Decimals Addition and Subtraction Exploring decimals Objectives Day

Decimals, Addition and Subtraction Exploring decimals Objectives Day 1 Y 5: Revise place value in numbers with three decimal places; Convert between kilograms and grams, litres and millilitres, metres and kilometres. Y 6: Revise place value in numbers with three decimal places; Convert between kilograms and grams, litres and millilitres, metres and kilometres. Day 2 Y 5: Compare and order numbers with three decimal places and place on a line. Y 6: Realise when a calculator has produced a rounding error. © hamilton-trust. org. uk 1 Year 5/6

Decimals, Addition and Subtraction Exploring decimals Short Mental Workouts Day 1 Count on and back in steps of 0. 002 Day 2 Round numbers with one or two decimal places to the nearest whole © hamilton-trust. org. uk 2 Year 5/6

Decimals, Addition and Subtraction Exploring decimals Short Mental Workout Count on and back in steps of 0. 002 © hamilton-trust. org. uk 3 Year 5/6

Decimals, Addition and Subtraction Exploring decimals Short Mental Workout Round numbers with one or two decimal places to the nearest whole © hamilton-trust. org. uk 4 Year 5/6

Decimals, Addition and Subtraction Exploring decimals Day 1 Y 5 and Y 6: Revise place value in numbers with three decimal places; Convert between kilograms and grams, litres and millilitres, metres and kilometres. © hamilton-trust. org. uk 5 Year 5/6

Day 1 Y 5 and Y 6: Revise place value in numbers with three decimal places. Convert between kilograms and grams, litres and millilitres, metres and kilometres. What is the digit 4 worth? 4. 378 What is the digit 8 worth? What is the digit 3 worth? What is the digit 7 worth? Write your own 4 -digit number with three decimal places. 2 3 5 6 7 1 4 9 8 © hamilton-trust. org. uk If you have this digit in your number, subtract its value, e. g. If you wrote first person 2. 783, The subtract 0. 08. Iftothe digit reach zeronumber, wins! subtract shown isn't in your nothing. 6 Year 5/6

Day 1 Y 5 and Y 6: Revise place value in numbers with three decimal places. Convert between kg and g, l and ml, m and km. Look at the weights written in grams on the jars and cans. We’re going to write these weights in kilograms. Remember that there are 1000 g in 1 kg. Look at this 100 g weight. Is this 0. 001 kg, 0. 01 kg or 0. 1 kg? What does each digit after the decimal point represent? Look at this 1 g weight. Is this 0. 001 kg, 0. 01 kg or Look at this 10 g weight. 0. 1 kg? Is this 0. 001 kg, 0. 01 kg or 0. 1 kg? Which is the heaviest can? Which is the lightest can? Is this the biggest can? Is this the smallest can? Let’s arrange the cans in order of weight. © hamilton-trust. org. uk 7 Year 5/6

Day 1 Y 5 and Y 6: Revise place value in numbers with three decimal places. Convert between kg and g, l and ml, m and km. 1275 ml 495 ml 350 ml 400 ml In pairs, convert each measure from millilitres to litres. Remember that there are 1000 ml in a litre. 2. 375 km 0. 208 km 2. 6 km 4. 25 km In pairs, convert each distance from kilometres to metres. Remember that there are 1000 m in a kilometre. © hamilton-trust. org. uk 8 Year 5/6

Challenge © hamilton-trust. org. uk 9 Year 5/6

Decimals, Addition and Subtraction Exploring decimals Day 2 Y 5: Compare and order numbers with three decimal places and place on a line. Y 6: Realise when a calculator has produced a rounding error. © hamilton-trust. org. uk 12 Year 5/6

Day 2: Compare and order numbers with three decimal places and place on a line. Realise when a calculator has produced a rounding error. □. □□□ > □. □□□ 7 5 © hamilton-trust. org. uk Where shall we put this card to try to make sure that the first number is greater than the second number? 1 8 Write on your whiteboards a number between the two numbers. 13 3 9 4 2 Year 5/6

Day 2: Compare and order numbers with three decimal places and place on a line. Realise when a calculator has produced a rounding error. □. □□□ < □. □□□ 2 3 5 Where shall we put this card to try to make sure that the first number is less than the second number? 6 © hamilton-trust. org. uk 1 9 Write on your whiteboards a number between the two numbers. 14 7 8 Year 5/6

Day 2: Compare and order numbers with three decimal places and place on a line. Realise when a calculator has produced a rounding error. 5. 289 On your whiteboards, write these numbers in order from smallest to largest. 5. 974 5. 278 Compare your list with a partner and explain how you put them in order. Together, think of a number between each neighbouring pair of numbers: one with one decimal place, one with two decimal places, and one with three decimal places. Numbers with more digits are bigger than those with fewer digits. © hamilton-trust. org. uk 5. 419 They all began with five ones, so what did you look at to help order them? Let’s place one pair’s numbers on this line. Discuss the statement in pairs, and then prepare an argument for why you think it is/isn’t true. 15 Year 5/6

