Monday, December 26, 2016

Different Answer Locations on Number Lines

Number lines are helpful for solving addition and subtraction problems, but what happens when the answer on the number line isn't at the end? Many of my students would get stuck on solving number lines because they would only look for the answer at the end. Well, that is just great and fine when you have an equation like this.

This is the most common type of addition problem that is used so often that students hardly give it any thought. The answer is at the end of the number line. Once students are familiar with solving this type of problem on a number line, they tend to go into auto mode. Add, answer at the end. Add, answer at the end. Enter in the second type of addition problem.

Not so easy this time! Students cannot find the answer by adding the numbers together. The answer lies in the middle and solving to find the answer is a bit different from the main type we are used to. What I love about this type of problem is that there is less auto mode in solving. Students who try to auto solve like before end up with the answer 113, which is information already known in the equation. This is why I focus on where the variable is when teaching. Look for the variable, that's what you are trying to find. Where it is matters in how you solve it!

The third type involves finding the variable at the beginning of an equation. As such, the answer on the number line with be at the beginning! Yes, the problem is addition but you solve it by working backyards with subtraction. Gotta love those inverse operations! This type of problem can be confusing for students since they will not add at all to find the answer. I like to model out a problem with manipulatives in my hand when introducing this problem type. I have some chocolate candy in my hands. I add another 3 pieces. Look! I have 5 in my hand! How many did I have at the start? Working backwards and taking out what was first added, the kids can easily subtract it to get the answer and we use that to work on more appropriately labeled problems.

Most of the first trimester is pirate-themed. Inevitably any resources I make for content taught during the first trimester is pirate-themed. And why not!? It's fun and the students love it. My video resource, Treasure Number Lines: Where is the Answer on a Number Line? is pirate-themed and covers the 3 addition problem types just mentioned. Each problem-type is taught step by step and puts the bare equation problems into some context.

The video also comes with a worksheet for each equation problem type following the same format as the video. Check it out here!

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