What Are Integers?

See my Do Now video in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, I want to know what students already know about negative numbers.   This helps me understand what background knowledge my students have and it may help me to identify student misconceptions. 

I have students participate in a Think Write Pair Share.  Then I ask students to share out their connections with the class.   

I have students work with a partner on this Temperature activity.  I walk around to observe student work.  I am curious to see what students do with -4 and -6.  A common mistake is that students confuse which one belongs on which side of -5.  I am also curious to see how students interpret “coldest” and “warmest”.

After a few minutes, we come together as a class.  I have students share out the locations of the temperatures.  For each answer, I ask for a student to explain if they agree of disagree and why.   Next I ask, “Which day was colder, Thursday or Sunday? Why?” (MP3)  I want students to recognize that the further the temperature is below 0 degrees, the colder it is.  

I share the Number Categories Review with the class. Students first saw this resource a couple lessons back: Where does that fall on the number line?. I begin by asking a student to read the definition of integers. 

• What is special about integers?  
• Is  -100 an integer?  
• Is 100 an integer?  

I want students to recognize that 100 can be considered a natural number, a whole number, and an integer.  I refer back to the circle diagram.  Is -14.5 an integer?  I want students to understand that although -14.5 is negative, it is not an integer, because integers have to be whole numbers.

In this section, I want students to quickly practice plotting integers on vertical and horizontal number lines.  A common mistake is that students confuse which integers are below on which side of a benchmark.  For example, for Number 6 a student may place -5 above -4, instead of below it. 

I have students complete the number line independently.  I walk around and monitor student progress.  If I see repeated mistakes I will address them as a class.  I ask for volunteers to share out their answer for problem 5.  Where is 0?  How do you know?  

Students need to be able to understand integers in context.  I have students work in partners for these problems.  Students may be unfamiliar with some vocabulary words (deposit, altitude, sea level).  If this is the case I will define these words for students. 

I give students a few minutes to write integers for the situations.  Students are working on MP2: Reason abstractly and quantitatively.  We come back together as a class to share ideas.  On the board, I draw a horizontal and vertical number line and I mark and label 0. For each question I have a volunteer explain their answer.  I reference the number lines on the board.  Why do you think this integer needs to be ______ (positive/negative). 

For problem 3 I explain that owing people money is a debt, and I connect it with students knowledge of loans from Unit 2.  If you owe someone money, that is a negative amount of money.  For problems 5-7, I ask students what sea level means?  I want students to understand that sea level is the same as 0 feet.  I ask students, “How can Badwater, CA be below sea level but not underwater?”  For the football examples I have a few volunteers help me act out a gain and a loss in front of the horizontal number line on the board. 

At this point in the year, my students are comfortable comparing positive numbers, but comparing integers may be new for them.  As a result, we fill in notes on the Comparing Integers worksheet together.  I stress that if you have a horizontal number line, the integer furthest to the right is greater.  If you have a vertical number line, the integer furthest up is greater.  A common mistake is that students think that -12 is greater than -8, since 12 > 8. 

Today, I plan to complete the first three examples together.  Students complete the rest of the problems on their own.  For each example I ask a student to explain which integer is greater and why.  

To begin this section, I go over the rules and expectations for Integer War.  I go through the example rounds with the class.  I tell students that if both players flip over the same integer, they both need to flip over another card and compare the new cards.  Some students may struggle with understanding that -12 is less than -1.  For each example I reference the number line and repeat that the integer that is greater is further to the right on the number line. 

Alternative Activity: Comparing Integers Dice Game

Another option for a comparing integers game is the Comparing Integers Dice Game.  Ask students what they notice about #3 on both sides.  Which player will win?  Always?  Why or why not?

Students play Integer War in groups of two.  I walk around and monitor student progress.

If students struggle, I may ask the following questions:

• Where is your integer on the number line?  Where is your partner’s integer?
• How do you know which one is greater?

If you have extra time, students can play Consecutive Capture in groups of 3. (This game is on the back side of the Integer War resource.)

 For Closure I ask students these questions:

• What it means for a number to be an integer?
• Why is it important that we are able to work with integers? 
• What strategies do you use for comparing integers? 
• What’s greater -100 or -1000?  Prove it.

I pass out the Ticket To Go for students to complete independently.  At the end of class I pass out the HW What are integers.