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Examples
Example: A hexagon can be decomposed into 6 triangles.Example: A semi-circle and a triangle can be composed to create a two-dimensional representation of an ice cream cone.
Clarifications
Clarification 1: Instruction focuses on the understanding of spatial relationships relating to part-whole, and on the connection to breaking apart numbers and putting them back together.Clarification 2: Composite figures are composed without gaps or overlaps.
Clarification 3: Within this benchmark, it is not the expectation to compose two- and three- dimensional figures at the same time.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Cone
- Cube
- Cylinder
- Hexagon
- Rectangle
- Rectangular Prism
- Square
- Trapezoid
- Triangle
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to promote students’ spatial reasoning. Students should begin to see figures as compositions of other figures. In Kindergarten, students combined triangles, rectangles, and squares to form composite figures.- Instruction should include guiding students to ensure that when composing a new three- dimensional figure those figures should have one set of the faces touching without gaps or overlaps.
- For example, the flat surface of a cone touching one face of a cube.
- Instruction includes making a connection to partitioning shapes.
Common Misconceptions or Errors
- Students may not initially recognize that a figure can be made using other figures. Class
activities should promote exploring what figures could make a given figure.
- SSFor example, using pattern blocks a student could manipulate two triangles to make a square, four triangles to make a rectangle, or six triangles to make a hexagon.
Strategies to Support Tiered Instruction
- Instruction provides opportunities to identify shapes around the school while transitioning between the classroom to other areas of the school. When possible, trace shapes with sidewalk chalk (such as the rectangles that make up sections of the sidewalks or the bricks in the wall). Students could include using colorful tape to highlight shapes around the classroom (windows, doors, cupboards, desks, etc.) to make them visible.
- For example, students may use pattern blocks to manipulate two triangles to make a square, four triangles to make a rectangle and six triangles to make a hexagon.
Instructional Tasks
Instructional Task 1 (MTR.5.1)
- Provide pattern blocks to students; be sure students get at least six triangles, two squares, two trapezoids and one hexagon. Read the directions to students and give students time to explore to find possible solutions. After students have come up with solutions, have discussion around whether all students found the same solution or if they had different solutions. Ask students if they could come up with a different response.
Instructional Items
Instructional Item 1
What three-dimensional figures make up the composite figure below?
Instructional Item 2
What two-dimensional figures make up the figure below?
Instructional Item 3
How many of the squares would you need to tile the rectangle below with no gaps or overlaps?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Teaching Idea
Problem-Solving Tasks
MFAS Formative Assessments
Students use different three dimensional shapes to compose a composite shape.
Note: This task includes the use of triangular prisms.
Students join right triangles together to compose a rectangle and then use the rectangle to compose a new shape. Students describe this new shape made from the composite shape.
Students compose new shapes from equilateral triangles and a trapezoid.
Students view a composite shape with a missing piece and identify shapes that can fill in the space.
Original Student Tutorials Mathematics - Grades K-5
Learn to combine simple shapes to compose larger shapes with Robbie the Robot in this interactive tutorial.
Student Resources
Original Student Tutorial
Learn to combine simple shapes to compose larger shapes with Robbie the Robot in this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
The purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment.
Type: Problem-Solving Task
The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares and stimulate interest as students compete to try to find the most squares.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
The purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment.
Type: Problem-Solving Task
The purpose of this task is to give students a hands-on experience with composing and decomposing geometric figures and is meant as an instructional task.
Type: Problem-Solving Task
The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares and stimulate interest as students compete to try to find the most squares.
Type: Problem-Solving Task
