Chapter 12: Comparing Quantities
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Comparing Quantities with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- More and fewer (a Grade 1 idea used in this chapter)
- Same amount (a Grade 1 idea used in this chapter)
- Comparing two sets (a Grade 1 idea used in this chapter)
- Comparing by matching objects (a Grade 1 idea used in this chapter)
- Comparing by counting (a Grade 1 idea used in this chapter)
- Using more than language (a Grade 1 idea used in this chapter)
- Using less than language (a Grade 1 idea used in this chapter)
- Using equal to language (a Grade 1 idea used in this chapter)
- Comparing real-life quantities (a Grade 1 idea used in this chapter)
- Explaining a comparison (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.
12.1 More and fewer
More and fewer 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 More and fewer mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: More and fewer is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: More and fewer 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 More and fewer.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: More and fewer 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 More and fewer.
Worked Example 3
Problem: Which tool could help with More and fewer?
- 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: More and fewer 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 More and fewer?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: More and fewer 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 More and fewer 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: More and fewer is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: More and fewer can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show More and fewer 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 More and fewer best through concrete examples and clear words.
Answer: A correct simple example of More and fewer.
Worked Example 7
Problem: Show More and fewer 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 More and fewer best through concrete examples and clear words.
Answer: A correct simple example of More and fewer.
Worked Example 8
Problem: Show More and fewer 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 More and fewer best through concrete examples and clear words.
Answer: A correct simple example of More and fewer.
Worked Example 9
Problem: Show More and fewer 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 More and fewer best through concrete examples and clear words.
Answer: A correct simple example of More and fewer.
Worked Example 10
Problem: Show More and fewer 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 More and fewer best through concrete examples and clear words.
Answer: A correct simple example of More and fewer.
Practice Exercise
Create one small question about More and fewer. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.2 Same amount
Same amount 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 amount mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Same amount is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Same amount 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 amount.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Same amount 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 amount.
Worked Example 3
Problem: Which tool could help with 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: Same amount 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 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: Same amount 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 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: Same amount is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Same amount can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Same amount 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 amount best through concrete examples and clear words.
Answer: A correct simple example of Same amount.
Worked Example 7
Problem: Show Same amount 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 amount best through concrete examples and clear words.
Answer: A correct simple example of Same amount.
Worked Example 8
Problem: Show Same amount 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 amount best through concrete examples and clear words.
Answer: A correct simple example of Same amount.
Worked Example 9
Problem: Show Same amount 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 amount best through concrete examples and clear words.
Answer: A correct simple example of Same amount.
Worked Example 10
Problem: Show Same amount 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 amount best through concrete examples and clear words.
Answer: A correct simple example of Same amount.
Practice Exercise
Create one small question about Same amount. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.3 Comparing two sets
Comparing two sets 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 two sets mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing two sets is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing two sets 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 two sets.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing two sets 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 two sets.
Worked Example 3
Problem: Which tool could help with Comparing two sets?
- 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 two sets 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 two sets?
- 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 two sets 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 two sets 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 two sets is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing two sets can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing two sets 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 two sets best through concrete examples and clear words.
Answer: A correct simple example of Comparing two sets.
Worked Example 7
Problem: Show Comparing two sets 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 two sets best through concrete examples and clear words.
Answer: A correct simple example of Comparing two sets.
Worked Example 8
Problem: Show Comparing two sets 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 two sets best through concrete examples and clear words.
Answer: A correct simple example of Comparing two sets.
Worked Example 9
Problem: Show Comparing two sets 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 two sets best through concrete examples and clear words.
Answer: A correct simple example of Comparing two sets.
Worked Example 10
Problem: Show Comparing two sets 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 two sets best through concrete examples and clear words.
Answer: A correct simple example of Comparing two sets.
Practice Exercise
Create one small question about Comparing two sets. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.4 Comparing by matching objects
Comparing by matching objects 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 by matching objects mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing by matching objects is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing by matching objects 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 by matching objects.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing by matching objects 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 by matching objects.
Worked Example 3
Problem: Which tool could help with Comparing by matching objects?
- 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 by matching objects 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 by matching objects?
- 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 by matching objects 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 by matching objects 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 by matching objects is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing by matching objects can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing by matching objects 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 by matching objects best through concrete examples and clear words.
Answer: A correct simple example of Comparing by matching objects.
Worked Example 7
Problem: Show Comparing by matching objects 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 by matching objects best through concrete examples and clear words.
Answer: A correct simple example of Comparing by matching objects.
Worked Example 8
Problem: Show Comparing by matching objects 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 by matching objects best through concrete examples and clear words.
Answer: A correct simple example of Comparing by matching objects.
Worked Example 9
Problem: Show Comparing by matching objects 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 by matching objects best through concrete examples and clear words.
Answer: A correct simple example of Comparing by matching objects.
Worked Example 10
Problem: Show Comparing by matching objects 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 by matching objects best through concrete examples and clear words.
Answer: A correct simple example of Comparing by matching objects.
Practice Exercise
Create one small question about Comparing by matching objects. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.5 Comparing by counting
Comparing by counting 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 Comparing by counting mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing by counting helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Comparing by counting 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 Comparing by counting.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing by counting 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 Comparing by counting.
Worked Example 3
Problem: Which tool could help with Comparing by counting?
- 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 by counting 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 Comparing by counting?
- 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 by counting 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 Comparing by counting 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 by counting helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Comparing by counting 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 Comparing by counting. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.6 Using more than language
Using more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Using more than 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 more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Worked Example 2
Problem: Show one small example of Using more than language.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: A correct small model or drawing can show the meaning of Using more than language.
Worked Example 3
Problem: Which tool could help with Using more than 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 more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Using more than 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 more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using more than 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 more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using more than language can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using more than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using more than language best through concrete examples and clear words.
