Chapter 32: Pattern Rules, Predictions, and Missing Elements
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Pattern Rules, Predictions, and Missing Elements in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
32.1 Writing a pattern rule in words
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 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 3
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 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 2, 4, 6, ... 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: 8, 10
Worked Example 7
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 8
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 9
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 10
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
Practice Exercise
Create and solve one new example of Writing a pattern rule in words. 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.
32.2 Start value and change
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 $3 for 5 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 A
Worked Example 2
Problem: Option A costs $11 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 3
Problem: Option A costs $7 for 1 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 B
Worked Example 4
Problem: Option A costs $9 for 3 items. Option B costs $12 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 5
Problem: Option A costs $10 for 3 items. Option B costs $2 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 6
Problem: Option A costs $4 for 2 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: Same value
Worked Example 7
Problem: Option A costs $8 for 3 items. Option B costs $4 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 8
Problem: Option A costs $12 for 1 items. Option B costs $2 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 9
Problem: Option A costs $6 for 3 items. Option B costs $7 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 10
Problem: Option A costs $10 for 1 items. Option B costs $5 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
Practice Exercise
Create and solve one new example of Start value and change. 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.
32.3 Using a rule to extend a pattern
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 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 2
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 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 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
Worked Example 5
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 6
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 7
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 8
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 9
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 10
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
Practice Exercise
Create and solve one new example of Using a rule to extend a pattern. 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.
32.4 Using a rule to find a missing term
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: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 4 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 Using a rule to find a missing term.
Worked Example 2
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 15 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 Using a rule to find a missing term.
Worked Example 3
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 3 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 Using a rule to find a missing term.
Worked Example 4
Problem: Create a simple Grade 4 example about Using a rule to find a missing term 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 Using a rule to find a missing term.
Worked Example 5
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 19 and 14.
- 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 Using a rule to find a missing term.
Worked Example 6
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 20 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 Using a rule to find a missing term.
Worked Example 7
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 10 and 14.
- 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 Using a rule to find a missing term.
Worked Example 8
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 8 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 Using a rule to find a missing term.
Worked Example 9
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 2 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 Using a rule to find a missing term.
Worked Example 10
Problem: Create a simple Grade 4 example about Using a rule to find a missing term using the numbers 9 and 9.
- 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 Using a rule to find a missing term.
Practice Exercise
Create and solve one new example of Using a rule to find a missing term. 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.
32.5 Making a prediction
Making a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. 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 Making a prediction using the numbers 14 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 Making a prediction.
Worked Example 2
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 3 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 Making a prediction.
Worked Example 3
Problem: Create a simple Grade 4 example about Making a prediction 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 Making a prediction.
Worked Example 4
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 5 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 Making a prediction.
Worked Example 5
Problem: Create a simple Grade 4 example about Making a prediction 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 Making a prediction.
Worked Example 6
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 20 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 Making a prediction.
Worked Example 7
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 10 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 Making a prediction.
Worked Example 8
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 11 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 Making a prediction.
Worked Example 9
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 5 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 Making a prediction.
Worked Example 10
Problem: Create a simple Grade 4 example about Making a prediction using the numbers 16 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 Making a prediction.
Practice Exercise
Create and solve one new example of Making a prediction. 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.
32.6 Justifying a prediction
Justifying a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. 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 Justifying a prediction using the numbers 17 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 Justifying a prediction.
Worked Example 2
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 13 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 Justifying a prediction.
Worked Example 3
Problem: Create a simple Grade 4 example about Justifying a prediction 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 Justifying a prediction.
Worked Example 4
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 4 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 Justifying a prediction.
Worked Example 5
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 13 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 Justifying a prediction.
Worked Example 6
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 11 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 Justifying a prediction.
Worked Example 7
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 12 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 Justifying a prediction.
Worked Example 8
Problem: Create a simple Grade 4 example about Justifying a prediction 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 Justifying a prediction.
Worked Example 9
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 15 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 Justifying a prediction.
Worked Example 10
Problem: Create a simple Grade 4 example about Justifying a prediction using the numbers 8 and 14.
- 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 Justifying a prediction.
Practice Exercise
Create and solve one new example of Justifying a prediction. 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.
32.7 Testing a pattern rule
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, 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
Worked Example 2
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 3
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 4
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
Worked Example 5
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
Worked Example 6
Problem: Continue 7, 9, 11, ... 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: 13, 15
Worked Example 7
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 8
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 9
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 10
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
Practice Exercise
Create and solve one new example of Testing a pattern rule. 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.
32.8 Correcting an incorrect rule
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: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 4 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 Correcting an incorrect rule.
