**National curriculum content**

- Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]

- Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
- Multiply one-digit numbers with up to two decimal places by whole numbers
- Use written division methods in cases where the answer has up to two decimal places
- Solve problems which require answers to be rounded to specified degrees of accuracy
- Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

**Lesson objectives**

- Recap – Decimals up to 2d.p.
- Recap – Understand thousandths
- Three decimal places
- Multiply by 10, 100 and 1,000
- Divide by 10, 100 and 1,000
- Multiply decimals by integers
- Divide decimals by integers
- Division to solve problems
- Decimals as fractions
- Fractions to decimals (1)
- Fractions to decimals (2)

**What we want children to know**

- Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375).
- For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context.
- Pupils multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers.
- Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money.
- Pupils are introduced to the division of decimal numbers by one-digit whole number, initially, in practical contexts involving measures and money.
- They recognise division calculations as the inverse of multiplication.
- Pupils also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.

**What skills we want children to develop**

Use knowledge to solve reasoning and problem solving questions such as:

**True or false?**

25% of 23km is longer than 0.2 of 20km. Convince me.

In all of the following numbers, the digit 6 is worth __more than__ 6 hundredths.

3.6 3.063 3.006 6.23 7.761 3.076

Is this true or false? Change some numbers so that it is true.

**Undoing**

I multiply a number with three decimal places by a multiple of 10. The answer is approximately 3.21

What was my number and what did I multiply by?

When I divide a number by 1000 the resulting number has the digit 6 in the units and tenths and the other digits are 3 and 2 in the tens and hundreds columns. What could my number have been?

**Another and another**

Write a unit fraction which has a value of less than 0.5 … and another, … and another, …

**Ordering**

Put the following amounts in order, starting with the largest.

23%, 5/8, 3/5, 0.8

**Vocabulary/Mathematical Talk**

- How many tenths/hundredths/thousandths are there in the number?
- Can you make the number on the place value chart?
- How many hundredths are the same as 5 tenths?
- What is the value of the zero in this number?
- What number is represented on the place value chart?
- Why is 0 important when multiplying by 10, 100 and 1,000? What patterns do you notice?
- What is the same and what is different when multiplying by 10, 100, 1,000 on the place value chart compared with the Gattegno chart?
- What happens to the counters/digits when you divide by 10, 100 or 1,000?
- What is happening to the value of the digit each time it moves one column to the right?
- What are the relationships between tenths, hundredths and thousandths?
- Which is bigger, 0.1, 0.01 or 0.001? Why?
- How many 0.1s do you need to exchange for a whole one?
- Can you draw a bar model to represent the problem?
- Can you think of another way to multiply by 5? (e.g. multiply by 10 and divide by 2).
- Are we grouping or sharing?
- How else could we partition the number 3.69? (For example, 2 ones, 16 tenths and 9 hundredths.) How could we check that our answer is correct?
- How would you record your answer as a decimal and a fraction? Can you simplify your answer?

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