Adding and Subtracting Integers on a Number Line
Lesson 5 of 17
Objective: SWBAT: • Add and subtract integers using a number line
See my Do Now in my Strategy folder that explains my beginning of class routines.
Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to review comparing integers.
I ask for a student to explain the order of the balances. I ask, “How is 10 greater than -20? Isn’t 20 larger than 10?” I have students share out ideas about how Terriana could have a negative balance in her bank account. She spent more money than she had in her account, so she owes the bank money.
If I have time I will ask the following questions:
- What do you think happened between Wednesday and Thursday?
- What do you think happened between Thursday and Friday?
I want students to recognize that her balance decreased between Wednesday and Thursday. She could have spent more money or been charged a fee by her bank. I want students to see that between Thursday and Friday her balanced increased from -20 to 0 dollars. This means money was deposited into her bank.
I ask students to share out what teams are trying to do in a football game. Some students may say they are trying to score points and to win. I share that we will be using football to help us add and subtract integers – it’s the Positive Yellow Team vs. the Negative Red Team.
I introduce the integer football rules. The yard lines are a little different than regular football. The middle of the field, where each problem starts, is the 0 yard line. To the left of 0 are negative yards (-1, -2, etc.) and to the right of 0 are the positive yards (1, 2, 3, etc.).
- For this lesson, each student will need a yellow and red writing utensil.
- The purpose of this lesson is for students to practice adding and subtracting on a number line and start to build conceptual understanding of what is actually happening. I am avoiding telling students shortcuts and teaching them procedures because I want them to start to build their own conceptual understanding of what is going on. This will not be easy and students will likely struggle, but I think it is important to build a conceptual foundation and have students figure out patterns.
- I would encourage you to go through the examples on your own and familiarize with how you would explain each problem in terms of the football teams. It took me time to become comfortable in explaining problems in terms of the team and the direction.
- In the guided examples, you may want to replace some of my drawings with blank number lines so students are accountable for drawing something.
We start with combining drives. This is when both numbers are either positive or negative and they are being added together. Students will obviously know right away that 5 +2 = 7, but it is important for them to understand what is happening in the context of our football game. I have students circle both numbers (not the addition sign) with the yellow marker, showing that both drives are by the Positive Yellow Team. That means that both arrows should be yellow. We go through problem 2 with the same language, except this time the Negative Red Team is driving towards their end zone. If they drive -5 yards and then another -2 yards they will end at the -7 yard line.
I have students work in partners. My students are in heterogeneous partner pairs. It is likely that this is new material for most students. I explain to students that the important thing they are doing right now is creating a model (MP4: Model with mathematics). It is not good enough for students to just write an answer, they need to show what is happening with the football teams.
As students work I walk around and monitor their progress. If students are struggling, I refer them back to problem 1 and 2 and have them follow the same steps. If a student just writes an answer, I require them to look at my examples and draw a model of the problem.
Again we go through problems 1 and 2 together. For problem 1 I have students circle the (-6) in red and the 2 in yellow. That means our first arrow will be red and our second arrow will be yellow.
Students work with their partners on the Interception Practice. I am looking that students are drawing the models. A common mistake is that students ignore the signs and add the numbers as if they were both positive or both negative. If I see students doing this I ask them to color the positive number yellow and the negative number red. I guide them through the problem the same way as the examples.
When most partners have finished the Interception practice, we come back together as a class. For each example I have one student come to the document camera to show and explain their thinking. If students just list steps I push them to explain the why they did each step. Then I ask a student if he/she agrees or disagrees with the student and why. Students are engaging with MP3: Construct viable arguments and critique the reasoning of others.
Last, I ask them to look at problem 1 and problem 3. I ask them what they notice. How can those two problems have the same answer? I want students to recognize that even though the problems started differently they both included a drive of 6 yards by the Negative Red Team and a drive of 2 yards by the Positive Yellow Team. Students are engaging with MP7: Look for and make use of structure.
Getting Pushed Back
Using football, if you subtract an integer it means that that color team gets pushed back, or pushed away from their end zone a particular number of yards. I ask a volunteer to act out this motion. I am on the Positive Yellow Team and I have the ball. The Negative Red Team overpowers me and pushes me back, away from my end zone. I don’t use the words “loss” or “gain” here because I don’t want students get confused.
We go through the example problems in a similar manner. I have students circle -3 in red and circle 2 in yellow. That means that the Negative Red Team will have a drive and then the Positive Yellow Team will intercept it. Because we are subtracting a positive 2, the Positive Yellow Team is getting pushed back 2 yards. The result is that the problem ends at negative 7.
We go through the other examples in a similar fashion. If needed, I have a student come up and help me act out what is going on, then we review it on the number line.
This section may prove to be the most confusing for students. Take it slowly and act it out. Emphasize that when we are subtracting integers, that team is getting push back, the opposite of adding integers.
Closure and Ticket to Go
For Closure I ask students these questions:
- What happens when we add two positive numbers together?
- What happens when we add two negative numbers together?
I want students to realize that if we add two positive numbers together, the result will always be a positive number and that if we add two negative numbers together, the result will always be a negative number. Students will look for more patterns in the next lesson using integer chips to model problems.
I pass out the Ticket to Go for students to complete independently. At the end of class I pass out the HW Adding and Subtracting Integers on a Number Line.