Last time I focused on some basics about learning the number bonds (combinations) of 10 as well as adding 10 to any number. Today I want to show the benefits of making a 10 when adding numbers with sums greater than 10 (such as 8 + 5).  Then I’ll show how to help students add up to apply that to addition and subtraction of larger numbers. I’ll model this using concrete and pictorial representations (which are both important before starting abstract forms).

Using a 10 Frame:

A ten frame is an excellent manipulative for students to experience ways to “Make a 10.” I am attaching a couple of videos I like to illustrate the point.

• Model this process with your students using 2 ten frames.
• Put 8 counters on one ten frame. (I love using 2-color counters.)
• Put 5 counters (in another color) on the second ten frame.
• Determine how many counters to move from one ten frame to the other to “make a 10.” In this example, I moved 2 to join the 8 to make a 10. That left 3 on the second ten frame. 10 + 3 = 13 (and 8 + 5 = 13).

The example below shows the same problem, but this time move 5 from the first ten frame to the second ten frame to “make a 10.” That left 3 on the first ten frame. 3 + 10 = 13 (and 8 + 5 = 13).

The making 10 strategy is also really helpful when adding 9.  For example:  9 + 7 — We tell students to think 10 + 6, but showing them with the ten frame makes it less abstract when first learning.

Decomposing Numbers:

This is a pictorial representation of the same problems showing how to decompose one of the addends to make a ten.

Here are 2 good resources for this method:

I LOVE, LOVE, LOVE using the add up strategy for most double+ digit subtraction problems. Making a 10 is the essential first step.  There are a few ways to show this. I’ll start with a concrete method first using place value disks.

The problem is 100 – 37.

1. Count up (Add up) from 37 to 100.
2. Ask, “What goes with 37 to make the next ten?” Answer = 3  (Using bond of 7 + 3 = 10)
3. Ask, “How many 10’s can be added to get from 40 to 100?” Ten at a time can be added while counting “50, 60, 70, 80, 90, 100.”
4. It’s easy to see that by adding up, the answer is 3 + 60.

Here’s the same problem using “The arrow way” from Eureka / Engage NY.

1. Count up (add up) from 37 to 100.
2. Write 37 and an arrow pointing to the next ten (which would be 40).
3. Above the arrow, write the amount added (3).
4. Add more arrows (or just one) to show the process of getting from 40 to 100. Depending on the students’ comfort, this can be done in one step or several.
5. Add the numbers above the arrows.

Open Number Line:

Here’s the same problem using an open number line, which is a great pictorial model showing the process. Using an open number line to count up / add up for a subtraction problem should help them see “the difference” between the two numbers.

1. Place 37 on the left side of the number line.
2. Put 100 on the right side of the number line. The task is to count up from 37 to 100.
3. Ask, “What goes with the 7 in 37 to make the next ten (40)?”  Answer = 3 (because 7 + 3 = 10)
4. Ask, “How many 10’s can be added to 40 to equal 100?” This can be done in several “jumps” if needed. Best is to ask, “What goes with 4 tens to make 10 tens?” Answer = 6 tens (because we know 4 + 6 = 10)
5. Total the “jumps” made on the number line: 3 + 60

See how this strategy also works well with a missing addend problem: 3,249 + n =  6,500

1. 3249 + 1 = 3250
2. 3250 + 50 = 3300
3. 3300 + 3000 = 6300
4. 6300 + 200 = 6500

Now I’m not suggesting that we should ignore the standard algorithm, but using the make a 10 strategy is very helpful when doing mental math. It’s a very helpful strategy when paper and pencil or a calculator are not available. It’s also a helpful strategy for children to check their work. Instead of students asking, “Did I get this right?” I tell them to try a different strategy — if they get the same answer they are probably correct.

I have often asked students this question to see what strategy they use: “What is 100 – 88?” So many go right away to the std. algorithm – crossing out zeros, etc. when the adding up strategy would have been more efficient (88 + 2 = 90 and 90 + 10 = 100)!!

Enjoy! Let us know your favorite “ten” lesson or activity.