Addition Subtraction and Decimals Column addition mental subtraction
Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 1 Y 4 Add pairs of 2 -digit numbers mentally; Add 2–digit numbers to 3 -digit numbers using mental strategies. Y 5 Use written addition to add pairs of 4 -digit numbers. Day 2 Y 4 Add two 3 -digit numbers using compact written addition. Y 5 Use written addition to add pairs of 5 -digit numbers. Day 3 Y 4 Add three 3 -digit numbers using compact written addition. Y 5 Add amounts of money using column addition. Day 4 Y 4 Find a difference by counting up. Y 5 Add amounts of money using column addition. Use rounding to check answers. Day 5 Y 4 Count up and use number bonds to subtract 2 -digit numbers from 100. Y 5 Find change from £ 20, £ 50 and £ 100 using counting up (Frog). Day 6 Y 4 Choose counting up/back to subtract 2 -digit numbers from numbers >100. Y 5 Find the difference between two prices using counting up (Frog). © hamilton-trust. org. uk 1 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workouts Day 1 Count on in 10 s from any 3 -digit number Day 2 Pairs to 20 and related subtractions Day 3 Add three 1 -digit numbers, spotting bonds to 10 and doubles Day 4 Complements to multiples of 10 Day 5 Count back in 10 s from any 3 -digit number, including crossing 100 s Day 6 Bonds to £ 1 © hamilton-trust. org. uk 2 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workout Count on in 10 s from any 3 -digit number © hamilton-trust. org. uk 3 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workout Pairs to 20 and related subtractions © hamilton-trust. org. uk 4 Year 4/5
© hamilton-trust. org. uk 5 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workout Add three 1 -digit numbers, spotting bonds to 10 and doubles © hamilton-trust. org. uk 6 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workout Complements to multiples of 10 © hamilton-trust. org. uk 7 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workout Bonds to £ 1 © hamilton-trust. org. uk 8 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Short Mental Workout Units of time © hamilton-trust. org. uk 9 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 1 Y 4 Add pairs of 2 -digit numbers mentally. Add 2–digit numbers to 3 -digit numbers using mental strategies. Y 5 Use written addition to add pairs of 4 -digit numbers. © hamilton-trust. org. uk 10 Year 4/5
Day 1: Add pairs of 2 -digit numbers mentally. Add 2–digit numbers to 3 -digit numbers using mental strategies. Use written addition to add pairs of 4 -digit numbers. Let’s remember how to add two numbers by partitioning. Partition the numbers into 10 s and 1 s. Add the 10 s, then the 1 s. Then add together to find the total. © hamilton-trust. org. uk + 2 04 4 08 8 2 0 4 4 0 2 0 + 4 0 = 6 0 = 1 02 + 4 8 + 1 02 6 0 11 = 7 02 Year 4/5
Day 1: Add pairs of 2 -digit numbers mentally. Add 2–digit numbers to 3 -digit numbers using mental strategies. Use written addition to add pairs of 4 -digit numbers. 3458 + 2477 3478 + 2827 3455 + 2327 Which do you think will have the biggest answer and which do you think will have the smallest answer? Talk to your partner to agree an order without calculating the answers. • Each number could be rounded to the nearest 1000 to give an approximation, in which case the first and last would have the same approximation. • Or each could be rounded to the nearest 100, and then knowledge of adding pairs of 2 -digit numbers used to find more accurate approximations. 3458 + 2477: 3500 + 2500 = 6000 3478 + 2827: 3500 + 2800 = 6300 3455 + 2327: 3500 + 2300 = 5800 © hamilton-trust. org. uk 12 Year 4/5
Day 1: Add pairs of 2 -digit numbers mentally. Add 2–digit numbers to 3 -digit numbers using mental strategies. Use written addition to add pairs of 4 -digit numbers. • Now let’s find the exact total for 3458 + 2477 using compact column addition. Add the 10 s. Add the. Add 1000 s. the 100 s. Remember to leave a blank row above the answer line. © hamilton-trust. org. uk Add the 1 s. 3458 + 2477 11 5 93 5 13 How does this answer compare with your estimate? Year 4/5
