Subject Area:
Pre-Algebra
Lesson Design
Mathematics
Grade Level:
7th
Benchmark Period
III
Duration of Lesson:
1 or 2 periods
Standard(s): MG 3.2 Understand & use coordinate graphs to plot simple figures, determine lengths &
areas related to them, & determine their image under translations & reflections.
Learning Objective: Students will find and draw the image of a geometric shape under a translation and / or a
reflection and find the area of both the original figure and its transformation.
Big Ideas involved in the lesson:
Length and area are preserved under translations and reflections, that is, they are isometries.
As a result of this lesson students will:
Know:
 Vocabulary: graph, coordinates, plot, pre-image, image, translation, slide, reflection, flip,
coordinate plane, x-axis, y-axis, x- and y- coordinates, origin, image, and prime (such as A
prime, A’).
 The reflection of an object is called its image.
 Translating an object is a slide.
 Reflecting a figure is taking a mirror image of the figure.
Understand:
 How to read and plot coordinate points on a coordinate plane
 Reflected objects are flipped over a line of reflection (where a mirror may be placed).
 The distance from a point to the line of reflection is the same as the distance from the point’s
image to the line of reflection.
 Translated or reflected objects preserve their original size and shape and they face the same
direction.
 Objects that are reflected over the x-axis are moving either from Quadrant IV to Quadrant I or
vice versa or from Quadrant II to Quadrant III or vice versa. A point that is reflected over the
x-axis keep the same x-coordinate, but the y-coordinate is the opposite of the original.
 Objects that are reflected over the y-axis are moving either from Quadrant I to Quadrant II or
vice versa or from Quadrant III to Quadrant IV or vice versa. A point that is reflected over the
y-axis keeps the same y-coordinate, but x-coordinate changes to the opposite of the original.
 Translated or reflected objects are labeled in the same manner as the original but with a prime
notation.
Be Able To Do:
 Calculate length of a line segment.
 Use distance found between the coordinates of a figure to determine the area
 Draw the image of a geometric figure under a translation
 Draw the image of a geometric figure under a reflection
 Label translated or reflected objects.
1
M&G 3.2
Assessments:
What will be evidence of
student knowledge,
understanding & ability?
Anticipatory Set:
a. T. focuses students
b. T. states objectives
c. T. establishes purpose of
the lesson
d. T. activates prior knowledge
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide examples
 Model
b. Check for Understanding
 Pose key questions
 Ask students to explain
concepts, definitions,
attributes in their own words
 Have students
discriminate between
examples and nonexamples
 Encourage students
generate their own
examples
 Use participation
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step along
w/students at the same time
b. Elicit overt responses from
2
Lesson Design
Mathematics
Formative: ABWA, closure,
review
Summative: unit test, CST
Checking for Understanding:
 What is the difference between an
object that is translated and an object
that is reflected?
 What happens to the coordinates of
an object that is reflected over the xaxis?
 What label do we use for an object
that has been translated or reflected?
 How does the area and the length
change when an object is translated
or reflected?
Lesson Plan
See powerpoint for M&G 3.2
Use powerpoint to introduce reflections and translations on a coordinate plan.
See file M&G 3.2 instruction for problems to do with students.
Check for understanding using whiteboards during the instruction for each
problem asking questions such as:
 What is the difference between an object that is translated and an object
that is reflected?
 What happens to the coordinates of an object that is reflected over the xaxis?
 What label do we use for an object that has been translated or reflected?
 How does the area and the length change when an object is translated or
reflected?
See file M&G 3.2 Guided practice
Do problems with students, ask questions such as those listed below as
students work out each problem on their white boards. Have students first
share answers in small groups before showing them to you.
 What is the difference between an object that is translated and an object
M&G 3.2
students that demonstrate
behavior in objectives
c. T. slowly releases student to
do more work on their own
(semi-independent)
d. Check for understanding
that students were correct at
each step
e. Provide specific knowledge
of results
f. Provide close monitoring
What opportunities will students
have to read, write, listen &
speak about mathematics?
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students can
describe the what and why
of the work
c. Have each student perform
behavior
Lesson Design
Mathematics
that is reflected?
 What happens to the coordinates of an object that is reflected over the xaxis?
 What label do we use for an object that has been translated or reflected?
 How does the area and the length change when an object is translated or
reflected?
With partners, students do a pair / share discussion of the result of each
transformation.
Teacher asks the students the following questions. Students will respond on
their white boards, or be called on randomly to answer. Correct student
responses are given:
1. The teacher will ask the students, “How can we find the length of horizontal
or vertical line segments?”
Ans. The students will respond with, “The length of a horizontal line segment
is the difference between the x values; the length of a vertical line segment
is the difference between the y-values.”
2. The teacher will ask the students what must be found first in order to
calculate the area of a simple figure such as triangle or rectangle on a
coordinate plane.
Ans. The students will say that they must find the length and width distance of
the rectangle or triangle first.
3. The teacher will ask, “Which value of the ordered pair changes when a
point is translated up or down? Left or right?”
Ans The students will say, “y-value, and x-value, respectively.”
4. The teacher will ask the students, “Which value changes in the ordered pair
when a point is reflected about the y-axis?”
Ans. The students will respond, “The x-value changes to the opposite value,
but not the y- value.”
5. The teacher will ask the students, “Which value changes in the ordered pair
when a point is reflected about the x-axis?”
Ans. The students will respond, “The y-value changes to the opposite value
but not the x -value.”
Independent Practice:
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
3
See file M&G 3.2 independent practice
M&G 3.2
Lesson Design
Mathematics
accuracy
c. Provide effective, timely
feedback
Resources: materials needed
to complete the lesson
4
Powerpoint
M&G 3.2 instruction
M&G 3.2 guided practice
M&G 3.2 independent practice
M&G 3.2