Chapter 31: Representing Patterns with Tables and Graphs
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Representing Patterns with Tables and Graphs in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
31.1 Pattern term number
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 10, 14, 18, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 22, 26
Worked Example 2
Problem: Continue 1, 3, 5, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 7, 9
Worked Example 3
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 4
Problem: Continue 3, 6, 9, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 15
Worked Example 5
Problem: Continue 6, 11, 16, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 21, 26
Worked Example 6
Problem: Continue 3, 7, 11, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 15, 19
Worked Example 7
Problem: Continue 7, 13, 19, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 31
Worked Example 8
Problem: Continue 8, 14, 20, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 26, 32
Worked Example 9
Problem: Continue 8, 11, 14, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 17, 20
Worked Example 10
Problem: Continue 5, 9, 13, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 17, 21
Practice Exercise
Create and solve one new example of Pattern term number. 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.
31.2 Pattern value
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 7, 10, 13, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 16, 19
Worked Example 2
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 3
Problem: Continue 8, 13, 18, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 23, 28
Worked Example 4
Problem: Continue 10, 16, 22, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 28, 34
Worked Example 5
Problem: Continue 2, 5, 8, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 11, 14
Worked Example 6
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 7
Problem: Continue 10, 16, 22, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 28, 34
Worked Example 8
Problem: Continue 6, 10, 14, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 18, 22
Worked Example 9
Problem: Continue 1, 4, 7, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 10, 13
Worked Example 10
Problem: Continue 5, 7, 9, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 11, 13
Practice Exercise
Create and solve one new example of Pattern value. 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.
31.3 Building a table of values
Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value. 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: Option A costs $10 for 1 items. Option B costs $4 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 2
Problem: Option A costs $2 for 2 items. Option B costs $8 for 5 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 3
Problem: Option A costs $2 for 3 items. Option B costs $9 for 4 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 4
Problem: Option A costs $3 for 3 items. Option B costs $6 for 3 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 5
Problem: Option A costs $11 for 2 items. Option B costs $3 for 1 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 6
Problem: Option A costs $9 for 1 items. Option B costs $9 for 4 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 7
Problem: Option A costs $7 for 4 items. Option B costs $4 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 8
Problem: Option A costs $8 for 1 items. Option B costs $4 for 1 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 9
Problem: Option A costs $4 for 5 items. Option B costs $12 for 5 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 10
Problem: Option A costs $8 for 3 items. Option B costs $4 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Practice Exercise
Create and solve one new example of Building a table of values. 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.
31.4 Reading a table of values
Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value. 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: Option A costs $8 for 1 items. Option B costs $3 for 3 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 2
Problem: Option A costs $12 for 1 items. Option B costs $5 for 4 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 3
Problem: Option A costs $5 for 5 items. Option B costs $8 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 4
Problem: Option A costs $7 for 5 items. Option B costs $11 for 1 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 5
Problem: Option A costs $10 for 4 items. Option B costs $10 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 6
Problem: Option A costs $5 for 4 items. Option B costs $6 for 5 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 7
Problem: Option A costs $7 for 4 items. Option B costs $3 for 5 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option B
Worked Example 8
Problem: Option A costs $9 for 5 items. Option B costs $11 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 9
Problem: Option A costs $8 for 5 items. Option B costs $7 for 4 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Worked Example 10
Problem: Option A costs $2 for 5 items. Option B costs $8 for 2 items. Which has the lower cost per item?
- Divide each price by its number of items.
- Compare the two costs per item.
Very beginner explanation: Value comparisons should compare equivalent quantities.
Answer: Option A
Practice Exercise
Create and solve one new example of Reading a table of values. 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.
