Connecting Benchmarks/Horizontal Alignment

• There are no direct connections outside of this standard; however, teachers are encouraged to find possible indirect connections.

 

Terms from the K-12 Glossary

• Composite Figures 
• Rectangles 
• Squares 
• Triangle

 

Vertical Alignment

Previous Benchmarks

• VPK

 

Next Benchmarks

• MA.1.GR.1.3

 

 

Purpose and Instructional Strategies

The purpose of this benchmark is to allow students opportunities to discover further connections and patterns with two-dimensional figures. Students should have an opportunity to investigate combining figures in a variety of sizes and orientations (MTR.2.1, MTR.5.1).

• Instruction includes composite figures that may be named based on previous benchmarks, as well as those not included in previous benchmarks, though there is no expectation of a formal name for new composite shapes outside of previously named figures. 
  • For example, a triangle and square forming a pentagon, may not need to be formally identified as a pentagon. Two triangles that form a rectangle can be formally identified as a rectangle. 
• Exploring with figures of different sizes and orientations allows students to continue to develop an understanding of spatial reasoning (MTR.2.1).

 

Common Misconceptions or Errors

• Students may attempt to compose figures without regard to aligning sides or vertices. The overlap may cause difficulty in naming or describing the new composite figures. 
• Students may avoid lining the edges of two figures if the sides aren’t the same length. 
  • For example, it could be appropriate to join several rectangles of various sizes to make a figure that looks like a building with towers.

 

Strategies to Support Tiered Instruction

• Instruction includes providing opportunities to compose shapes using pattern blocks. Begin by having students compose rectangles using squares. 
  • Example: 

• Teacher provides opportunities for students to explore what happens when they compose shapes.
  • For example, teacher provides right triangles, squares, and rectangles in the middle of the workspace. The teacher may ask, “What shapes can you combine to make a square?” and places the square in front of the student.
  • To differentiate this activity, the teacher may place a different shape in front of each student.
• Teacher provides a set of tangram pieces for the students to explore how they can compose shapes to create a larger figure. If tangram pieces are not available to the teacher, the teacher may use a search engine to print a set of tangram pieces to copy.

Instructional Tasks

Instructional Task 1 (MTR.2.1, MTR.4.1, MTR.5.1, MTR.7.1) 

Provide each student in a group or whole class with a plethora of rectangles, squares and triangles in a variety of shapes and sizes (be intentional in assuring that various sides are congruent for the purpose of composing new figures). Ask students, “can you make a new figure using two of the figures I have given you?” Give students time to explore, then opportunities to share. Record the findings, focusing on what may be considered “key” compositions (two squares making a rectangle, two triangles making a rectangle, a “house” from a rectangle and triangle, or an octagon from triangles).

 

Instructional Items

Instructional Item 1 

Jamie says that you cannot make a rectangle using the 2 triangles below. Is she correct? Justify your answer.

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.