Reflection: Rigor All That and a Bag of Chips! Using Counters to Combine Integers - Section 4: Closing


This is my 5th year teaching 7th grade, and therefore my 5th time teaching operations with integers. Each year I try something different in terms of HOW I give my students the rules for all the operations. Each time I wondered what format looked best, what the vocabulary should look like on the sheet. And each year I would get so angry when I would see my beautifully crafted “rules sheets” thrown away in garbage cans or stomped on the floor.

This year I had an epiphany: what if the problem was not formatting and vocabulary on the sheet, but instead the fact that I was giving them anything at all?! This may seem common sense to some of us (it seems common sense to me now), but each time in years past I was worried about arming students with information. This year I am continuing to use Cornell Notes, but I am not giving students copied sheets to write on and keep in their binders. Instead, I opted to get each student a composition notebook. The pages may not be torn out and students must take their own notes every day. The advantage to taking these notes is that I allow students to use them to take their quizzes (not their unit test).

For this lesson using chips to illustrate integer addition, I ended with a review of any rules students noticed while working to illustrate each problem with their integer chips. The following questions cover the hierarchy of questions I asked during the review to attempt to get students themselves to write out the rules for adding positive and negative integers:

-          For each problem you answered, I want you to imagine what would happen if the numbers got much bigger/smaller. What if the problem was -144 + -155 and you didn’t have this many chips to lay out (or maybe you don’t even want to aly out that many chips)?

-          What operation could you use to find the answer faster?

-          How would you know what sign the answer should be?

-          Is there a rule you could write that tells you what operation to use and what sign the answer will be for this problem?

-          What is it called when we add/subtract the numbers “without the sign” or “ignoring the sign”? what vocabulary term do we know that says this? (This question tries to elicit students to use the vocabulary term “absolute value”)

This year I have found that my students are more likely to recall information, rules, or key ideas they explained themselves, rather than listening to me recite the rules. The cognitive lifting is on them and as a result they are better able to retain and understand the rules. 

  Rigor: Student Cognitive Lift
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All That and a Bag of Chips! Using Counters to Combine Integers

Unit 1: Integers
Lesson 8 of 20

Objective: SWBAT combine and simplify integers by making zero pairs with counters

Big Idea: Students work with partners to model integer operations with red and blue chips/counters.

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