Decimals, Percentages and Fractions Understanding place value in 3-place decimals Objectives Day 1 Revise 2-place decimals. Day 2 Introduce 3-place decimals. Day 3 Multiply and divide by 10, 100 and 1000. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. You will need a set of large 0 to 9 cards. On Day 2 children will need mini-whiteboards and pens. You will need a metre stick. On Day 3 you will need a set of large 0 to 9 cards and a card with a decimal point. Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Starters Day 1 Count in steps of 0.01 (pre-requisite skills) Day 2 Count in steps of 0.001 (pre-requisite skills) Day 3 Convert between m and cm (pre-requisite skills) Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day. Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Starter Count in steps of 0.01 Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Count in steps of 0.01 from 8.85 to 9.15. What is 8.89 add 0.01? What is 0.01 more than 8.99? What is 9.1 subtract 0.01? Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Starter Count in steps of 0.001 Pre-requisite skills – to use this starter, drag this slide to the start of Day 2 Count in steps of 0.001 from 2.995 to 3.005, on a counting stick. What is 0.001 more than 2.999? What is 0.001 more than 3? Write 5.345. What number is 0.001 more? 0.01 more? 0.1 more? 0.001 less? 0.01 less? 0.1 less? Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Starter Convert between m and cm Pre-requisite skills – to use this starter, drag this slide to the start of Day 3 Draw on the board a 4 × 3 grid and enter distances in centimetres, e.g. 43cm, 245cm, 30cm, 240cm. Children copy the grid but write the measurements in metres. Ensure to use numbers that challenge understanding of place value, e.g. 38cm, 308cm and 380cm. Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Objectives Day 1 Revise 2-place decimals. Year 5

What does the first digit represent? Day 1: Revise 2-place decimals. What does the first digit represent? 3.33 And the third digit? And the second digit? Let’s write the number in a place value grid to check. 1s 1/10s (0.1s) 1/100s (0.01s) 3 Split the class into two teams. For each team, assign a missing number template: □.□□. Shuffle a set of number cards 0–9. One child from team A picks a card and writes the digit it into their number, with the aim of making the largest number possible. Repeat for team B. Repeat for until all three spaces in each number are filled. Ask all children to write a number between the two numbers that the teams make. Repeat, but this time teams try to make the smallest number. Ask children to round each number to the nearest whole, then tenth. Round each number to the nearest whole, then tenth. Write a number between these two numbers. Year 5

Whole class investigation Day 1: Revise 2-place decimals. Whole class investigation • Work in pairs to find out how many numbers between 1 and 10, with one or two decimal places, contain a digit ‘9’. • How can you be sure you have found them all? Challenge! Do you think the answer will be the same for numbers that contain a zero? Today’s GROUP ACTIVITY is a whole class investigation. You can find more details in the unit’s TEACHING AND GROUP ACTIVITIES download. WT: Children find out how many numbers between 1 and 2, with one or two decimal places, contain a digit ‘9’. Can they extend their findings to numbers between 1 and 10? ARE/GD: Complete a short investigation to revisit numbers with two decimal places, as above. Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE/GD: Compare order and round numbers with 2 decimal places (Sheet 1) Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Objectives Day 2 Introduce 3-place decimals. Year 5

Which labels belong with each row in this place value chart? Day 2: Introduce 3-place decimals. Which labels belong with each row in this place value chart? tens thousands hundredths ones thousandths hundreds tenths Year 5

Which labels belong with each row in this place value chart? Day 2: Introduce 3-place decimals. We may not have come across this one before – why might we need to divide something into such a small amount? Which labels belong with each row in this place value chart? thousandths hundredths tenths ones tens hundreds thousands Note that 1 metre is 1 thousandth of a kilometre. Show a metre ruler. 1 millimetre is one thousandth of a metre! What happens to the digit 5 on the place value chart, as each number is multiplied by 10? What happens as each number is divided by 10? Year 5

And the next biggest? And then? Day 2: Introduce 3-place decimals. I can make this number by pointing to five numbers on the place value chart. What is the biggest number I would point to? And the next biggest? And then? 25.895 20 + 5 + 0.8 + 0.09 + 0.005 Year 5

Record the total of the ringed numbers on your whiteboards. Day 2: Introduce 3-place decimals. Record the total of the ringed numbers on your whiteboards. 351.637 Year 5

Record the total of the ringed numbers on your whiteboards. Day 2: Introduce 3-place decimals. Record the total of the ringed numbers on your whiteboards. 7351.637 Year 5

Record the total of the ringed numbers on your whiteboards. Day 2: Introduce 3-place decimals. Record the total of the ringed numbers on your whiteboards. 6350.249 Year 5

