## Geometric Twins

### Sandi Tidwell

#### Description

This lesson explores the concept of congruency using dot paper so that a student can visualize, draw, and replicate different congruent shapes.

#### Objectives

The student understands the concepts of spatial relationships, symmetry, reflections, congruency, and similarity.

#### Materials

-Pencil
-Dot Paper
-Scissors
-Vis-à-vis Pen or other overhead pen
-Liquid Glue or glue stick
-Software entitled Number Heroes or other software that provides practice with congruency (optional)

#### Preparations

2. Copy and pass out dot paper to each student.
3. Make a task card to explain where to go on the Beacon online student lesson or bookmark the site (see Materials).
4. Be sure the computer software you are using is loaded, or the students know how to load it.
5. Visit the lesson entitled Create Your Save and Rave Box as listed in the Extensions before teaching this lesson.

#### Procedures

1. The teacher begins the lesson by calling attention to the overhead, where she has placed blank overhead dot paper. The teacher draws any quadrilateral shape on the dot paper. Then she challenges students to replicate this quadrilateral on their dot paper (which has already been passed out).

2. The teacher walks around while students are drawing to observe if students understand the concept.

3. After all students have finished, the teacher tells students that what she is looking for is to see if their shapes are congruent to the one she has drawn. Then she asks for a volunteer to explain the meaning of congruent (same size AND same shape).The teacher then asks, -Can you think of an example of why you would need to know about congruency in the real world?- (ex. answer: If you are putting a puzzle together, you need to be able to look at the space that needs filling, and put the right puzzle piece there. OR, As an adult and you are a contractor building a house for someone, you need to be able to visualize what kind of cabinets would fit in a certain space and build cabinets to fit that space.)

4. The teacher asks students to check their shapes using the definition given. (Give a hint that counting their dots will help them determine this.)

5. The teacher reminds students of an earlier lesson called, Create Your Save and Rave Box (see Extensions). This lesson used pattern blocks to explore congruency with concrete models. If you choose not to use this lesson as an introduction, you need to review the concept.

6. The teacher now draws a congruent shape to the one she has already drawn on the overhead, except she draws it turned in a different position.
(You will want to emphasize this step because many students might think that the shapes are not congruent because they are in a different position. Re-emphasize that congruent means same size AND same shape.)

7. Have students draw a congruent shape in a different position on their dot paper next to the one they have already drawn.

8. To make sure they are congruent, have them cut out one of the shapes they have drawn and place it over the other one to see if they match (same size AND same shape).

9. Pair students up in groups of two to work together for the remainder of the lesson.

10. Have one person in the group draw a shape on the dot paper. Have the other student try to replicate a congruent shape on the dot paper, cut it out, place it over the other student's shape to see if it is congruent, and glue it to the congruent shape. Have them reverse roles until they have created five sets of congruent shapes.

11. Students will turn in their dot paper with the glued congruent shapes to be assessed. (Be sure both names are on the paper.)

12. (This last step is completely optional and does not have to be done for the lesson to be complete.) If students have access to the Internet, they can complete a Beacon online student lesson entitled Carol's Congruent Concentration (see Materials).
They could also complete a lesson using the computer software Number Heroes or another computer software that contains geometry skills that deal with congruency. (Number Heroes contains a computerized geo-board that lends itself well to extending this lesson.)

#### Assessments

1) Students self-assess by gluing their congruent shapes together. (They can see if they are not congruent because they don't fit. They can self-correct at this point.)
2) Teacher assessment can be used if you want to take a grade using the task the students performed on dot paper in their groups. Since there are five sets of figures, they each count 20 points.
3) Teacher observation will informally assess whether students are working together in their groups cooperatively.
4) To assess effective communication and content learning, students will write in their journals a paragraph answering the following question, or the teacher may orally interview each group asking the following questions:
1. What did you learn about learning to visualize, draw, and replicate congruent shapes?
2. What problems did you encounter?