Katie Danner

1

Congruent, Noncongruent, and Similar

Context/Grade Level: Third Grade, 24 students

Objective(s): TSW use problem solving, mathematical communication, mathematical reasoning, connections, and representations to identify examples of congruent and noncongruent figures and verify their congruence by laying one on top of the other using drawings or models. TSW also determine and explain why plane figures are congruent or noncongruent, using tracing procedures.

SOL Strand: Geometry

SOL: 3.16 TSW identify and describe congruent and noncongruent plane figures.

Materials/Resources:

  • 26 sets of print-out notes
  • individual students’ Math Journals
  • 2 same textbooks; two different-size chairs (student chair and adult chair); two different-length pencils
  • 26 sheets centimeter dot paper
  • scissors, glue, crayons
  • 12 manila folders, each with a pair of shapes and physical exercise instructions inside
  • 4 desktop computers, 4 laptop computers
  • 26 homework pages

Approximate time required: 75 minutes

Content and Instructional Strategies:

  1. Opening activity: hold up various pairs of objects to the class and ask the students to make three observations for each pair (with their seat partner) about how they are similar and/or different. For example, two identical math textbooks—response should be “They are the same book; they are the same size; they have the same colors; etc.”; gesture to large and small chairs—responses should be “They are both chairs; One is big and one is small; They are both silver and blue; etc.”; hold up two pencils, one long and one short—responses should be “They are both pencils; They are both yellow; One is long and one is sharpened to very short; etc.” Praise students for their observations. Tell them, “In geometry, we use special words for these descriptions: ‘same size and shape’ is congruent, and ‘different size and different shape,’ is noncongruent. Noncongruent objects can also be ‘same shape, different size,’ which is called similar.” Have students say the new vocabulary out-loud. Draw a Venn diagram to represent these terms (5 minutes)
  2. Ask students to take out a pencil and fill out their note sheet with the teacher. During notes discussion, demonstrate for the students that orientation of the shapes does not affect whether objects are congruent, noncongruent, or similar. Model and ask students to draw two rectangles on their dot paper—connecting five dots for two parallel sides and four dots for the other two parallel sides. Cut out the shapes. Orient them in various ways; then lay one atop the other—they are still the same size. Therefore, they are congruent. Then, draw and cut out two squares that are similar—one square is 4 dots by 4 dots; the other is 3 dots by 3 dots. Lay small atop large, and notice that the area around the small square is evenly 1 dot wider than the large square all the way around. The small square is a “shrunken” version of the large square—they are similar. Glue notes into their Math Journals on the next available page, after “Angles.” (15 minutes)
  3. Explain the three stations for math groups today.

The first station has 12 manila envelopes, each with a pair of shapes and a physical exercise action. Students will walk to each envelope in pairs of two. Use the station chart to record whether each pair of shapes is congruent or noncongruent. Then, do each physical activity, solving the multiplication fact to know how many repetitions of how much time to spend.

The second station is an individual activity. Using the remainder of their dot paper, students will draw, color in, and cut out AT LEAST five pairs of shapes—shapes can be irregular, “funny” shapes; check if they are congruent, similar, or noncongruent by laying them atop one another and comparing the shapes and sizes. Glue into Math Journals and label the examples.

The third station is on the computer. Students log into IXL.com and complete the skills for R.4 and R.6. If they finish early, they may also review their multiplication facts on IXL.com. (5 minutes)

  1. Students break into their already-established math groups (Groups 1, 2, and 3), and spend 14 minutes in each station. (45 minutes)
  2. Come together as whole group to look over the homework assignment. Explain the directions, point out that it is two-sided. Do one of the word problems together, which describes the perimeters of two shapes and asks if they are congruent. (5 minutes)
  3. Dismiss for lunch.

Evaluation/Assessment:

Collect the Math Journals and evaluate how each student did on the shape design and comparison individual activity. .

Differentiation and Adaptation: Students who finish their work in stations early can do extensions—12 manila envelopes: practice multiplication and division flashcards; Cut out shapes: cut out extra pairs with extra dot paper; IXL: practice multiplication, then division facts.

If students do not have enough time, they may complete the station activities when they return from lunch and choice time, before transitioning to Reading class.

Sources:

Mrs. Holloway’s original note page; Mrs. Holloway’s manila envelope activity; Math textbook homework worksheets; Katie Danner’s original dot paper activity; Katie Danner’s original classroom object comparison and Venn diagram activity.

10/31/18