Make It Visual

Sep 23

With Integers

The second of four things we need to do when teaching math so kids will remember.

There are 4 very important things we as educators (whether you are a parent or classroom teacher) need to keep in mind when teaching math. In this 4 part series, I will be elaborating on each of these 4 things as they relate to the teaching of integers (positive and negative numbers). Keep in mind, these 4 things could relate to any math concept we are trying to instill on our children.

Thing Two - Make It Visual

One of the keys to being able to effectively process and strategically think mathematically is the ability to visualize any given problem either mentally or through the use of tools.

One study by Delinda van Garderen found that for students of all ability levels “successful mathematical problem solving was positively correlated with the use of schematic representations.” This correlation shows that we as parents and teachers must be prepared to create and teach lessons that help our children find ways to visualize the concepts we are presenting

**Do you remember the old adage,**
**“A picture is worth a thousand words”?**
**Make it Visual!**

Screenshot 2020-09-22 at 2.37.23 PM.png — One of My Favorite Activities

to introduce the concept of integers is Draw Me A Story. I usually start by showing my students the picture I drew of my son high on a cliff above the ocean. The picture includes a vertical number line. I ask questions like:
● If Tommy jumped off the cliff and went 20 ft under the water how far did he travel?
● How far below the boat is the whale?
● What is the distance between the octopus and the airplane?

Next, my students think of a situation they could draw that would represent both positive and negative numbers. I let them brainstorm with a partner or small group. Students draw their pictures (remembering to include a number line) and create a few questions to accompany them. These are posted around the room. The class does a gallery walk, answering each other’s Draw Me A Story questions. An extension activity would be to have students use post-it notes to add questions to the other team’s picture. (Some scenarios my students have drawn: swimming pool with different levels of diving boards, a tree fort with escape tunnels underground, a jungle with animals above and below ground, a marathon race with zero as the starting line and people at different stages - including behind the line - the situations are endless!)

What story could you draw that would would have representation of both positive and negative numbers?

Screenshot 2020-09-22 at 2.46.56 PM.png — Another way that we as educators can help students “see” integers is to use two-color counters. Two-color counters can be used to model all 4 operations. Here is a good video showing how to use two-color counters with subtraction. There are many more videos out there so look around. I also show my students how to model integer problems by drawing pluses (+) and minuses (-) to represent the two-color counters. This is important for students that needed visual assistance when counters aren’t available.

Early in my career, I did not have access to manipulatives so for this activity I used pennies. Heads were positive and tails were negative.

Another vital tool students should have experience with is the number line. See my other blog posts about the importance of number lines. Regularly using an open number line is a fabulous learning activity for all students. Clotheslines and a drawn number line with post-it notes are two different ways to create an interactive open number line for whole-class or parent/child number talks.

Showing students how to create their own number line to help them visualize and solve integer problems can be taught after children have some experience with the whole class or parent supported number line activities. Here is a great video demonstrating adding integers with the use of a number line.