Patterns and rules · Usually met around P4
Greater than and less than
Find the number that makes it equal, then go bigger or smaller.
How to do it
Method
Find the number that makes it equal, then go bigger or smaller
□ + 4 < 10: □ + 4 = 10 when □ = 6, so □ < 6
Another way
Try each number
5 + 4 = 9 < 10 ✓, 6 + 4 = 10 ✗
In full
□ > 3 means “□ is greater than 3”: 4, 5, 6, … all work, but 3 itself doesn't, because 3 is not greater than 3. □ < 3 means “□ is less than 3”. Such a sentence usually has many answers, so find every number that works. On a number line, draw an open circle at 3 (3 is not included) and an arrow to the right (the numbers greater than 3 are to its right); if 3 is allowed too, fill the circle in. For □ + 4 < 10, first find when □ + 4 = 10: □ is 6. Then think: □ must be less than 6. Or try the numbers one by one.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
□ + 13 < 44, where □ is a whole number greater than 0. What is the largest □ can be?
Show the answer and working
Answer: 30
First find when it is equal: □ + 13 = 44 when □ = 31. To be less than 44, □ must be less than 31: at most 30.
Example 2
The open circle and arrow on the number line show which numbers □ can be. Which sentence does it show?
- A. □ > 15
- B. □ < 13
- C. □ < 14
- D. □ > 14
Choose the right answer
Show the answer and working
Answer: D. □ > 14
The circle is at 14, and open means 14 isn't included; the arrow points to the side where □ can be.
Example 3
□ > 29 and □ < 36, where □ is a whole number. How many different numbers can □ be?
Show the answer and working
Answer: 6
□ can be 30, …, 35; neither 29 nor 36: 6 in all.
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