Place Value Place numbers on a line compare

Place Value Place numbers on a line: compare and order Objectives Day 1 Place 2 -digit numbers on landmarked and empty number lines. Place 3 -digit numbers on landmarked and empty number lines. Day 2 Place numbers on landmarked and empty 100– 200 number lines. Place 4 -digit numbers on landmarked and empty number lines. Day 3 Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines. Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. © hamilton-trust. org. uk 1 Year 3/4

Place Value Place numbers on a line: compare and order Short Mental Workouts Day 1 In between Day 2 Count on and back Day 3 Compare © hamilton-trust. org. uk 2 Year 3/4

Place Value Place numbers on a line: compare and order Short Mental Workout In between © hamilton-trust. org. uk 3 Year 3/4

Place Value Place numbers on a line: compare and order Short Mental Workout Count on and back © hamilton-trust. org. uk 5 Year 3/4

Place Value Place numbers on a line: compare and order Short Mental Workout Compare © hamilton-trust. org. uk 7 Year 3/4

Place Value Place numbers on a line: compare and order Objectives Day 1 Place 2 -digit numbers on landmarked and empty number lines. Place 3 -digit numbers on landmarked and empty number lines. © hamilton-trust. org. uk 8 Year 3/4

Day 1: Place 2 -digit numbers on landmarked and empty number lines; Place 3 -digit numbers on landmarked and empty number lines. 0 10 20 30 40 23 50 60 70 80 79 45 Talk to your partner – where would you mark 45, 79, 95, and 23 on the beaded line? 90 100 95 Let’s check. . . 45 …. count on 5 beads 7995 …. one …. five more 23 than …. 3 more than 20. from 40. 80. before 90. © hamilton-trust. org. uk 9 Year 3/4

Day 1: Place 2 -digit numbers on landmarked and empty number lines; Place 3 -digit numbers on landmarked and empty number lines. 0 10 20 23 30 40 45 50 Now let’s try 45, 79, 95, and 23 on this 0 -100 landmarked number line. 60 70 80 79 90 95 100 If you get stuck, think how close the numbers are to the 10 s. 23…. halfway …. after 20. . getting 45 …. halfway between 95 between 79 …. just before 80. towards halfway and 50. to 30. 9040 and 100. © hamilton-trust. org. uk 10 Year 3/4

Day 1: Place 2 -digit numbers on landmarked and empty number lines; Place 3 -digit numbers on landmarked and empty number lines. 0 25 4750 75 100 Where would Talk to your partner – we mark 47 onwould you mark where this line? 25 and 75? What would be a is to halfway is 75 halfway good 25 number mark between 50 and 50. 100. onbetween first? Why is that? 47 will be a little before that. © hamilton-trust. org. uk 11 Year 3/4

Day 1: Place 2 -digit numbers on landmarked and empty number lines; Place 3 -digit numbers on landmarked and empty number lines. 50 150 675 450 Y 4: What number halfway Y 3: Y 4: What hownumber can weisis mark halfway 450, between 100 and 200? 675 between and 840 0 and on the 100? line? 840 Let’s check those… Y 4: explain to Y 3 how you can use your knowledge of placing numbers between 0 and 100 to place numbers between larger neighbouring multiples of 100! © hamilton-trust. org. uk 12 Year 3/4

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

Place Value Place numbers on a line: compare and order Objectives Day 2 Place numbers on landmarked and empty 100– 200 number lines. Place 4 -digit numbers on landmarked and empty number lines. © hamilton-trust. org. uk 15 Year 3/4

Day 2: Place numbers on landmarked and empty 100– 200 number lines; Place 4 digit numbers on landmarked and empty number lines. 0 10 20 100 110 120 100 130 140 150 but what We can…count alongif we changed the bead bar it into this 10 s…one… © hamilton-trust. org. uk 160 170 180 190 200 Let’s count in 10 s from 100 to 200. 16 Year 3/4

Day 2: Place numbers on landmarked and empty 100– 200 number lines; Place 4 digit numbers on landmarked and empty number lines. 125 149 199 49 is just before 50 so is just before 150. 0 25149 is halfway between and 50 125 is halfway 175 is so halfway Where will 199 between go? between 100 and 150 and 200, know? who 150. can How do you explain why? Where should we mark 149 on this line? 125? 175? 199? How do you know? © hamilton-trust. org. uk 175 17 Year 3/4

Day 2: Place numbers on landmarked and empty 100– 200 number lines; Place 4 digit numbers on landmarked and empty number lines. 50 250 550 750 Where should we mark 50 on this line? Let’s count in 100 s. Where can we mark 250? 550? 750? How do you know? © hamilton-trust. org. uk 18 Year 3/4

Day 2: Place numbers on landmarked and empty 100– 200 number lines; Place 4 digit numbers on landmarked and empty number lines. 50 125 250 475 550 699 750 999 Where can we mark 125? 475? 699? 999? How do you know? Let’s check those… © hamilton-trust. org. uk 19 Year 3/4

Day 2: Place 4 -digit numbers on landmarked and empty number lines. 1750 6500 4250 Let’s count in 1000 s. 9999 Where can we place 6500, 4250, 1750 and 9999 on this line? How do you know? Let’s check those… Using a number line is a good way to order numbers, can you see why? © hamilton-trust. org. uk 21 Year 3/4

