Teaching how to find the unknown number takes time. It’s a concept that you will need to re-visit throughout the school year if you want students to be proficient with it. As a new teacher I think I spent a couple weeks (in total) with it and my students struggle. But now, it’s “know better, do better!”

## To Find the Unknown, Start At the Beginning

What do you know about the progression of addition and subtraction? Regardless of the grade you are teaching, you need to know where your students have been and what they have learned. One of the biggest mistakes I made early in on my teaching career, was to assume that students would come into my class having learned the previous grade’s concepts. They might have, but they didn’t act like that had.

In the primary grades, there is a lot of counting, 1:1 correspondence with objects, and then a move towards “sets of”. Many, even in kindergarten, will be introduced to 5 frames and 10 frames. With these, adding and subtracting are introduced. Have you seen Graham Fletchy’s website? I’ve used it for the first time last year and the videos worked great for our number talks. He has a video on the progression of addition and subtraction here.

## Give Students Strategies

There is not one way to teach addition or subtraction, so teaching students to find the unknown number will be the same. Give them strategies. Ask yourself, “how do I solve unknown numbers?”

**Strategies to Teach**:

- Fact families are popular, for example, if 6 + 4 = 10, then 4 + 6 = 10, 10 – 6 = 4, 10 – 4 = 6. If students understand that addition and subtraction are related, then to solve for 6 + ___ = 10, then students can solve 10 – 6 = _____
- Using manipulatives/objects to solve, for this one students need to understand “counting on” and “counting backwards”
- Guess and check, there are some students will be guess. This is not the best strategy but if you can get them to check their answer, this can be a strategy worth showing. However, many students will not check their work.
- Part – Part – Whole, this is another way of teaching how addition and subtraction are related. When searching for the unknown number, students need to know whether they are searching for the part or the whole number. Determine which numbers are parts and which are whole numbers. In addition, the parts are the sum of the whole so the part will be a number less than the whole. For example, if 6 + 4 = 10, then 6 and 4 are parts and 10 is the whole. Take away the 6. To solve the equation: ____ + 4 = 10, ask the students if they are looking for a part or a whole?
- Word problems are a great activity to reinforce this concept. Instead of “what plus what equals what”, move the known numbers around. If you are a creator, make powerpoint games or Boom Cards and project them onto the screen for whole class instruction

## When To Teach Students The Strategies To Find The Unknown Number

There are 2 different times that I teach strategies: formal instruction and during number talks. Both formal instruction and number talks are short, less than 20 minutes, sometimes less than 10 minutes. If you have tried number talks, I highly recommend it. You can read more about it in my “Number Talks” post. Though teaching the unknown number is a whole class concept, working on it in small groups is a good place to assess student understanding and proficiency.

If you are interested in pursuing this math concept, let me know. I have started a picture book list and teacher resource list. They will eventually be uploaded to the Math Resources page.

Until then,

*Happy Teaching!*

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