31.5 Representing a repeating pattern in a table
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 1, 6, 11, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 16, 21
Worked Example 2
Problem: Continue 8, 10, 12, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 16
Worked Example 3
Problem: Continue 3, 5, 7, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 9, 11
Worked Example 4
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 5
Problem: Continue 2, 6, 10, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 18
Worked Example 6
Problem: Continue 2, 7, 12, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 17, 22
Worked Example 7
Problem: Continue 6, 9, 12, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 15, 18
Worked Example 8
Problem: Continue 5, 10, 15, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 25
Worked Example 9
Problem: Continue 1, 3, 5, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 7, 9
Worked Example 10
Problem: Continue 4, 6, 8, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 10, 12
Practice Exercise
Create and solve one new example of Representing a repeating pattern in a table. 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.
31.6 Representing a growing pattern in a table
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 2, 8, 14, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 26
Worked Example 2
Problem: Continue 10, 15, 20, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 30
Worked Example 3
Problem: Continue 4, 7, 10, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 13, 16
Worked Example 4
Problem: Continue 4, 10, 16, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 22, 28
Worked Example 5
Problem: Continue 2, 8, 14, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 26
Worked Example 6
Problem: Continue 9, 12, 15, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 18, 21
Worked Example 7
Problem: Continue 5, 10, 15, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 25
Worked Example 8
Problem: Continue 10, 15, 20, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 30
Worked Example 9
Problem: Continue 7, 13, 19, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 31
Worked Example 10
Problem: Continue 2, 8, 14, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 26
Practice Exercise
Create and solve one new example of Representing a growing pattern in a table. 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.
31.7 Graphing pattern points
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 1, 7, 13, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 19, 25
Worked Example 2
Problem: Continue 1, 6, 11, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 16, 21
Worked Example 3
Problem: Continue 3, 5, 7, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 9, 11
Worked Example 4
Problem: Continue 6, 10, 14, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 18, 22
Worked Example 5
Problem: Continue 5, 9, 13, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 17, 21
Worked Example 6
Problem: Continue 6, 10, 14, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 18, 22
Worked Example 7
Problem: Continue 9, 13, 17, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 21, 25
Worked Example 8
Problem: Continue 2, 6, 10, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 18
Worked Example 9
Problem: Continue 8, 10, 12, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 16
Worked Example 10
Problem: Continue 5, 8, 11, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 17
Practice Exercise
Create and solve one new example of Graphing pattern points. 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.
31.8 Reading a simple pattern graph
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 9, 14, 19, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 24, 29
Worked Example 2
Problem: Continue 1, 7, 13, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 19, 25
Worked Example 3
Problem: Continue 9, 12, 15, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 18, 21
Worked Example 4
Problem: Continue 10, 13, 16, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 19, 22
Worked Example 5
Problem: Continue 6, 9, 12, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 15, 18
Worked Example 6
Problem: Continue 3, 8, 13, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 18, 23
Worked Example 7
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 8
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 9
Problem: Continue 3, 6, 9, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 15
Worked Example 10
Problem: Continue 7, 12, 17, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 22, 27
Practice Exercise
Create and solve one new example of Reading a simple pattern graph. 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.
31.9 Connecting table and graph
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, 12, 6, 14, 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 [7, 14, 4, 2, 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 3
Problem: A data set is [3, 8, 11, 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 4
Problem: A data set is [15, 6, 4, 10, 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 5
Problem: A data set is [13, 7, 6, 15, 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 6
Problem: A data set is [10, 7, 7, 14, 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 7
Problem: A data set is [13, 2, 15, 9, 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 8
Problem: A data set is [2, 11, 13, 10, 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: 13
Worked Example 9
Problem: A data set is [13, 2, 6, 4, 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 10
Problem: A data set is [5, 11, 11, 15, 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
Practice Exercise
Create and solve one new example of Connecting table and graph. 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.
31.10 Translating shape patterns to numbers
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 7, 12, 17, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 22, 27
Worked Example 2
Problem: Continue 10, 13, 16, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 19, 22
Worked Example 3
Problem: Continue 10, 12, 14, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 16, 18
Worked Example 4
Problem: Continue 7, 13, 19, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 31
Worked Example 5
Problem: Continue 10, 15, 20, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 30
Worked Example 6
Problem: Continue 10, 16, 22, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 28, 34
Worked Example 7
Problem: Continue 3, 5, 7, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 9, 11
Worked Example 8
Problem: Continue 1, 7, 13, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 19, 25
Worked Example 9
Problem: Continue 10, 14, 18, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 22, 26
Worked Example 10
Problem: Continue 5, 8, 11, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 17
Practice Exercise
Create and solve one new example of Translating shape patterns to numbers. 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.
