Greater than and less than worksheet

Part A: Working out and filling in

1. 1. 11

   7 itself doesn't count. Count from the number after 7 up to 18.

   The numbers greater than 7 are 8, …, 18; 7 itself isn't: 11 in all.

2. 2. 17

   3 itself doesn't count. Count from the number after 3 up to 20.

   The numbers greater than 3 are 4, …, 20; 3 itself isn't: 17 in all.

3. 3. 12

   First find when it is equal: what makes □ + 16 = 29? Then think whether □ must be bigger or smaller.

   First find when it is equal: □ + 16 = 29 when □ = 13. To be less than 29, □ must be less than 13: at most 12.

4. 4. 10

   First find when it is equal: what makes □ + 6 = 17? Then think whether □ must be bigger or smaller.

   First find when it is equal: □ + 6 = 17 when □ = 11. To be less than 17, □ must be less than 11: at most 10.

5. 5. 9

   First find when it is equal: what makes □ + 2 = 12? Then think whether □ must be bigger or smaller.

   First find when it is equal: □ + 2 = 12 when □ = 10. To be less than 12, □ must be less than 10: at most 9.

6. 6. 8

   Neither 16 nor 25 counts. Count from 1 more than 16 up to 1 less than 25.

   □ can be 17, …, 24; neither 16 nor 25: 8 in all.

7. 7. 37

   Neither 2 nor 40 counts. Count from 1 more than 2 up to 1 less than 40.

   □ can be 3, …, 39; neither 2 nor 40: 37 in all.

Part B: Choose, or true or false

1. 8. D. 13

   □ < 15 needs □ less than 15, and 15 itself doesn't count. Compare each option with 15.

   □ < 15 needs □ less than 15: 13 is, so it works.

2. 9. D. 14

   □ < 17 needs □ less than 17, and 17 itself doesn't count. Compare each option with 17.

   □ < 17 needs □ less than 17: 14 is, so it works.

3. 10. B. 9

   □ < 10 needs □ less than 10, and 10 itself doesn't count. Compare each option with 10.

   □ < 10 needs □ less than 10: 9 is, so it works.

4. 11. False

   □ > 20 means □ is greater than 20. Put 20 in the box and read the sentence: does it hold?

   □ > 20 needs □ greater than 20; 20 itself doesn't count. Is 20 greater than 20?

5. 12. B. □ < 6

   First see which number the circle is on, then whether the arrow points left or right.

   The circle is at 6, and open means 6 isn't included; the arrow points to the side where □ can be.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 3 people

   More than 15 doesn't include exactly 15. What is the fewest people that is more than 15?

   “More than 15” doesn't include 15, so at least 16 are needed: 16 − 13 = 3.

2. 14. 7 notebooks

   $10 must be kept for the bus, so how much can be spent? Work out 70 − 10 first.

   At most 70 − 10 = 60 can be spent. 8 × □ can't go over 60, so □ is at most 7.

3. 15. 1 child

   Taller than 125 cm doesn't include exactly 125 cm. Compare each child with 125.

   Height > 125: the child of exactly 125 cm can't ride; count only those taller, 1 in all.

4. 16. 10 people

   More than 16 doesn't include exactly 16. What is the fewest people that is more than 16?

   “More than 16” doesn't include 16, so at least 17 are needed: 17 − 7 = 10.

5. 17. 6 notebooks

   $10 must be kept for the bus, so how much can be spent? Work out 62 − 10 first.

   At most 62 − 10 = 52 can be spent. 8 × □ can't go over 52, so □ is at most 6.

6. 18. 3 children

   Taller than 125 cm doesn't include exactly 125 cm. Compare each child with 125.

   Height > 125: the child of exactly 125 cm can't ride; count only those taller, 3 in all.