Algebra prerequisite skills – Integers

Why are integers so important to review?

High school students often struggle with operations on integers. Since integer operations are essential for just about everything in middle and high school math, I do spend some time at the beginning of the semester explicitly teaching operations on integers. It is a review for many of my students, but I have still found that it is an excellent use of time because the review applies directly to our work with variables. In this post we also have some suggestions for quick and easy games to reinforce understanding of operations on integers using number lines and/or playing cards.

Using number lines to review integers

Using both vertical and horizontal number lines is a great precursor to graphing on a coordinate plane. It is also a great way to visually represent different types of real-world problems. Many textbooks and worksheets introduced integers with the horizonal number line, but I have found that I can reach more students when I give the option of both.

Completing integer word problems using number lines are great warm-ups throughout the year. They are quick, they allow students practice using a visual to model a real-world situation, and they help to address previous misconceptions about integers. I like to pair students up with two integer word problems. Each student can model one, then they can write the expressions and solutions. This is low-stakes and fast. It is a great way to ease into math class.

Examples of Word Problems for Vertical Number Lines

Temperature – Sarah left her house this morning and the temperature was . Now, the temperature has gone up .  What is the temperature now?

Elevator – An elevator is on the ninth floor. It goes down 12 floors and then up 5 floors. What floor is the elevator on now?

Examples of Word Problems for Horizontal Number Lines

Football – Harry is watching a football game. He decided to list yardage gained as positive integers and yardage lost as negative integers. Harry recorded , , and . What was the net gain or loss?

Timeline – The Roman emperor Claudius was born in 10 BC. Tiberius was born in 14 AD. How many years apart were they born?

Freebie: Click here for -20 to 20 vertical and horizontal number line templates.

Using playing cards to review integers

Playing cards are a great way to get students solving problems with integers with very little teacher prep. Think about the skill you would like your students to practice. Set the rules and let teams play in five-minute intervals. This makes for a great brain break from the lesson you are teaching, but provides a math focus and great review.

Things you want to establish before beginning an integer game with cards.

• Red cards are negative integers and black cards are positive integers.
• Are you using the face cards or removing them? If you are using them, what is a Jack, King, Queen, and Ace worth?
• What operation are you focusing on (addition, subtraction, multiplication, or division)?
• How many students are in each group? Are there four in each group with two teams of two? Do you have two students in each group working together or playing against each other? What dynamics work best for your class?

Using playing cards is great because students can check each others’ mistakes.  Also, cards are an inexpensive investment and there are so many iterations of games students can play throughout the year if you tweak the rules.

Freebie: Here are several integers playing card game boards to get you started.

If you would like step-by-step guidance for working with your students on Integers, we have an in-depth guided notes product. It really sets the stage for all future Algebra concepts. You can check out our Integers guided notes product here.