by C. Elkins, OK Math and Reading Lady

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.

- Video 1: Make a Ten video
- Video 2: Make a Ten strategy
- Ten frame template (FREE): Making 10 activity board by Louise Leger

Let’s say the task is to add 8 + 5:

- 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:

- Video: Decomposing to Make a 10
- This link is a free practice page from Donna Boucher (aka Math Coachs Corner):Friends of Ten

**Adding Up:**

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.

- Count up (Add up) from 37 to 100.
- Ask, “What goes with 37 to make the next ten?” Answer = 3 (Using bond of 7 + 3 = 10)
- 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.”
- 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.

- Count up (add up) from 37 to 100.
- Write 37 and an arrow pointing to the next ten (which would be 40).
- Above the arrow, write the amount added (3).
- 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.
- 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.

- Place 37 on the left side of the number line.
- Put 100 on the right side of the number line. The task is to count up from 37 to 100.
- Ask, “What goes with the 7 in 37 to make the next ten (40)?” Answer = 3 (because 7 + 3 = 10)
- 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)
- 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

- 3249 +
**1**= 3250 - 3250 +
**50**= 3300 - 3300 +
**3000**= 6300 - 6300 +
**200**= 6500

Answer (add the bold # above): n = 3,251

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.**