Math 106 - Cooley Math for Elementary Teachers II OCC
Classroom Activity #7 – Slope Exploration using Geoboards
In this lesson students explore the slopes of line segments using a rectangular geoboard.
v Learning Objectives
Students will:
· be able to identify the slope of a line segment on a geoboard.
· be able construct (or draw) line segments on the geoboard given the slope and length of the line segment.
v Materials
· Geoboards, preferably 5´5 grids
· Rubber Bands
· Slopes & Geoboards Activity Sheet – 1 per student
v Instructional Plan
Distribute the Slopes & Geoboards Activity Sheet to each student. Introduce (or
re-introduce) the concept of slope as it is developed in the opening paragraph of
this activity. Show students how to recreate the triangle having hypotenuse AB
(this is your line segment) and legs of lengths 2 (rise) and 3 (run). This is done by
first stretching the rubber band between points A and B, then pulling one side of the
rubber band down to create a triangular opening. Finally, position this opening over
the peg the corresponds to the corner of the right angle.
Have students work on the activity in groups or on their own. From each question to the next you may want to demonstrate part a) and then have students work on the remaining parts independently. Students may be called on for correctness and to demonstrate competency and understanding.
v Extensions
Create additional problems that involve negative slope, provided that negative slope has
been taught.
v NCTM Standards and Expectations
Algebra – Analyze change in various contexts – Grades 3-5:
· Investigate how a change in one variable relates to a change in a second variable.
v References
This lesson was obtained from Mathematics for Elementary Teachers, A Conceptual Approach
by Bennett, Burton, & Nelson. This lesson has been modified by TopCatMath.com.
NAME ______
Slope Exploration using Geoboards Activity Sheet
The slope of the line segment from point A to B on the geoboard to the right is .
Notice that you can move from point A to B by moving horizontally 3 spaces to
the right (called the run) and vertically 2 spaces up (called the rise). These distances
form the lengths of the legs of a right triangle.
· The slope of a line is the rise (vertical distance) divided by the run
(horizontal distance) in moving from one point to another on the line.
Slope =
· The slope is generally expressed as a fraction in lowest terms.
In this activity we will only consider the slopes of line segments that rise as you look left to right on the geoboard.
1) a) For each of the following line segments, label the rise, run, and indicate the slope.
Slope = ______Slope = ______Slope = ______Slope = ______
b) As the line segments get “steeper”, what happens to the numerical value of the slope?
2) Sketch a line segment on each geoboard below to satisfy the given condition.
a) Slope of b) Slope of c) Slope of 2 d) Slope of
The line through points C and D on the geoboard to the right is horizontal, that is, has
no “steepness.”
· This line has a rise of 0 and a run of 3.
· Since , the slope of a horizontal line is 0.
The line through points E and F on the geoboard to the right is vertical.
· This line has a rise of 2 and a run of 0.
· Since the formula for the slope is rise/run and is undefined, we say that
the slope of a vertical line is “undefined”. (Recall that division by 0 is undefined.)
3) Sketch a line segment on each geoboard below to satisfy the given condition.
a) Length of 4 and b) Length of 3 and c) Length of 1 and d) Length of 5 and
slope of 0. undefined slope. undefined slope. slope of .
4) On the large geoboard below,
a) Draw as many line segments as you can that will have the largest slope.
b) Draw as many line segments as you can that will have the smallest non-zero slope.
5) There are 20 possible non-vertical line segments corresponding to 12 distinct slopes that have the
lower left point on the geoboard as one end point.
a) Sketch 12 of these 20 possible line segments corresponding to 12 distinct slopes.
· Each line segment should have the lower left point on the geoboard as one endpoint.
· Remember only non-vertical line segments may be used.
b) Identify the slope of each line segment. (You should have 12 distinct numbers.)
c) Fill in the blanks at the bottom to list these 12 distinct slopes in increasing numerical order.
Slope = ______Slope = ______Slope = ______Slope = ______
Slope = ______Slope = ______Slope = ______Slope = ______
Slope = ______Slope = ______Slope = ______Slope = ______
Ordered from smallest to largest:
______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______, ______.