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This lesson provided by:
Author: Valerie Harden
System:Mobile County
School:Dixon Elementary School
Lesson Plan ID: 26401
Title:

Shape Makers

Overview/Annotation:

In this Five E’s AMSTI lesson, students discover relationships between shapes. Students discover multiple ways to combine shapes to fill the area of a given shape using real and virtual pattern blocks, and share their solutions with peers. Children create puzzles for a partner and play an online game to reinforce their learning.

This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

Content Standard(s):
MA2013(K) 17. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. [K-G1]
MA2013(K) 18. Correctly name shapes regardless of their orientations or overall size. [K-G2]
MA2013(K) 19. Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). [K-G3]
MA2013(1) 19. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. [1-G1]
MA2013(1) 20. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as "right rectangular prism.") [1-G2]
MA2013(1) 21. Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. [1-G3]
MA2013(2) 24. Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2-G1]
MA2013(2) 25. Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them. [2-G2]
MA2013(2) 26. Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. [2-G3]
Local/National Standards:

2009 Mathematics ACOS Standards (Kindergarten):

8. Identify two-dimensional (plane) shapes, including rectangle, square, circle, triangle, hexagon, trapezoid, and rhombus, and three-dimensional (solid) figures, including sphere, cone, and cylinder.

· Combining shapes to fill in the area of a given shape

Example: covering a rectangle with two triangles

 

National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics:

Expectations for Kindergarten Students:

Geometry:

· Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes

· Describe attributes and parts of two- and three-dimensional shapes

· Create mental images of geometric shapes using spatial memory and spatial visualization

 

Process Standards:

Communication: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

Problem Solving:

  • Build new mathematical knowledge through problem solving
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Monitor and reflect on the process of mathematical problem solving

 

Primary Learning Objective(s):

The student will be able to name shapes and combine them to fill in the area of another shape.

Additional Learning Objective(s):

Students will develop problem solving skills by attempting to discover multiple ways to fill a given shape. Students will clearly communicate their reasoning strategies.

Approximate Duration of the Lesson: 31 to 60 Minutes
Materials and Equipment:

Then and Now on Old MacDonald’s Farm by Dr. T. E. Foster

Pattern blocks

Pattern block puzzles (two of each puzzle)

Paper pattern blocks (click pattern block templates) lklkj

Triangle Challenge worksheet, from Pattern Block Puzzle site above (one per student)

AMSTI Investigations users may choose to substitute the following:

Pattern Block Puzzles: Unit 5, masters M20-29

Paper Pattern Blocks: Unit 5, masters M14-19

Technology Resources Needed:

Interactive white board

Computer with LCD projector

Web access

Student computer(s) with web access

 

Background/Preparation:

After downloading the pattern block puzzles above, you might want to white out the interior lines. This encourages students to find more than one way to solve the puzzles.

Procedures/Activities:

Engage:

1. Read Then and Now on Old MacDonald’s Farm by Dr. T. E. Foster. Ask children how they think the illustrator made the animals. What shapes do they see?

2. On the interactive whiteboard, display the Virtual Pattern Block activity. Tap the purple shape in the upper left corner to choose a puzzle. Ask children to suggest which puzzle pieces you should use to fill the puzzle. Continue to add pieces until the puzzle is full, following students’ directions. As it becomes necessary to rotate, flip, or erase pieces, demonstrate use of these game controls (note: hovering the mouse over each tool provides an animated display of what it does). Purposely try to fit shapes where they don’t belong, and discuss the idea that the outline must be filled completely “with no white space”, but that nothing can hang over the edge.

3. After the puzzle is finished, ask children what they noticed about the shapes. Did they see any places on the puzzle where two different shapes could fit? How could they use two shapes to fill a spot where there is one shape now? Invite volunteers to the front to demonstrate their explanations.

4. Clear the puzzle, and, as a group, attempt to fill it using different blocks, again following children’s suggestions. Challenge children to find multiple ways to fill the puzzles in the following activity.

AMSTI Investigations users may choose to substitute the interactive pattern blocks puzzles available on the Shapes software CD.

 

Explore:

1. Distribute the pattern block puzzles to pairs of children, so that both partners have the same puzzle. (Note: differentiate the activity by giving the more difficult puzzles to the above level students and the simplest puzzles to those below level). Challenge each pair to fill the puzzles two different ways. Remind children that the shape must be completely covered, but no blocks may “stick out” of the lines.

2. As children work, prompt them to see relationships between shapes using dialog such as: What other shapes could you use here? Do you see two shapes that you could put together to match this shape? (ex. two trapezoids form a hexagon) Can you fill in this part with more shapes? With less shapes? How did you figure out that this fits here? Also note whether students seem to understand the idea of filling a shape completely with no blocks outside of the area.

