There are 24 counters. How many counters could you add without having to regroup? Why?

You could add 5. If you added 6, the answer would be 30 and you'd need to regroup.

29

25

To determine the number of counters that can be added without regrouping, we need to understand the concept of regrouping in the context of addition. Regrouping, also known as carrying, occurs when the sum of two or more digits in one place value column exceeds the base of that column (usually 10).

In this case, we are adding counters, which can be considered as whole numbers. Assuming that we are working in a base-10 system (which is customary), we can add numbers without regrouping if the sum of the digits in each place value column does not exceed 9.

Given that there are 24 counters, we need to determine the largest number of counters we can add without exceeding the value of 9 in any of the columns. Let's start by analyzing the columns:

- The ones column: Since the largest digit in the ones column is 4, we can add up to 5 counters without regrouping (e.g., 4 + 5 = 9).
- The tens column: Since there are no counters in the tens column, we can add up to 9 counters without regrouping (e.g., 0 + 9 = 9).

Therefore, we can add a total of 5 + 9 = 14 counters without having to regroup in this scenario.