different ways.
Worked Example 7
Problem: Show Same total in different ways with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Same total in different ways best through concrete examples and clear words.
Answer: A correct simple example of Same total in different ways.
Worked Example 8
Problem: Show Same total in different ways with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Same total in different ways best through concrete examples and clear words.
Answer: A correct simple example of Same total in different ways.
Worked Example 9
Problem: Show Same total in different ways with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Same total in different ways best through concrete examples and clear words.
Answer: A correct simple example of Same total in different ways.
Worked Example 10
Problem: Show Same total in different ways with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Same total in different ways best through concrete examples and clear words.
Answer: A correct simple example of Same total in different ways.
Practice Exercise
Create one small question about Same total in different ways. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.6 Using objects to show equality
Using objects to show equality 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 objects to show equality mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using objects to show equality builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using objects to show equality 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 objects to show equality.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using objects to show equality 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 objects to show equality.
Worked Example 3
Problem: Which tool could help with Using objects to show equality?
- 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 objects to show equality 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 objects to show equality?
- 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 objects to show equality 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 objects to show equality 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 objects to show equality builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using objects to show equality 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 objects to show equality. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.7 Using drawings to show equality
Using drawings to show equality 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 drawings to show equality mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using drawings to show equality builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using drawings to show equality 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 drawings to show equality.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using drawings to show equality 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 drawings to show equality.
Worked Example 3
Problem: Which tool could help with Using drawings to show equality?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Using drawings to show equality 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 drawings to show equality?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Using drawings to show equality 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 drawings to show equality in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Using drawings to show equality builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using drawings to show equality 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 drawings to show equality. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.8 Comparing both sides
Comparing both sides 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 Comparing both sides mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing both sides is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing both sides 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 Comparing both sides.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing both sides 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 Comparing both sides.
Worked Example 3
Problem: Which tool could help with Comparing both sides?
- 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: Comparing both sides 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 Comparing both sides?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Comparing both sides 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 Comparing both sides 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: Comparing both sides is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing both sides can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing both sides 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 Comparing both sides best through concrete examples and clear words.
Answer: A correct simple example of Comparing both sides.
Worked Example 7
Problem: Show Comparing both sides 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 Comparing both sides best through concrete examples and clear words.
Answer: A correct simple example of Comparing both sides.
Worked Example 8
Problem: Show Comparing both sides 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 Comparing both sides best through concrete examples and clear words.
Answer: A correct simple example of Comparing both sides.
Worked Example 9
Problem: Show Comparing both sides 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 Comparing both sides best through concrete examples and clear words.
Answer: A correct simple example of Comparing both sides.
Worked Example 10
Problem: Show Comparing both sides 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 Comparing both sides best through concrete examples and clear words.
Answer: A correct simple example of Comparing both sides.
Practice Exercise
Create one small question about Comparing both sides. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.9 Fixing an unequal sentence
Fixing an unequal sentence 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 Fixing an unequal sentence mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Fixing an unequal sentence builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Fixing an unequal sentence 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 Fixing an unequal sentence.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Fixing an unequal sentence 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 Fixing an unequal sentence.
Worked Example 3
Problem: Which tool could help with Fixing an unequal sentence?
- 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: Fixing an unequal sentence 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 Fixing an unequal sentence?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Fixing an unequal sentence 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 Fixing an unequal sentence 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: Fixing an unequal sentence builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Fixing an unequal sentence 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 Fixing an unequal sentence. Show it with objects, a picture, or numbers, then check by counting or comparing again.
35.10 Equality review
Equality review 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 Equality review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Equality review builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Equality review 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 Equality review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Equality review 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 Equality review.
Worked Example 3
Problem: Which tool could help with Equality review?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Equality review 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 Equality review?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Equality review 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 Equality review in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Equality review builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Equality review 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 Equality review. Show it with objects, a picture, or numbers, then check by counting or comparing again.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read or listen to the question before solving.
- Use objects, a drawing, ten frame, number line, table, graph, or simple number sentence when useful.
- Explain your thinking and check by counting, comparing, or using another simple model.
Extra Practice
- Create and solve one original problem about Equals means the same amount.
- Create and solve one original problem about Balancing two sides.
- Create and solve one original problem about True number sentences.
- Create and solve one original problem about False number sentences.
- Create and solve one original problem about Same total in different ways.
- Create and solve one original problem about Using objects to show equality.
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 Equals means the same amount?
Answer: Equals means the same amount builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q2. What is the main idea in Balancing two sides?
Answer: Balancing two sides 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 True number sentences?
Answer: True number sentences helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q4. What is the main idea in False number sentences?
Answer: False number sentences helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q5. What is the main idea in Same total in different ways?
Answer: Same total in different ways 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 objects to show equality?
Answer: Using objects to show equality builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q7. What is the main idea in Using drawings to show equality?
Answer: Using drawings to show equality builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q8. What is the main idea in Comparing both sides?
Answer: Comparing both sides is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q9. What is the main idea in Fixing an unequal sentence?
Answer: Fixing an unequal sentence builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q10. What is the main idea in Equality review?
Answer: Equality review builds early algebra thinking by showing that both sides of the equals sign must have the same value.
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.