This lesson accommodates all three different types of learners, auditory, visual, and kinesthetic. The auditory learners will benefit from the class discussion and reviewing the problems orally. The visual learners will be able to draw and see the translated figures as well as writing the coordinates of the translated figures on their worksheets. Finally, the kinesthetic learners will love to cut out the quadrilaterals and physically move the figure on the coordinate plane to see how it is translated.
Lesson: Diagonal Translations (8.2)
New Jersey Core Curriculum Content Standards
4.2B Transforming Shapes
1. Understand and apply transformations.
4.2C Coordinate Geometry
1. Use coordinates in four quadrants to represent geometric concepts.
2. Use a coordinate grid to model and quantify transformations.
Focus: Representation and Connections
Learning Objectives
· Given a figure in a coordinate plane, students will identify the relationship between coordinates of the original figure and coordinates of the translated figure.
· Students will be able to perform horizontal, vertical, and diagonal translations correctly, given the direction and number of units of translation.
Lesson Strategy
The teacher will begin by reviewing homework from the previous night. The teacher will then introduce the concept of diagonal translations, through use of an example in the textbook. Discussion will take place regarding the topic of congruent figures. Students will use then use two different pre-cut quadrilaterals to perform specific diagonal translations, and record the coordinates of the original and translated figures in a chart. After the task has been completed, the teacher will discuss the characteristics of diagonal translations with the students. The teacher and students will orally review similar problems about different types of translations to reinforce important ideas about the topic. The teacher will have students respond to two translation problems in their journals. Homework will be assigned, and students will be informed that this homework will be collected and graded.
This lesson accommodates every type of learner. Visual learners will benefit from drawing the translated figures and writing the coordinates of the translated figures on their worksheets. They will also enjoy the opportunity to write responses to given problems in their journals. Auditory learners will be adept in discussing their findings from their charts, and reviewing problems orally. Kinesthetic learners will benefit from cutting out the quadrilaterals on their own, and translating the figures on graph paper.
Adaptations: If students are having difficulty translating the given figure, the teacher can guide the class through the first translation, on the overhead projector, to ensure that all students understand the task. Additionally, the teacher could help individual students by actually translating the figure for them, so that the students can focus on the differences in the coordinates between the original and translated figures. If students finish the activity quickly, they will be instructed to begin working on the worksheet Diagonal Translations (3), which they will finish for homework.
Materials
· Pencils
· Graph Paper
· Quadrilateral Cut-Outs
· Colored Pencils
· Worksheets: Diagonal Translations (1, 2, 3)
Preparation
The teacher must prepare worksheets Diagonal Translations (1, 2). The teacher must determine the coordinates of each translated quadrilateral to ensure that the students perform the translations correctly. A transparency containing the two problems to which the students must respond in their journals must be prepared prior to this lesson. The teacher must also develop Diagonal Translations (3) worksheet, integrating a variety of translation problems.
The students should have completed the Horizontal and Vertical Translations (3) worksheet for homework. This lesson incorporates horizontal, vertical, and diagonal translations so it is important for students to have an understanding of the previous day’s material prior to this lesson.
Procedure
Before
· Review students’ homework
· Introduce topic of diagonal translations through use of problem in textbook
· Have students record definition of congruent in vocabulary list
· Ask for volunteers to pass out materials to each student
- Quadrilateral Cut-Outs
- Worksheets: Diagonal Translations (1, 2, 3)
- Colored Pencils
Activity
· Discuss how to perform the given translations on worksheet
- Show students how to perform translation on overhead projector if necessary
- Instruct students to trace translated figure with colored pencil to distinguish between figures
· Allow students to complete task individually
· Discuss change of coordinates depending on translation
- Ask students about the similarities and differences between the translations performed
Summary and Reinforcement
· Review problems #1 and #2 (p. 382, textbook) orally with students
· Instruct students to complete Journal Entry B
- Two pairs of figures will be given, one in which a rotation has been performed and one in which the figures are similar but not congruent
- Students should correctly determine why these pairs of figures do not represent translations
- Journal entries are to be completed individually
· Instruct students to complete Diagonal Translations (3) worksheet for homework
Assessment
During the activity, the teacher will observe whether or not students are performing translations and determining coordinates of the figures correctly. The students will be assessed during class discussion, as well, to ensure that they can verbally explain the differences between horizontal and vertical translations, and diagonal translations. The teacher will evaluate students’ responses while reviewing problems at the end of the lesson to determine if students are using correct vocabulary and solving problems correctly. The journal responses will be assessed prior to the next lesson, as well. The homework assignment will be graded, and will count as a quiz grade for each student.
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