We need to find strategies that will help us solve mathematical problems in different ways.

             Here is an example.

Problem:

Jeremy and his sister collected shells at the beach. Jeremy found 8 shells and his sister found 7. How many shells did they find altogether?

Solution #1

One way to solve this would be to use the break apart method. In this problem, you could think about it in a different way. Working in groups of tens is easier to add mentally.

• You think that "8 + 2 = 10."
• So, take 2 out of the 7 and put it with the 8 to make 10.
• When you take 2 from 7, you are left with 5.
• So, 10 + 5 = 15.

Solution #2

Another way would be to use doubling plus or minus one. Remembering addition using doubling is easier to do mentally. In this problem you can double the number and add one more step to come up with the answer.

• You know the two numbers you need to work with are 8 and 7. Choose the smaller number to start with and double it.
• This is shown by the following number sentence:        7 + 7 = 14 But you're not done yet.
• You need to add 7 + 8 and 8 is one more than 7, so add one more to your first step.
• This is shown as 14 + 1 = 15.

Solution #3

Try doubling and subtracting one this time.

• Start with the higher number, 8 and double it.
• 8 + 8 = 16.
• 7 is one less than 8, so take one away from your first step.
• 16 - 1 = 15

No matter which way you figure it out, the answer is 15.

These strategies can work for many different problems. Try out a few using each of the strategies and find the one that work best for you.

Click on the shell for practice.

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