Answer: A correct simple example of Using more than language.
Worked Example 7
Problem: Show Using more than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using more than language best through concrete examples and clear words.
Answer: A correct simple example of Using more than language.
Worked Example 8
Problem: Show Using more than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using more than language best through concrete examples and clear words.
Answer: A correct simple example of Using more than language.
Worked Example 9
Problem: Show Using more than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using more than language best through concrete examples and clear words.
Answer: A correct simple example of Using more than language.
Worked Example 10
Problem: Show Using more than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using more than language best through concrete examples and clear words.
Answer: A correct simple example of Using more than language.
Practice Exercise
Create one small question about Using more than language. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.7 Using less than language
Using less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Using less than 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 less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Worked Example 2
Problem: Show one small example of Using less than language.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: A correct small model or drawing can show the meaning of Using less than language.
Worked Example 3
Problem: Which tool could help with Using less than 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 less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Using less than 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 less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using less than 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 less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Using less than language can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using less than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using less than language best through concrete examples and clear words.
Answer: A correct simple example of Using less than language.
Worked Example 7
Problem: Show Using less than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using less than language best through concrete examples and clear words.
Answer: A correct simple example of Using less than language.
Worked Example 8
Problem: Show Using less than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using less than language best through concrete examples and clear words.
Answer: A correct simple example of Using less than language.
Worked Example 9
Problem: Show Using less than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using less than language best through concrete examples and clear words.
Answer: A correct simple example of Using less than language.
Worked Example 10
Problem: Show Using less than language with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using less than language best through concrete examples and clear words.
Answer: A correct simple example of Using less than language.
Practice Exercise
Create one small question about Using less than language. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.8 Using equal to language
Using equal to language 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 equal to 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 equal to language builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using equal to language 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 equal to language.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using equal to language 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 equal to language.
Worked Example 3
Problem: Which tool could help with Using equal to 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 equal to language 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 equal to 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 equal to language 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 equal to 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 equal to language builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Answer: Using equal to language 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 equal to language. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.9 Comparing real-life quantities
Comparing real-life quantities 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 real-life quantities mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing real-life quantities is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing real-life quantities 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 real-life quantities.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing real-life quantities 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 real-life quantities.
Worked Example 3
Problem: Which tool could help with Comparing real-life quantities?
- 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 real-life quantities 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 real-life quantities?
- 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 real-life quantities 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 real-life quantities 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 real-life quantities is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing real-life quantities can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing real-life quantities 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 real-life quantities best through concrete examples and clear words.
Answer: A correct simple example of Comparing real-life quantities.
Worked Example 7
Problem: Show Comparing real-life quantities 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 real-life quantities best through concrete examples and clear words.
Answer: A correct simple example of Comparing real-life quantities.
Worked Example 8
Problem: Show Comparing real-life quantities 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 real-life quantities best through concrete examples and clear words.
Answer: A correct simple example of Comparing real-life quantities.
Worked Example 9
Problem: Show Comparing real-life quantities 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 real-life quantities best through concrete examples and clear words.
Answer: A correct simple example of Comparing real-life quantities.
Worked Example 10
Problem: Show Comparing real-life quantities 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 real-life quantities best through concrete examples and clear words.
Answer: A correct simple example of Comparing real-life quantities.
Practice Exercise
Create one small question about Comparing real-life quantities. Show it with objects, a picture, or numbers, then check by counting or comparing again.
12.10 Explaining a comparison
Explaining a comparison 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 Explaining a comparison mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Explaining a comparison is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Explaining a comparison 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 Explaining a comparison.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Explaining a comparison 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 Explaining a comparison.
Worked Example 3
Problem: Which tool could help with Explaining a comparison?
- 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: Explaining a comparison 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 Explaining a comparison?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Explaining a comparison 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 Explaining a comparison 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: Explaining a comparison is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Explaining a comparison can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Explaining a comparison 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 Explaining a comparison best through concrete examples and clear words.
Answer: A correct simple example of Explaining a comparison.
Worked Example 7
Problem: Show Explaining a comparison 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 Explaining a comparison best through concrete examples and clear words.
Answer: A correct simple example of Explaining a comparison.
Worked Example 8
Problem: Show Explaining a comparison 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 Explaining a comparison best through concrete examples and clear words.
Answer: A correct simple example of Explaining a comparison.
Worked Example 9
Problem: Show Explaining a comparison 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 Explaining a comparison best through concrete examples and clear words.
Answer: A correct simple example of Explaining a comparison.
Worked Example 10
Problem: Show Explaining a comparison 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 Explaining a comparison best through concrete examples and clear words.
Answer: A correct simple example of Explaining a comparison.
Practice Exercise
Create one small question about Explaining a comparison. 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 More and fewer.
- Create and solve one original problem about Same amount.
- Create and solve one original problem about Comparing two sets.
- Create and solve one original problem about Comparing by matching objects.
- Create and solve one original problem about Comparing by counting.
- Create and solve one original problem about Using more than language.
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 More and fewer?
Answer: More and fewer 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 Same amount?
Answer: Same amount 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 Comparing two sets?
Answer: Comparing two sets is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q4. What is the main idea in Comparing by matching objects?
Answer: Comparing by matching objects is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q5. What is the main idea in Comparing by counting?
Answer: Comparing by counting helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q6. What is the main idea in Using more than language?
Answer: Using more than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q7. What is the main idea in Using less than language?
Answer: Using less than language is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q8. What is the main idea in Using equal to language?
Answer: Using equal to language builds early algebra thinking by showing that both sides of the equals sign must have the same value.
Q9. What is the main idea in Comparing real-life quantities?
Answer: Comparing real-life quantities is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q10. What is the main idea in Explaining a comparison?
Answer: Explaining a comparison is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
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.