3. Children who finish early may try to complete another (slightly harder) puzzle, or find a third way to fill the puzzle

 

Explain:

1. Gather children in a central location (ask them not to clean up their materials). As a group, visit each workspace, and have the pair of children share their strategies with the group. If necessary, ask questions such as; How did you decide which piece to use here? I see you have different pieces here on your other puzzle. Show us how you figured that out. Does anyone see another way this part of the puzzle could be filled? Show us. As students explain their thinking encourage them to use math vocabulary such as square, triangle, hexagon, rhombus, etc. Make sure student understand these concepts.

2. Return to the meeting area. Display the Virtual Pattern Block activity on the interactive whiteboard, with no puzzle visible (remove puzzles by clicking the purple shape at the upper left and selecting the blank board in the pop-up window) Drag a red trapezoid (diamond) onto the workmat. Ask students if anyone can cover the rhombus with two other shapes. Have volunteers demonstrate. (Review vocabulary by asking students to name the shapes) Can someone cover it with three other shapes

3. Ask children to list other sets of blocks they have discovered, in which two or more shapes can completely cover another shape. Teacher may wish to list these on chart paper or ask students to demonstrate on the whiteboard.

 

Extend

1. For additional practice in combining shapes, have each child create a shape with pattern blocks, and trace the outer outline of the shape onto a blank paper. Have another child fill in the shape with pattern blocks. Children may record their solutions by gluing paper pattern blocks in place.

2. Use the Make My Shape worksheet (attached) to extend the above activity. One child creates a design in the work area with pattern blocks, and then traces the outside edges. A second child fills the outline with paper pattern blocks, glues them down, and records the number of each block used.

3. Students can use the Virtual Pattern Blocks individually to produce a variety of shapes. Encourage children to:

a. form the same shape in different ways and/or

b. completely cover a larger block with smaller blocks

Students can print out finished projects or record them with paper pattern blocks on blank paper. For an additional challenge, ask another student to reproduce the design with real or virtual pattern blocks.

More advanced students can create with pattern blocks using a larger variety of tools at this Shape Tools site. Have students describe their creations to the class.

Evaluate:

Distribute the Triangle Challenge worksheet from the PreKinders website(scroll down, and click to download pdf file), and paper pattern blocks to each child. Challenge them to fill the triangles as many ways as possible, using the paper pattern block shapes (tip: require children to completely fill the triangle before gluing any of the shapes). Use the following rubric to assess the children’s ability to combine shapes:

4 -- Student found three or more ways to fill the triangles.

3 -- Student found one or two ways to fill the triangles.

2 – Student filled one shape correctly, but other shapes are not full or have shapes glued outside of triangle.

1 – Student glued shapes outside triangle and/or didn’t completely cover shape.

 


Attachments:**Some files will display in a new window. Others will prompt you to download. MakeMyShape.rtf
Assessment Strategies:

Distribute the Triangle Challenge worksheet from the PreKinders website (scroll down, and click to download pdf file), and paper pattern blocks to each child. Challenge them to fill the triangles as many ways as possible, using the paper pattern block shapes (tip: require children to completely fill the triangle before gluing any of the shapes). Use the following rubric to assess the children’s ability to combine shapes:

4 -- Student found three or more ways to fill the triangles.

3 -- Student found one or two ways to fill the triangles.

2 – Student filled one shape correctly, but other shapes are not full or have shapes glued outside of triangle.

1 -- Student glued shapes outside triangles and/or didn't completely cover the shape.

 

Extension:

1. For additional practice in combining shapes, have each child create a shape with pattern blocks, and trace the outer outline of the shape onto a blank paper. Have another child fill in the shape with pattern blocks. Children may record their solutions by gluing paper pattern blocks in place.

2. Use the Make My Shape worksheet (attached) to extend the above activity. One child creates a design in the work area with pattern blocks, and then traces the outside edges. A second child fills the outline with paper pattern blocks, glues them down, and records the number of each block used.

3. Students can use the Virtual Pattern Blocks individually to produce a variety of shapes. Encourage children to:

a. form the same shape in different ways and/or

b. completely cover a larger block with smaller blocks

Students can print out finished projects or record them with paper pattern blocks on blank paper. For an additional challenge, ask another student to reproduce the design with real or virtual pattern blocks.

More advanced students can create with pattern blocks using a larger variety of tools at this Shape Tools site. Have students describe their creations to the class.

Remediation:

Children who are having trouble combining shapes and/or filling in shape outlines can play Beaver Dam Jammer . To stop water from leaking through a dam, students must drag correctly shaped pieces to fill the hole. Audio directions are included.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

Hosted by Alabama Supercomputer Authority
The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
Thinkfinity
Thinkfinity
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