Intoduction to

for Middle Years Mathematics





by Murray Bruce


CELs
1994
S105.15




Table of Contents







Analytic Geometry



TOPIC: INTRODUCTION TO SLOPE FOR MIDDLE YEARS MATHEMATICS

Precis:
This topic deals with the Cartesian grid and linear equations with some analysis of the graph of the line and its relationship to the equation of the line. This topic was completed in five - fifty minute periods.

I. BACKGROUND


Grades: 1-5 Saskatchewan Curriculum

Strand: Geometry

Topic:Plane

Objectives:

G-17

Recognize, Draw, Name:

G-30
Locate and plot ordered number pairs in the first quadrant Grade 5
Grades 7/8 Geometry
Coordinate grid-plotting points
Definitions of Euclidean concepts


II. RESOURCES


III. SEQUENCE

Coordinate System


Relations:
Forms


Slopes of Lines
Use equations
y = 2x
y = 3x
y = -2x
y = -3x
to explain m = (rise)/(run)


The students were instructed on use of the Emulator program and were to, with supervision, key in a couple of equations to graph. This topic took 4.5 classes of instruction with 0.5 of a class for an OPEN BOOK QUIZ.


IV. STUDENT MATERIALS


V. CELs

  1. Communication
  2. Creative and Critical Thinking
  3. Numeracy
  4. Technological Literacy


VI. LESSONS





Lesson One

Plotting Points on a Cartesian Grid Using the Geoboard

Learning Objective

The students will be able to plot and recognize points on a Cartesian coordinate grid. Use of a geoboard may be useful

Cartesian Coordinate Grid (Descartes)


Direct Instruction: structured overview and demonstration of:
  1. Grid Systems
  2. Grid

    Key:
    1. x axis
    2. y axis
    3. positive x
    4 negative x
    5. positive y
    6. negative y
    7. quadrant 1, 2, 3, 4


  3. Locating Coordinates

  4. Geoboard

Interactive

peer practice (groups)




CLASSROOM MANAGEMENT
Monitor use of nonpermanent markers
when students plot points L, M, and N.








Relations

Direct Instruction: explicit teaching of examples.


Equations of Lines (results will be as ordered pairs with x, y elements of the set of integers)


x, y charts


Results will be ordered pairs as (x,y), with x, y elements of the set of integers

ASSIGNMENT 1





Lesson 2


Graphing Lines on the Cartesian Grid




Learning Objective


Indirect Instruction: reflective discussion on x, y charts using the set of integers.

Correct Assignment One


Students graph on blackboard using different colored chalk (plot check).


Direct Instruction: compare and contrast; demonstration




CLASSROOM MANAGEMENT: First complete instructions on how to use equipment, e.g. elastics and geoboards and then pass equipement out.



Slope



Direct Instruction: structured overview of:


SET 1:
a) y = x + 1
b) y = x - 1
c) y = -x + 1
d) y = -x - 1
examine similarities and differences.

SET 2:
a) y = 2x - 1
b) y = 2x - 3
c) y = 2x + 1
d) y = 2x - 3
examine similarities and differences.





LESSON 3


Determining the Slope and Y-Intercept of the Line



Learning Objective

Students will be able to determine the slope and y-intercept of the line given:


Independent Learning: computer assisted instruction


Direct Instruction: structured overview and demonstration.


ASSIGNMENT 2


  1. Determine the slope and the y-intercept of the following equations:
    	a) y = x 		b) y = 7x
    c) y = -4x d) y = 2x + 7
    e) y = 8x + 6 f) y = -4x 2
    g) y = -6 - 3x h) 2x + y = 4
    i) 7x + 6y = 4 j) 12y + 3x = 14

  2. Determine the equation of the line in:

The instructor and the students went through these questions as a group (except 1hij and 2def).




Lesson 4


Determining the Slope Using Coordinate Points


Learning Objective

Students will be able to determine the slope of the line given two coordinate points.

Direct Instruction: structured overview

ASSIGNMENT 3



Determine the slope of:

AB where A(2,1) and B(-4,3)

CD where C(-3,5) and D(5,1)

EF where E(-11,5) and F(-5,7)

GH where G(-6,-5) and H(3,-1)

IJ where I(7,-5) and J(10,1)

KL where K(-3,8) and L(2,-2)

MN where M(3,3) and N(7,3)

OP where O(2,2) and P(2,4)

Indicate to students that the last two sets may have surprising results. Class time was given to work on the assignment and was corrected in the same class.

Horizontal and Vertical Lines




Lesson 5


Parallel and Intersection Lines in Relation to Slope



Learning Objective

Students will be able to determine whether lines are parallel or intersecting based on their slope given:

Direct Instruction: structured overview and demonstration




VII. SUMMARY FOR STUDENTS

- review of learning objectives


VIII. EVALUATION



The rationale for the open book nature was that this was the first visual representation of the equation of the line as it relates to the cartesian grid. GRID.





OPEN BOOK QUIZ

ANALYTIC GEOMETRY NAME :________________________




1. What are the coordinates for the points on the grid (3 marks)
(Use first graph)


A _____, B _____,

C _____, D _____,

E _____, F _____ .



2. Plot the points on the grid: (3 marks)

(Use second graph)

A(2,3); B(0,4); C(5,-3); D(2,0); E(-4,-6), F(-1,1)




3. Complete the x, y chart for the following equations: (2 marks)


4. What is the slope for the following equations: (3 marks)
a) y = 7x - 3
b) y = -3x + 3
c) 3x + 2y = 5



5. What is the slope and y-intercept of the following equations: (4 marks)
a) y = -2x
b) y = 7x + 6


6. Determine the slope: (6 marks)
a) (-3,6) (-1,3)
b) (7,0) (2,1)
c) (0,3) (0,6)


7. For the equation sets given determine which are parallel and which intersect: (3 marks)

	a) y = 7x - 2 		b) y = 3x + 2		 c) y = x - 1
y = -7x - 2 y = 3x - 3 y = x + 1

This unit comes from the The Stewart Resources Centre which provides library resources and teacher-prepared materials for teachers in Saskatchewan. To borrow materials or obtain a free catalogue listing unit and lesson plans contact :
Stewart Resources Centre,
Sask. Teachers' Federation,
2317 Arlington Avenue,
Saskatoon, SK S7J 2H8;
phone 306-373-1660; fax 306-374-1122,
e-mail src@stf.sk.ca.
http://www.stf.sk.ca/

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