Chapter 42: Sorting and Classifying Data
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Sorting and Classifying Data with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Sorting by one attribute (a Grade 1 idea used in this chapter)
- Sorting by colour (a Grade 1 idea used in this chapter)
- Sorting by shape (a Grade 1 idea used in this chapter)
- Sorting by size (a Grade 1 idea used in this chapter)
- Making categories (a Grade 1 idea used in this chapter)
- Putting each item in a category (a Grade 1 idea used in this chapter)
- Counting each category (a Grade 1 idea used in this chapter)
- Comparing categories (a Grade 1 idea used in this chapter)
- Explaining a sorting rule (a Grade 1 idea used in this chapter)
- Sorting-data 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.
42.1 Sorting by one attribute
Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by one attribute mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Sorting by one attribute.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Sorting by one attribute.
Worked Example 3
Problem: Which tool could help with Sorting by one attribute?
- 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: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by one attribute?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Sorting by one attribute 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: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by one attribute can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Sorting by one attribute. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.2 Sorting by colour
Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by colour mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Sorting by colour.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Sorting by colour.
Worked Example 3
Problem: Which tool could help with Sorting by colour?
- 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: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by colour?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Sorting by colour 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: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by colour can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Sorting by colour. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.3 Sorting by shape
Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by shape mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Sorting by shape.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Sorting by shape.
Worked Example 3
Problem: Which tool could help with Sorting by shape?
- 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: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by shape?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Sorting by shape 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: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by shape can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Sorting by shape. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.4 Sorting by size
Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by size mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Sorting by size.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Sorting by size.
Worked Example 3
Problem: Which tool could help with Sorting by size?
- 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: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting by size?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Sorting by size 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: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting by size can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Sorting by size. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.5 Making categories
Making categories 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 Making categories mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Making categories 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 Making categories.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making categories 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 Making categories.
Worked Example 3
Problem: Which tool could help with Making categories?
- 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 categories 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 Making categories?
- 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 categories 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 Making categories 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 categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Making categories can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Making categories 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 Making categories best through concrete examples and clear words.
Answer: A correct simple example of Making categories.
Worked Example 7
Problem: Show Making categories 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 Making categories best through concrete examples and clear words.
Answer: A correct simple example of Making categories.
Worked Example 8
Problem: Show Making categories 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 Making categories best through concrete examples and clear words.
Answer: A correct simple example of Making categories.
Worked Example 9
Problem: Show Making categories 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 Making categories best through concrete examples and clear words.
Answer: A correct simple example of Making categories.
Worked Example 10
Problem: Show Making categories 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 Making categories best through concrete examples and clear words.
Answer: A correct simple example of Making categories.
Practice Exercise
Create one small question about Making categories. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.6 Putting each item in a category
Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Putting each item in a category mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Putting each item in a category.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Putting each item in a category.
Worked Example 3
Problem: Which tool could help with Putting each item in a category?
- 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: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Putting each item in a category?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Putting each item in a category 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: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Putting each item in a category can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Putting each item in a category. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.7 Counting each category
Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Counting each category mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Worked Example 2
Problem: Show one small example of Counting each category.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: A correct small model or drawing can show the meaning of Counting each category.
Worked Example 3
Problem: Which tool could help with Counting each category?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Counting each category?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Counting each category in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Answer: Counting each category can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Count to 6. What number comes just before 6?
- Count forward until 6.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 5
Worked Example 7
Problem: Count to 12. What number comes just before 12?
- Count forward until 12.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 11
Worked Example 8
Problem: Count to 19. What number comes just before 19?
- Count forward until 19.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 18
Worked Example 9
Problem: Count to 27. What number comes just before 27?
- Count forward until 27.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 26
Worked Example 10
Problem: Count to 44. What number comes just before 44?
- Count forward until 44.
- Move back one number.
Very beginner explanation: The number before is one less.
Answer: 43
Practice Exercise
Create one small question about Counting each category. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.8 Comparing categories
Comparing categories 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 categories mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing categories 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 categories.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing categories 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 categories.
Worked Example 3
Problem: Which tool could help with Comparing categories?
- 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 categories 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 categories?
- 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 categories 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 categories 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 categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing categories can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing categories 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 categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing categories.
Worked Example 7
Problem: Show Comparing categories 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 categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing categories.
Worked Example 8
Problem: Show Comparing categories 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 categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing categories.
Worked Example 9
Problem: Show Comparing categories 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 categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing categories.
Worked Example 10
Problem: Show Comparing categories 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 categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing categories.
Practice Exercise
Create one small question about Comparing categories. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.9 Explaining a sorting rule
Explaining a sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 sorting rule 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 sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Explaining a sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Explaining a sorting rule.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Explaining a sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Explaining a sorting rule.
Worked Example 3
Problem: Which tool could help with Explaining a sorting rule?
- 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 sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 sorting rule?
- 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 sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Explaining a sorting rule 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 sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Explaining a sorting rule can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Explaining a sorting rule. Show it with objects, a picture, or numbers, then check by counting or comparing again.
42.10 Sorting-data review
Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting-data review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Worked Example 2
Problem: Show one small example of Sorting-data review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: A correct small model or drawing can show the meaning of Sorting-data review.
Worked Example 3
Problem: Which tool could help with Sorting-data 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: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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 Sorting-data 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: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Sorting-data 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: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Sorting-data review can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: A simple data record shows cats: 3 and dogs: 5. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: dogs
Worked Example 7
Problem: A simple data record shows red: 4 and blue: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: red
Worked Example 8
Problem: A simple data record shows apples: 6 and bananas: 3. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: apples
Worked Example 9
Problem: A simple data record shows walk: 5 and bus: 4. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: walk
Worked Example 10
Problem: A simple data record shows books: 7 and games: 2. Which category has more?
- Read both category counts.
- Compare the two numbers.
Very beginner explanation: The category with the larger count has more responses.
Answer: books
Practice Exercise
Create one small question about Sorting-data 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 Sorting by one attribute.
- Create and solve one original problem about Sorting by colour.
- Create and solve one original problem about Sorting by shape.
- Create and solve one original problem about Sorting by size.
- Create and solve one original problem about Making categories.
- Create and solve one original problem about Putting each item in a category.
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 Sorting by one attribute?
Answer: Sorting by one attribute helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q2. What is the main idea in Sorting by colour?
Answer: Sorting by colour helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q3. What is the main idea in Sorting by shape?
Answer: Sorting by shape helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q4. What is the main idea in Sorting by size?
Answer: Sorting by size helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q5. What is the main idea in Making categories?
Answer: Making categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q6. What is the main idea in Putting each item in a category?
Answer: Putting each item in a category helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q7. What is the main idea in Counting each category?
Answer: Counting each category helps Grade 1 learners build strong number sense with small numbers, objects, drawings, and number lines.
Q8. What is the main idea in Comparing categories?
Answer: Comparing categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q9. What is the main idea in Explaining a sorting rule?
Answer: Explaining a sorting rule helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q10. What is the main idea in Sorting-data review?
Answer: Sorting-data review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
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.