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Learning Experience/Unit

Adding and Subtracting Integers Using a Number Line by St. Lawrence-Lewis BOCES

Grade Levels

Intermediate, 7th Grade, 8th Grade


Assessment

Homework-corrected and graded.
Unit exam including integer questions-scored.

Learning Context/ Introduction

I learned this method of adding and subtracting integers on the number line from Jerry Peters, while at his workshop on distributed practice (see related resources).

The traditional method of adding and subtracting integers consists of teaching students several "rules" to memorize and follow. The beauty and convenience of Jerry Peter's number line method is that there is only one "rule" students must follow.

The rule is "always go right on the number line unless you get turned around by a subtraction or negative sign."

After practicing adding and subtracting integers on the number line, students will find it intuitive and will eventually drop the need for the number line and be able to add or subtract integers without memorizing the many traditional rules.

Duration

3 to 4 days

Essential Question

How can the number line be used to combine integers?

Procedure

    Day 1:
  1. Students are given a worksheet with the day's problems (see attached).
  2. Start the PowerPoint presentation Adding and Subtracting Integers (included below). Play through lesson 1 until you get to the worksheet slide.
  3. Help class complete the day’s worksheet.

    The procedure is the same regardless if students are adding or subtracting two integers.
    • Students draw a number line, locating and labeling the zero. (It is not necessary to fill in the number line by locating and labeling other integers to the left and right of zero.)
    • Students locate and label the first integer in the problem on the number line. Then students place their pencils above that integer. Since the only "rule" for this method is "always go right unless you get turned around by a negative or subtraction sign", students will look at the remainder of the problem to decide if they should draw a line to the left or right. lf the first integer in the problem is followed by an addition sign (adding a positive number), students will draw a line to the right the number of spaces they are adding.
    • If the first integer in the problem is followed by an addition sign AND a negative sign (adding a negative number), students will "turn around" and draw a line to the left the number of spaces they are adding.
  4. Give out homework.

    Day 2:
  1. Students are given a worksheet with the day's problems attached (see attached).
  2. Continue the PowerPoint at Lesson 2 until you come to the practice worksheet slide. If the first integer in the problem is followed by a subtraction sign (subtracting a positive integer), students will "turn around" and go left the number of spaces they are subtracting.
  3. Students complete the day's worksheet.
  4. Give out homework.

    Day 3:
  1. Students are given a worksheet with the day's problems attached (see attached).
  2. Continue the PowerPoint at Lesson 3 until you come to the practice worksheet slide. If the first integer in the problem is followed by a subtraction sign AND a negative sign (subtracting a negative integer), students will "turn around" twice, hence going right the number of spaces they are subtracting.
  3. Students draw their lines by counting the number of spaces left or right. Where they stop on the number line is the answer to the problem.
  4. Students complete the day's worksheet.
  5. Give out homework.
  • Adding and Subtracting Integers PowerPoint
  • Day 1 - Adding Integers Worksheet
  • Day 2 - Subtracting and Adding Integers Worksheet
  • Day 3 - Subtracting and Adding Integers Worksheet
  • Reflections and Feedback

    I taught this method of adding and subtracting integers using a number line to students who were beginning eighth grade. Since this is a seventh grade standard, students had already learned the topic, but I felt a review was necessary. Many students remembered the many traditional "rules" for adding and subtracting integers from seventh grade and resisted the number line method. For subtraction in particular, they preferred the "SMATO" rule (subtraction means add the opposite), and a few students said they found the number line cumbersome or confusing. Therefore, even though I like this method and will use it again for eighth grade, I would suggest introducing it seventh grade.

    Student Work

    • Students will complete practice worksheets in class.
    • Students will complete homework assignments.
    See attached samples:
    Student Sample A
    Student Sample B
    Student Sample C

    Related Resource

    The following are resources from Jerry Peter's distributed practice workshop.

  • Jerry Peter's Basic Lesson Format with Bell Ringer
  • Spreadsheet using J. Peter's Distributed Practice

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