Level 3 Decimals

1. Level 3 Decimals

2. Level 3 decimals • Begin to use decimal notation in contexts such as money, e.g. - order decimals with one dp, or two dp in context of money - know that £3.06 equals 306p

3. Overcoming Barriers L2-3 • Can I use and explain decimal notation for tenths and hundredths Teaching tips • Make sure that children understand that the decimal point is used to separate whole amounts and parts of the whole. You might use place value cards and the Decimal number line ITP, or pounds and pence with money notation, to illustrate this point. • Help children become aware of the relative size of decimal numbers by ordering a set of amounts of money or lengths. Link this to ordering numbers on a number line. Make sure that you include numbers to overcome misconceptions such as mistaking the length of the number with its size, for example thinking that 4.05 is larger than 4.5. • Ensure that as children are introduced to decimal notation they hear and use the language of tenths and hundredths, i.e. they can read 3.6 as ‘three units and six tenths’ and not just as ‘three point six’. • Use a simple number line marked in divisions of 0.5 to familiarise children with counting forwards and backwards in steps of 0.5. Extend this to other number lines to develop counting in other step sizes (e.g. 0.2). • Use money and length as practical examples of decimals to place decimal numbers in context and compare size of numbers. For example: - Which is the larger amount, £0.75 or 90p? - Which is longer, 3.06 m or 3.6 m?

4. Progression of models and images • Place value – grid and charts (Moving Digits ITP and Place Value charts spreadsheet) • Counting stick – forwards and back • Number lines – Leads on from counting stick (Decimal number line ITP) • Ordering decimal numbers – one and two dp • Money/measures in context – Big coins

5. Level 4 decimals • Order decimals to three decimal places • Use efficient written methods of addition and subtraction - add and subtract decimals to two decimal places • Multiply a simple decimal by a single digit, e.g. calculate 36.2 x 8

6. Overcoming Barriers L3-4 • Can I read, write, partition and order decimal numbers? • Can I use my tables to work out multiplication and division facts with decimals

7. Level 4 decimals Ordering decimals to three decimal places: • Extend Place Value spreadsheet and explain values using appropriate vocabulary • Extend Decimal number line ITP • Use in the context of measures (mixed number of decimal places) Use efficient written methods of addition and subtraction: • Refer back to Place Value grid to model addition and subtraction of decimal numbers • Use the counting stick and Decimal number line ITP to add on and subtract (refer back to counting on and back) • Move on to efficient written methods (column methods) – money and measures contexts

8. Level 4 decimals cont… Multiply a simple decimal by a single digit: • Ensure children confidently multiply and divide by 10 and 100 and that they understand that multiplying by 10/100 gives an answer that is bigger than the original number and all the digits move one/two places to the left, while dividing by 10/100 gives an answer that is smaller than the original number and all the digits move one/two places to the right. • Start with known multiplication facts before relating these to decimal multiplication facts. Encourage children to explain the relationship between the two sets of numbers. • Ensure that children meet and can interpret multiplication and division calculations that are written in a variety of different ways, e.g. ? X 0.8 = 5.6 9 = 5.4 ÷ ? 0.3 x 8 = 6 x ? • Reinforce the division facts corresponding to multiplication facts. When solving a missing number question, it is helpful to write down the other three number sentences and then decide which one is most useful to use to help find the missing number • Model the use of jottings and encourage children to use jottings to help keep track of the stages within a mental calculation. • Spider diagrams of known facts • Number dials ITP

9. Fractions, decimals and percentages

10. Level 4 combined FDP • Recognise approximate proportions of a whole and use simple fractions and percentages to describe these: - recognise simple equivalence between fractions, decimals and percentages, e.g. ½, ¼, 1/10, ¾

11. Progression in combined FDP Fractions to decimals: - Relate to Place Value grids and Moving digits ITP using language of 10ths and 100ths - Top two rows of coloured number line (include common misconceptions, e.g. ½, ¼, ¾) - Use a calculator to divide and check Include percentages: - Understand parts out of 100 - Link to 100ths - Third line of coloured number line - Fractions ITP - Known facts spider diagrams (e.g. 100% = £1) Begin to find simple % equivalence mentally (High Level 4, links to Level 5) - Reason equivalence in problem solving

12. Summary • Teach explicit skills and understanding then link to context • Use a range of models and images to support teaching and learning (practical and ICT) • Ensure understanding of progression and build up understanding gradually (not jump from written methods) • Make links where appropriate, including with vocabulary • Plan for regular opportunities for children to reason, explain and compare fractions, decimals and percentages in their many forms