Describing and Partitioning Two- and Three-Dimensional Shapes
Describing and Partitioning Two- and Three-Dimensional Shapes
Objectives
In this unit, students will analyze, draw, and name two- and three-dimensional shapes having specified attributes and partition two-dimensional shapes into halves, thirds, and fourths. Students will:
- recognize and draw shapes having specified attributes.
- identify triangles, quadrilaterals, pentagons, hexagons, and three-dimensional shapes.
- partition circles and rectangles into two, three, or four equal shares, recognizing that equal shares of identical wholes do not need to have the same shape.
Essential Questions
How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems?
How can geometric properties and theorems be used to describe, model, and analyze situations?
How can patterns be used to describe relationships in mathematical situations?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving?
- How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving?
- How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations or solve problems?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- Shapeville: http://www.tvokids.com/games/shapeville
- Shapes, Shapes, Shapes by Tana Hogan. Greenwillow Books, 1996.
- Windows, Rings, and Grapes—A Look at Different Shapes by Brian P. Cleary. Millbrook Press, 2009.
- Let’s Fly a Kite by Stuart J. Murphy. Harper Collins, 2000.
- 3-D Shapes Game: http://www.adrianbruce.com/maths/3dshapes/3d_math_game.htm
- Captain Invincible and the Space Shapes by Stuart J. Murphy. Harper Collins, 2001.
- Cubes, Cones, Cylinders, & Spheres by Tana Hoban. Greenwillow Books, 2000
- http://edgalaxy.com/numeracy/2012/8/22/great-collection-of-3d-shape-nets-to-print-and-make.html
Formative Assessment
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View
Short-Answer Items
Circle the shape you can make by tracing the face of these objects.
1.
2.
3. Draw a line matching each shape to its correct name.
4. Draw a line in each shape to divide the shape into two equal halves.
5. Fill in the chart.
Shape
Name
Number of Sides
Number of Vertices
6. Clue: “I drew a shape with four sides.”
Draw four examples of what this shape might look like.
7. Clue: “I drew a shape with six sides.”
Draw two examples of what this shape might look like.
8. What is the difference between a circle and a sphere?
9. I’m thinking of a three-dimensional shape. It has six faces. Each face is a square. It looks like a box. What shape am I thinking of?
10. Circle all of the shapes that are divided into thirds.
11. Use words to describe a cylinder.
12. What is the name of a shape with five sides?
Short-Answer Key:
Circle the shape you can make by tracing the face of these objects.
1.
2.
3. Draw a line matching each shape to its correct name.
4. Draw a line in each shape to divide the shape into two halves.
5. Fill in the chart.
Shape
Name
Number of Sides
Number of Vertices
square
4
4
pentagon
5
5
6. Clue: “I drew a shape with four sides.”
Draw four examples of what this shape might look like.
Answers will vary. Examples: square, rectangle, trapezoid.
7. Clue: “I drew a shape with six sides.”
Draw two examples of what this shape might look like.
Answers will vary.
8. What is the difference between a circle and a sphere?
A circle is two-dimensional and a sphere is three-dimensional, or a circle is flat and a sphere can roll like a ball.
9. I’m thinking of a three-dimensional shape. It has six faces. Each face is a square. It looks like a box. What shape am I thinking of?
The shape is a cube.
10. Circle all of the shapes that are divided into thirds.
11. Use words to describe a cylinder.
This shape has two faces that are circles. This shape can roll. It is like a soda can or pencil container. This shape does not have any vertices.
12. What is the name of a shape with five sides?
A pentagon.
Performance Assessment:
Find the number of edges, faces, and vertices of a cube and a pyramid with a square base.
Cube: edges ____ faces ____ vertices ____
Pyramid: edges ____ faces ____ vertices ____
How are the two shapes the same? How are they different?
Performance Assessment Key and Scoring Rubric:
If possible, provide three-dimensional models for students to refer to.
Find the number of edges, faces, and vertices of a cube and a pyramid with a square base
Cube: edges 12 faces 6 vertices 8
Pyramid: edges 8 faces 5 vertices 5
How are the two shapes the same? How are they different?
Answers will vary.
Both shapes have a square face. Both shapes are three-dimensional. The cube is made of squares, but the pyramid is made of squares and triangles. The cube has more edges, faces, and vertices than the pyramid. The cube has sides that are straight up and down, but the pyramid has slanted sides.
Points
Description
5
- Mathematics is correct with complete work shown.
- Written explanations are thorough, detailed, and clear.
- Student displays excellent understanding of the mathematical concepts involved.
- Student performs beyond the requirements of the problem.
- Pictorial representation is appropriate, of excellent quality, and creative.
4
- Mathematics is correct with work shown.
- Written explanations are thorough and clear.
- Student displays good understanding of the mathematical concepts involved.
- Student meets all requirements of the problem.
- Pictorial representation is appropriate, of good quality, and neat.
3
- Mathematics is correct with minimal or no work shown.
- Written explanations are present but lacking some detail.
- Student displays partial understanding of the mathematical concepts involved.
- Student meets most of the requirements of the problem.
- Pictorial representation is complete but may have errors.
2
- Mathematics is incorrect with some work shown.
- Written explanations are incomplete and lack detail.
- Student displays little understanding of the mathematical concepts involved.
- Student does not meet a majority of the requirements of the problem.
- Pictorial representation is incomplete, inappropriate for the situation, or missing.
1
- Mathematics is incorrect with no work shown.
- Written explanations are illogical or not present.
- Student displays no understanding of mathematical concepts involved.
- Student does not meet the requirements of the problem.
- Pictorial representation is missing.
0
- Student does not participate.
Final 3/28/14