Day 2: Place 4 -digit numbers on landmarked and empty number lines. Think, pair, share how we can find 5000, 2500 and 7500 on the line. 0 2000 2500 is halfway between 0 and What multiple of 5000. 1000 goes here? © hamilton-trust. org. uk 5000 6000 7500 10, 000 7500 is halfway 5000 is halfway What multiple of between 5000 between 0 and 1000 goes here? and 10, 000. 22 Year 3/4

Place Value Place numbers on a line: compare and order Objectives Day 3 Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines. Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. © hamilton-trust. org. uk 24 Year 3/4

Day 3: Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines; Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. I’m going to pick 3 cards and choose someone from Year 3 to pick 3. Take a set of 0 – 9 cards and put them face down! Teacher chooses 2, 7 and 4. Yasmin chooses 0, 1 and 8. Who can make the largest 3 -digit number? © hamilton-trust. org. uk 25 Year 3/4

Day 3: Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines; Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. 742 Let’s mark our numbers on a The 0 -1000 person number with theline. . . highest Replace number canthat keepcard onewith of another of thefor same number their cards later. …andand useplay < oragain. > to write a number sentence… © hamilton-trust. org. uk 810 > 742 or 742 < 810 26 Year 3/4

Day 3: Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines; Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. I’m going to pick 4 cards and choose someone from Year 4 to pick 4. Let’s try with Year 4. Teacher chooses 6, 3, 9 and 5. Michael chooses 7, 1, 2 and 8. Who can make the largest 4 -digit number? © hamilton-trust. org. uk 27 Year 3/4

Day 3: Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines; Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. 8721 Let’s mark our numbers on a The person with theline. . . highest 0 -10, 000 number can keep one of their cards for later. …and use < or > to write a number sentence… © hamilton-trust. org. uk 9653 After several rounds the > 8721 isorthe 8721< 9653 game 9653 champion player who can use their winner’s digit cards to make the bigger number. 28 Year 3/4

Place Value Place numbers on a line: compare and order Well Done! You’ve completed this unit. Objectives Day 1 Place 2 -digit numbers on landmarked and empty number lines. Place 3 -digit numbers on landmarked and empty number lines. Day 2 Place numbers on landmarked and empty 100– 200 number lines. Place 4 -digit numbers on landmarked and empty number lines. Day 3 Compare 3 -digit numbers; Place 3 -digit numbers on 0– 1000 landmarked lines. Compare 4 -digit numbers; Place 4 -digit numbers on 0– 10, 000 landmarked lines. © hamilton-trust. org. uk 31 Year 3/4

Problem solving and reasoning questions Year 3 Sketch a line 0– 1000. Mark 500. Draw arrows to 250, 350 and 850? True or false? • There always four numbers between two multiples of 5. • There always nine numbers between two multiples of 10. • The number next to a multiple of 10 always ends in 9. What number will be marked halfway between 125 and 151 on the number line? © hamilton-trust. org. uk 32 Year 3/4

Problem solving and reasoning answers Year 3 Sketch a line 0– 1000. Mark 500. Draw arrows to 250, 350 and 850? Ask children how they have identified the numbers. What strategies do they use? e. g. 250 is halfway between 0 and 500; 350 is between 250 and 350 but closer to 250. 850 is more than halfway between 500 and 1000, closer to 750 than 1000. True or false? • There always four numbers between two multiples of 5. True. Multiples of 5 always end in 0 or 5, so, for example, between 20 and 25 there are 4 numbers, 21, 22, 23 and 24 and between 25 and 30 there also 4, 26, 27, 28 and 29. Watch for children who include the multiples of 5 themselves and so think that this statement is false. • There always nine numbers between two multiples of 10. True by a similar logic to the previous question. E. g. between 30 and 40 go 31, 32, 33, 34, 35, 36, 37 38 and 39. • The number next to a multiple of 10 always ends in 9. True. e. g. 19 is before 20, 29 is before 30. Check on a 100 grid. What number will be marked halfway between 125 and 151 on the number line? 138 © hamilton-trust. org. uk 33 Year 3/4

Problem solving and reasoning questions Year 4 Sketch a line 0 -10, 000. Mark 5, 000. Draw arrows to 7500, 3200, 8700, 5500. How many numbers between 8500 and 9500 contain just 1 zero? Count in 1 s. Work out what digits a and b are. Write the next number: 54 aa, 54 ab, 54 b 0, _____ © hamilton-trust. org. uk 34 Year 3/4

Problem solving and reasoning answers Year 4 Sketch a line 0 -10, 000. Mark 5, 000. Draw arrows to 7500, 3200, 8700, 5500. Ask children how they have identified the numbers. What strategies do children use to identify the numbers marked? e. g. locating 5000 as halfway along the line then using that to identify the arrow drawn to 7500, halfway between 5000 and 7500. Children should be able to identify arrows drawn to 1000 s and say if numbers are slightly greater or less than that. Note that although in Y 3 children may have completed a similar exercise with numbers to 1000, some may find the larger numbers intimidating so ensure lots of practice correctly reading and writing 4 -digit numbers. Count in 1 s. Work out what digits a and b are. Write the next number: 54 aa, 54 ab, 54 b 0, 54 b 1 a = 8, b = 9. b must equal 9 since the number following 54 ab ends in a zero. 54 b 0 is therefore 5490 and, working backwards, the previous numbers are 5489 and 5488. © hamilton-trust. org. uk 35 Year 3/4