Mini Lesson Topic
Drawing Shapes on a Coordinate Grid (Cartesian Plane)
Materials
Paper, pencils, extra worksheets, centimetre paper
Connection
Tell them what you taught the previous lesson.
“The last class, we learned how to…”
Explicit Instruction
Tell them what you will teach today.
“Today I’m going to teach you…”
Today we are going to be using ordered pairs to describe the
position of a shape on a coordinate grid or cartesian plane.
Let’s take a look at how Aria does this.
Show them exactly how to do it.
“Watch ​ me do it,” ​or “Let’s take a look at how (individual, text)
does this when he/she…”
Aria is designing a rectangular playground for a local park in
Victoria. To help plan the playground, Aria drew a rectangle on a
coordinate grid. She used the scale 1 square represents 2m.
To describe the rectangle, we label its vertices with letters.
The letters are written in order as you move around the
perimeter of the shape.
We then use coordinates to describe the locations of the
vertices.
Point A has coordinates (4, 6)
Point B has coordinates (4, 18)
Point C has coordinates (20, 18)
Point D has coordinates (20, 6)
Guided Practice
Ask them to try it out with a partner, or with you for a few
minutes.
“Now try it out with a partner...”
With a partner, try and use a coordinate grid to help find the
length and width of the playground.
Strategy #1 - Counting Squares
There are 8 squares along the horizontal segment AD.
The side length of each square represents 2 m.
So, the playground has length:
8 x 2 m = 16 m
There are 6 squares along the vertical segment AB.
The side length of each square represents 2 m.
So, the playground has width:
6 x 2 m = 12 m
Strategy #2 - Using the Coordinates
Jarrod used the coordinates of the points.
The first coordinate of an ordered pair tells how far you move
right.
The horizontal distance between D and A is:
20 - 4 = 16
So, the playground has length 16 m.
The second coordinate of an ordered pair tells how far you move
up.
The vertical distance between B and A is:
18 - 6 = 12
So, the playground has width 12 m.
Independent Practice
Remind students how the teaching point can be used in
independent work. There should be a link between the mini
lesson and the students’ independent lives.
Group Wrap Up
Restate the teaching point.
“Did you try what was taught?”
“Did it work for you?”
“How will it affect your future problem solving?”
On your own, try and answer the following question.
Draw and label a coordinate grid.
a)
Plot each point on the grid.
What scale will you use? Explain your choice.
J (4, 2) K (4, 10) L (10, 12) M (10, 4)
b)
Join the points in order. Then describe the shape you
have drawn.
In the future, when describing a shape, you can use a coordinate
grid (or cartesian plane) to be specific and accurate in your
descriptions of position, length, widths, etc.
How do you decide which scale to use when plotting a set of
points on a grid?
Is more than one scale sometimes possible? Explain.
Mini Lesson Topic
Transformations on a Coordinate Grid - Translations
Materials
Paper, pencils, extra worksheets, centimetre paper, onion paper
Connection
Tell them what you taught the previous lesson.
“The last class, we learned how to…”
We have already learned how to describe the position of a shape
on a coordinate grid.
Explicit Instruction
Tell them what you will teach today.
“Today I’m going to teach you…”
Now we are going to transform the positions of these shapes.
We will still use the cartesian plane to accurately describe the
beginning and end positions of the shapes.
Show them exactly how to do it.
“Watch me do it,” ​or “Let’s take a look at how (individual, text)
does this when he/she…”
If possible, watch Pearson Animation Video.
Let’s examine the following example:
Triangle ABC was translated 5 squares right and 2 squares
down. It’s translation image is triangle A’B’C’.
Each vertex moved 5 squares right and 2 squares down to its
image position.
After a translation, a shape and its image face the same way.
The shape and its image are congruent.
That is, corresponding sides and corresponding angles are
equal.
We can show this by measuring.
Guided Practice
Ask them to try it out with a partner, or with you for a few
minutes.
“Now try it out with a partner...”
With a partner, try and answer the following question:
Copy this triangle on a grid:
D (6, 10) E (10, 7) (7, 6)
a)
Draw the image of triangle DEF after the translation 6
squares left and 1 square down.
b)
Write the coordinates of the vertices of the image
triangle. How are the coordinates related to the
coordinates of the vertices of the prime triangle?
Independent Practice
Remind students how the teaching point can be used in
independent work. There should be a link between the mini
lesson and the students’ independent lives.
On your own, try and answer the following question.
Group Wrap Up
Restate the teaching point.
“Did you try what was taught?”
“Did it work for you?”
“How will it affect your future problem solving?”
Translations are only one type of transformation that shapes can
undergo.
