Year 4 - Maths
Explain how making the dividend 10 times the size affects the quotient
Understand what happens when a number is multiplied or divided by 10 and 100
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will explain the relationship between multiplying and dividing a number by 10 and multiples of 10.
Lesson Summary
You will learn to explain how making the dividend 10 times the size affects the quotient.
Key Notes
- If the dividend is multiplied by 10 then the quotient will be ten times the size.
- The dividend is equivalent to the product in the inverse calculation.
- 18 divided by 6 is equal to 3 so 180 divided by 6 is equal to 30 or 18 tens divided by 6 is equal to 3 tens.
Vocabulary To Learn
- Dividend: The dividend is the number being divided.
- Divisor: The divisor is the number we are dividing by.
- Quotient: The quotient is the result after division has taken place. It is a whole number.
Common Mistakes To Avoid
- Place value counters don't have proportionality in the same way that Base 10 does which can make the concepts here more abstract.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
If the dividend is multiplied by 10 then the quotient will be ten times the size. The dividend is equivalent to the product in the inverse calculation.
2. Use this key word in a maths sentence and explain it clearly. 'Dividend'
The dividend is the number being divided. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Place value counters don't have proportionality in the same way that Base 10 does which can make the concepts here more abstract. Correction: Smaller divisions can be used with Base 10 to model scaling to start off with. Try 2 ÷ 2 or 4 ÷ 2 scaling up to become 20 ÷ 2 or 40 ÷ 2 with Base 10 and then put this modelling side-by-side with place value counters to make the links.
More Lessons In This Unit
- Explain how making a factor 10 times the size affects the product Study Guide
- Explain how making a factor 100 times the size affects the product Study Guide
- Explain how making the dividend 100 times the size affects the quotient Study Guide
- Explain the relationship between multiplying a number by 10 and multiples of 10 Study Guide
- Explain the relationship between multiplying a number by 100 and multiples of 100 Study Guide
- Explain the removal of placeholders when dividing whole numbers by 100 Study Guide
- Explain the use of placeholders when multiplying whole numbers by 100 Study Guide
- Scale division facts derived from multiplication facts by 100 Study Guide
- Scale known multiplication facts by 100 Study Guide
- Understand that dividing a number by 10 makes it one-tenth times the size Study Guide
- Understand that multiplying by 10 makes a number ten times the size Study Guide
- Use knowledge of the composition of 100 to multiply and divide by 100 in different ways Study Guide
- Use place value to explain placing a zero after the final digit when we multiply whole numbers by 10 Study Guide
- Use place value to explain removing the zero in the ones from a multiple of ten when we divide by 10 Study Guide
Browse all guides in the Year 4 Maths guide library.