© hamilton-trust. org. uk 14 Year 4/5
Day 1: Add pairs of 2 -digit numbers mentally. Add 2–digit numbers to 3 -digit numbers using mental strategies. Let’s try 178 + 31. Let’s check how to add a 2 -digit number to a 3 -digit number. First partition the numbers: 178 = 100 + 70 + 8 and 31 = 30 + 1 Then re-order the 10 s and 1 s, and then add: 178 + 31 = 100 + 70 + 30 + 8 + 1 = 100 + 9 = 209 © hamilton-trust. org. uk It’s OK to do some jottings to help! 15 Year 4/5
Day 1: Add pairs of 2 -digit numbers mentally. Add 2–digit numbers to 3 -digit numbers using mental strategies. Now look at these four additions: 125 + 26 154 + 27 22 + 195 What do you think is the most efficient strategy for each? e. g. For 137 + 19 you can add 20 and subtract 1. Talk to your partner… How would you do each one? Try with some jottings. © hamilton-trust. org. uk 137 + 19 16 Year 4/5
Y 4 Investigation: Adult Sheet © hamilton-trust. org. uk 17 Year 4/5
Y 4 Investigation: Child Sheet © hamilton-trust. org. uk 18 Year 4/5
Challenge © hamilton-trust. org. uk 19 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 2 Y 4 Add two 3 -digit numbers using compact written addition. Y 5 Use written addition to add pairs of 5 -digit numbers. © hamilton-trust. org. uk 20 Year 4/5
Day 2: Add two 3 -digit numbers using compact written addition. Use written addition to add pairs of 5 -digit numbers. Try 324 + 439 on your whiteboards using a written method – it could be expanded or compact addition. © hamilton-trust. org. uk 21 Year 4/5
Day 2: Add two 3 -digit numbers using compact written addition. Use written addition to add pairs of 5 -digit numbers. 324 + 439 Today, we will focus on compact written addition. Set the numbers out with 100 s, 10 s and 1 s lined up. Don’t forget the space above the line for any extra 10 s digits from adding 1 s, or 100 s digits from the 10 s. © hamilton-trust. org. uk 22 Year 4/5
Day 2: Add two 3 -digit numbers using compact written addition. Use written addition to add pairs of 5 -digit numbers. 324 + 439 1 3 First add the 1 s. 4+9=? Look where the digits go. © hamilton-trust. org. uk 324 + 439 1 63 324 + 439 1 763 Next the 10 s. 20 + 30 + 10 = ? Don’t forget that last 10. 23 Finally add the 100 s. 300 + 400 = ? Year 4/5
Challenge © hamilton-trust. org. uk 24 Year 4/5
Day 2: Use written addition to add pairs of 5 -digit numbers. Roughly how many people visited the website on Sunday (am and pm)? HINT! Round to the nearest thousand, then add the 2 -digit numbers of 1000 s (36, 000 and 57, 000). • Now let’s find the exact total using compact column addition. 36432 + 57478 1 11 How does this compare with your estimate? © hamilton-trust. org. uk 25 939 10 Year 4/5
Day 2: Use written addition to add pairs of 5 -digit numbers. Roughly how many people visited the website on Monday (am and pm)? • How does this compare with your estimate? © hamilton-trust. org. uk 26 Now let’s find the exact total using compact column addition. 19758 + 24642 1 111 4 440 0 Year 4/5
Y 5 Investigation: Adult Sheet © hamilton-trust. org. uk 27 Year 4/5
Y 5 Investigation: Child Sheet © hamilton-trust. org. uk 28 Year 4/5
Y 5 Investigation: Adult Sheet © hamilton-trust. org. uk 29 Year 4/5
Y 5 Investigation: Child Sheet © hamilton-trust. org. uk 30 Year 4/5
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Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 3 Y 4 Add three 3 -digit numbers using compact written addition. Y 5 Add amounts of money using column addition. © hamilton-trust. org. uk 32 Year 4/5
Day 3: Add three 3 -digit numbers using compact written addition. Add amounts of money using column addition. • • Two DVDs cost £ 14. 79 and £ 12. 49. Now let’s find the exact total using column addition – first the expanded method then the compact method. £ 14 + £ 12 £ 1 £ 27 70 p 9 p 40 p 9 p 10 p 20 p 8 p £ 14. 79 +£ 12. 49 1 1 £ 27. 28 © hamilton-trust. org. uk 33 Year 4/5
