Chapter 40: Mathematical Modelling for Real Life
Learn Grade 1 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Mathematical Modelling for Real Life with simple language, step-by-step reasoning, and original worked examples. Math words are explained in simple Grade 1 language.
Key Technical Terms
- Understanding a real-life question (a Grade 1 idea used in this chapter)
- Choosing important information (a Grade 1 idea used in this chapter)
- Using objects to model a situation (a Grade 1 idea used in this chapter)
- Using drawings to model a situation (a Grade 1 idea used in this chapter)
- Trying one solution (a Grade 1 idea used in this chapter)
- Trying another solution (a Grade 1 idea used in this chapter)
- Comparing solutions (a Grade 1 idea used in this chapter)
- Choosing a reasonable solution (a Grade 1 idea used in this chapter)
- Explaining the solution (a Grade 1 idea used in this chapter)
- Modelling 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.
40.1 Understanding a real-life question
Understanding a real-life question 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 Understanding a real-life question mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Understanding a real-life question is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Understanding a real-life question 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 Understanding a real-life question.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Understanding a real-life question 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 Understanding a real-life question.
Worked Example 3
Problem: Which tool could help with Understanding a real-life question?
- 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: Understanding a real-life question 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 Understanding a real-life question?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Understanding a real-life question 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 Understanding a real-life question 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: Understanding a real-life question is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Understanding a real-life question can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Understanding a real-life question 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 Understanding a real-life question best through concrete examples and clear words.
Answer: A correct simple example of Understanding a real-life question.
Worked Example 7
Problem: Show Understanding a real-life question 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 Understanding a real-life question best through concrete examples and clear words.
Answer: A correct simple example of Understanding a real-life question.
Worked Example 8
Problem: Show Understanding a real-life question 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 Understanding a real-life question best through concrete examples and clear words.
Answer: A correct simple example of Understanding a real-life question.
Worked Example 9
Problem: Show Understanding a real-life question 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 Understanding a real-life question best through concrete examples and clear words.
Answer: A correct simple example of Understanding a real-life question.
Worked Example 10
Problem: Show Understanding a real-life question 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 Understanding a real-life question best through concrete examples and clear words.
Answer: A correct simple example of Understanding a real-life question.
Practice Exercise
Create one small question about Understanding a real-life question. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.2 Choosing important information
Choosing important information 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 Choosing important information mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Choosing important information is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Choosing important information 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 Choosing important information.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Choosing important information 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 Choosing important information.
Worked Example 3
Problem: Which tool could help with Choosing important information?
- 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: Choosing important information 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 Choosing important information?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Choosing important information 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 Choosing important information 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: Choosing important information is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Choosing important information can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Choosing important information 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 Choosing important information best through concrete examples and clear words.
Answer: A correct simple example of Choosing important information.
Worked Example 7
Problem: Show Choosing important information 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 Choosing important information best through concrete examples and clear words.
Answer: A correct simple example of Choosing important information.
Worked Example 8
Problem: Show Choosing important information 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 Choosing important information best through concrete examples and clear words.
Answer: A correct simple example of Choosing important information.
Worked Example 9
Problem: Show Choosing important information 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 Choosing important information best through concrete examples and clear words.
Answer: A correct simple example of Choosing important information.
Worked Example 10
Problem: Show Choosing important information 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 Choosing important information best through concrete examples and clear words.
Answer: A correct simple example of Choosing important information.
Practice Exercise
Create one small question about Choosing important information. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.3 Using objects to model a situation
Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Using objects to model a situation mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Worked Example 2
Problem: Show one small example of Using objects to model a situation.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: A correct small model or drawing can show the meaning of Using objects to model a situation.
Worked Example 3
Problem: Which tool could help with Using objects to model a situation?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Using objects to model a situation?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using objects to model a situation in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Using objects to model a situation can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using objects to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using objects to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using objects to model a situation.
Worked Example 7
Problem: Show Using objects to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using objects to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using objects to model a situation.
Worked Example 8
Problem: Show Using objects to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using objects to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using objects to model a situation.
Worked Example 9
Problem: Show Using objects to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using objects to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using objects to model a situation.
Worked Example 10
Problem: Show Using objects to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using objects to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using objects to model a situation.
Practice Exercise
Create one small question about Using objects to model a situation. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.4 Using drawings to model a situation
Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Using drawings to model a situation mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Worked Example 2
Problem: Show one small example of Using drawings to model a situation.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: A correct small model or drawing can show the meaning of Using drawings to model a situation.
Worked Example 3
Problem: Which tool could help with Using drawings to model a situation?
- Think about counters, fingers, a ten frame, number line, picture, table, or real object.
- Choose the tool that makes the idea easiest to see.
Very beginner explanation: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Using drawings to model a situation?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Using drawings to model a situation in everyday life?
- Think about toys, snacks, books, classroom objects, calendars, shapes, or money.
- Choose one situation.
- Explain how the math helps.
Very beginner explanation: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Using drawings to model a situation can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Using drawings to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using drawings to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using drawings to model a situation.
