The main purpose of this lesson is stated in the essential question. However, in order for students to be able to answer the question, I first must make sure they know how to add integers on a number line. That is the purpose of the introduction. I personally don't find much meaning in the tradional representation (as represented in many textbooks) of integer addition on the number line. I find it easier to always think of addition problems as being in a right facing vehicle (or arrow) starting from the first addend. The second addend tells you to move forward for a positive value and backwards (or reverse) for negative values. I find this a powerful tool (MP5) for adding integers. Using this model has served me well in thinking about adding integers, despite the fact that I have long been comfortable with integer operations without models. It helps to deepen the understanding of quantities and their relationships (MP2).
As a way to make this even more fun, I will have prepared enough vehicles for every student to use during class time. These will be made using a popsicle stick with a vehicle (helipcopters, spaceships, cars, etc...) glued to the top. Each stick will have a labeled addition side (right facing) and subtraction side (left facing). Of course, today we will only use the addition side.
I have included 8 problems to make sure that students can find sums before exploring the essential questions. While students are working on these problems, I will walk around to make sure they understand the procedure for adding on a number line. If I see any incorrect answers, I will ask that student questions that guide students through the steps of adding on a number line. Even better, if a student or pair of students are struggling, I will ask one student to read each line of the steps for adding while the other student acts them out on the number line. They can then change roles for each problem.
In the problem solving section, students will now engage with the essential question. The table and questions are desinged to help students develop and make use of MP2 as mentioned in the introduction, as well as MP7 and MP8. Students will work on these problems in their pairs or trios. Again, I will initially walk around to make sure students are using the table properly and are finding sums correctly. As students answer these questions, I will be looking for mathematical language such as less than, greater than, addend, sum (MP6). Question 4 is an opportuntiy for students to finalize their responses to the essential question using a viable argument and to critique the reasoning of others when we share out. As students are sharing their responses to #4, the audience will be listening to see if the speaker provides enough detail that would make sense to anyone trying to understand the question.
We answered the essential question in problem solving, now in independent practice it is time to apply the concept. Here students will work independently without help from their partners. Question 1-3 assess to see if students see the structure of a positive and negative sum and whether the sum is less than or greater than the first addend (MP7). Questions 4-6 use algebraic notation to develop MP2. Question 7-10 use require MP2 as well.
While students are working, I will either be working with a small (hopefully!) group of students who still having difficulty answering the essential question. Otherwise, as students work through these problems, I will require them to first refer to their responses from the previous section as an aid.
The extension questions see how students can apply their understanding of the essential question to rational numbers, equations, and number line diagrams.
The exit ticket has two general questions just to assess how well students understand the essential question. An answer to question 1 could be as simple as: "For the expression X + M to be greater than X, M must be a positive number. Adding a positive number to X on a number line moves the vehicle (or pointer) to the right on the number line for a greater value."