Day 3: Add three 3 -digit numbers using compact written addition. Add amounts of money using column addition. • Two DVDs cost £ 15. 79 and £ 12. 45. • Y 5 s - Find the exact total using column addition. Choose either the expanded or the compact layout. • Y 4 s - Round to the nearest pound add to make an approximation. • Check your answer with a neighbour. • Y 5 s - Did you both get £ 28. 24? Y 4 s - Did you both get £ 28? © hamilton-trust. org. uk 34 Year 4/5
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Day 3: Add three 3 -digit numbers using compact written addition. 592 + 235 Try 592 + 235 on your whiteboards using the compact written method. 592 + 235 7 592 + 235 1 27 Let’s check the steps. 592 + 235 1 827 First add the 1 s. Place the answer carefully. Next the 10 s. 90 + 30 = ? Don’t forget the 1 under the 100 s. © hamilton-trust. org. uk 36 Finally add the 100 s. 500 + 200 + 100. Year 4/5
Day 3: Add three 3 -digit numbers using compact written addition. 123 474 + 332 Let’s try the same method to add 3 numbers! 123 474 + 332 9 Add the 1 s. 3+4+2=? © hamilton-trust. org. uk Let’s check the steps. 123 474 + 332 1 929 123 474 + 332 1 29 Next the 10 s. 20 + 70 + 30 = ? 37 Don’t forget the extra 100! Lastly, the 100 s. 100 + 400 + 300 + 100 = ? Year 4/5
Day 3: Add three 3 -digit numbers using compact written addition. 238 111 + 216 Now try 238 + 111 + 216 on your whiteboards. 238 111 + 216 1 5 Add the 1 s. 8 + 1 + 6 = 15 Where did you put the digits? © hamilton-trust. org. uk 238 111 + 216 1 65 Next the 10 s. 30 + 10 = ? 38 Set it out neatly! 238 111 + 216 1 565 Lastly, the 100 s. 200 + 100 + 200 = ? Year 4/5
Challenge © hamilton-trust. org. uk 39 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 4 Y 4 Find a difference by counting up. Y 5 Add amounts of money using column addition. Use rounding to check answers. © hamilton-trust. org. uk 40 Year 4/5
Day 4: Find a difference by counting up. Add amounts of money using column addition. Use rounding to check answers. £ 27. 85 + £ 14. 29 £ 45. 69 + £ 34. 49 £ 14. 67 + £ 18. 75 Y 4 s - Use rounding to the nearest pound to write an approximate total for each. Y 5 s - Split into 3 s and each calculate an exact answer for one of the questions. © hamilton-trust. org. uk 41 Year 4/5
Day 4: Find a difference by counting up. Add amounts of money using column addition. Use rounding to check answers. £ 27. 85 + £ 14. 29 £ 45. 69 + £ 34. 49 £ 14. 67 + £ 18. 75 Here are the answers to the nearest pound: £ 27. 85 + £ 14. 29: £ 28 + £ 14 = £ 42 £ 45. 69 + £ 34. 49: £ 46 + £ 34 = £ 80 £ 14. 67 + £ 18. 75: £ 15 + £ 19 = £ 34 Y 5 s - How close to the estimates were your exact answers? © hamilton-trust. org. uk 42 Year 4/5
© hamilton-trust. org. uk 43 Year 4/5
Day 4: Find a difference by counting up. Add the jumps to find the answer. to to find 78 – 47. He wants helps us subtract numbers by counting up from Do you Frog remember Maths Frog? 20 + 8 + 3 = ? Draw the a line on your whiteboards smaller number to the larger number; he finds a and recorddifference Frog’s jumps. between two numbers. Frog always jumps left to right along the number line to – 47 = 31 So 78 the next ‘friendly number’, e. g. 10, 100, £ 10. Frog hops 3 to 50… … then 8 to hop from 70 to 78. 20 3 47 … and another 20 to jump from 50 to 70. . . 50 © hamilton-trust. org. uk 8 70 44 78 Year 4/5
Day 4: Find a difference by counting up. Sometimes, Frog can solve questions with only 2 jumps… Add the jumps to find the answer … First jump 3 to the next 10… 28 3 50 47 © hamilton-trust. org. uk So 78 – 47 = 31 … and then one more jump from 50 to 78. 78 45 Year 4/5
