The first time I taught students to use compatible numbers, I was totally unprepared.  I am guessing that my teachers did the same thing I did.  I read what the book said, followed its examples, and then told the kids to just round.  The next day we recycled their homework and moved on. EEK!

I saw the light after attending a workshop with Greg Tang. It transformed my teaching and how I help my students think about numbers. The goal is to see familiar facts within a given problem and make use of them.

Successfully using compatible numbers requires two things:
1. Make 10 Fact Fluency: Students need to quickly recognize ways to make ten/tens with the numbers in the problem. A few minutes a day investing in practicing these 11 facts makes a huge impact on lots of math skills. Click here to download a poster

2. Ability to Decompose Numbers: Understanding that numbers are flexible and how to apply Addition and Multiplication Properties is essential.  When students do not understand that they can break numbers apart to make them easier to work with, they will not understand how to use compatible numbers to their advantage.

Check this out:

I could add these using a standard algorithm, but students are likely to make simple errors trying to keep track of all of those steps.  It would be a lot easier for me to add 36 + 44 (see the Make 10 fact 6+4?)  How do I make that happen?  By breaking apart my numbers.

By taking away 1 from 45 I am left with two numbers that are easy for me to add in my head. BTW-You could have just as easily taken 1 away from 36 to add 35 + 45. The facts most familiar to the person solving it will be the ones that they see.

If I want an estimate, this is where I would complete my problem.

If I am looking for an exact answer, I would add the 1 that I took away when making my compatible numbers.

This is very similar to the Near Doubles addition strategy that students learn. They only have to fluently learn a small number of facts, then they are able to use those with strategy to add a large set of facts. Revisit Near Doubles strategies to scaffold using compatible numbers with multi-digit addition and subtraction.

Awesome Resources:
Whack a Number: Addition with Compatible Numbers without Regrouping

Whack a Number: Addition with Compatible Numbers with Regrouping

Whack a Number: Subtraction with Compatible Numbers without Regrouping

Whack a Number: Subtraction with Compatible Numbers with Regrouping

Greg Tang Math Break Apart

Greg Tang Math Printables do teachers survive without it?  Sometimes I barely feel like I am surviving WITH it!  I'm pretty sure I have trained my brain to require over stimulation.

I know that I am not the only one who has to make sure that everything they do is deeply meaningful and accomplishes multiple goals.  Priorities when developing activities: flexible, assessable, and engaging.

One of my go-to activities is Popcorn Quiz.  It is crazy easy to manage and is flexible enough to use with several different grade levels and skills. I also love that it works if you have 5 minutes or 30.

The combination of those qualities make it perfect for math rotations as skill practice and spiral review.

This is how it all started. While working with my students on make 10 addition facts, I wanted a way to assess them.  Now, I am not capable of giving something as simple as a worksheet that asks them to fill in the missing addends-too boring. I told them we were going to have a pop quiz. Enter Popcorn Quiz.

I put all of the make 10 facts on paper kernels of popcorn, crumpled them up, and put them in a popcorn box.  The kids went around the table answering the question on the popcorn kernel they pulled out of the box.  Instant success!  I didn't have to do anything, but sit back and collect data.

My students began asking when we were going to have another popcorn quiz. Yes, you read that right, they asked for a quiz. So, I started making them for other skills and will continue making more.

Target and Dollar Tree sometimes have plastic popcorn boxes that are super cute. Any box, bag, or bowl will work though. It's fun to print the kernels on white and yellow paper to really bring home the popcorn look.  BTW- I do not waste time cutting out the kernels along the lines. #notimeforthat I just chop them in the paper cutter as rectangles and crumple them up.

If you have an idea for a topic for a popcorn quiz, put it in the comments. Don't forget your email address.  If I make one with that topic, I will send you a copy!

Get a copy free of the Make 10 Popcorn Quiz by clicking here.

Other skills:
Doubles Addition Facts
Compare Fractions with 1/2 Benchmark
Multiply by 5 & 10
Multiply by 2 & 4
Multiply by 3, 6, & 7
Multiply by 8 & 9

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