Year 5 - Maths
Multiplying and dividing a number by 10, 100 and 1,000
Calculating with decimal fractions
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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 effect of multiplying and dividing a number by 10, 100 and 1,000 and use their knowledge of multiplying decimal fractions by whole numbers to solve measures problems.
Lesson Summary
You will learn to explain the effect of multiplying and dividing a number by 10, 100 and 1,000.
Key Notes
- To multiply a number by 1,000 move the digits three places to the left - this makes the number 1,000 times the size.
- To divide a number by 1,000 move the digits three places to the right - this makes the numbers 1,000th times the size.
- A place value chart can be used to explain how the digits move when you multiply or divide by 10, 100 and 1,000.
- Use a Gattengo chart can be used to explain how the digits move when you multiply divide by 10, 100 and 1,000.
- Dividing by 10, 100 or 1,000 is equivalent to multiplying by 0.1, 0.01 or 0.001 respectively.
Vocabulary To Learn
- Thousandth: One-thousandth is one part in one thousand equal parts.
- Equivalent: If something is equivalent, it has the same value. For example, £1 is equivalent to 100 p - they have the same value.
Common Mistakes To Avoid
- Children may confuse use of the Base 10 equipment. They may also confuse the equivalence between dividing by 10/100/1,000 and multiplying by 0.1/0.01/0.001.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
To multiply a number by 1,000 move the digits three places to the left - this makes the number 1,000 times the size. To divide a number by 1,000 move the digits three places to the right - this makes the numbers 1,000th times the size.
2. Use this key word in a maths sentence and explain it clearly. 'Thousandth'
One-thousandth is one part in one thousand equal parts. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Children may confuse use of the Base 10 equipment. They may also confuse the equivalence between dividing by 10/100/1,000 and multiplying by 0.1/0.01/0.001. Correction: The large cube now represents one whole. The smaller blocks represent decimal fraction numbers. Use stem sentences to support common mistakes: when a number is divided by ___, it is the same as multiplying by ___.
More Lessons In This Unit
- Converting units of length Study Guide
- Converting units of mass and capacity Study Guide
- Divide decimal fractions by 1-digit numbers Study Guide
- Divide decimal fractions by 1-digit numbers using written methods Study Guide
- Explain how to multiply and divide a number by 10, 100 and 1,000 Study Guide
- Multiply 1-digit numbers by decimal fractions using written methods Study Guide
- Multiply 1-digit numbers by decimals Study Guide
- Multiply hundredths by whole numbers Study Guide
- Multiply tenths by whole numbers Study Guide
- Multiplying and dividing a number by 10, 100 and 1,000 including bridging 1 Study Guide
- Predicting the size of a product Study Guide
- Solve measures problems using knowledge of multiplying decimal fractions Study Guide
- The relationship between multiplying by 0.01 and dividing by 100 Study Guide
- The relationship between multiplying by 0.1 and dividing by 10 Study Guide
Browse all guides in the Year 5 Maths guide library.