Chapter 3: Standard, Word, and Expanded Form
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Standard, Word, and Expanded Form with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Standard form (a Grade 3 idea used in this chapter)
- Word form (a Grade 3 idea used in this chapter)
- Expanded form (a Grade 3 idea used in this chapter)
- Matching standard and word form (a Grade 3 idea used in this chapter)
- Matching standard and expanded form (a Grade 3 idea used in this chapter)
- Writing 3-digit numbers in words (a Grade 3 idea used in this chapter)
- Writing words as numbers (a Grade 3 idea used in this chapter)
- Writing expanded form from a model (a Grade 3 idea used in this chapter)
- Composing numbers in different ways (a Grade 3 idea used in this chapter)
- Decomposing numbers in different ways (a Grade 3 idea used in this chapter)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
3.1 Standard form
Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Standard form?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Worked Example 2
Problem: What should you identify first before solving a problem about Standard form?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Standard form.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Standard form problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Standard form.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Standard form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Standard form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.2 Word form
Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Word form?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Worked Example 2
Problem: What should you identify first before solving a problem about Word form?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Word form.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Word form problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Word form.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Word form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Word form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.3 Expanded form
Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Expanded form?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Worked Example 2
Problem: What should you identify first before solving a problem about Expanded form?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Expanded form.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Expanded form problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Expanded form.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Expanded form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Write 638,420,715 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 600,000,000 + 30,000,000 + 8,000,000 + 400,000 + 20,000 + 700 + 10 + 5
Worked Example 7
Problem: Write 92,305,004 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 90,000,000 + 2,000,000 + 300,000 + 5,000 + 4
Worked Example 8
Problem: Write 704,090,650 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 700,000,000 + 4,000,000 + 90,000 + 600 + 50
Worked Example 9
Problem: Write 18,765,432 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 10,000,000 + 8,000,000 + 700,000 + 60,000 + 5,000 + 400 + 30 + 2
Worked Example 10
Problem: Write 999,500,001 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 900,000,000 + 90,000,000 + 9,000,000 + 500,000 + 1
Practice Exercise
Create one new question about Expanded form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.4 Matching standard and word form
Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Matching standard and word form?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Worked Example 2
Problem: What should you identify first before solving a problem about Matching standard and word form?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Matching standard and word form.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Matching standard and word form problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Matching standard and word form.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Matching standard and word form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Matching standard and word form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.5 Matching standard and expanded form
Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Matching standard and expanded form?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Worked Example 2
Problem: What should you identify first before solving a problem about Matching standard and expanded form?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Matching standard and expanded form.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Matching standard and expanded form problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Matching standard and expanded form.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Matching standard and expanded form can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Write 638,420,715 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 600,000,000 + 30,000,000 + 8,000,000 + 400,000 + 20,000 + 700 + 10 + 5
Worked Example 7
Problem: Write 92,305,004 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 90,000,000 + 2,000,000 + 300,000 + 5,000 + 4
Worked Example 8
Problem: Write 704,090,650 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 700,000,000 + 4,000,000 + 90,000 + 600 + 50
Worked Example 9
Problem: Write 18,765,432 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 10,000,000 + 8,000,000 + 700,000 + 60,000 + 5,000 + 400 + 30 + 2
Worked Example 10
Problem: Write 999,500,001 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 900,000,000 + 90,000,000 + 9,000,000 + 500,000 + 1
Practice Exercise
Create one new question about Matching standard and expanded form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.6 Writing 3-digit numbers in words
Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Writing 3-digit numbers in words?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Writing 3-digit numbers in words?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Writing 3-digit numbers in words.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Writing 3-digit numbers in words problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Writing 3-digit numbers in words.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Writing 3-digit numbers in words can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Writing 3-digit numbers in words in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing 3-digit numbers in words becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Writing 3-digit numbers in words and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing 3-digit numbers in words becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Writing 3-digit numbers in words using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing 3-digit numbers in words becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Writing 3-digit numbers in words problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing 3-digit numbers in words becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Writing 3-digit numbers in words could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing 3-digit numbers in words becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Writing 3-digit numbers in words. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.7 Writing words as numbers
Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Writing words as numbers?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Writing words as numbers?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Writing words as numbers.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Writing words as numbers problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Writing words as numbers.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Writing words as numbers can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Writing words as numbers in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing words as numbers becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Writing words as numbers and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing words as numbers becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Writing words as numbers using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing words as numbers becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Writing words as numbers problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing words as numbers becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Writing words as numbers could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Writing words as numbers becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Writing words as numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.8 Writing expanded form from a model
Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Writing expanded form from a model?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Worked Example 2
Problem: What should you identify first before solving a problem about Writing expanded form from a model?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Writing expanded form from a model.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Writing expanded form from a model problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Writing expanded form from a model.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Answer: Writing expanded form from a model can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Write 638,420,715 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 600,000,000 + 30,000,000 + 8,000,000 + 400,000 + 20,000 + 700 + 10 + 5
Worked Example 7
Problem: Write 92,305,004 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 90,000,000 + 2,000,000 + 300,000 + 5,000 + 4
Worked Example 8
Problem: Write 704,090,650 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 700,000,000 + 4,000,000 + 90,000 + 600 + 50
Worked Example 9
Problem: Write 18,765,432 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 10,000,000 + 8,000,000 + 700,000 + 60,000 + 5,000 + 400 + 30 + 2
Worked Example 10
Problem: Write 999,500,001 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 900,000,000 + 90,000,000 + 9,000,000 + 500,000 + 1
Practice Exercise
Create one new question about Writing expanded form from a model. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.9 Composing numbers in different ways
Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Composing numbers in different ways?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Composing numbers in different ways?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Composing numbers in different ways.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Composing numbers in different ways problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Composing numbers in different ways.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Composing numbers in different ways can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Composing numbers in different ways in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Composing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Composing numbers in different ways and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Composing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Composing numbers in different ways using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Composing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Composing numbers in different ways problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Composing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Composing numbers in different ways could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Composing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Composing numbers in different ways. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
3.10 Decomposing numbers in different ways
Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Decomposing numbers in different ways?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Decomposing numbers in different ways?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Decomposing numbers in different ways.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Decomposing numbers in different ways problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Decomposing numbers in different ways.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Decomposing numbers in different ways can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Decomposing numbers in different ways in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Decomposing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Decomposing numbers in different ways and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Decomposing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Decomposing numbers in different ways using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Decomposing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Decomposing numbers in different ways problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Decomposing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Decomposing numbers in different ways could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Decomposing numbers in different ways becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Decomposing numbers in different ways. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Standard form.
- Create and solve one original problem about Word form.
- Create and solve one original problem about Expanded form.
- Create and solve one original problem about Matching standard and word form.
- Create and solve one original problem about Matching standard and expanded form.
- Create and solve one original problem about Writing 3-digit numbers in words.
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 key idea in Standard form?
Answer: Standard form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Q2. What is the key idea in Word form?
Answer: Word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Q3. What is the key idea in Expanded form?
Answer: Expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Q4. What is the key idea in Matching standard and word form?
Answer: Matching standard and word form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Q5. What is the key idea in Matching standard and expanded form?
Answer: Matching standard and expanded form helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Q6. What is the key idea in Writing 3-digit numbers in words?
Answer: Writing 3-digit numbers in words is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q7. What is the key idea in Writing words as numbers?
Answer: Writing words as numbers is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q8. What is the key idea in Writing expanded form from a model?
Answer: Writing expanded form from a model helps learners understand how digits represent quantities and how whole numbers can be written, compared, or used in everyday situations.
Q9. What is the key idea in Composing numbers in different ways?
Answer: Composing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q10. What is the key idea in Decomposing numbers in different ways?
Answer: Decomposing numbers in different ways is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 3 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Standard, Word, and Expanded Form effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Standard, Word, and Expanded Form effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Standard, Word, and Expanded Form effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Standard, Word, and Expanded Form effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Standard, Word, and Expanded Form effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.