Order Up! Ordering and Comparing Integers

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SWBAT order and compare integers by graphing on a number line.

Big Idea

Students will gain a deeper understanding of ordering integers by using both vertical and horizontal number lines.

Do Now

7 minutes

Students enter and follow the Daily Entrance Routine. The directions for the Do Now will be written on the smartboard (ppt) and students will also have a half sheet of paper on their desk with the same directions. At the end of the Do Now, students are reminded to leave this half sheet of paper on their desk for the next class.

Journal: Positive and negative numbers are opposites. For example, gaining 3 pounds is the opposite of losing 3 pounds. In football, gaining 10 yards is the opposite of losing 10 yards.

Consider the following statement: If °F is really cold, then °F is really hot. Do you agree or disagree? Explain your answer.

Students write for 4 minutes. Then, they turn to their partner and share their answers. I take this opportunity for students to work on MP3: Student pairs must coincide in their agreement with the statement. This means that if they disagree with each other, they must persuade each other until one person’s logic is undeniable.  At the end of 2 minutes, I will ask each pair to tell me if they agree or disagree with the statement (as a pair). One group will be selected to share their opinion and justification. I usually ask for a student who was “persuaded” by their neighbor to change their answer. Once that student has participated I distribute Cornell Notes and give students 1 minute to fill our their headings and copy the aim.

Class Notes + Intro to Lesson

10 minutes

The power point is used to explain some of the basic facts of the structure of a number line. I’ve found over the years that it is helpful to review some of the following facts and I review them in the following order:

  • Number lines can appear in horizontal and vertical forms
  • On a horizontal number line positive numbers are to the right of zero and negatives are to the left of zero
    • As numbers continue to the left they get smaller, or colder if we’re talking about temperature. As they continue to the right they get larger, or hotter in temperature.
    • On a vertical number line positive numbers are above zero and negatives are below zero.
      • As numbers continue on a downward path they get smaller, or colder, ad they continue upward they get larger, or hotter.

Students see the words “smaller” and “larger” in blue and red lettering, respectively. Tomorrow’s lesson will expose students to red and blue counter chips. Red will represent positive numbers and blue will represent negative numbers in a continued effort to discuss temperature and tie it to the first examples of integer operations.

I then distribute the “Task” worksheets and we complete the sample problem together (super cooling points of insects). I ask students to graph the temperatures in the table with their neighbor after I model this with one temperature (-54°C). I begin by drawing a red and green arrow above two different intervals on the number line, the interval between -40 and -50 and the interval between -50 and -60. I ask them to first tell their neighbor in which interval the number belongs, red or green. This allows me to listen for any misunderstandings. Then I ask one person to share which interval I should use for the integer -54. I then cold call for a couple of questions (what integer is to the left of -10? What integer is to the right of -40? etc). I make sure to emphasize plotting the point by drawing a dot on the approximate location of the number and also labeling the location if there is not a number already there. Finally, I ask one person to answer the following questions:

  • How does this number line help me list numbers in order from Least to Greatest or Greatest to Least? What is the only thing I would have to do? (read the numbers written on the number line from left to right or right to left)

Group Work + Task

15 minutes

There are 6 total problems on the task that ask students to list integers in order from least to greatest. Students are instructed to work in groups to complete the task. I walk around during group practice with chart paper for each group. I select one student from each group and one question for this student to draw on a vertical number line on the chart paper. This student needs to be someone who works quickly or who needs to be able to get up and engage in active movement to remain engaged in the task. If they finish early as a group, they are given the homework to get a head start.

Check for understanding: as I walk around the room to look at students’ work I watch out for students who are not placing the integers (especially the negatives) in the correct intervals on the number line. When this happens I stop to ask the student to name the negative integers starting at 0. I skip some of the numbers until we get to the targeted and incorrect interval in an attempt to get students to identify the correct interval on their own.

Closing - Positive Feedback

5 minutes

 At the end of independent practice, a different student from each group than the artist stands to stick their chart paper on the black board. Each problem is numbered and graphed on a vertical number line. I ask students to pack up their materials and line up silently in front of these papers to observe their classmates representation of each problem on a vertical number line. I encourage them to write positive feedback on the chart paper regarding the way the work was displayed (for ex: “I like the way you labeled each point on the number line and also listed the numbers in order from least to greatest”).