Day 4: Find a difference by counting up. Add the jumps to find the answer. 30 + 5 + 3 = ? Now, on your boards try 85 – 47. You can take 2 jumps or 3 jumps. First hop 3 to 50… … and another 30 to jump from 50 to 80. . . … then 5 to hop from 80 to 85. 30 3 47 So 85 – 47 = 38 50 © hamilton-trust. org. uk 5 80 46 85 Year 4/5
Day 4: Find a difference by counting up. Who tried it with 2 jumps? Add the jumps to find the answer … The first jump is the same… 35 3 50 47 © hamilton-trust. org. uk So 85 – 47 = 38 … and then one more jump of 35 from 50 to 85. 85 47 Year 4/5
Challenge © hamilton-trust. org. uk 48 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 5 Y 4 Count up and use number bonds to subtract 2 -digit numbers from 100. Y 5 Find change from £ 20, £ 50 and £ 100 using counting up (Frog). © hamilton-trust. org. uk 49 Year 4/5
Day 5: Count up and use number bonds to subtract 2 -digit numbers from 100. Find change from £ 20, £ 50 and £ 100 using counting up (Frog). How can Frog solve 100 – 85 on the number line? +5 + 10 85 First mark on 85. Jump 5 to 90. Then 10 to 100 – 85 = ? © hamilton-trust. org. uk 50 Year 4/5
Day 5: Count up and use number bonds to subtract 2 -digit numbers from 100. Find change from £ 20, £ 50 and £ 100 using counting up (Frog). Use number bonds when you know them. What is 85 + 15? So what is 100 – 85 ? © hamilton-trust. org. uk 51 Year 4/5
Day 5: Count up and use number bonds to subtract 2 -digit numbers from 100. Find change from £ 20, £ 50 and £ 100 using counting up (Frog). Talk to your partner… For these questions is it more efficient to count up to the nearest 10 and then 100 OR can you recall the number bonds to do one big hop to 100? 100 – 75 100 – 65 100 – 78 100 – 57 © hamilton-trust. org. uk 52 Year 4/5
Day 5: Count up and use number bonds to subtract 2 -digit numbers from 100. Find change from £ 20, £ 50 and £ 100 using counting up (Frog). Use number bonds when you know them. What is 75 + 25? So what is 100 – 75? © hamilton-trust. org. uk 53 Year 4/5
Day 5: Count up and use number bonds to subtract 2 -digit numbers from 100. Find change from £ 20, £ 50 and £ 100 using counting up (Frog). 100 82 Talk to your partner… For this bar model, could you use Frog OR use number bonds to find the missing number…? I could Frog jump 8 to 90 then 10 to 100. I know the number bond: 82 + 18 = 100. © hamilton-trust. org. uk 54 Year 4/5
Challenge © hamilton-trust. org. uk 55 Year 4/5
Day 5: Find change from £ 20, £ 50 and £ 100 using counting up (Frog). What would you like to buy for less than £ 20? Frog hops 21 p to £ 19… The price is £ 18. 79. We can use Frog to help us to find how much change we would get from £ 20. … and another £ 1 to jump from £ 19 to £ 20. £ 1 21 p £ 18. 79 © hamilton-trust. org. uk So how much change would we get? Add the hops! £ 19 £ 20 56 Year 4/5
Day 5: Find change from £ 20, £ 50 and £ 100 using counting up (Frog). The price is £ 43. 49. Use Frog to help us to find how much change we would get from £ 50… What would you like to buy for between £ 40 and £ 50? £ 50 £ 43. 49 Frog hops 51 p to £ 44… ? … and another £ 6 to jump from £ 44 to £ 50. £ 6 51 p £ 43. 49 © hamilton-trust. org. uk So how much change would we get? Add the hops! £ 44 £ 50 57 Year 4/5
Day 5: Find change from £ 20, £ 50 and £ 100 using counting up (Frog). • Two items are bought for £ 43. 49 and £ 18. 79, and then the change found from £ 100. • Find the exact total using column addition. Choose either the expanded or the compact layout. • Then use Frog to calculate the change from £ 100 £ 43. 49 £ 18. 79 ? • Check your answer with a neighbour. • Did you both get £ 37. 72? © hamilton-trust. org. uk 58 Year 4/5
