Chapter 33: Whole-Number and Decimal-Tenth Patterns
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Whole-Number and Decimal-Tenth Patterns in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
33.1 Adding 10 repeatedly
Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 2,713 + 119.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 2,832
Worked Example 2
Problem: Calculate 3,888 + 457.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 4,345
Worked Example 3
Problem: Calculate 2,522 + 1,274.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 3,796
Worked Example 4
Problem: Calculate 2,465 + 876.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 3,341
Worked Example 5
Problem: Calculate 3,498 + 668.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 4,166
Worked Example 6
Problem: Calculate 2,580 + 1,511.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 4,091
Worked Example 7
Problem: Calculate 2,211 + 655.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 2,866
Worked Example 8
Problem: Calculate 836 + 1,323.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 2,159
Worked Example 9
Problem: Calculate 2,768 + 2,049.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 4,817
Worked Example 10
Problem: Calculate 1,348 + 2,684.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 4,032
Practice Exercise
Create and solve one new example of Adding 10 repeatedly. 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.
33.2 Adding 100 repeatedly
Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 3,234 + 2,268.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 5,502
Worked Example 2
Problem: Calculate 3,364 + 2,792.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 6,156
Worked Example 3
Problem: Calculate 2,306 + 1,161.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 3,467
Worked Example 4
Problem: Calculate 2,600 + 213.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 2,813
Worked Example 5
Problem: Calculate 3,070 + 2,302.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 5,372
Worked Example 6
Problem: Calculate 3,222 + 299.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 3,521
Worked Example 7
Problem: Calculate 405 + 2,331.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 2,736
Worked Example 8
Problem: Calculate 3,577 + 2,703.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 6,280
Worked Example 9
Problem: Calculate 3,377 + 2,694.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 6,071
Worked Example 10
Problem: Calculate 429 + 2,468.
- Line up place values.
- Add from right to left.
- Regroup when needed.
Very beginner explanation: Place-value alignment keeps like places together.
Answer: 2,897
Practice Exercise
Create and solve one new example of Adding 100 repeatedly. 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.
33.3 Subtracting 10 repeatedly
Subtraction finds what remains or the difference between quantities. Addition is a useful way to check. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 4,649 − 1,038.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 3,611
Worked Example 2
Problem: Calculate 6,302 − 1,286.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 5,016
Worked Example 3
Problem: Calculate 1,679 − 1,588.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 91
Worked Example 4
Problem: Calculate 2,489 − 2,222.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 267
Worked Example 5
Problem: Calculate 7,129 − 2,959.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 4,170
Worked Example 6
Problem: Calculate 7,170 − 6,085.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 1,085
Worked Example 7
Problem: Calculate 4,838 − 1,216.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 3,622
Worked Example 8
Problem: Calculate 4,036 − 201.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 3,835
Worked Example 9
Problem: Calculate 1,538 − 1,233.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 305
Worked Example 10
Problem: Calculate 2,868 − 1,588.
- Line up place values.
- Subtract from right to left.
- Regroup when needed.
Very beginner explanation: Addition can be used to check subtraction.
Answer: 1,280
Practice Exercise
Create and solve one new example of Subtracting 10 repeatedly. 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.
33.4 Multiplying patterns by 10
Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Calculate 11 × 4.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 44
Worked Example 2
Problem: Calculate 7 × 6.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 42
Worked Example 3
Problem: Calculate 8 × 5.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Worked Example 4
Problem: Calculate 6 × 9.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 54
Worked Example 5
Problem: Calculate 12 × 5.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 60
Worked Example 6
Problem: Calculate 9 × 3.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 27
Worked Example 7
Problem: Calculate 7 × 4.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 28
Worked Example 8
Problem: Calculate 6 × 9.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 54
Worked Example 9
Problem: Calculate 3 × 6.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 10
Problem: Calculate 6 × 9.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 54
Practice Exercise
Create and solve one new example of Multiplying patterns by 10. 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.
33.5 Decimal-tenth addition patterns
A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Worked Example 2
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 3
Problem: Write 6/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.6
Worked Example 4
Problem: Write 1/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.1
Worked Example 5
Problem: Write 2/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.2
Worked Example 6
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 7
Problem: Write 0/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.0
Worked Example 8
Problem: Write 9/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.9
Worked Example 9
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 10
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Practice Exercise
Create and solve one new example of Decimal-tenth addition patterns. 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.
33.6 Decimal-tenth subtraction patterns
A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 2
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Worked Example 3
Problem: Write 0/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.0
Worked Example 4
Problem: Write 1/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.1
Worked Example 5
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Worked Example 6
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 7
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 8
Problem: Write 2/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.2
Worked Example 9
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 10
Problem: Write 1/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.1
Practice Exercise
Create and solve one new example of Decimal-tenth subtraction patterns. 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.
