Chapter 45: Picture Graphs
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Picture Graphs with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- What is a picture graph (a Grade 1 idea used in this chapter)
- One picture means one item (a Grade 1 idea used in this chapter)
- Making a picture graph (a Grade 1 idea used in this chapter)
- Reading a picture graph (a Grade 1 idea used in this chapter)
- Finding the most (a Grade 1 idea used in this chapter)
- Finding the least (a Grade 1 idea used in this chapter)
- Finding how many altogether (a Grade 1 idea used in this chapter)
- Comparing two categories (a Grade 1 idea used in this chapter)
- Answering questions from a picture graph (a Grade 1 idea used in this chapter)
- Picture-graph 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.
45.1 What is a picture graph
What is a picture graph 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 What is a picture graph mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: What is a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: What is a picture graph 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 What is a picture graph.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: What is a picture graph 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 What is a picture graph.
Worked Example 3
Problem: Which tool could help with What is a picture graph?
- 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: What is a picture graph 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 What is a picture graph?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: What is a picture graph 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 What is a picture graph 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: What is a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: What is a picture graph 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 What is a picture graph. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.2 One picture means one item
One picture means one item 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 One picture means one item mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: One picture means one item is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: One picture means one item 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 One picture means one item.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: One picture means one item 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 One picture means one item.
Worked Example 3
Problem: Which tool could help with One picture means one item?
- 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: One picture means one item 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 One picture means one item?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: One picture means one item 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 One picture means one item 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: One picture means one item is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: One picture means one item can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show One picture means one item 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 One picture means one item best through concrete examples and clear words.
Answer: A correct simple example of One picture means one item.
Worked Example 7
Problem: Show One picture means one item 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 One picture means one item best through concrete examples and clear words.
Answer: A correct simple example of One picture means one item.
Worked Example 8
Problem: Show One picture means one item 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 One picture means one item best through concrete examples and clear words.
Answer: A correct simple example of One picture means one item.
Worked Example 9
Problem: Show One picture means one item 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 One picture means one item best through concrete examples and clear words.
Answer: A correct simple example of One picture means one item.
Worked Example 10
Problem: Show One picture means one item 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 One picture means one item best through concrete examples and clear words.
Answer: A correct simple example of One picture means one item.
Practice Exercise
Create one small question about One picture means one item. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.3 Making a picture graph
Making a picture graph 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 Making a picture graph mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Making a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Making a picture graph 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 Making a picture graph.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Making a picture graph 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 Making a picture graph.
Worked Example 3
Problem: Which tool could help with Making a picture graph?
- 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 a picture graph 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 Making a picture graph?
- 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 a picture graph 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 Making a picture graph 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 a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Making a picture graph 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 Making a picture graph. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.4 Reading a picture graph
Reading a picture graph 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 Reading a picture graph mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Reading a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Reading a picture graph 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 Reading a picture graph.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Reading a picture graph 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 Reading a picture graph.
Worked Example 3
Problem: Which tool could help with Reading a picture graph?
- 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: Reading a picture graph 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 Reading a picture graph?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Reading a picture graph 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 Reading a picture graph 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: Reading a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Reading a picture graph 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 Reading a picture graph. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.5 Finding the most
Finding the most 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 Finding the most mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding the most is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding the most 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 Finding the most.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding the most 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 Finding the most.
Worked Example 3
Problem: Which tool could help with Finding the most?
- 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: Finding the most 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 Finding the most?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Finding the most 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 Finding the most 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: Finding the most is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding the most can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Finding the most 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 Finding the most best through concrete examples and clear words.
Answer: A correct simple example of Finding the most.
Worked Example 7
Problem: Show Finding the most 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 Finding the most best through concrete examples and clear words.
Answer: A correct simple example of Finding the most.
Worked Example 8
Problem: Show Finding the most 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 Finding the most best through concrete examples and clear words.
Answer: A correct simple example of Finding the most.
Worked Example 9
Problem: Show Finding the most 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 Finding the most best through concrete examples and clear words.
Answer: A correct simple example of Finding the most.
Worked Example 10
Problem: Show Finding the most 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 Finding the most best through concrete examples and clear words.
Answer: A correct simple example of Finding the most.
Practice Exercise
Create one small question about Finding the most. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.6 Finding the least
Finding the least 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 Finding the least mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding the least is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding the least 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 Finding the least.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding the least 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 Finding the least.
Worked Example 3
Problem: Which tool could help with Finding the least?
- 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: Finding the least 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 Finding the least?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Finding the least 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 Finding the least 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: Finding the least is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding the least can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Finding the least 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 Finding the least best through concrete examples and clear words.
Answer: A correct simple example of Finding the least.
