Chapter 8: Counting by Unit Fractions
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Counting by Unit Fractions in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
8.1 Counting by halves
Counting by halves is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 14 and 13.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 2
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 19 and 12.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 3
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 3 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 4
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 12 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 5
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 17 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 6
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 13 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 7
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 12 and 16.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 8
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 11 and 11.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 9
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 17 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Worked Example 10
Problem: Create a simple Grade 4 example about Counting by halves using the numbers 8 and 2.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting by halves.
Practice Exercise
Create and solve one new example of Counting by halves. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.2 Counting by thirds
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 6 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/6
Worked Example 2
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Worked Example 3
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 4
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 5
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Worked Example 6
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 7
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 8
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 9
Problem: A model has 10 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/10
Worked Example 10
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Practice Exercise
Create and solve one new example of Counting by thirds. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.3 Counting by fourths
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 2
Problem: A model has 8 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/8
Worked Example 3
Problem: A model has 5 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/5
Worked Example 4
Problem: A model has 8 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/8
Worked Example 5
Problem: A model has 8 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/8
Worked Example 6
Problem: A model has 10 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/10
Worked Example 7
Problem: A model has 10 equal parts and 6 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 6/10
Worked Example 8
Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/6
Worked Example 9
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Worked Example 10
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Practice Exercise
Create and solve one new example of Counting by fourths. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.4 Counting by fifths
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 2
Problem: A model has 5 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/5
Worked Example 3
Problem: A model has 10 equal parts and 6 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 6/10
Worked Example 4
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 5
Problem: A model has 10 equal parts and 8 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 8/10
Worked Example 6
Problem: A model has 10 equal parts and 6 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 6/10
Worked Example 7
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 8
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 9
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 10
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Practice Exercise
Create and solve one new example of Counting by fifths. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.5 Counting by sixths
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 10 equal parts and 9 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 9/10
Worked Example 2
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 3
Problem: A model has 5 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/5
Worked Example 4
Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/6
Worked Example 5
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 6
Problem: A model has 10 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/10
Worked Example 7
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 8
Problem: A model has 8 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/8
Worked Example 9
Problem: A model has 8 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/8
Worked Example 10
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Practice Exercise
Create and solve one new example of Counting by sixths. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.6 Counting by eighths
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Worked Example 2
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 3
Problem: A model has 4 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/4
Worked Example 4
Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/3
Worked Example 5
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 6
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 7
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 8
Problem: A model has 5 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/5
Worked Example 9
Problem: A model has 8 equal parts and 8 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 8/8
Worked Example 10
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Practice Exercise
Create and solve one new example of Counting by eighths. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.7 Counting by tenths
A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Write 8/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.8
Worked Example 2
Problem: Write 6/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.6
Worked Example 3
Problem: Write 9/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.9
Worked Example 4
Problem: Write 0/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.0
Worked Example 5
Problem: Write 8/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.8
Worked Example 6
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Worked Example 7
Problem: Write 6/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.6
Worked Example 8
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 9
Problem: Write 6/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.6
Worked Example 10
Problem: Write 2/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.2
Practice Exercise
Create and solve one new example of Counting by tenths. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.8 Counting beyond one whole
Counting beyond one whole is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 6 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 2
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 16 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 3
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 4 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 4
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 15 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 5
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 20 and 17.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 6
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 4 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 7
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 5 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 8
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 15 and 3.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 9
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 7 and 19.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Worked Example 10
Problem: Create a simple Grade 4 example about Counting beyond one whole using the numbers 8 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Counting beyond one whole.
Practice Exercise
Create and solve one new example of Counting beyond one whole. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.9 Mixed numbers while counting
Mixed numbers while counting is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 18 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 2
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 11 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 3
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 13 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 4
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 11 and 17.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 5
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 20 and 15.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 6
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 4 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 7
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 10 and 2.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 8
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 13 and 15.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 9
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 19 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Worked Example 10
Problem: Create a simple Grade 4 example about Mixed numbers while counting using the numbers 19 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Mixed numbers while counting.