Worked Example 7
Problem: Show Using drawings to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using drawings to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using drawings to model a situation.
Worked Example 8
Problem: Show Using drawings to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using drawings to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using drawings to model a situation.
Worked Example 9
Problem: Show Using drawings to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using drawings to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using drawings to model a situation.
Worked Example 10
Problem: Show Using drawings to model a situation with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Using drawings to model a situation best through concrete examples and clear words.
Answer: A correct simple example of Using drawings to model a situation.
Practice Exercise
Create one small question about Using drawings to model a situation. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.5 Trying one solution
Trying one solution 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 Trying one solution mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Trying one solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Trying one solution 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 Trying one solution.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Trying one solution 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 Trying one solution.
Worked Example 3
Problem: Which tool could help with Trying one solution?
- 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: Trying one solution 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 Trying one solution?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Trying one solution 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 Trying one solution 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: Trying one solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Trying one solution can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Trying one solution 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 Trying one solution best through concrete examples and clear words.
Answer: A correct simple example of Trying one solution.
Worked Example 7
Problem: Show Trying one solution 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 Trying one solution best through concrete examples and clear words.
Answer: A correct simple example of Trying one solution.
Worked Example 8
Problem: Show Trying one solution 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 Trying one solution best through concrete examples and clear words.
Answer: A correct simple example of Trying one solution.
Worked Example 9
Problem: Show Trying one solution 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 Trying one solution best through concrete examples and clear words.
Answer: A correct simple example of Trying one solution.
Worked Example 10
Problem: Show Trying one solution 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 Trying one solution best through concrete examples and clear words.
Answer: A correct simple example of Trying one solution.
Practice Exercise
Create one small question about Trying one solution. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.6 Trying another solution
Trying another solution 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 Trying another solution mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Trying another solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Trying another solution 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 Trying another solution.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Trying another solution 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 Trying another solution.
Worked Example 3
Problem: Which tool could help with Trying another solution?
- 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: Trying another solution 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 Trying another solution?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Trying another solution 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 Trying another solution 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: Trying another solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Trying another solution can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Trying another solution 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 Trying another solution best through concrete examples and clear words.
Answer: A correct simple example of Trying another solution.
Worked Example 7
Problem: Show Trying another solution 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 Trying another solution best through concrete examples and clear words.
Answer: A correct simple example of Trying another solution.
Worked Example 8
Problem: Show Trying another solution 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 Trying another solution best through concrete examples and clear words.
Answer: A correct simple example of Trying another solution.
Worked Example 9
Problem: Show Trying another solution 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 Trying another solution best through concrete examples and clear words.
Answer: A correct simple example of Trying another solution.
Worked Example 10
Problem: Show Trying another solution 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 Trying another solution best through concrete examples and clear words.
Answer: A correct simple example of Trying another solution.
Practice Exercise
Create one small question about Trying another solution. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.7 Comparing solutions
Comparing solutions 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 solutions mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Comparing solutions is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing solutions 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 solutions.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Comparing solutions 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 solutions.
Worked Example 3
Problem: Which tool could help with Comparing solutions?
- 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 solutions 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 solutions?
- 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 solutions 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 solutions 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 solutions is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Comparing solutions can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Comparing solutions 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 solutions best through concrete examples and clear words.
Answer: A correct simple example of Comparing solutions.
Worked Example 7
Problem: Show Comparing solutions 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 solutions best through concrete examples and clear words.
Answer: A correct simple example of Comparing solutions.
Worked Example 8
Problem: Show Comparing solutions 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 solutions best through concrete examples and clear words.
Answer: A correct simple example of Comparing solutions.
Worked Example 9
Problem: Show Comparing solutions 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 solutions best through concrete examples and clear words.
Answer: A correct simple example of Comparing solutions.
Worked Example 10
Problem: Show Comparing solutions 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 solutions best through concrete examples and clear words.
Answer: A correct simple example of Comparing solutions.
Practice Exercise
Create one small question about Comparing solutions. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.8 Choosing a reasonable solution
Choosing a reasonable solution 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 Choosing a reasonable solution mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Choosing a reasonable solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Choosing a reasonable solution 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 Choosing a reasonable solution.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Choosing a reasonable solution 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 Choosing a reasonable solution.
Worked Example 3
Problem: Which tool could help with Choosing a reasonable solution?
- 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: Choosing a reasonable solution 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 Choosing a reasonable solution?
- Look at the objects, drawing, or numbers again.
- Count or compare one more time.
- Make sure the answer matches the question.
Very beginner explanation: Choosing a reasonable solution 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 Choosing a reasonable solution 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: Choosing a reasonable solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Choosing a reasonable solution can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Choosing a reasonable solution 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 Choosing a reasonable solution best through concrete examples and clear words.
Answer: A correct simple example of Choosing a reasonable solution.
Worked Example 7
Problem: Show Choosing a reasonable solution 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 Choosing a reasonable solution best through concrete examples and clear words.
Answer: A correct simple example of Choosing a reasonable solution.
