What's up with that? The Connection Between Addition and Subtraction of Integers

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SWBAT explain the relationship between addition and subtraction of integers by using counters and zero pairs.

Big Idea

Students use integer chips to understand the abstract connection between addition, subtraction, and the additive inverse.

Do Now

6 minutes

Students enter silently. They will all have their journals on their desks. Many have been falling behind during the opening part of class in the last two weeks and will get an opportunity to complete missing journal entries. Those who are finished with their journal entry will work on an operations puzzle that allows for the opportunity to earn achievement points. As students complete each puzzle, they may raise their hands to have their work checked and earn stars on their achievement card. After 5 minutes all students will be asked to turn in their homework form the weekend and get ready for the task.

Lesson Intro + Task

20 minutes

Essential Question: How is subtracting signed numbers related to adding signed numbers?

Ask a student to sit at the table with the document camera to model the intro to this lesson. We will use the essential question above to guide how we think about the exercises on counters. For each expression, students will model with their chips and draw a representation of their model on their paper. I first start out by asking them to place 3 red chips on their desk for the first problem and also draw three circles with a positive sign in front. I ask them to volunteer the integer that represents this model. We write 3 on our paper. Then I ask them to show me 3+2 by modeling 3 red chips in a group and 2 red chips in another group. I remind them to draw the representation and fill in their answer. Then I read the 3rd problem as “3 take away 2” and ask someone to model 3 and then “take away two”. Some students may want to place two blue chips opposites of two blue chips. This is not entirely wrong. It is in fact the aim of the lesson, but it is important to translate the problem as “take away”, so that other students can connect the dots later. We ask this particular student to write down 3+(-2) as the expression for their drawing and ask them to continue thinking about the differences and similarities between the two expressions. We come back to ask this student about his comparison once we get closer to forming the relationship between addition and subtraction as a class.

As we move through examples, I ask student volunteers to take turns at the document camera to display their model and draw their representation. Students continue with examples #4-9.  I encourage students to speak with their neighbor and share out as a classif they are noticing a relationship between addition and subtraction. If any student gives an explanation that is too vague or broad, I offer counter examples and ask them to continue to think about the relationship (i.e. student states, “addition and subtraction are the same”, teacher responds, “what do you mean they are the same? So 9-5 is the same as 9+5? How are they the same?”). If a student words something in a succinct and mathematically correct way, we ask the student to repeat what he stated so that we can write it in our journals. I write it on a sheet of paper and project it on the document camera.

I stop the class after 3-4 minutes to complete #1-9 and ask them to complete #10 with me. We start out with 3 blue chips. We read the problems as “negative 3 take away 3”. I ask students whether we need to take away 3 negatives or 3 positives. When we see that we need to take away positives, or red chips, and we have none, I ask if there is a way we can add red chips without adding any more value to the number currently on the table (use of zero pairs). If we add two zero pairs, we can take away the 2 red chips (+) and we’re left with a total of 5 blue chips. Students volunteer the use of the additive inverse to re-write the expression as an addition sentence. Students complete #12 with partners and are asked to try #13 in their pairs as well. I walk around until I find the first group that correctly models #13 and ask one of them to draw it on the white board using red and blue markers.

To close the lesson, I will ask students to discuss the answer to today’s essential question with their neighbor and then I’ll have 2-3 students share out.

Closing - Exit Ticket

6 minutes

Exit ticket – Students are given an exit ticket to complete before they leave. Homework is placed on student desks while they work.

Exit Ticket includes 6 addition and subtraction questions (i.e. 8+(-4), -46-(-5))

Homework includes 8 addition/subtraction questions, 1 error analysis, and 1 word problem and change.