8165.042 Day 2: Introduce 3-place decimals. Record the total of the ringed numbers on your whiteboards. How do we show that there are no tenths? 8165.042 Year 5

Record the total of the ringed numbers on your whiteboards. Day 2: Introduce 3-place decimals. Record the total of the ringed numbers on your whiteboards. Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Write place value additions to match numbers with three decimal places. ARE/GD: Write place value additions to match numbers with three decimal places. Derive missing numbers. 307.003 Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE: Complete place value partitioning additions for numbers with 3 decimal places (Sheet 1). GD: Complete place value partitioning additions for numbers with 3 decimal places (Sheet 2) Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Objectives Day 3 Multiply and divide by 10, 100 and 1000. Year 5

6 4 2 6 Day 3: Multiply and divide by 10, 100 and 1000. 6 4 2 6 What is each 6 worth? Read the number together: six point four two six (not ‘six point four hundred and twenty-six’). Year 5

Stand on either side of the decimal point to show 1.234 Day 3: Multiply and divide by 10, 100 and 1000. 4 2 Stand on either side of the decimal point to show 1.234 1 3 Now multiply 1.234 by 10. Move to show the answer. The decimal point must NOT move! Does everyone else agree with the answer? What is the 4 worth now? Now multiply by 10 again. What is the 3 worth now? Choose a child to hold a card showing a decimal point. Make a fuss of them, saying they have today’s MOST IMPORTANT JOB – to STAND ABSOLUTELY STILL! Give four children number cards, e.g. 1, 2, 3 and 4. Ask them to stand on either side of the decimal point to show 1.234. Ask them to multiply their number by 10 and move accordingly. Decimal point –I’m watching you – don’t move! Does the class agree with the result of multiplication? Repeat with four new children showing 4567, ÷ 1000, × 10, etc. Occasionally pause and ask questions such as: What is the 6 worth now? And if we multiply by 10? What operation do we need to change the place value of the 7 from 7 tens to 7 thousandths? Today would be a great day to use a problem-solving investigation – Greater Than or Less Than – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website. Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Move digit cards on a place value grid to multiply and divide by 10 and 100. ARE/GD: Multiply and divide a number by 10, 100 and 1000. Divide capacities in ml to convert to litres. Now divide by 100. Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE: Work out the outputs for ×10, ÷10, ×100, ÷100, ×1000 and ÷1000 function machines (Sheet 1) ARE/GD: Work out the outputs for ×10, ÷10, ×100, ÷100, ×1000 and ÷1000 function machines (Sheet 2) Year 5

Decimals, Percentages and Fractions Understanding place value in 3-place decimals Well Done! You’ve completed this unit. Objectives Day 1 Revise 2-place decimals. Day 2 Introduce 3-place decimals. Day 3 Multiply and divide by 10, 100 and 1000. You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide. Year 5

Problem solving and reasoning questions Write the next numbers in each sequence. 41 4.1 ____ ____ 0.009 0.09 ____ ____ 20 2 ____ ____ ____ Divide 65 by 10 repeatedly until you get a number that is less than 0.1. Write that number. True or false? • 4.3 ÷ 100 = 0.43 • 109 = 1.009 x 100 • 0.005 x 100 = 0.5 • 71 ÷ 1000 = 0.0071 • 164 = 0.164 x 1000 • 804 ÷ 1000 = 0.084 Year 5

Problem solving and reasoning: Answers Write the next numbers in each sequence. 41 4.1 0.41 0.041 0.009 0.09 0.9 9 20 2 0.2 0.02 Look for the children who do not appropriately multiply or divide by 10, often evidenced in including unnecessary zeroes, for example, 41, 4.1, 4.10, 4.100. Divide 65 by 10 repeatedly until you get a number that is less than 0.1. Write that number. 0.065 An answer of 0.65 suggests child has misread the question and given the first number found less than 1. 65 needs to divided by ten 3 times to get to 0.065 True or false? • 4.3 ÷ 100 = 0.43 False, should be 0.043. • 109 = 1.009 x 100 False, should be 109 = 1.09 x 100 or 1.009 x 100 = 100.9 • 0.005 x 100 = 0.5 True • 71 ÷ 1000 = 0.0071 False, should be 71 ÷ 1000 = 0.071 or 71 ÷ 10,000 = 0.0071 • 164 = 0.164 x 1000 True • 804 ÷ 1000 = 0.084 False, should be 804 ÷ 1000 = 0.804 or 84 ÷ 1000 = 0.084 Check children have actually carried out the calculation, moving the digits to the right or left the appropriate number of places. Year 5