Investigation: Adult Sheet © hamilton-trust. org. uk 16 Year 5/6

Investigation: Child Sheet © hamilton-trust. org. uk 17 Year 5/6

Challenge © hamilton-trust. org. uk 18 Year 5/6

Day 2: Realise when a calculator has produced a rounding error. Enter 1 ÷ 3 into the calculator. If you multiply this answer by 3, what should you get? Try it. What happens? Let’s use the computer’s calculator (or one on a phone) to carry out the same key sequence. . . This calculator gets 1 as an answer, why do you think that happens? © hamilton-trust. org. uk 19 Year 5/6

Day 2: Realise when a calculator has produced a rounding error. Now divide 1 by 4, then multiply by 4. What happens this time? Do you think the calculator will give the correct answer when dividing, then multiplying 1 by 5? Why? What about dividing by 6? Try it! © hamilton-trust. org. uk 20 Year 5/6

Challenge © hamilton-trust. org. uk 21 Year 5/6

Decimals, Addition and Subtraction Exploring decimals Well Done! You’ve completed this unit. Objectives Day 1 Y 5: Revise place value in numbers with three decimal places; Convert between kilograms and grams, litres and millilitres, metres and kilometres. Y 6: Revise place value in numbers with three decimal places; Convert between kilograms and grams, litres and millilitres, metres and kilometres. Day 2 Y 5: Compare and order numbers with three decimal places and place on a line. Y 6: Realise when a calculator has produced a rounding error. © hamilton-trust. org. uk 22 Year 5/6

Problem solving and reasoning questions Year 5 Write the value of each digit as a fraction: 0. 375 Write the total of this addition as a decimal: Ali’s homework needs marking. Write the correct answers for those he has wrong. Explain any mistakes Ali is making… Write < or > or = between each pair of numbers: (a) 0. 34 < 0. 099 (b) 1. 075 > 1. 08 (c) 6. 006 < 6. 06 (d) 5. 264 > 5. 27 (e) 9. 999 > 10. 001 © hamilton-trust. org. uk 23 Year 5/6

Problem solving and reasoning questions Year 6 Write the value of each digit as a fraction: 3. 726 Write the total of this addition as a decimal: Sadi’s homework needs marking. Write the correct answers for any she has wrong. Explain any mistakes Sadi is making… Write < or > or = between each pair of numbers: (a) 0. 27 < 0. 088 (b) 1. 075 > 1. 09 (c) 3. 003 < 3. 03 (d) 5. 148 > 5. 32 © hamilton-trust. org. uk 24 Year 5/6

Problem solving and reasoning answers Year 5 Write the value of each digit as a fraction: 0. 375 Write the total of this addition as a decimal: An answer of 0. 643 suggests the denominators have been ignored. Suggest children order to the fractions largest to smallest; that will then determine the order of the digits after the decimal place. © hamilton-trust. org. uk 25 Year 5/6

Problem solving and reasoning answers Year 5 continued a) b) c) d) e) 0. 34 < 0. 099 1. 075 > 1. 08 6. 006 < 6. 06 5. 264 > 5. 27 9. 999 > 10. 001 0. 34 > 0. 099 1. 075 < 1. 08 Correct 5. 264 < 5. 27 9. 999 < 10. 001 The most likely sources of Ali’s errors is thinking that the number in each pair with the greater number of digits is the larger or reading the decimal part as a whole number (e. g. ‘thirty four’ and ‘ninety nine’ in question a). In e) the presence of so many 9 s may give the appearance of 9. 999 being a larger number than 10. 001. Ali may also be confused about the greater than and less than symbols. Remind children that the ‘open end of the crocodile’s mouth’ always faces the larger number. © hamilton-trust. org. uk 26 Year 5/6

Problem solving and reasoning answers Year 6 Write the value of each digit as a fraction: 3. 726 Write the total of this addition as a decimal: An answer of 0. 937 suggests the denominators have been ignored. Suggest children order to the fractions largest to smallest; that will then determine the order of the digits after the decimal place. Sadi’s homework needs marking. Write the correct answers for any she has wrong. Explain any mistakes Sadi is making. Write < or > or = between each pair of numbers: (a) 0. 27 < 0. 088 0. 27 > 0. 088 (b) 1. 075 > 1. 09 1. 075 < 1. 09 (c) 3. 003 < 3. 03 Correct (d) 5. 148 > 5. 32 5. 148 < 5. 32 The most likely sources of errors is reading the decimal part as a whole number, e. g. ‘eighty eight’ and ‘twenty seven’ in question (a). © hamilton-trust. org. uk 27 Year 5/6