Number and Place Value Objectives Day 1 Partition

Number and Place Value Objectives Day 1 Partition and represent 3 -digit numbers using place value cards and base-10 equipment. Practise place value addition and subtraction. Day 2 Order 3 -digit numbers and place on an empty number line; find a number inbetween. Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. Day 3 Place 3 -digit numbers on landmarked lines and round to nearest 10/100. Place 4 -digit numbers on landmarked lines and round to nearest 1000. © hamilton-trust. org. uk 1 Year 3/4

Number and Place Value Short Mental Workouts Day 1 Count in steps of 100 Day 2 Place 3 -digit numbers on an empty number line Day 3 Multiply and divide by 10 © hamilton-trust. org. uk 2 Year 3/4

Number and Place Value Short Mental Workout Count in steps of 100 © hamilton-trust. org. uk 3 Year 3/4

Number and Place Value Short Mental Workout Place 3 -digit numbers on an empty number line © hamilton-trust. org. uk 4 Year 3/4

Number and Place Value Short Mental Workout Multiply and divide by 10 © hamilton-trust. org. uk 5 Year 3/4

Number and Place Value Day 1 Y 3: Partition and represent 3 -digit numbers using place value cards and base-10 equipment. Y 4: Practise place value addition and subtraction. © hamilton-trust. org. uk 6 Year 3/4

Day 1 Partition and represent 3 -digit numbers using place value cards and base-10 equipment. Practise place value addition and subtraction. 100 200 300 400 500 600 700 800 900 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 9 Find the total of the highlighted numbers and write it on your whiteboards. © hamilton-trust. org. uk 7 0 0 8 0 5 7 08 005 4 0 0 6 0 1 4 06 001 3 0 0 8 3 0 08 7 Year 3/4

Day 1 Partition and represent 3 -digit numbers using place value cards and base-10 equipment. Practise place value addition and subtraction. We can draw blocks, sticks and cubes to represent numbers. For example for 327. On your whiteboards, sketch blocks to show 145, then 451. © hamilton-trust. org. uk 8 Year 3/4

Day 1 Practise place value addition and subtraction. 4375 You should have done this really quickly… Why is this a ‘no-work’ calculation? Subtract 305. Write the answer on your whiteboard. © hamilton-trust. org. uk 10 Year 3/4

Day 1 Practise place value addition and subtraction. 4375 This time subtract 4005. Write the answer on your whiteboard. Now subtract 4070. Write the answer on your whiteboard. Now calculate 4375 + 202. © hamilton-trust. org. uk Finally, calculate 4375 - 1002. 11 Year 3/4

Day 1 Practise place value addition and subtraction. 4375 5555 In pairs, think about what place value additions and subtractions you could do to 4375 to make 5555. You are looking for an efficient way to do this! Here’s one way. 4375 + 1200 = 5575 – 20 = 5555 © hamilton-trust. org. uk 12 Year 3/4

Challenge © hamilton-trust. org. uk 13 Year 3/4

Number and Place Value Day 2 Y 3: Order 3 -digit numbers and place on an empty number line; find a number in-between. Y 4: Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. © hamilton-trust. org. uk 14 Year 3/4

Day 2 Order 3 -digit numbers and place on an empty number line; find a number in-between. Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. 0 100 153 200 300 400 500 Let’s play Lowest, Highest, In-between on a 0 -1000 line. . . 700 756 800 900 1000 Take two numbers from the pile and place them on the line. Where will 153 and 756 go? © hamilton-trust. org. uk 600 Those are our lowest and highest numbers. 15 Year 3/4

Day 2 Order 3 -digit numbers and place on an empty number line; find a number in-between. Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. 0 100 200 135 153 300 400 500 440 700 756 800 861 900 1000 572 …. it goes in-between. Take more numbers … are they lower than, higher than or in-between our two numbers? 135 …. we have a new low number, it replaces 153. 861 …. we have a new high number, it replaces 756. © hamilton-trust. org. uk 600 572 440 …. it goes in-between. 16 Year 3/4

Day 2 Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. 4600 4654 ? ? 4700 4660 ? ? The Discuss, number in is pairs between / groups, Imagine a number line 4650 and 4660! what from the mystery going 4600 to 4700. Whatnumber could itmight be? be. Is it more than 4630? Less than 4670? Which two multiples of 10 is the number between? © hamilton-trust. org. uk 18 Year 3/4

Day 2 Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. 4650 4654 4660 Can you agree a number Is 4654 nearer to 4650 between 4650 and 4660 which or to 4660? rounds up to 4660? We can use down our skills 4654 rounds to in rounding 2 -digit numbers 4650 when rounding to to thethe nearest 10, 10. to round nearest 4 -digit numbers to the nearest 10! What about 4655? Who can remember the rule? © hamilton-trust. org. uk 19 Year 3/4

Number and Place Value Day 3 Y 3: Place 3 -digit numbers on landmarked lines and round to nearest 10/100. Y 4: Place 4 -digit numbers on landmarked lines and round to nearest 1000. © hamilton-trust. org. uk 21 Year 3/4

Day 3 Place 3 -digit numbers on landmarked lines and round to nearest 10/100. Place 4 -digit numbers on landmarked lines and round to nearest 1000. 2379 ? 5842 ? 7756 ? 2379 Y 4: What about 3 the second We have mystery about thecan third number? tell do numbers on our Y 4: What Which of. How these sixyou numbers number? 1000 s number it is? 0 -10, 000 number line. is? youwhich think. What the first number will it round to? What number will it Which 1000 s numbers can’t it be? round to? 2739 5482 5842 7576 Y 4: It is Docloser you think to 2000 it isso 2379 it or must 2739? be 2379. Why? © hamilton-trust. org. uk 22 7756 Year 3/4

