Describing, Composing, and Partitioning Shapes
Describing, Composing, and Partitioning Shapes
Objectives
In this unit, students will compose and distinguish between two-dimensional and three-dimensional shapes based on their attributes and partition two-dimensional shapes into halves and quarters. Students will:
- recognize and draw two-dimensional shapes having specified attributes, including circles, triangles, squares, and rectangles,
- partition circles and rectangles into two or four equal shares.
- compose and recognize three-dimensional shapes, including: cubes, prisms, cones and cylinders.
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.
- Circus Shapes by Stuart J. Murphy. Harper Collins, 1998
- A Fair Bear’s Share by Stuart J. Murphy. Harper Collins, 1997
- Captain Invincible and the Space Shapes by Stuart J. Murphy. Harper Collins, 2001
- The Greedy Triangle by Marilyn Burns. Scholastic, reprint 2008.
- Shapes That Roll by Karen Nagel. Blue Apple Books, 2009
- 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.
- Cubes, Cones, Cylinders, & Spheres by Tana Hoban. Greenwillow Books, 2000
- math dictionary with pictures http://www.mathsisfun.com/definitions/index.html
- three-dimensional math game http://www.adrianbruce.com/maths/3dshapes/3d_math_game.htm
- Shapeville http://www.tvokids.com/games/shapeville
- three-dimensional nets to print http://edgalaxy.com/numeracy/2012/8/22/great-collection-of-3d-shape-nets-to-print-and-make.html
- National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/topic_t_3.html
- Illuminations Patch Tool http://illuminations.nctm.org/activitydetail.aspx?id=27
Formative Assessment
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View
Short-Answer Items
- Draw a line matching each shape to its correct name.
- Circle the shape that doesn’t belong. Then explain why.
Shape _______ does not belong because _________________________________.
- Fill in the chart.
Shape
Name of Shape
Number of Sides
Number of Corners
3 sides
- Look at the two shapes.
How are they similar? __________________________________________
How are they different? _____________________________________
- Draw a line in each shape to divide the shape into two halves.
- Draw line(s) in each shape to divide the shape into fourths.
- What is the difference between a half circle and a whole circle? Use pictures and/or words to explain your answer.
- Circle all of the shapes that are divided into quarters.
- Circle the two shapes that make up the three-dimensional shape.
- Circle the two shapes that make up the three-dimensional shape.
- Look at the picture. Circle the name that best describes the picture.
- Look at the picture. Circle the word that best describes the picture.
Short-Answer Key
- Draw a line matching each shape to its correct name.
- Circle the shape that doesn’t belong. Then explain why.
Shape C does not belong because it has 4 sides that are straight. The others are curved lines and do not have sides. (Accept reasonable answers, as there can be more than one answer.)
- Fill in the chart.
Shape
Name of Shape
Number of Sides
Number of Corners
Square
4
4
Triangle
3 sides
3
- Look at the two shapes.
How are they similar?
Answers could include
Both have straight sides.
Both have sides that are slanted.
How are they different?
Accept reasonable answers.
One has 6 sides and the other has 4 sides.
One has dots and the other is a solid color.
- Draw a line in each shape to divide the shape into two halves. Accept all correct answers. Examples shown.
- Draw a line in each shape to divide the shape into fourths. Accept all correct answers. Examples shown.
- What is the difference between a half circle and a whole circle? Use pictures and/or words to explain your answer. Accept all correct answers. Examples shown.
This is a whole circle.
This is a half circle.
There are two half circles in a whole circle.
- Circle all of the shapes that are divided into quarters.
- Circle the two shapes that make up the three-dimensional shape.
- Circle the two shapes that make up the three-dimensional shape.
- Look at the picture. Circle the name that best describes the picture.
- Look at the picture. Circle the name that best describes the picture.
Performance Assessment:
Read or verbally give the following directions to students. (You can reword the directions so students understand the task.)
- Draw and color two shapes. You can only use two different crayons.
- Describe each shape. Give at least two details of each shape.
- Explain how the shapes are the same.
- Explain how the shapes are different.
Shape 1
Shape 2
Describe Shape 1.
Describe Shape 2.
Shape 1 is similar to Shape 2 because
Shape 1 is different than Shape 2 because
Performance Assessment Key and Scoring Rubric:
Example answers are shown.
Shape 1
Shape 2
Describe Shape 1.
The blue shape is a circle. It is round.
Describe Shape 2.
The red shape is a triangle. It has 3 corners.
Shape 1 is similar to Shape 2 because
The shapes are both two-dimensional.
Shape 1 is different than Shape 2 because
The blue shape is round, but the red shape is not.
Points
Description
4
- Student answers all 4 parts of the problem correctly.
- Mathematics is correct with complete work shown.
- Written explanations are thorough, detailed, and clear.
- Student displays excellent understanding of the mathematical concepts involved.
- Pictorial representation is appropriate.
3
- Student answers 3 of the 4 parts correctly.
- Mathematics is correct with work shown.
- Written explanations are thorough and clear.
- Student displays good understanding of the mathematical concepts involved.
- Pictorial representation is appropriate.
2
- Student answers 2 of the 4 parts correctly.
- 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.
1
- Student answers 1 of the 4 parts correctly.
- 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 could be incomplete, inappropriate for the situation, or missing.
0
- Student answers 0 of the 4 parts correctly.
- Mathematics is incorrect with no work shown.
- Written explanations are illogical or not present.
- Student displays no understanding of the mathematical concepts involved.
- Student does not meet the requirements of the problem.
- Pictorial representation is missing.
Final 3/7/14