Mini Lesson Topic
Transformations on a Coordinate Grid - Reflections
Materials
Paper, pencils, extra worksheets, centimetre paper, onion paper
Connection
Tell them what you taught the previous lesson.
“The last class, we learned how to…”
We have already learned how to describe the position of a shape
on a coordinate grid.
Explicit Instruction
Tell them what you will teach today.
“Today I’m going to teach you…”
Now we are going to transform the positions of these shapes.
We will still use the cartesian plane to accurately describe the
beginning and end positions of the shapes.
Show them exactly how to do it.
“Watch me do it,” ​or “Let’s take a look at how (individual, text)
does this when he/she…”
If possible, watch Pearson Animation Video.
Another point on this grid is G (10, 2). Using the translation
above (6 squares left and 1 square down), predict the
coordinates of point G’ after the same translation.
Let’s examine the following example:
Quadrilateral JKLM was reflected in a vertical line through the
horizontal axis at 5.
Its reflection image is Quadrilateral J’K’L’M’.
Each vertex moved horizontally so the distance between the
vertex and the line of reflection is equal to the distance between
its image and the line of reflection.
After a reflection, a shape and its image face opposite ways.
The shape and its image are congruent.
We can show this by tracing the shape, then flipping the tracing.
The tracing and its image match exactly.
Guided Practice
Ask them to try it out with a partner, or with you for a few
minutes.
“Now try it out with a partner...”
With a partner, try and answer the following question:
Copy this triangle on a grid:
S (2, 9) T (5, 7) U (8, 10)
a)
Draw the image of triangle STU after a reflection in the
line of reflection.
b)
Write the coordinates of the vertices of the image
triangle. Describe how the positions of the vertices have
changed from the vertices of the prime triangle.
Independent Practice
Remind students how the teaching point can be used in
independent work. There should be a link between the mini
lesson and the students’ independent lives.
On your own, try and answer the following question.
Group Wrap Up
Restate the teaching point.
“Did you try what was taught?”
“Did it work for you?”
“How will it affect your future problem solving?”
Translations and reflections are only two types of
transformations that shapes can undergo.
Mini Lesson Topic
Transformations on a Coordinate Grid - Rotations
Materials
Paper, pencils, extra worksheets, centimetre paper, onion paper
Connection
Tell them what you taught the previous lesson.
“The last class, we learned how to…”
We have already learned how to describe the position of a shape
on a coordinate grid.
Explicit Instruction
Tell them what you will teach today.
“Today I’m going to teach you…”
Now we are going to transform the positions of these shapes.
We will still use the cartesian plane to accurately describe the
beginning and end positions of the shapes.
Another point on this grid is V (4, 3).
Predict the location of point V’ after a reflection in the same line.
How did you make your prediction?
Show them exactly how to do it.
“Watch me do it,” ​or “Let’s take a look at how (individual, text)
does this when he/she…”
If possible, watch Pearson Animation Video.
Let’s examine the following example:
When a shape is turned about a point, it is rotated.
A complete turn measures 360°.
So we can name fractions of turns in degrees.
A 1/4 turn in a 90° rotation.
A 1/2 turn is a 180° rotation.
A 3/4 turn is a 270° rotation.
Trapezoid PQRS was rotated a 3/4 turn clockwise about vertex
R. Its rotation image is Trapezoid P’Q’R’S’.
The sides and their images are related.
For example,
● The distances of S and S’ from the point of rotation, R,
are equal; that is, SR = RS’
● Reflex angle SRS’ = 270°, which is the angle of
rotation.
After a rotation, a shape and its image may face different ways.
Since we trace the shape and use the tracing to get the image,
the shape and its image and its image are congruent.
Guided Practice
Ask them to try it out with a partner, or with you for a few
minutes.
“Now try it out with a partner...”
With a partner, try and answer the following question:
Copy this quadrilateral on a coordinate grid.
A (4, 2) B (3, 4) C (4, 7) D (6, 3)
Trace the quadrilateral on tracing paper.
Independent Practice
Remind students how the teaching point can be used in
independent work. There should be a link between the mini
lesson and the students’ independent lives.
Group Wrap Up
Restate the teaching point.
“Did you try what was taught?”
“Did it work for you?”
“How will it affect your future problem solving?”
a)
Draw the image of the quadrilateral after a rotation of
90° clockwise about vertex B.
b)
Write the coordinates of the vertices.
On your own, try and answer the following question.
Using the same quadrilateral.
a)
Draw the image of the quadrilateral after a rotation of
270° clockwise about vertex B.
b)
Draw the image of the quadrilateral after a rotation of
270° counterclockwise about vertex B.
Translations, reflections, and rotations are some of the
transformations that shapes can undergo.
How does a coordinate grid help you describe a transformation
of a shape?