Worked Example 7
Problem: Show Finding the least 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 Finding the least best through concrete examples and clear words.
Answer: A correct simple example of Finding the least.
Worked Example 8
Problem: Show Finding the least 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 Finding the least best through concrete examples and clear words.
Answer: A correct simple example of Finding the least.
Worked Example 9
Problem: Show Finding the least 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 Finding the least best through concrete examples and clear words.
Answer: A correct simple example of Finding the least.
Worked Example 10
Problem: Show Finding the least 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 Finding the least best through concrete examples and clear words.
Answer: A correct simple example of Finding the least.
Practice Exercise
Create one small question about Finding the least. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.7 Finding how many altogether
Finding how many altogether 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 Finding how many altogether mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Finding how many altogether is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding how many altogether 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 Finding how many altogether.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Finding how many altogether 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 Finding how many altogether.
Worked Example 3
Problem: Which tool could help with Finding how many altogether?
- 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: Finding how many altogether 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 Finding how many altogether?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Finding how many altogether 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 Finding how many altogether 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: Finding how many altogether is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Finding how many altogether can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Finding how many altogether 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 Finding how many altogether best through concrete examples and clear words.
Answer: A correct simple example of Finding how many altogether.
Worked Example 7
Problem: Show Finding how many altogether 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 Finding how many altogether best through concrete examples and clear words.
Answer: A correct simple example of Finding how many altogether.
Worked Example 8
Problem: Show Finding how many altogether 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 Finding how many altogether best through concrete examples and clear words.
Answer: A correct simple example of Finding how many altogether.
Worked Example 9
Problem: Show Finding how many altogether 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 Finding how many altogether best through concrete examples and clear words.
Answer: A correct simple example of Finding how many altogether.
Worked Example 10
Problem: Show Finding how many altogether 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 Finding how many altogether best through concrete examples and clear words.
Answer: A correct simple example of Finding how many altogether.
Practice Exercise
Create one small question about Finding how many altogether. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.8 Comparing two categories
Comparing two 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 two 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 two categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing two 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 two categories.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing two 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 two categories.
Worked Example 3
Problem: Which tool could help with Comparing two 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 two 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 two 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 two 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 two 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 two categories is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing two categories can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing two 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 two categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing two categories.
Worked Example 7
Problem: Show Comparing two 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 two categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing two categories.
Worked Example 8
Problem: Show Comparing two 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 two categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing two categories.
Worked Example 9
Problem: Show Comparing two 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 two categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing two categories.
Worked Example 10
Problem: Show Comparing two 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 two categories best through concrete examples and clear words.
Answer: A correct simple example of Comparing two categories.
Practice Exercise
Create one small question about Comparing two categories. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.9 Answering questions from a picture graph
Answering questions from a picture graph 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 Answering questions from a picture graph mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Answering questions from a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Answering questions from a picture graph 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 Answering questions from a picture graph.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Answering questions from a picture graph 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 Answering questions from a picture graph.
Worked Example 3
Problem: Which tool could help with Answering questions from a picture graph?
- 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: Answering questions from a picture graph 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 Answering questions from a picture graph?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Answering questions from a picture graph 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 Answering questions from a picture graph 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: Answering questions from a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Answering questions from a picture graph 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 Answering questions from a picture graph. Show it with objects, a picture, or numbers, then check by counting or comparing again.
45.10 Picture-graph review
Picture-graph 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 Picture-graph review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Picture-graph review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Picture-graph 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 Picture-graph review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Picture-graph 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 Picture-graph review.
Worked Example 3
Problem: Which tool could help with Picture-graph 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: Picture-graph 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 Picture-graph 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: Picture-graph 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 Picture-graph 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: Picture-graph review helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Answer: Picture-graph 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 Picture-graph 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 What is a picture graph.
- Create and solve one original problem about One picture means one item.
- Create and solve one original problem about Making a picture graph.
- Create and solve one original problem about Reading a picture graph.
- Create and solve one original problem about Finding the most.
- Create and solve one original problem about Finding the least.
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 What is a picture graph?
Answer: What is a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q2. What is the main idea in One picture means one item?
Answer: One picture means one item 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 Making a picture graph?
Answer: Making a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q4. What is the main idea in Reading a picture graph?
Answer: Reading a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q5. What is the main idea in Finding the most?
Answer: Finding the most 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 Finding the least?
Answer: Finding the least 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 Finding how many altogether?
Answer: Finding how many altogether 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 Comparing two categories?
Answer: Comparing two 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 Answering questions from a picture graph?
Answer: Answering questions from a picture graph helps learners collect, sort, show, and talk about information so they can answer simple questions with evidence.
Q10. What is the main idea in Picture-graph review?
Answer: Picture-graph 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.