Chapter 28: Equal Sharing and Fractions
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Equal Sharing and Fractions with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Sharing fairly (a Grade 1 idea used in this chapter)
- Making equal groups (a Grade 1 idea used in this chapter)
- Equal parts of a whole (a Grade 1 idea used in this chapter)
- Equal parts of a set (a Grade 1 idea used in this chapter)
- Fair shares between two people (a Grade 1 idea used in this chapter)
- Fair shares between four people (a Grade 1 idea used in this chapter)
- Recognizing unequal shares (a Grade 1 idea used in this chapter)
- Using fraction language (a Grade 1 idea used in this chapter)
- Fractions in everyday sharing (a Grade 1 idea used in this chapter)
- Equal-sharing 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.
28.1 Sharing fairly
Sharing fairly 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 Sharing fairly mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Sharing fairly is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Sharing fairly 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 Sharing fairly.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Sharing fairly 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 Sharing fairly.
Worked Example 3
Problem: Which tool could help with Sharing fairly?
- 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: Sharing fairly 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 Sharing fairly?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Sharing fairly 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 Sharing fairly 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: Sharing fairly is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Sharing fairly can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Sharing fairly 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 Sharing fairly best through concrete examples and clear words.
Answer: A correct simple example of Sharing fairly.
Worked Example 7
Problem: Show Sharing fairly 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 Sharing fairly best through concrete examples and clear words.
Answer: A correct simple example of Sharing fairly.
Worked Example 8
Problem: Show Sharing fairly 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 Sharing fairly best through concrete examples and clear words.
Answer: A correct simple example of Sharing fairly.
Worked Example 9
Problem: Show Sharing fairly 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 Sharing fairly best through concrete examples and clear words.
Answer: A correct simple example of Sharing fairly.
Worked Example 10
Problem: Show Sharing fairly 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 Sharing fairly best through concrete examples and clear words.
Answer: A correct simple example of Sharing fairly.
Practice Exercise
Create one small question about Sharing fairly. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.2 Making equal groups
Making equal groups 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 Making equal groups mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making equal groups builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Making equal groups 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 Making equal groups.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making equal groups 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 Making equal groups.
Worked Example 3
Problem: Which tool could help with Making equal 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: Making equal groups 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 Making equal 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: Making equal groups 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 Making equal 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: Making equal groups builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Making equal groups 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 Making equal groups. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.3 Equal parts of a whole
Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Equal parts of a whole mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Equal parts of a whole.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Equal parts of a whole.
Worked Example 3
Problem: Which tool could help with Equal parts of a whole?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Equal parts of a whole?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Equal parts of a whole in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Equal parts of a whole can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Equal parts of a whole. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.4 Equal parts of a set
Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Equal parts of a set mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Equal parts of a set.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Equal parts of a set.
Worked Example 3
Problem: Which tool could help with Equal parts of a set?
- 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: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Equal parts of a set?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Equal parts of a set 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: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Equal parts of a set can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Equal parts of a set. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.5 Fair shares between two people
Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Fair shares between two people mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Fair shares between two people.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Fair shares between two people.
Worked Example 3
Problem: Which tool could help with Fair shares between two people?
- 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: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Fair shares between two people?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Fair shares between two people 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: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Fair shares between two people can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Fair shares between two people. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.6 Fair shares between four people
Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Fair shares between four people mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Fair shares between four people.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Fair shares between four people.
Worked Example 3
Problem: Which tool could help with Fair shares between four people?
- 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: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Fair shares between four people?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Fair shares between four people 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: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Fair shares between four people can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Fair shares between four people. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.7 Recognizing unequal shares
Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Recognizing unequal shares mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Recognizing unequal shares.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Recognizing unequal shares.
Worked Example 3
Problem: Which tool could help with Recognizing unequal shares?
- 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: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Recognizing unequal shares?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Recognizing unequal shares 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: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Recognizing unequal shares can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Recognizing unequal shares. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.8 Using fraction language
Using fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 fraction language mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Using fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Using fraction language.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Using fraction language.
Worked Example 3
Problem: Which tool could help with Using fraction language?
- 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 fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 fraction language?
- 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 fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using fraction language 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 fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Using fraction language can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Using fraction language. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.9 Fractions in everyday sharing
Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Fractions in everyday sharing mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Worked Example 2
Problem: Show one small example of Fractions in everyday sharing.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: A correct small model or drawing can show the meaning of Fractions in everyday sharing.
Worked Example 3
Problem: Which tool could help with Fractions in everyday sharing?
- 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: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
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 Fractions in everyday sharing?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Fractions in everyday sharing 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: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Answer: Fractions in everyday sharing can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Share 6 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Worked Example 7
Problem: Share 8 counters equally among 2 groups. How many are in each group?
- Make 2 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 4
Worked Example 8
Problem: Share 4 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 1
Worked Example 9
Problem: Share 8 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 2
Worked Example 10
Problem: Share 12 counters equally among 4 groups. How many are in each group?
- Make 4 groups.
- Give one counter to each group again and again.
- Stop when all counters are shared.
Very beginner explanation: Equal sharing gives every group the same amount.
Answer: 3
Practice Exercise
Create one small question about Fractions in everyday sharing. Show it with objects, a picture, or numbers, then check by counting or comparing again.
28.10 Equal-sharing review
Equal-sharing 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 Equal-sharing review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Equal-sharing review builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Equal-sharing 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 Equal-sharing review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Equal-sharing 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 Equal-sharing review.
Worked Example 3
Problem: Which tool could help with Equal-sharing 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: Equal-sharing 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 Equal-sharing 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: Equal-sharing 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 Equal-sharing 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: Equal-sharing review builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Equal-sharing 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 Equal-sharing 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 Sharing fairly.
- Create and solve one original problem about Making equal groups.
- Create and solve one original problem about Equal parts of a whole.
- Create and solve one original problem about Equal parts of a set.
- Create and solve one original problem about Fair shares between two people.
- Create and solve one original problem about Fair shares between four people.
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 Sharing fairly?
Answer: Sharing fairly is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q2. What is the main idea in Making equal groups?
Answer: Making equal groups builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q3. What is the main idea in Equal parts of a whole?
Answer: Equal parts of a whole introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q4. What is the main idea in Equal parts of a set?
Answer: Equal parts of a set introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q5. What is the main idea in Fair shares between two people?
Answer: Fair shares between two people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q6. What is the main idea in Fair shares between four people?
Answer: Fair shares between four people introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q7. What is the main idea in Recognizing unequal shares?
Answer: Recognizing unequal shares introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q8. What is the main idea in Using fraction language?
Answer: Using fraction language introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q9. What is the main idea in Fractions in everyday sharing?
Answer: Fractions in everyday sharing introduces fractions through fair sharing and equal parts. Learners check that every share is the same size or has the same number of objects.
Q10. What is the main idea in Equal-sharing review?
Answer: Equal-sharing 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.