Q1.
For each of the cases below, write the expression and identify its terms: If the teacher had called out ‘4’, Ruby would write ____________ . If the teacher had called out ‘7’, Ruby would write ____________ . Write expressions like the above for your class size.
Answer
There are 33 students playing, so we split 33 into complete groups plus those left out.
Teacher calls ‘4’: 33 ÷ 4 → 8 groups, 1 left out
Ruby would write 8 × 4 + 1
Terms: 8 × 4 and 1 (value 32 + 1 = 33)
Teacher calls ‘7’: 33 ÷ 7 → 4 groups, 5 left out
Ruby would write 4 × 7 + 5
Terms: 4 × 7 and 5 (value 28 + 5 = 33)
Ruby would write 8 × 4 + 1
Terms: 8 × 4 and 1 (value 32 + 1 = 33)
Teacher calls ‘7’: 33 ÷ 7 → 4 groups, 5 left out
Ruby would write 4 × 7 + 5
Terms: 4 × 7 and 5 (value 28 + 5 = 33)
For your own class: suppose 40 children are playing.
| Teacher calls | Expression | Terms |
|---|---|---|
| 3 | 13 × 3 + 1 | 13 × 3, 1 |
| 5 | 8 × 5 + 0 | 8 × 5 |
| 6 | 6 × 6 + 4 | 6 × 6, 4 |
| 7 | 5 × 7 + 5 | 5 × 7, 5 |
Why it happens: The first term always counts children inside the groups and the second term counts children who are out. Their sum must come back to the class size.
Check it yourself: Count the students in your own class and repeat the game on paper for the numbers 2 to 9.