Transformations

1. Transformations Unit of Study: Transformations and Symmetry Global Concept Guide: 1 of 3

2. Content Development • “Younger students generally ‘prove’ that two shapes are congruent by physically fitting one on top of the other. But students in grades 3-5 can develop greater precision as they describe the motions needed to show congruence (‘rotate it 90 degrees or reflect it vertically, then rotate it 180 degrees).” NCTM 2000, p. 167 • “Let students explore puzzles, pattern blocks, attribute blocks, or tangram puzzles. They will naturally use transformations when they create pictures or designs using these materials. Asking them to explain how their design or picture was made reinforces transformational vocabulary.” - Math Misconceptions, p. 97 • Lesson 11.3 uses turns of both degrees and fractions. FCAT will assess rotations in degrees, but students can be exposed to fractional turns to help make a connection to benchmark rotations. For instance, of 360° is 90°. 360 split into 4 equal amounts would have 90 in each group. This will be applied to rotational symmetry in GCG 2. • Per the 3rd grade Item Specs, students have already been exposed to transformations, including the common and geometric terminology. Because this is not a new concept, there is not an entire day devoted to differentiated instruction in this GCG. Use daily informal assessments to make instructional decisions, and utilize reteach and enrich activities and online tutorials as appropriate.

3. Day 1 • Essential Question: How can you use precise geometric terms to identify a transformation? • Using a pattern block under the ELMO, perform a transformation and have the students turn and talk to identify the transformation as a slide, flip or turn and justify their thinking. This is an opportunity for informal assessment of prior knowledge, specifically students’ familiarity with the geometric terms for these transformations. Be sure to add both the common and geometric terms to your word wall. • Student discussion can be used to create a class anchor chart . • Students can create a foldable to record their thinking as they further explore transformations throughout this unit, and use it as a resource when describing shapes as the results of transformations. A modified Frayer Model can be incorporated into the foldable. • By the end of day one, students should be able to use precise geometric terms to identify transformations.

4. Day 2 • How can you accurately describe and perform translations and reflections? • Students play “Secret Transformation”. Pairs of students are given the same pentamino, pattern block or tangram. Put a divider between the two students. Both students start with their figure in the same position. One of the students performs a transformation and describes the transformation. The other student tries to replicate the transformation, without asking questions. Students then remove the divider and compare the location of the figures. • This activity will set a purpose for being even more precise when describing transformations. In reflecting on the activity, students will share that directions and knowing how far to move their figure would have made the task a lot easier. • Model using more precise, accurate vocabulary to describe translations and reflections to play “Secret Transformations”. Translations are the easiest to describe, using directional terms “left, right, up, down, diagonal”, possibly accompanied by units on grid paper. Reflections require describing the line of reflection as horizontal, vertical or diagonal . • Give students the opportunity to add these terms to their foldable and then revisit the “Secret Transformation” game, this time on top of grid paper, so that students can be more accurate in their descriptions of translations and reflections. Encourage students to use their foldable as a resource. • By the end of day 2, students should be able to accurately describe and perform translations and reflections.

5. Day 3 • Essential Question: How can you accurately describe and perform rotations? • Access students prior knowledge of angles within circles (Unit 12) by giving students Judy clocks. With all students starting at 12 o’clock, have students model benchmark angles (90, 180, 270 and 360 degrees) and fractions (1/4, ½, ¾) using the directional terms clockwise and counter-clockwise. • Explain to students that there is precise vocabulary to describe rotations, just like there is for translations and reflections. Give students clock paper and a pentamino, tangram or pattern block. Have students start with their figure at 12 o’clock and trace their figure on the clock. Identify the center of the clock as the point of rotation. Give students directions just as you did at the start of the lesson, and have them trace the results of the rotations. Look for students who are not keeping the point of rotation constant, and model this if necessary. It also may be helpful for students to divide the clock into fourths. • Give students the opportunity to add to their foldable, and revisit the “Secret Transformations” game from Day 2, so students can apply more precise descriptions of rotations. Encourage students to perform more than one transformation. • By the end of day 3, students should be able to accurately describe and perform rotations.

6. Enrich/Reteach/Intervention • Reteach: • Give students mirrors when performing reflections. • Online Florida Intervention Skill: 51- online tutorial on transformations • Icy Slides, Flips and Turns- have partners play game and describe the transformations they see using more precise vocabulary • Core: • Mega Math Shapes Ahoy: Ship Shapes Lesson O (turns and slides) and Lesson P (flips), Mega Math Ice Station Exploration: Polar Planes Lesson M (transformations) • Enrich: • Students work in pairs to create tangram pictures or play “If the Key Fits” using precise geometric terms to describe each transformation they apply to the shapes or play • RoboPacker – students apply transformations

7. Literature for your Classroom Library