Chapter 6: Fraction Models and Number Lines
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Fraction Models and Number Lines in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
6.1 Fraction notation
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 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 2
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 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 8 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: 6/8
Worked Example 5
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 6
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 7
Problem: A model has 5 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: 2/5
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 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
Practice Exercise
Create and solve one new example of Fraction notation. 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.
6.2 Area models
Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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 data set is [8, 9, 9, 5, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 9
Worked Example 2
Problem: A data set is [14, 15, 4, 12, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 3
Problem: A data set is [4, 3, 9, 15, 15]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 4
Problem: A data set is [15, 11, 11, 6, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 5
Problem: A data set is [14, 6, 5, 12, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 6
Problem: A data set is [12, 10, 9, 14, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 7
Problem: A data set is [3, 13, 7, 3, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 8
Problem: A data set is [15, 14, 13, 5, 12]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 9
Problem: A data set is [5, 8, 12, 4, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 10
Problem: A data set is [14, 5, 15, 15, 12]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Practice Exercise
Create and solve one new example of Area models. 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.
6.3 Set models
Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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 data set is [14, 11, 3, 3, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 2
Problem: A data set is [5, 10, 13, 10, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 3
Problem: A data set is [3, 8, 8, 13, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 4
Problem: A data set is [10, 14, 4, 13, 15]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 5
Problem: A data set is [12, 12, 7, 13, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 6
Problem: A data set is [6, 9, 6, 15, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 7
Problem: A data set is [6, 13, 10, 8, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 8
Problem: A data set is [10, 11, 10, 9, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 9
Problem: A data set is [4, 9, 5, 13, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 10
Problem: A data set is [6, 3, 5, 8, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Practice Exercise
Create and solve one new example of Set models. 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.
6.4 Length models
Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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 data set is [15, 15, 8, 9, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 2
Problem: A data set is [6, 8, 3, 8, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 8
Worked Example 3
Problem: A data set is [4, 5, 10, 4, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 10
Worked Example 4
Problem: A data set is [5, 14, 12, 13, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 5
Problem: A data set is [7, 7, 13, 15, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 6
Problem: A data set is [9, 12, 6, 11, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 7
Problem: A data set is [15, 11, 14, 11, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 8
Problem: A data set is [12, 9, 9, 8, 12]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 9
Problem: A data set is [3, 15, 2, 3, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [9, 4, 12, 2, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Practice Exercise
Create and solve one new example of Length models. 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.
6.5 Number-line models
Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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 data set is [11, 3, 11, 5, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 2
Problem: A data set is [12, 3, 12, 6, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 3
Problem: A data set is [5, 14, 3, 2, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 4
Problem: A data set is [12, 3, 7, 15, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 5
Problem: A data set is [5, 3, 12, 12, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 6
Problem: A data set is [11, 6, 14, 4, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 7
Problem: A data set is [10, 8, 7, 10, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 10
Worked Example 8
Problem: A data set is [5, 5, 5, 14, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 9
Problem: A data set is [5, 15, 9, 6, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [10, 15, 14, 6, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Practice Exercise
Create and solve one new example of Number-line models. 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.
6.6 Fraction strips
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 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 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 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 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 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 6
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 7
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 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 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 10
Problem: A model has 5 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: 4/5
Practice Exercise
Create and solve one new example of Fraction strips. 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.
6.7 Drawing a fraction
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 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 2
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 3
Problem: A model has 5 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: 2/5
Worked Example 4
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 5
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 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 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 8
Problem: A model has 5 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: 4/5
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 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
Practice Exercise
Create and solve one new example of Drawing a fraction. 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.
6.8 Naming a shaded fraction
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 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 3
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 4
Problem: A model has 5 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: 4/5
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 8 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: 6/8
Worked Example 7
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 8
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
Worked Example 9
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 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 Naming a shaded fraction. 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.
6.9 Naming an unshaded fraction
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 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 2
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 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 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 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 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 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 8
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 9
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 10
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
Practice Exercise
Create and solve one new example of Naming an unshaded fraction. 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.
6.10 Fractions as division
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: Calculate 81 ÷ 5.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 16 remainder 1
Worked Example 2
Problem: Calculate 9 ÷ 2.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 4 remainder 1
Worked Example 3
Problem: Calculate 164 ÷ 8.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 20 remainder 4
Worked Example 4
Problem: Calculate 65 ÷ 4.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 16 remainder 1
Worked Example 5
Problem: Calculate 25 ÷ 2.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 12 remainder 1
Worked Example 6
Problem: Calculate 68 ÷ 6.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 11 remainder 2
Worked Example 7
Problem: Calculate 24 ÷ 3.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 8
Worked Example 8
Problem: Calculate 53 ÷ 3.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 17 remainder 2
Worked Example 9
Problem: Calculate 44 ÷ 8.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 5 remainder 4
Worked Example 10
Problem: Calculate 51 ÷ 6.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 8 remainder 3
Practice Exercise
Create and solve one new example of Fractions as division. 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.
6.11 Locating 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 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: 4/10
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 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 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 5
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 6
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 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 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
Worked Example 9
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 10
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
Practice Exercise
Create and solve one new example of Locating 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.
6.12 Connecting models to symbols
Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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 data set is [12, 4, 10, 10, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 2
Problem: A data set is [5, 15, 7, 10, 12]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 3
Problem: A data set is [6, 15, 3, 5, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 4
Problem: A data set is [10, 8, 5, 12, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 5
Problem: A data set is [15, 5, 4, 2, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 6
Problem: A data set is [3, 6, 3, 11, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 7
Problem: A data set is [7, 8, 7, 14, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 8
Problem: A data set is [6, 7, 4, 11, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 9
Problem: A data set is [3, 5, 10, 15, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [14, 10, 12, 10, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Practice Exercise
Create and solve one new example of Connecting models to symbols. 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 Fraction notation?
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.
Q2. What is important to understand about Area models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q3. What is important to understand about Set models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q4. What is important to understand about Length models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q5. What is important to understand about Number-line models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q6. What is important to understand about Fraction strips?
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 Drawing a fraction?
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.
Q8. What is important to understand about Naming a shaded fraction?
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.
Q9. What is important to understand about Naming an unshaded fraction?
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.
Q10. What is important to understand about Fractions as division?
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 Locating 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.
Q12. What is important to understand about Connecting models to symbols?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q13. How would you explain Fraction notation?
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.
Q14. How would you explain Area models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q15. How would you explain Set models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q16. How would you explain Length models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q17. How would you explain Number-line models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q18. How would you explain Fraction strips?
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 Drawing a fraction?
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.
Q20. How would you explain Naming a shaded fraction?
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.
Q21. How would you explain Naming an unshaded fraction?
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.
Q22. How would you explain Fractions as division?
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 Locating 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.
Q24. How would you explain Connecting models to symbols?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q25. What should a beginner check when working with Fraction notation?
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.
Q26. What should a beginner check when working with Area models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q27. What should a beginner check when working with Set models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q28. What should a beginner check when working with Length models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q29. What should a beginner check when working with Number-line models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q30. What should a beginner check when working with Fraction strips?
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.