Worked Example 2
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 10 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 Correcting an incorrect rule.
Worked Example 3
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 8 and 9.
- 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 Correcting an incorrect rule.
Worked Example 4
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 4 and 14.
- 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 Correcting an incorrect rule.
Worked Example 5
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 8 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 Correcting an incorrect rule.
Worked Example 6
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 16 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 Correcting an incorrect rule.
Worked Example 7
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 17 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 Correcting an incorrect rule.
Worked Example 8
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 18 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 Correcting an incorrect rule.
Worked Example 9
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 2 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 Correcting an incorrect rule.
Worked Example 10
Problem: Create a simple Grade 4 example about Correcting an incorrect rule using the numbers 5 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 Correcting an incorrect rule.
Practice Exercise
Create and solve one new example of Correcting an incorrect rule. 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.
32.9 Comparing two rules
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: Create a simple Grade 4 example about Comparing two rules using the numbers 8 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 Comparing two rules.
Worked Example 2
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 4 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 Comparing two rules.
Worked Example 3
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 7 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 Comparing two rules.
Worked Example 4
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 11 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 Comparing two rules.
Worked Example 5
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 8 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 Comparing two rules.
Worked Example 6
Problem: Create a simple Grade 4 example about Comparing two rules 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 Comparing two rules.
Worked Example 7
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 12 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 Comparing two rules.
Worked Example 8
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 8 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 Comparing two rules.
Worked Example 9
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 19 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 Comparing two rules.
Worked Example 10
Problem: Create a simple Grade 4 example about Comparing two rules using the numbers 20 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 Comparing two rules.
Practice Exercise
Create and solve one new example of Comparing two rules. 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.
32.10 Finding a later term informally
Finding a later term informally is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. 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 Finding a later term informally using the numbers 10 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 Finding a later term informally.
Worked Example 2
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 9 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 Finding a later term informally.
Worked Example 3
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 3 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 Finding a later term informally.
Worked Example 4
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 16 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 Finding a later term informally.
Worked Example 5
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 5 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 Finding a later term informally.
Worked Example 6
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 16 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 Finding a later term informally.
Worked Example 7
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 19 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 Finding a later term informally.
Worked Example 8
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 16 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 Finding a later term informally.
Worked Example 9
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 3 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 Finding a later term informally.
Worked Example 10
Problem: Create a simple Grade 4 example about Finding a later term informally using the numbers 9 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 Finding a later term informally.
Practice Exercise
Create and solve one new example of Finding a later term informally. 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.
32.11 Pattern word problems
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 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 3
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 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 9, 11, 13, ... 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: 15, 17
Worked Example 6
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 7
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 8
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 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 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
Practice Exercise
Create and solve one new example of Pattern word problems. 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.
32.12 Explaining pattern reasoning
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 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 3
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 4
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 5
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
Worked Example 6
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 7
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 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 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 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
Practice Exercise
Create and solve one new example of Explaining pattern reasoning. 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 Writing a pattern rule in words?
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 Start value and change?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q3. What is important to understand about Using a rule to extend a pattern?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q4. What is important to understand about Using a rule to find a missing term?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q5. What is important to understand about Making a prediction?
Answer: Making a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q6. What is important to understand about Justifying a prediction?
Answer: Justifying a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q7. What is important to understand about Testing a pattern rule?
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 Correcting an incorrect rule?
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 Comparing two rules?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q10. What is important to understand about Finding a later term informally?
Answer: Finding a later term informally is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q11. What is important to understand about Pattern word problems?
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 Explaining pattern reasoning?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q13. How would you explain Writing a pattern rule in words?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q14. How would you explain Start value and change?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q15. How would you explain Using a rule to extend a pattern?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q16. How would you explain Using a rule to find a missing term?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q17. How would you explain Making a prediction?
Answer: Making a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q18. How would you explain Justifying a prediction?
Answer: Justifying a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q19. How would you explain Testing a pattern rule?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q20. How would you explain Correcting an incorrect rule?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q21. How would you explain Comparing two rules?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q22. How would you explain Finding a later term informally?
Answer: Finding a later term informally is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q23. How would you explain Pattern word problems?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q24. How would you explain Explaining pattern reasoning?
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 Writing a pattern rule in words?
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 Start value and change?
Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.
Q27. What should a beginner check when working with Using a rule to extend a pattern?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q28. What should a beginner check when working with Using a rule to find a missing term?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q29. What should a beginner check when working with Making a prediction?
Answer: Making a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q30. What should a beginner check when working with Justifying a prediction?
Answer: Justifying a prediction is an important Grade 4 mathematics idea in Pattern Rules, Predictions, and Missing Elements. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.