PARCC Sample Lesson Plans for Math Grade 8

1. Lesson
14:
PBA
–
Geometry
Translations
Page
1
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
Rationale
Students use compasses, protractors, rulers or technology to explore figures created from
translations, reflections and rotations. Characteristics of figures, such as lengths of line
segments, angle measures and parallel lines are explored before and after a
transformation. Students understand that rigid transformations produce images of exactly
the same size and shape as the pre-image since the measures of the corresponding angles
and corresponding line segments remain equal (are congruent). They identify resulting
coordinates from translations, reflections and rotations (90°, 180° and 270° both
clockwise and counterclockwise), recognizing the relationship between the coordinates
and the transformation.
Goals
To translate a figure in the coordinate system
To describe translations, using appropriate mathematical language
Objectives
Students will use transformations, reflections and rotations on a coordinate grid.
Students must be able to quantify a transformation with direction and distance.
Students must be able to draw a reflection or a rotation given the number of degrees.
Standards
8.G.2. Understand that a two-dimensional figure is congruent to another if the second can
be obtained from the first by a sequence of rotations, reflections, and translations; given
two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-
dimensional figures using coordinates.
Materials
Performance-Based Assessment Tasks-There are two separate Type II tasks.
Journal
Class Folder Labeled: Lesson 14: Performance-Based Assessment – Geometry. (At the
end of the lesson, place the class papers in the folder. If students used “scratch” paper,
please have students attach the “scratch” paper to their Mathematics Items handout.)
PARCC Grade 8 Mathematics
Lesson 14: Performance-Based Assessment
Geometry
Translations

2. Lesson
14:
PBA
–
Geometry
Translations
Page
2
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
Procedures
Say, “This year, you will be taking the math PARCC Assessment. It will test all of the
things you have learned this year in math in order to find out if you have mastered the
concepts or if you still need more practice. Today we will be learning about what you
will need to know for the test. You will determine what is easy for you and what is
challenging for you. We will then work on a plan for improving the areas which are
difficult for you right now.”
Assign students to groups of 2 or 3. Give them the Performance-Based Assessment. Tell
students that this is an example of what a Performance-Based Assessment may look like.
Review the directions for the Tasks. Instruct students to record their answers on the
assessment.
Ask students to work in pairs and discuss each Task. Each student should complete their
own assessment. Remind students to use clear explanations in their justification of their
answers.
While the students are working, circulate the room and monitor students’ approaches.
Note patterns of difficulty and/or errors.
When students have finished, ask them to share their answers to the questions.
Assessment or Check for Understanding
Journal writing: in the last 2-3 minutes of class, students should record what they learned
about themselves regarding test taking strategies and the content of the CCSS.
Follow-up
During any Performance-Based Assessment mathematics lesson, engage students in a
discussion of why one task was less challenging and another task more challenging.
PARCC Technology Tips
PARCC equation editors are provided as the answer boxes for responses that include
math, utilizing special mathematical functions. In this lesson, a written response is
needed and the Open Response Equation Editor is provided. It is possible to respond
with a combination of words and math.
It is suggested that letters, numbers, and punctuation symbols from the standard keyboard
be used. Any part of the response that indicates mathematical processes can be described
using the function keys provided in the Open Response Equation Editor. When the
pointer (curser) hovers over a function key, the name of the function appears as a pop-up.
It is NOT possible to create diagrams, models and/or step-by-step solution processes in a
vertical format (such as solving with an algorithm).
See: PARCC Practice with Equation Editors for online practice with the equation editors.

3. Lesson
14:
PBA
–
Geometry
Translations
Page
3
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
Task # 1 (PARCC 8.C.5.2)
Quilt Design Contest
A collection of original designs are being created to compete in a quilt design
contest.
PART A
A shape within a design is drawn in Quadrant II. Add to the design by drawing the
following translations:
Step 1: Reflect the shape across the vertical axis.
Step 2: Next, reflect both shapes across the horizontal axis.
PARCC Grade 8 Mathematics
Lesson 14: Performance-Based Assessment
Geometry
Translations

4. Lesson
14:
PBA
–
Geometry
Translations
Page
4
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
PART B
Another design is represented below. Add to the design by drawing the following
translations:
Step 1. Rotate the shape a 90° turn clockwise about the origin.
Step 2. Repeat Step 1 twice. When completed, each quadrant should have a shape.
Is there another way to describe the translations needed to complete the design?
Explain your reasoning.

5. Lesson
14:
PBA
–
Geometry
Translations
Page
5
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
Task # 2 (PARCC 8.C.5.2)
Quilt Design Contest
A collection of original designs are being created to compete in a quilt design
contest.
PART A
The shape in Quadrant II has been translated to create this design. Describe two
different ways the shape could have been translated to complete the design.

6. Lesson
14:
PBA
–
Geometry
Translations
Page
6
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
PART B
The shape in Quadrant II has been translated to create this design.
Figure A is similar to Figure A’. What is the scale factor?
Scale Factor: Choose
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2
4

7. Lesson
14:
PBA
–
Geometry
Translations
Page
7
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
Task # _1___ Part A
Score Description
1 Student correctly translates the portions
0 Student Response is incorrect or irrelevant.
Task # ___1_ Part B
Score Description
2
Student response includes each of the following 2 elements:
• Student correctly translates the portions

8. Lesson
14:
PBA
–
Geometry
Translations
Page
8
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
• Valid explanation other translations that can be used to complete the design.
Sample Student Response:
Another way to translate the figure is with these steps:
Step 1. Rotate the shape a 90° turn counter clockwise about the origin.
Step 2. Repeat Step 1 twice.
This translation is nearly the same as the translation that was given in the problem but it reverses the
direction. Quadrant I would be drawn in step 1. In step 2, Quadrant II would be drawn, followed by
Quadrant III.
1 Student Response includes 1 of the 2 elements.
0 Student Response is incorrect or irrelevant.

9. Lesson
14:
PBA
–
Geometry
Translations
Page
9
©
2014
Standards
Solution,
LLC.
All
Rights
Reserved.
Task # __2__ Part A
Score Description
2
Student response includes each of the following 2 elements:
• Student correctly describes the translations one way.
• Student correctly describes the translations a different way.
Sample Student Response:
There are different ways to describe the translation of the shape in Quadrant II to create the
complete design.
One way is: Reflects the shape over the vertical line, then translate the two shapes down seven units.
Another way is: Translate the shape down seven units, then reflect both shapes over the vertical line.
1 Student Response includes 1 of the 2 elements.
0 Student Response is incorrect or irrelevant.
Task # __2__ Part B
Score Description
1 !
!
0 Student Response is incorrect or irrelevant.