Worked Example 8
Problem: Show Choosing a reasonable solution 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 Choosing a reasonable solution best through concrete examples and clear words.
Answer: A correct simple example of Choosing a reasonable solution.
Worked Example 9
Problem: Show Choosing a reasonable solution 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 Choosing a reasonable solution best through concrete examples and clear words.
Answer: A correct simple example of Choosing a reasonable solution.
Worked Example 10
Problem: Show Choosing a reasonable solution 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 Choosing a reasonable solution best through concrete examples and clear words.
Answer: A correct simple example of Choosing a reasonable solution.
Practice Exercise
Create one small question about Choosing a reasonable solution. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.9 Explaining the solution
Explaining the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Beginner Note
Start with real objects, fingers, or a picture. Say the idea aloud, try one small example, and check it by counting or comparing again.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: What does Explaining the solution mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Explaining the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Explaining the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Worked Example 2
Problem: Show one small example of Explaining the solution.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Explaining the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: A correct small model or drawing can show the meaning of Explaining the solution.
Worked Example 3
Problem: Which tool could help with Explaining the solution?
- 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 the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Use a simple tool that lets you see and check the quantities or shapes.
Worked Example 4
Problem: How can you check your work in Explaining the solution?
- 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 the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Explaining the solution 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 the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Answer: Explaining the solution can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Explaining the solution with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Explaining the solution best through concrete examples and clear words.
Answer: A correct simple example of Explaining the solution.
Worked Example 7
Problem: Show Explaining the solution with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Explaining the solution best through concrete examples and clear words.
Answer: A correct simple example of Explaining the solution.
Worked Example 8
Problem: Show Explaining the solution with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Explaining the solution best through concrete examples and clear words.
Answer: A correct simple example of Explaining the solution.
Worked Example 9
Problem: Show Explaining the solution with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Explaining the solution best through concrete examples and clear words.
Answer: A correct simple example of Explaining the solution.
Worked Example 10
Problem: Show Explaining the solution with a simple Grade 1 example.
- Use small numbers, objects, or a drawing.
- Explain what the example shows.
Very beginner explanation: Grade 1 learners understand Explaining the solution best through concrete examples and clear words.
Answer: A correct simple example of Explaining the solution.
Practice Exercise
Create one small question about Explaining the solution. Show it with objects, a picture, or numbers, then check by counting or comparing again.
40.10 Modelling review
Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
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 Modelling review mean?
- Say the topic in simple words.
- Use objects, fingers, a drawing, or a number example.
- Tell what you notice.
Very beginner explanation: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Worked Example 2
Problem: Show one small example of Modelling review.
- Choose small numbers or a simple shape/object.
- Make a model or drawing.
- Describe what the model shows.
Very beginner explanation: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: A correct small model or drawing can show the meaning of Modelling review.
Worked Example 3
Problem: Which tool could help with Modelling 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: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
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 Modelling 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: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Check by recounting, comparing, or using a second simple model.
Worked Example 5
Problem: Where might you use Modelling 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: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Answer: Modelling review can help with a simple everyday task such as counting, sharing, comparing, measuring, organizing, or deciding.
Worked Example 6
Problem: Show Modelling review 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 Modelling review best through concrete examples and clear words.
Answer: A correct simple example of Modelling review.
Worked Example 7
Problem: Show Modelling review 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 Modelling review best through concrete examples and clear words.
Answer: A correct simple example of Modelling review.
Worked Example 8
Problem: Show Modelling review 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 Modelling review best through concrete examples and clear words.
Answer: A correct simple example of Modelling review.
Worked Example 9
Problem: Show Modelling review 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 Modelling review best through concrete examples and clear words.
Answer: A correct simple example of Modelling review.
Worked Example 10
Problem: Show Modelling review 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 Modelling review best through concrete examples and clear words.
Answer: A correct simple example of Modelling review.
Practice Exercise
Create one small question about Modelling 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 Understanding a real-life question.
- Create and solve one original problem about Choosing important information.
- Create and solve one original problem about Using objects to model a situation.
- Create and solve one original problem about Using drawings to model a situation.
- Create and solve one original problem about Trying one solution.
- Create and solve one original problem about Trying another solution.
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 Understanding a real-life question?
Answer: Understanding a real-life question is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q2. What is the main idea in Choosing important information?
Answer: Choosing important information 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 Using objects to model a situation?
Answer: Using objects to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Q4. What is the main idea in Using drawings to model a situation?
Answer: Using drawings to model a situation uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
Q5. What is the main idea in Trying one solution?
Answer: Trying one solution 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 Trying another solution?
Answer: Trying another solution 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 Comparing solutions?
Answer: Comparing solutions 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 Choosing a reasonable solution?
Answer: Choosing a reasonable solution 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 the solution?
Answer: Explaining the solution is a Grade 1 mathematics idea. Learn it with objects or pictures first, then explain it with numbers or words.
Q10. What is the main idea in Modelling review?
Answer: Modelling review uses simple mathematics to understand a real situation, try possible solutions, and explain a reasonable choice.
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.