Monday
Math Instructional Model
Goals/Standards/Mathematical/Objectives:
Goals:
The students will be able to describe the similarities and differences between the image and pre image;
under translation.
The students will be able to describe, apply, and demonstrate the properties of translations.
CCSS.MATH.CONTENT.8.G.A.1
Verify experimentally the properties of translations:
CCSS.MATH.CONTENT.8.G.A.1.A
Lines are taken to lines, and line segments to line segments of the same length under a translation.
CCSS.MATH.CONTENT.8.G.A.1.B
Angles are taken to angles of the same measure under a translation.
CCSS.MATH.CONTENT.8.G.A.1.C
Parallel lines are taken to parallel lines under a translation.
CCSS.MATH.CONTENT.8.G.A.2
Understand that a two-dimensional figure is congruent to another if the second can be obtained from
the first by a sequence of translation; given two congruent figures, describe a sequence that exhibits the
congruence between them.
CCSS.MATH.CONTENT.8.G.A.3
Describe the effect of translation on two-dimensional figures using coordinates.
Understandings:
The students will understand translations have direction. This can be explained by using words such as
up, down, left, right, and the amount of units moved.
The students will understand translations have a pre-image and image that are congruent. This means
that students will understand that angle measures, parallel lines, and sides of the figure of the image
and pre-image are always the same.
I.
Engagement Block (Launch)
10 mins
II.
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III.
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IV.
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Tell students to find a partner.
Tell students to get out one piece of paper per group and then to go to the following link https://www.geogebratube.org/student/m18530.
Instruct students to explore the site moving the points of the triangle and typing in different
coordinate points for the image.
Have the students write down any observations they notice about image and the pre – image.
Have students write down what they are noticing about the size and shape of the triangle.
After students have explored the site and wrote down some observations we will then pass out
the worksheet on Exploring Translations.(See Below)
Investigation Work Block
10 min
Have students work with their partner and complete the work sheet.
The teacher should be walking around asking questions and assessing understanding.
Questions to ask?
What happens when you move the vector to a different point? We want students to
see the points of the triangle are moved according to the vector.
What do you see about the angles, side lengths, and shape of the image and pre-image?
We want students to see the angles of the pre-image and image are the same.
Issues to address
They may not know the vector can move. If we notice students are not moving the
vector ask them to move the vector and explain the effect this has on the image and
pre-image.
Students may only move the entire shape of the triangle and not explore moving
specific points to create other triangle shapes. If we notice students are doing this we
can ask them to try moving different points on the triangle.
Summary Block
22 mins
After students have completed their worksheets, have them form groups of four. 2 mins
Have each group take a large sheet of paper.
Ask each group to collectively write their ideas, (drawings, rules, descriptions) about translations
on a large sheet of paper. 5 mins.
After each group has written down their ideas on a large sheet of paper each group will present
their paper in front of their peers for two minutes. Each group will leave their sheet of paper on
the board. 10 minutes
After each group has presented there will be an entire class discussion on everyone’s thoughts
of translation. 5 minutes
Then collectively we will all come up with a class definition of what we think translation means.
Application/Extension/Practice Block
Then students will be given their exit ticket.
8 min
In this exit ticket students will be creating a translation by hand using coordinate points
and on a plan without coordinates. (see attatched)
Homework
Go home and find 5 translations around your home be sure to either take pictures, or draw the
movement. Write a description of why this movement is a translation. Be specific. Please make sure to
use the google doc we have provided the link for you and post pictures and the descriptions on the
translations you find. Put your name and then numbers one through five and then your pictures or
descriptions. Tomorrow we will pull up the document and discuss what you all found.