Question

Break up 31 into 3 tens and 1 one
Break up 11 into 1 ten and 1 one
So we're going to make an array using base ten blocks, that has ? columns and 11 ?.

Answer 1

how many columns

Answer 2

Let's break down your request step by step.

1. **Breaking up 31 into base ten blocks**:
- 31 can be represented as 3 tens (which equals 30) and 1 one.
- So, \( 31 = 3 \times 10 + 1 \times 1 \).

2. **Breaking up 11 into base ten blocks**:
- 11 can be represented as 1 ten and 1 one.
- So, \( 11 = 1 \times 10 + 1 \times 1 \).

3. **Creating an array using base ten blocks**:
- You mentioned that we're going to make an array that has "? columns" and "11 ?".
- From the breakdowns:
- We already established that 31 can be arranged in columns of tens and ones. To find out how to represent 11 in a similar format, we could see how they relate.

**Arranging in columns**:
- If we're considering the number **11**, we can interpret it as having:
- 1 column of tens (representing 1 ten).
- 1 column of ones (representing 1 one).

Putting it together, if we're making an array using base ten blocks for **31** and **11**, it seems like you would be interested in:

- **Array representation for 31**: 3 columns (for the 3 tens) and 1 column (for the 1 one).
- **Array representation for 11**: 1 column (for the 1 ten) and 1 column (for the 1 one).

So, the final interpretation would be:
- You can create an array with **1 column of tens and 1 column of ones** to represent **11**. If you're directly constructing, you could be looking for an array with **3 columns for tens and 1 column for ones** to give a visual representation of **31**.

If you're asking how many columns the total array would have:
- If you're looking at the maximum representation of either, you can use **3 columns for tens** (from 31) and if you align the **1 column of tens from 11**, the total makes **4 columns** (3 for the tens and possibly 1 for the ones for 31).

In summary:
- **The array has 3 columns for tens and 1 column for ones, for a total of 4 columns visually if you track the sum resemblance.**

Answer 3

To clarify how many columns there are based on your earlier descriptions of breaking up 31 and 11:

1. **For 31**:
- You have **3 columns for tens** (from breaking down 31 into 3 tens) and **1 column for ones**.

2. **For 11**:
- You have **1 column for tens** (from breaking down 11 into 1 ten) and **1 column for ones**.

Now, if we consider how many columns are created for both numbers in an array:

- For **31**, you could say it creates **4 columns** total:
- 3 columns (tens) + 1 column (ones) = **4 columns**.

Thus, if we are structuring it based on the largest number (which can potentially represent both depending on context), you would typically represent the columns based on the composition of the larger number:

- If we only consider **31** for the entirety of the array, we have **4 columns** (3 tens + 1 one).

So to directly answer your question: **The array has 4 columns** when considering how we can break down 31.