33.7 Place-value patterns
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 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 3
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 4
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
Worked Example 5
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 6
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 7
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 8
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
Worked Example 9
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 10
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
Practice Exercise
Create and solve one new example of Place-value patterns. 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.
33.8 Patterns crossing a whole 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 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 2
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 3
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 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 4, 8, 12, ... 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: 16, 20
Worked Example 6
Problem: Continue 4, 8, 12, ... 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: 16, 20
Worked Example 7
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 8
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 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 4, 8, 12, ... 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: 16, 20
Practice Exercise
Create and solve one new example of Patterns crossing a whole 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.
33.9 Tables for decimal patterns
A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Write 9/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.9
Worked Example 2
Problem: Write 9/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.9
Worked Example 3
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Worked Example 4
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 5
Problem: Write 1/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.1
Worked Example 6
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Worked Example 7
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 8
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Worked Example 9
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Worked Example 10
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Practice Exercise
Create and solve one new example of Tables for decimal patterns. 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.
33.10 Graphs for decimal patterns
A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Write 9/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.9
Worked Example 2
Problem: Write 4/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.4
Worked Example 3
Problem: Write 6/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.6
Worked Example 4
Problem: Write 8/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.8
Worked Example 5
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Worked Example 6
Problem: Write 8/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.8
Worked Example 7
Problem: Write 3/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.3
Worked Example 8
Problem: Write 7/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.7
Worked Example 9
Problem: Write 8/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.8
Worked Example 10
Problem: Write 5/10 as a decimal.
- The denominator 10 means tenths.
- Put the numerator in the tenths place.
Very beginner explanation: Tenths can be written as either fractions or decimals.
Answer: 0.5
Practice Exercise
Create and solve one new example of Graphs for decimal patterns. 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.
33.11 Predicting later terms
Predicting later terms is an important Grade 4 mathematics idea in Whole-Number and Decimal-Tenth Patterns. 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 Predicting later terms using the numbers 12 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 Predicting later terms.
Worked Example 2
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 5 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 Predicting later terms.
Worked Example 3
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 11 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 Predicting later terms.
Worked Example 4
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 15 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 Predicting later terms.
Worked Example 5
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 3 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 Predicting later terms.
Worked Example 6
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 10 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 Predicting later terms.
Worked Example 7
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 19 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 Predicting later terms.
Worked Example 8
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 20 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 Predicting later terms.
Worked Example 9
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 11 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 Predicting later terms.
Worked Example 10
Problem: Create a simple Grade 4 example about Predicting later terms using the numbers 19 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- Check that the result or representation makes sense.
Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.
Answer: A correct example that demonstrates Predicting later terms.
Practice Exercise
Create and solve one new example of Predicting later terms. 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.
33.12 Connecting patterns to mental math
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 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 3
Problem: Continue 6, 12, 18, ... 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: 24, 30
Worked Example 4
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 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 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 7
Problem: Continue 6, 12, 18, ... 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: 24, 30
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 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 10
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
Practice Exercise
Create and solve one new example of Connecting patterns to mental math. 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 Adding 10 repeatedly?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q2. What is important to understand about Adding 100 repeatedly?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q3. What is important to understand about Subtracting 10 repeatedly?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q4. What is important to understand about Multiplying patterns by 10?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q5. What is important to understand about Decimal-tenth addition patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q6. What is important to understand about Decimal-tenth subtraction patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q7. What is important to understand about Place-value patterns?
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 Patterns crossing a whole number?
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 Tables for decimal patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q10. What is important to understand about Graphs for decimal patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q11. What is important to understand about Predicting later terms?
Answer: Predicting later terms is an important Grade 4 mathematics idea in Whole-Number and Decimal-Tenth Patterns. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q12. What is important to understand about Connecting patterns to mental math?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q13. How would you explain Adding 10 repeatedly?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q14. How would you explain Adding 100 repeatedly?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q15. How would you explain Subtracting 10 repeatedly?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q16. How would you explain Multiplying patterns by 10?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q17. How would you explain Decimal-tenth addition patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q18. How would you explain Decimal-tenth subtraction patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q19. How would you explain Place-value patterns?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q20. How would you explain Patterns crossing a whole number?
Answer: A pattern follows a predictable rule. Repeating patterns repeat a core; growing patterns change in a consistent way.
Q21. How would you explain Tables for decimal patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q22. How would you explain Graphs for decimal patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q23. How would you explain Predicting later terms?
Answer: Predicting later terms is an important Grade 4 mathematics idea in Whole-Number and Decimal-Tenth Patterns. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q24. How would you explain Connecting patterns to mental math?
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 Adding 10 repeatedly?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q26. What should a beginner check when working with Adding 100 repeatedly?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q27. What should a beginner check when working with Subtracting 10 repeatedly?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q28. What should a beginner check when working with Multiplying patterns by 10?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q29. What should a beginner check when working with Decimal-tenth addition patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.
Q30. What should a beginner check when working with Decimal-tenth subtraction patterns?
Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.