A Math Explanation for Parents

Understanding Common Core Number Bonds

Suppose I walked up to you, gave you a handful of change and asked, How much money is this?”

How would you tackle counting the coins? Would you add left to right?

Or write them down and sum by column?

This column is so long, I’m not even going try to write all the numbers down!

Either way we get the right answer, so why would I want to learn another way to add coins? Can’t we stick with what works, what we’re familiar with?

We have to keep an open mind because there might be an easier way!

I’m betting at some point someone taught you a faster way to count coins. They demonstrated how to group coins together by denomination and count up using multiples, something like this:

Strategic grouping not only increases our efficiency, it also increases our accuracy. Because I am better at skip counting by 5’s and 10’s, I am less likely to make a mistake.

Utilizing This Strategy With All Numbers

This counting strategy is easy to accept with coins. They’re physical objects. Expanding this methodology to all addition is, of course, a little less obvious.

Remember numbers are components of a system. Components can be broken apart, rearranged and regrouped. This is easy with addition because of the commutative and associative properties.

Commutativity means we can change the order of addition without changing the outcome.

Associativity is closely related. It means we can group numbers together however we like when adding and the answer will remain the same.

Grouping 8 + 2 together first makes this problem easier to sum.

Number Bonds

Number bonds can be a useful strategy for some problems. Numbers are bonded together if they help make a multiple of ten.

In this problem I will break 8 into 6 + 2. How do I know to do this? Because of the following number pairs:

These number pairs all add to ten. Notice how 6 and 4 are a pair? That’s how I know 6 is a great value to add to a number ending in 4.

Now use the associative property to change the grouping to 14 + 6.

Then complete the sum.

Many people naturally do this process in their mind without even noticing it. Perhaps you do too?

Common Core Style Diagrams

Common Core uses a diagram technique to make this method kid friendly and easy to grade.

Step 1: Begin by writing 6 + 2 underneath the 8.

Step 2: Draw a circle to group the 14 and 6 together.

Step 3: Combine 14 and 6 to make 20. Write down the final problem: 20 + 2 = 22.

This process will eventually become a mental math technique, therefore how we write it is less important the concept itself.

Place Value Grouping Method

The beauty of math is once we realize numbers are components we can come up with many creative and effective ways to add. Another popular method is breaking numbers apart by place value.

Begin by splitting the numbers into tens and ones.

Tens are easy to add, so combine them first.

Then either add the 8 and 4 individually by counting up, or add them together first like this.

Think: “50 plus 10 is 60, plus 2 is 62.

Either way the answer is 62.

Common Core Column Notation

Again, Common Core has its own notation.

Step 1: Write the numbers with the place values separated.

Step 2: Add each column.

Step 3: Recognizing that 12 is equal to 10 + 2, write it below 12.

Step 4: Draw the circle to show summing 50 + 10.

Step 5: Write out the final addition.

The process looks lengthy, but keep in mind that the purpose is to build number sense. Rest assured, the traditional carrying algorithm is still a viable and useful technique and is still being taught.

Some fear that when carrying students aren’t always recognizing that they are adding a multiple of the place value. These methods are meant to complement the traditional algorithm, bridge understanding, and offer students multiple perspectives on numbers.


I teach a very similar mental math technique for addition in part 2 of my mental math series. Check out Addition Tricks to Increase Your Speed.

Next Lesson: The Martian Potato Paradox & A Review of Percents


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