Looking for "friends of ten", or two single addends that equal 10, is a great strategy to help children develop an understanding of math that can enable them to more quickly calculate large sums mentally. In this section, we take four addends, look for the friends of ten and use that to help us solve the problem quickly.

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Breaking apart and adding like units is a way for students to learn mental math strategies. Many of us learned the standard algorithm where we add the ones, then carry over and add the tens. At this age, the concept of carrying over causes a lot of frustration because it is not fully understood that we are trading place values when we do that. For this reason, we first teach about trading place value and then later introduce carrying over.

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Compensating is a way of making numbers more manageable to calculate mentally. Students can either take the compensated amount from the other addend, or they may take it out at the end (borrowing and giving back).

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Understanding how to make the next ten is an important concept for students to master when it comes to mental math strategies. As we learn to do this, it will take a lot of time and effort. However, mastering this will allow students to quickly manipulate numbers into numbers that are easier to work with mentally.

Using concrete models to compose a ten is a great way for students to not only "carry the one" over to the tens place, but helps them to truly understand what is happening when we do this. Trading out ten of one value for one of the next higher value is helping them learn why we do this when we begin to do it later using the standard algorithm.

It may seem like we are taking extra and unnecessary steps, however, our goal is not to solve it as quickly as possible. Our goal is to have a solid understanding of the reasoning behind why this process works.

Using a place value chart helps students to actually see the concept of borrowing in subtraction. This sets them up for greater success later.

Using an open number line can help students correlate the relationship between addition and subtraction within facts.

Breaking numbers down is one of the core skills necessary to allow students to do mental math. Encourage your child to break apart the numbers to enable them to get to numbers that are easier for them to work with.

When one of the digits in the ones place is an 8 or 9, students can quickly and easily add one or two (to make a ten) to both numbers in the math fact to create a balanced equation that is easier for them to work with. For example, a balanced equation for 56-19=37 would be (56+1)+(19+1)=37, which would be simplified to 57-20=37. It is much easier to mentally subtract 20 from 57 than it is to subtract 19 from 56.