Family Night Chair Rows
Family Night at Riverside Elementary needs 74 folding chairs set up on the gym floor. The custodian wants the chairs in rows of 8. He tells a parent volunteer, “Nine rows will be enough.” The volunteer notices that some chairs would be left over and asks the third graders to help check the plan. The gym can fit up to 12 rows, so there is room if another row is needed. Later, 6 more parents arrive and need chairs, and the custodian still wants every row except possibly the last to have 8 chairs. Students must explain what the quotient and remainder mean in this situation, decide whether the custodian’s statement is correct, and figure out how many extra chairs are needed after the 6 parents arrive so that all 80 people have seats.
1. Write a division equation for 74 ÷ 8. What do the quotient and remainder mean in this chair situation?
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74 ÷ 8 = 9 R2. The quotient 9 means 9 full rows of 8 chairs: 9 × 8 = 72 chairs. The remainder 2 means 2 chairs are left over, so they cannot fit in a full row of 8. Those 2 chairs still need a place, which would make a 10th row with only 2 chairs.
2. The custodian says, “Nine rows will be enough.” Is he correct? Use the remainder to explain.
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No. Nine rows hold 9 × 8 = 72 chairs. But there are 74 chairs, and 74 − 72 = 2 chairs are left. Since the custodian wants every person seated, those 2 chairs need one more row. So 9 rows are not enough; 10 rows are needed, with the last row having 2 chairs.
3. After 6 more parents arrive, there are 80 people. How many additional chairs are needed so everyone sits in full rows of 8?
Read the worked answer
First find the new total: 74 + 6 = 80 people. A full setup of rows of 8 would use 80 ÷ 8 = 10 rows. The school already has 74 chairs, so it needs 80 − 74 = 6 more chairs. Check: 74 + 6 = 80, and 10 × 8 = 80, so 6 additional chairs make exactly 10 full rows.