This post is a collaborative product of the MathTwitterBlogosphere

During our second trimester this school year some of our instructional goals centered around integers and integer arithmetic.

6.NS.C.5 – Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.C.6 – Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

7.NS.A.1 – Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

We began our investigation of integers using a sequence of open number sentences from Project Z. This came as a result of posts from Michael Pershan and Kent Haines. Students were able to make sense of and discuss the actions taking place during integer arithmetic.

The green and red arrows should be pointing to the same space on the line. My bad!

Then after some twitter collaboration with Michael and Kent we continued to investigate open number sentences.

We practiced integer arithmetic through a game designed by Kent.

We also integrated algebraic thinking with integers through unit 2 of the Transition to Algebra curriculum, which I was led to by David Wees. During the unit the context of temperature is used to help students make sense of integers in their everyday lives.

We supplemented this work with problems culled from Illustrative Mathematics. Kent and Mary Bourassa also have a posts related to contexts for the study of integers.

Just as the temperature context was introduced to the students a post from Andrew Stadel crossed my path. We transitioned from the temperature contexts in the TtA curriculum to an assignment related to Andrew’s concrete context of his ski trip to Brian Head, Utah.

We asked the students to find the temperature changes between each of his screenshots and write a story that made sense of those temperature changes. Here are their final products.

So that was our study of integers. I am personally very pleased with the progress the students made making sense of integer arithmetic and I believe they have a very firm grasp on this concept now.

A question for you, the dear reader, what would you add or subtract (pun intended!) from the our study of integers?

More Resources:

Yummy Math 3-act Task

For more integer posts from #MTBoS math teachers, here’s a link to the #MTBoS search engine