Understanding Integers

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Objective

SWBAT represent negative numbers in writing and express their relationship to zero.

Big Idea

What is the lowest elevation in United States? How would you represent it as an integer?

DO NOW

10 minutes

Students will be working with number lines to represent the location of fractions and decimals.  This activity sets them up for looking at numbers on number lines.  Today we will be including integers to our number line. (SMP 5)

Students may have difficulty with placing fractions on the number line.  Remind students they can use fraction bars to help them figure out where it goes.  By drawing a rectangle around the whole numbers and then cutting the rectangle into equal parts will help students visualize the parts on the number line.

When students have completed this worksheet, have them do a HUSUPU to go over answer with a partner.  Remind students that the conversation should sound something like this… “I know that this fractions belongs here because…” (SMP 3)  

Integers on the number line

15 minutes

This portion of the lesson is strictly teacher directed.  I’m going to use this slide to go over common vocabulary and to show the students that the number line extends in both directions.  It is here that we get our negative numbers.  At this time, students should be filling in vocabulary in their notes and listening to the teacher.

I will explain to the students about zero as this number is important when looking at writing integers and explaining their meaning.  Students need to know that zero is neither positive nor negative.  Zero is the line of symmetry on our number line. I will also be pointing out about opposites.  The idea of opposites being the same distance from zero will help when we start using absolute value.

Students will have difficulty understanding that the farther away from zero you go, the smaller the number where as it is the opposite when going in a positive direction.  I always say to the kids… “would you rather owe someone $10 or $100”.  These types of scenarios help students understand this concept.

To wrap things up, I’m going to ask the students these questions:

Is -3 above or below zero?  How do you know?

What is the opposite of 10?

What number is 5 units from zero?

This will give me a good indication of their understanding of our vocabulary

Number system and placing numbers on the number line

20 minutes

I’m going to go over our number system using the flow chart on slide 4.  Students will fill in this information in their notes.  Students need to know that rational numbers can be broken into integers and fractions and that we can have both positive and negative of both sets of numbers.  The blank boxes are for examples of each.

On the next slide, I’m going to have students place several numbers and their opposites on the number line. 

I’m expecting that students will have troubles placing the negative fractions on the number line, especially because it is not a blank number line.  So, I’m going to have students use their knowledge of benchmark fractions to assist in the placement.  I will say, “ let’s just look at the fraction and not worry about the negative sign. Is this fraction closer to 0,1/2, or 1”?  When students decide the benchmark, then I will remind them that this means it’s between 0 and -1, but closest to….. Students should then be able to place the number on the number line.

(SMP 1,5,6)

Writing Integers

20 minutes

Give students the opportunity to write in some integer words to know in their notes.  When students are done writing, ask them how they would know if they were dealing with a positive or negative number?  Students should say that positive words indicate going up and negative words indicate going down.  If they don’t say left is negative and right is positive, you could ask them that as well.

Use the scenarios to help them write integers.  For each scenario, I’ve included the statement, which means.  I want the students to make a connection to zero each time.  For example, owing someone $30 is -30 which means you are below zero. One step farther would be to say that zero means you owe or are owed nothing. 

Credit/Debit Game

20 minutes

You will need a deck of playing cards for each group of two.

Students need to be in partners.  This is a great activity to make real world connections to integers.

Directions for the game:

(SMP1,2,3,5,6)

Pretend that you are an accountant for a business.  Your job is to keep track of the company’s current balance.  The current balance is also called the “bottom line.”  As credits and debits are reported, you will record them and then adjust the bottom line.

 

1) Shuffle the deck and lay it facedown between the two players.

2) The black numbered cards are the “credits (+),” and the red numbered cards are the “debits (-).”

3) Each player begins with a bottom line of +$10.

4) Players take turns.  On your turn, do the following:

  • Draw a card.  The card tells you the dollar amount and whether it is a credit or debit to the bottom line.
  • Record the credit or debit in the “Change” column.
  • Use the credit or debit to adjust the bottom line and record it in the “End Value.”
  • Use your “End Value” as the new “Bottom Line (Start Value)” for the next round.

5) Game ends after each player has completed the 10 rounds.

 

Winner: The player with the most money or if both players have negative dollar amounts, the player whose amount is closest to 0 wins.

Closure

10 minutes

The students will be answering 3 questions in their notes about their learning for today.  I want them to be able to relate integers to their lives.  They have had much exposure to real world integers so the leap to come up with one on their own should be easy.  If time permits, have students share their responses with their tablemates. (SMP 1,2,3)