Day 3 Place 3 -digit numbers on landmarked lines and round to nearest 10/100. Place 4 -digit numbers on landmarked lines and round to nearest 1000. 2379 5842 7756 Write two numbers between 3000 and 4000, one which rounds down to 3000 and one which rounds up to 4000. Let’s check your ideas… © hamilton-trust. org. uk 23 Year 3/4

Investigation Use ‘The Thousands Game’ from NRICH Each child in Class 4 took four numbers out of the bag. Who had made the highest even number? © hamilton-trust. org. uk 24 Year 3/4

Day 3 Place 3 -digit numbers on landmarked lines and round to nearest 10/100. 600 700 What number could 684 rounds to go here? 700 if rounding to nearest 100. Is 684 closer to Is 600 it more than 650? or 700? What 2 multiples 684 rounds to of 10 it between? 680 ifis rounding to nearest 10. 684 closer Is it less thanto 670? 680 or 690? 680 690 684 What could it be? © hamilton-trust. org. uk 26 Year 3/4

Day 3 Place 3 -digit numbers on landmarked lines and round to nearest 10/100. 500 600 579 rounds to What could 600 number if rounding go here? 100. to nearest Is 579 closer to Is it more 500 orthan 600? 590? 5792 rounds to of 10 What multiples 580 if between? rounding is it to nearest 10. Is it 579 closer less thanto 560? 570 or 580? 570 579 580 What could it be? © hamilton-trust. org. uk 27 Year 3/4

Investigation: Adult Sheet © hamilton-trust. org. uk 28 Year 3/4

Investigation: Child Sheet 2. Now try to work out this mystery 3 -digit number:

Challenge © hamilton-trust. org. uk 30 Year 3/4

Number and Place Value Well Done! You’ve completed this unit. Objectives Day 1 Partition and represent 3 -digit numbers using place value cards and base-10 equipment. Practise place value addition and subtraction. Day 2 Order 3 -digit numbers and place on an empty number line; find a number inbetween. Place 4 -digit numbers on a landmarked line; round to nearest 10 and 100. Day 3 Place 3 -digit numbers on landmarked lines and round to nearest 10/100. Place 4 -digit numbers on landmarked lines and round to nearest 1000. © hamilton-trust. org. uk 31 Year 3/4

Problem solving and reasoning questions Year 3 Use drawings or equipment to represent 562 in three different ways. Write the missing numbers: • 529 – ☐ = 509 • 446 = 406 + ☐ • 1 = 801 – ☐ • 418 – ☐ = 400 • 999 = 990 + ☐ • 302 + ☐ = 302 Write two numbers which round to 300 as the nearest 100. One must be less than 300 and one must be more. Write two numbers that round to 120 as the nearest 10. One must be less than 120, and one must be more. Round 448 to the nearest 10. Round the same number to the nearest 100. © hamilton-trust. org. uk 32 Year 1/2

Problem solving and reasoning questions Year 4 Estimate the number shown by the arrow on this number line: Circle the number which is closer to 2000: 1997 2007 Explain how you know. Round 7483 to the nearest 10, nearest 100 and nearest 1000. Round these numbers to the nearest 100: 127, 1272, 12, 727. © hamilton-trust. org. uk 33 Year 1/2

Problem solving and reasoning answers Year 3 Use drawings or equipment to represent 562 in three different ways. Place value cards: 500, 60 and 2 Base-10 blocks: five 100 -‘squares’, six 10 -‘sticks’ and two 1 -‘cubes’. Coins: (562 p) five £ 1 coins, six 10 ps and two 1 ps. Write the missing numbers: • • • 529 – 20 = 509 446 = 406 + 40 1 = 801 – 800 418 – 18 = 400 999 = 990 + 9 302 + 0 = 302 © hamilton-trust. org. uk 34 Year 1/2

Problem solving and reasoning answers Year 3 continued Write two numbers which round to 300 as the nearest 100. One must be less than 300 and one must be more. One number should be 250 -299 and one 301 – 349 (note not 350). Model this and the following questions on a number line if children are unclear. Write two numbers that round to 120 as the nearest 10. One must be less than 120, and one must be more. One number should be 115 -119 and one 121 – 124 (note not 125). Round 448 to the nearest 10. 450. Round the same number to the nearest 100. 400 (not 500), children need to refer to the original number 448, not the one they have rounded to 10. © hamilton-trust. org. uk 35 Year 1/2

Problem solving and reasoning answers Year 4 Estimate the number shown by the arrow on this number line: Circle the number which is closer to 2000: 1997 2007 Explain how you know. 1997 is closer – it is only 3 away from 2000, 2007 is 7 away. Round 7483 to the nearest 10, nearest 100 and nearest 1000. 7480 (nearest 10); 7500 (nearest 100); 7000 (nearest 1000). Note that in each instance children should refer to the original number when rounding. Round these numbers to the nearest 100: 127, 1272, 12, 727. 100, 1300, 12, 700 respectively. Note that when rounding to the nearest 100, the last two digits will be zeros. © hamilton-trust. org. uk 36 Year 1/2