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# Week 1 - 2 Decimals

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

1. Recap – Decimals up to 2d.p.
2. Recap – Understand thousandths
3. Three decimal places
4. Multiply by 10, 100 and 1,000
5. Divide by 10, 100 and 1,000
6. Multiply decimals by integers
7. Divide decimals by integers
8. Division to solve problems
9. Decimals as fractions
10.   Fractions to decimals (1)
11.   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?