Practice Exercise
Create and solve one new example of Mixed numbers while counting. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.10 Improper fractions while counting
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 10 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/10
Worked Example 2
Problem: A model has 8 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/8
Worked Example 3
Problem: A model has 10 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/10
Worked Example 4
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 5
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 6
Problem: A model has 6 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/6
Worked Example 7
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 8
Problem: A model has 8 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/8
Worked Example 9
Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 5/6
Worked Example 10
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Practice Exercise
Create and solve one new example of Improper fractions while counting. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.11 Counting backward by unit fractions
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 4 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/4
Worked Example 2
Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 1/2
Worked Example 3
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 4
Problem: A model has 6 equal parts and 6 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 6/6
Worked Example 5
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 6
Problem: A model has 10 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/10
Worked Example 7
Problem: A model has 4 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/4
Worked Example 8
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 9
Problem: A model has 4 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/4
Worked Example 10
Problem: A model has 8 equal parts and 7 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 7/8
Practice Exercise
Create and solve one new example of Counting backward by unit fractions. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
8.12 Unit fractions on a number line
A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: A model has 10 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/10
Worked Example 2
Problem: A model has 6 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/6
Worked Example 3
Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/2
Worked Example 4
Problem: A model has 4 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/4
Worked Example 5
Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/3
Worked Example 6
Problem: A model has 4 equal parts and 4 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 4/4
Worked Example 7
Problem: A model has 4 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/4
Worked Example 8
Problem: A model has 4 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/4
Worked Example 9
Problem: A model has 3 equal parts and 3 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 3/3
Worked Example 10
Problem: A model has 6 equal parts and 2 are selected. What fraction is selected?
- Count all equal parts for the denominator.
- Count selected parts for the numerator.
Very beginner explanation: Fractions describe equal-sized parts.
Answer: 2/6
Practice Exercise
Create and solve one new example of Unit fractions on a number line. Show the steps and explain how you checked it.
Common Mistake
Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.
30 Review Questions and Answers
Q1. What is important to understand about Counting by halves?
Answer: Counting by halves is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q2. What is important to understand about Counting by thirds?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q3. What is important to understand about Counting by fourths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q4. What is important to understand about Counting by fifths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q5. What is important to understand about Counting by sixths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q6. What is important to understand about Counting by eighths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q7. What is important to understand about Counting by tenths?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q8. What is important to understand about Counting beyond one whole?
Answer: Counting beyond one whole is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q9. What is important to understand about Mixed numbers while counting?
Answer: Mixed numbers while counting is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q10. What is important to understand about Improper fractions while counting?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q11. What is important to understand about Counting backward by unit fractions?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q12. What is important to understand about Unit fractions on a number line?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q13. How would you explain Counting by halves?
Answer: Counting by halves is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q14. How would you explain Counting by thirds?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q15. How would you explain Counting by fourths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q16. How would you explain Counting by fifths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q17. How would you explain Counting by sixths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q18. How would you explain Counting by eighths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q19. How would you explain Counting by tenths?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q20. How would you explain Counting beyond one whole?
Answer: Counting beyond one whole is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q21. How would you explain Mixed numbers while counting?
Answer: Mixed numbers while counting is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q22. How would you explain Improper fractions while counting?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q23. How would you explain Counting backward by unit fractions?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q24. How would you explain Unit fractions on a number line?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q25. What should a beginner check when working with Counting by halves?
Answer: Counting by halves is an important Grade 4 mathematics idea in Counting by Unit Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q26. What should a beginner check when working with Counting by thirds?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q27. What should a beginner check when working with Counting by fourths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q28. What should a beginner check when working with Counting by fifths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q29. What should a beginner check when working with Counting by sixths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.
Q30. What should a beginner check when working with Counting by eighths?
Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.