Developing Mathematical Thinking Institute DMTI Professional Development Curricular

Developing Mathematical Thinking Institute (DMTI) Professional Development Curricular Resources Assessment Jonathan Brendefur, Ph. D jonathan@dmtinstitute. com © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 1

Geometry Warm- Ups: K-2 Grades The following slides contain 5 different warm-ups. Each warm-up activity is intended to be used briefly at the start or in the middle of a lesson and should only last approximately 5 -10 minutes. Each of the five warm-ups has 2 -3 variations or suggested areas of focus with guiding questions so the activity can be repeated a variety of times with slightly different outcomes for students. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 2

Shape Drawing WARM-UP 1 © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 3

Shape Drawing: Warm-up 1 Have students use their index fingers to draw shapes in the air. Have students turn and move the shapes and ask them to state that the shape is still a (circle, rectangle, square, triangle, etc. ) even though it is in different location or different orientation. Then have students physically “stretch” or “squish” the shape to transform its shape. For example, changing a square into a rectangle (that is not a square) or changing a circle into an oval. Students should describe how they changed the shape and what was the same and different between the two shapes. Have students use appropriate academic language (e. g. sides, vertices) to describe the shapes. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 4

Shape Drawing: Warm-up 1 Variations and Areas of Focus: A) Symmetry: Have students “slice” any shape into two equal parts. Make sure students describe this process as decomposing (or more specifically partitioning). Then have students “move” one half by folding it on top of the other. Then have them trace this new figure. If one half folds directly on top of the other, the shape is symmetrical. If not, then the halves are just congruent the line where the shape was “sliced” is not a line of symmetry. B) Shape Hierarchy: Students should draw any quadrilateral and then manipulate it to become another quadrilateral. Students should discuss what is the same and different between the two quadrilaterals. C) Decomposing Shapes: Have students decompose any given shape into some combination of other shapes. For example, drawing a hexagon and finding how to “slice” (decompose) the hexagon into triangles. Use a whiteboard to test students’ ideas for accuracy. Pay particular attention to the way quadrilaterals can be decomposing into two triangles by using vertices as the starting point of the decomposing. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 5

Shape Quick Draws A WARM-UP 2 © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 6

Shape Quick Draws A: Warm-up 2 Draw any shape on the board. Have students copy the shape. Then have students draw a larger and smaller version of the shape. Students should discuss what is the same and different about the similar figures. Then give students directions to draw a shape without drawing it for them (e. g. “A shape with 3 sides. Make all the sides equal. ”) Check for accuracy by drawing your shape on the board. Have students use appropriate academic language (e. g. sides, vertices) to describe the shapes. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 7

Shape Quick Draws A: Warm-up 2 Variations and Areas of Focus: A) Directions for Shape Drawings: Have students turn away from the board. Describe what you are drawing and have them follow along in their math journals without looking. When the shape is done, have students turn around to see how close their shape is. Discuss what part of the directions were the most difficult or what you could have said to make the shape easier to draw. B) Classification: After students copy a drawn shape on the board, have them create another version of the same shape that is not similar (e. g. not the same shape but just larger a smaller). For example, if you draw an equilateral triangle, challenge students to draw a different triangle that doesn’t have all equal sides. Students can share their ideas as a class. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 8

Shape Quick Draws B WARM-UP 3 © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 9

Shape Quick Draws B: Warm-up 3 Have students draw the following shape. Have them focus on the lengths and proportions. Have them edit their work if it is not correct. Then, have them imagine the shape turned 90 or 180 degrees to the right or to the left and draw that shape. You do not need to use the terms “ 90 degrees” or “ 180 degrees”. Instead, you may choose to guide students to use the sides or the given letters to match the rotation path. For example say, “Turn the shape so that the letter is right here. ” The following slides provide several examples. Be sure to animate the first example by playing the Slide Show. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 10

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. Now turn the shape so the letter O is on the bottom. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the turned shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. X © DMTI (2018) | RESOURCE MATERIALS

Shape Quick Draws B: Warm-up 3 Draw the following shape as precisely as possible. © DMTI (2018) | RESOURCE MATERIALS

Shape Walking WARM-UP 4 © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 27

Shape Walking: Warm-up 4 Students should start by moving to the sides of the room or to a space where they have room to move. Decide on a shape to “walk. ” In this example, the shape is a square. Give students directions: “Walk two steps forward. If that is the side of a square, turn and walk the next side. ” Note: students can be asked to use steps that are from heel to toe if space is limited. Have students continue walking out the shape’s form after naming the shape. Then discuss how they had to turn or how the number of steps were the same or different and what that means about the shape. In this example, they should note that they turned the same way each time (like the corner of the room or piece of paper, which is a right angle) and they took the same number of steps for each side because squares have all equal sides © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 28

Shape Walking: Warm-up 4 Variations and Areas of Focus: A) Properties: After students have paced out a particular shape, have them go back to the starting point and walk a different shape that is of a similar type. For example, if pacing out a square first, have them then walk out a rectangle. Students should discuss how their second path needed to change from the first to walk the new shape. B) Decomposing: After pacing out a shape, have students mentally “slice” (decompose) the shape and then have them pace out the new shapes they have created. For example, decomposing a square across a diagonal creates two triangles. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 29

Shape Making Groups WARM-UP 5 © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 30

Shape Making Groups: Warm-up 5 Students should work in small groups. Give each group a card or slip of paper with a shape name on it. Have the groups decide how to “make” (compose) the shape with their bodies. Remind them they can lay on the floor if needed. In some cases, there may be more students in the group than the number of sides of the shape (e. g. triangles). Have students decide how they could still create the shape (e. g. having a student bend his/her body for a vertex as opposed to have having two students’ bodies meet at a vertex). Groups should then present their shape to the class and discuss the key attributes of the shape and define it for the class. If time and materials are available, have the class draw the shapes as groups create them. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 31

Shape Making Groups: Warm-up 5 Variations and Areas of Focus: A) Properties: After a group has presented their shape, ask the rest of the class if they can think of a way the group could have made another version of the same shape that is slightly different. For example, if the group presents an equilateral triangle, have the class describe how to create another triangle that does not have all equal sides. B) Transformations: Have the class describe how they group could make the same shape but larger or smaller. How many people would be needed? How large/small would the new shape be. © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 32

“The. Developing Mathematical “The Mathematical. Thinking Institute (DMTI) is dedicated to enhancing students’ learning of students’ of mathematicsbyby supporting educators in supporting inthe theimplementation of of research-based instructional strategiesthrough research-based instructional strategies through high-quality professional development, curricular resources and assessments. ” assessments. " For more information contact For. Brendefur more information contact Dr. at jonathan@dmtinstitute. com Dr. Brendefur at jonathan@dmtinstitute. com © DMTI (2019) | RESOURCE MATERIALS | WWW. DMTINSTITUTE. COM 33