Challenge © hamilton-trust. org. uk 59 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Objectives Day 6 Y 4 Choose counting up/back to subtract 2 -digit numbers from numbers >100. Y 5 Find the difference between two prices using counting up (Frog). © hamilton-trust. org. uk 60 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. Find the difference between two prices using counting up (Frog). I went shopping and to start with had £ 37. 28 in my purse. I spent £ 18. 98. Discuss in pairs how we could use Frog to calculate how much money I had left. So how much money is left? Add the jump and hops! Does that answer seem about right? … and another £ 18 … then 28 p to hop from Frog’s first hop is tiny: to jump from £ 19 to £ 37. 28. 2 p to £ 19… £ 37. . . 2 p £ 18. 98 £ 19 © hamilton-trust. org. uk 28 p £ 37 61 £ 37. 28 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. Find the difference between two prices using counting up (Frog). £ 23. 67 £ 32. 25 £ 45. 49 £ 29. 78 Discuss in pairs which two prices you think have a difference between £ 5 and £ 6. Now predict which pair has a difference between £ 13 and £ 14 and which a difference between £ 2 and £ 3. © hamilton-trust. org. uk 62 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. Find the difference between two prices using counting up (Frog). Y 5 investigation • With a partner, write an amount with four consecutive digits, e. g. £ 34. 56. • Reverse the digits, i. e. £ 65. 43. • Subtract the smaller amount from the larger amount using Frog. • Repeat with other amounts with consecutive digits. • What do you notice? • What happens if the digits are different by 2, e. g. £ 24. 68? © hamilton-trust. org. uk 63 Year 4/5
Challenge © hamilton-trust. org. uk 64 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. Talk to your partner… How might you solve 123 – 41? © hamilton-trust. org. uk 65 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. So 123 – 41 = 82 123 – 41 = ? Let’s have a go using Frog… First hop 9 to 50… … and another 50 to jump from 50 to 100. . . … then 23 to hop from 100 to 123. 50 9 41 Add the jumps to find the answer. 50 + 23 + 9 = ? 50 © hamilton-trust. org. uk 23 100 66 123 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. 123 – 41 = ? Count back four 10 s from 123… Sometimes it can be more efficient to count back. … 113, 103, 93, 83. Which way did you prefer… Why? © hamilton-trust. org. uk Count back another 1 makes 82. 67 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. 123 – 89 Talk to your partner… For each of these, would it be more efficient to count back or to count up using Frog? 123 – 32 123 – 50 It’s OK to disagree! © hamilton-trust. org. uk 68 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. So 123 – 89 = 34 123 – 89 = ? Add the jumps to find the answer. 23 + 10 + 1 = ? Let’s try this with Frog… … and another 10 to jump from 90 to 100. . . First hop 1 to 90… 10 1 89 90 © hamilton-trust. org. uk … then 23 to hop from 100 to 123. 23 100 123 69 Year 4/5
Day 6: Choose counting up/back to subtract 2 -digit numbers from numbers >100. 123 – 32 = ? Count back three 10 s from 123… Let’s try this one by counting back. … 113, 103, 93. Count back 2 more makes 91. © hamilton-trust. org. uk 70 Year 4/5
Challenge © hamilton-trust. org. uk 71 Year 4/5
Addition, Subtraction and Decimals Column addition; mental subtraction Well Done! You’ve completed this unit. Day 1 Y 4 Add pairs of 2 -digit numbers mentally; Add 2–digit numbers to 3 -digit numbers using mental strategies. Y 5 Use written addition to add pairs of 4 -digit numbers. Day 2 Y 4 Add two 3 -digit numbers using compact written addition. Y 5 Use written addition to add pairs of 5 -digit numbers. Day 3 Y 4 Add three 3 -digit numbers using compact written addition. Y 5 Add amounts of money using column addition. Day 4 Y 4 Find a difference by counting up. Y 5 Add amounts of money using column addition. Use rounding to check answers. Day 5 Y 4 Count up and use number bonds to subtract 2 -digit numbers from 100. Y 5 Find change from £ 20, £ 50 and £ 100 using counting up (Frog). Day 6 Y 4 Choose counting up/back to subtract 2 -digit numbers from numbers >100. Y 5 Find the difference between two prices using counting up (Frog). © hamilton-trust. org. uk 72 Year 4/5
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