Answer :

Let's solve the given problem by applying specific strategies to find the sums step-by-step.

1. Strategy 4 make a 10: This strategy involves combining numbers to make a total of 10. We use the numbers 4 and 6.
- [tex]\(4 + 6 = 10\)[/tex]
- The sum is 10.

2. Strategy 3 make a 10: Similar to the previous strategy but using the numbers 3 and 7 to make 10.
- [tex]\(3 + 7 = 10\)[/tex]
- The sum is 10.

3. Strategy doubles: This strategy involves doubling a number. Let's consider the number 3.
- Doubling 3 means [tex]\(3 + 3\)[/tex] or [tex]\(2 \times 3 = 6\)[/tex].
- Another double for the number 4.
- Doubling 4 means [tex]\(4 + 4\)[/tex] or [tex]\(2 \times 4 = 8\)[/tex].

4. Strategy +4 count on: This strategy starts at a given number and counts on 4 more.
- Starting at 5, count on 4 more to get: [tex]\(5 + 4 = 9\)[/tex].

5. Strategy count on: This involves starting at a specific number and then counting on a specific number.
- Starting at 7, count on 3 more to get: [tex]\(7 + 3 = 10\)[/tex].

To summarize, here are the sums we found using different strategies:

1. Strategy 4 make a 10: [tex]\(4 + 6 = 10\)[/tex]
2. Strategy 3 make a 10: [tex]\(3 + 7 = 10\)[/tex]
3. Strategy doubles (Considering 3): [tex]\(2 \times 3 = 6\)[/tex]
4. Strategy doubles (Considering 4): [tex]\(2 \times 4 = 8\)[/tex]
5. Strategy +4 count on: [tex]\(5 + 4 = 9\)[/tex]
6. Strategy count on: [tex]\(7 + 3 = 10\)[/tex]

Thus, the results from applying these strategies are:

1. [tex]\( 10 \)[/tex]
2. [tex]\( 10 \)[/tex]
3. [tex]\( 6 \)[/tex]
4. [tex]\( 8 \)[/tex]
5. [tex]\( 9 \)[/tex]
6. [tex]\( 10 \)[/tex]