ALEX Learning Activity

  

Lining Up With Integers

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  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2289
Title:
Lining Up With Integers
Digital Tool/Resource:
 
Web Address – URL:
Not Applicable
Overview:

The students will create integer cards (using positive and negative whole numbers and decimals) and then work with classmates to put them in order in a number line diagram.  The activity is progressive to help scaffold understanding.

This activity was created as a result of the ALEX  Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
10. Locate integers and other rational numbers on a horizontal or vertical line diagram.

a. Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

b. Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Create and interpret number line diagram.
  • Given any rational number (positive or negative).
  • Locate the number on a number line.
  • Identify opposite signs of numbers as indicating the same distance from zero on the opposite side of zero, the opposite of the opposite, or a representation of its opposite as the point itself [-(-3) = 3], and zero as its own opposite.
Teacher Vocabulary:
  • Integers
  • Rational numbers
  • Horizontal line diagram
  • Vertical line diagram
Knowledge:
Students know:
  • Strategies for creating number line models of rational numbers (marking off equal lengths by estimation or recursive halving).
  • Strategies for locating numbers on a number line.
  • Notation for positive and negative numbers and zero.
Skills:
Students are able to:
  • Represent rational numbers and their opposites on a number line including both positive and negative quantities.
  • Explain and justify the creation of number lines and placement of rational numbers on a number line.
  • Explain the meaning of 0 in a variety of real-world contexts.
Understanding:
Students understand that:
  • Representing rational numbers on number lines requires using both a distance and a direction,
  • Locating numbers on a number line provides a representation of a mathematical context which aids in visualizing ideas and solving problems.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.10.1: Define integers, positive and negative numbers.
M.6.10.2: Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
M.6.10.3: Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
M.6.10.4: Discuss the measure of centering of 0 in relationship to positive and negative numbers.
M.6.10.5: Discover that the opposite of the opposite of a number is the number itself.
M.6.10.6: Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
M.6.10.7: Define rational number.
M.6.10.8: Plot pairs of integers and/or rational numbers on a coordinate plane.
M.6.10.9: Arrange integers and /or rational numbers on a horizontal or vertical number line.
M.6.10.10: Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
M.6.10.11: Identify a rational number as a point on the number line.
M.6.10.12: Name the pairs of integers and /or rational numbers of a point on a coordinate plane.

Prior Knowledge Skills:
  • Model writing ordered pairs.
  • Identify the x- and y- values in ordered pairs.
  • Label the vertical axis (y).
  • Label the horizontal axis (x).
  • Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
  • Locate positive numbers on a vertical number line.
    Examples: thermometer, map.
  • Locate positive numbers on a horizontal number line.
  • Locate negative numbers on a horizontal number line.
  • Label x- and y-axis and zero on a coordinate.
  • Illustrate vertical and horizontal number lines.
  • Specify locations on the coordinate system.
  • Define x-axis, y-axis, and zero on a coordinate.
  • Define ordered pair of numbers.
  • Define parentheses, braces, and brackets.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.9 Describe quantities with positive and negative numbers (e.g. temperature, sea level, etc.).
Learning Objectives:

The students will find and position integers and other rational numbers on a number line diagram.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

Begin by reviewing the number zero, and how integers are less than zero. Have students give examples of a situation that can be described with a positive or negative value (ex. giving away money, swimming up through the water, driving back to get something you forgot).

Give each student four index cards. They should listen carefully and place a different value on each card:

  • A positive whole number between 1 and 10

  • A negative whole number between -1 and -10

  • A positive decimal number between 1 and 10

  • A negative decimal number between -1 and -10

After the students have written their four numbers, have them put them in order from smallest to largest on their desks. Check for accuracy.

Next, have the students combine cards with a partner and put them in order from largest to smallest. Check for accuracy.

Next, students in each group should combine and order cards (16-20 numbers). This one can be a competition, whoever finishes first gets bragging rights.

Finally, have all of the kids put the cards back in random order facing down in the middle of the group. Each student should pick one card without looking at it or showing other students.

When the teacher says go, the object of the last activity is to order the students in the class from smallest to largest. Each student places their integer card on their forehead, and they can’t look at it. The students have to stay silent the entire time. They must arrange each other in order without knowing what their own number is.

After everyone has been arranged, check for accuracy.

Choose a few students at random to leave the line and pick a new number card from the desks. They now have to figure out how to place themselves back in the line. Continue until all students have been moved around.

In order to leave the line and go sit at their seat, students have to come up with a situation that describes their integer card.

In closing, ask questions such as:

  • How is 3 greater than -25, even though 25 is a bigger number? The negative sign tells you that you are moving backward away from zero. -25 is like owing 25 before I can even get back to zero. Three is positive.

  • Why do we need negative numbers? So we can describe situations less than zero.

  • Is a negative decimal number still a negative number? Yes, whole numbers, decimals, and fractions can all be negative.
Assessment Strategies:

Students can show Fist-to-Five at the beginning and end of the lesson as an informal pre- and post-assessment. (They hold up fingers to show their understanding, a fist means they didn't understand at all, one finger means they understood a little, all five fingers means they understand it perfectly and could teach it to a friend.)

Observation during the practice will show which students need further support.

The exit ticket (Ordering Integers Exit Ticket) shows whether students can compare and order integers.
Advanced Preparation:

Gather enough index cards for each student.  Copy exit tickets for the students (there are four on a page).
Variation Tips (optional):
 
Notes or Recommendations (optional):
 
  Keywords and Search Tags  
Keywords and Search Tags: decimal, integers, negative, number line, numbers, opposite, positive, rational