When I was younger I remember thinking math was all about memorizing formulas and just plugging in numbers. If I made an error, I obviously did something wrong along the way in the procedure. That’s what it was – just prescribed methods and rules. I could tell you instantly how to solve complex algebra problems, but I had NO idea why. I didn’t have number sense.
Children with good number sense are able to reason flexibly with numbers and see numbers as useful. They explore numbers and visualize them in a variety of contexts other than traditional algorithms. As teachers, we can help build number sense in children when we focus less on memorization and more on sensemaking.
Sensemaking in Math: Steps to Build Number Sense
In order to make sensemaking in math, we need to basically offer opportunities for exploration, encourage communication, and frequently discuss reasoning.
Step 1 – Pose a real-life problem. Provide students with a relatable problem in a real-world context. Verify that they understand it. If possible, make it concrete.
Example: Provide each student with a package of animal crackers. These animals all need to be placed in a cage for the local zoo exhibit. Each animal needs to be in its own cage and their cage must have four walls. Find all of the possible perimeters of the cages.
Step 2 – Begin a small group discussion. Together discuss how you can find the solution and what needs to be done. Have students share with one another what they are going to try.
Example: Students may discuss that they are going to sketch all the possibilities so that they can keep track of them.
Step 3 – Have students explore and come up with possible solutions. Give students time to come up with some solutions to the real-life problem. Circulate and assist. You may want to pose some guiding questions during this time but don’t offer any solutions. If students think they are done, ask if they can find another way.
Example: Students may make a cage that looks like this below:
Step 4 – Encourage explanations. Try to encourage students to share as many different strategies or solutions as possible. Have them discuss which they found most comfortable and justify why.
Step 5 – Encourage students to question, debate and prove their solutions. This one goes along with step 4. Students should watch carefully as others present their solutions. They may not always be accurate. They should be able to question their peers (respectfully) and they should always be able to prove their own solutions.
Step 6 – Support Students. As students are discussing their strategies and solutions listen for opportunities to assist or clarify misconceptions. It’s important that students aren’t reinforcing ideas that aren’t accurate.
In some cases, students will need more of a challenge. For instance, in the example above you could state each toothpick equals 6 cm. What is the perimeter of your cage now? Or find the area now.
To help children build number sense, students really need to go through these steps that focus on the process rather than the answer.
Grab Your FREEBIE!
You can grab this sheet, Caging the Animals by clicking here.
Looking for more ideas to build students’ number sense? Check out these posts to learn new strategies and get a few awesome freebies to use with students as you work to develop number sense in all students!
Strategies for Developing Number Sense with Decimals | Mix and Math
How to Improve Number Sense in Upper Elementary | The Stellar Teacher Company
3 Tried & True Tips for Developing Number Sense | Tried & True Teaching Tools
Steps to Build Number Sense | The Owl Teacher