31.11 Translating number patterns to graphs
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 5, 9, 13, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 17, 21
Worked Example 2
Problem: Continue 5, 11, 17, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 23, 29
Worked Example 3
Problem: Continue 9, 14, 19, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 24, 29
Worked Example 4
Problem: Continue 7, 13, 19, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 31
Worked Example 5
Problem: Continue 4, 9, 14, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 19, 24
Worked Example 6
Problem: Continue 10, 15, 20, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 25, 30
Worked Example 7
Problem: Continue 10, 12, 14, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 16, 18
Worked Example 8
Problem: Continue 2, 7, 12, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 17, 22
Worked Example 9
Problem: Continue 8, 12, 16, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 24
Worked Example 10
Problem: Continue 1, 5, 9, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 13, 17
Practice Exercise
Create and solve one new example of Translating number patterns to graphs. 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.
31.12 Choosing a useful pattern representation
A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way. 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: Continue 8, 14, 20, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 26, 32
Worked Example 2
Problem: Continue 9, 13, 17, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 21, 25
Worked Example 3
Problem: Continue 2, 8, 14, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 20, 26
Worked Example 4
Problem: Continue 6, 9, 12, ... for two more terms.
- The rule is add 3.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 15, 18
Worked Example 5
Problem: Continue 2, 6, 10, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 14, 18
Worked Example 6
Problem: Continue 3, 9, 15, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 21, 27
Worked Example 7
Problem: Continue 9, 14, 19, ... for two more terms.
- The rule is add 5.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 24, 29
Worked Example 8
Problem: Continue 6, 8, 10, ... for two more terms.
- The rule is add 2.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 12, 14
Worked Example 9
Problem: Continue 8, 14, 20, ... for two more terms.
- The rule is add 6.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 26, 32
Worked Example 10
Problem: Continue 9, 13, 17, ... for two more terms.
- The rule is add 4.
- Apply the same rule twice.
Very beginner explanation: A growing pattern changes according to a consistent rule.
Answer: 21, 25
Practice Exercise
Create and solve one new example of Choosing a useful pattern representation. 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 Pattern term number?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q2. What is important to understand about Pattern value?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q3. What is important to understand about Building a table of values?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q4. What is important to understand about Reading a table of values?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q5. What is important to understand about Representing a repeating pattern in a table?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q6. What is important to understand about Representing a growing pattern in a table?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q7. What is important to understand about Graphing pattern points?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q8. What is important to understand about Reading a simple pattern graph?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q9. What is important to understand about Connecting table and graph?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q10. What is important to understand about Translating shape patterns to numbers?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q11. What is important to understand about Translating number patterns to graphs?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q12. What is important to understand about Choosing a useful pattern representation?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q13. How would you explain Pattern term number?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q14. How would you explain Pattern value?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q15. How would you explain Building a table of values?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q16. How would you explain Reading a table of values?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q17. How would you explain Representing a repeating pattern in a table?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q18. How would you explain Representing a growing pattern in a table?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q19. How would you explain Graphing pattern points?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q20. How would you explain Reading a simple pattern graph?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q21. How would you explain Connecting table and graph?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q22. How would you explain Translating shape patterns to numbers?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q23. How would you explain Translating number patterns to graphs?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q24. How would you explain Choosing a useful pattern representation?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q25. What should a beginner check when working with Pattern term number?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q26. What should a beginner check when working with Pattern value?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q27. What should a beginner check when working with Building a table of values?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q28. What should a beginner check when working with Reading a table of values?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q29. What should a beginner check when working with Representing a repeating pattern in a table?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q30. What should a beginner check when working with Representing a growing pattern in a table?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.