Standard #: MA.6.GR.2.4

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.6.NSO.2.1
• MA.6.NSO.2.2
• MA.6.NSO.2.3
• MA.6.NSO.3.5
• MA.6.AR.2.3

 

Terms from the K-12 Glossary

• Area
• Net
• Rectangular Prism
• Rectangular Prism

 

Vertical Alignment

Previous Benchmarks

• MA.5.GR.2.1

Next Benchmarks

• MA.7.GR.2.2

 

Purpose and Instructional Strategies

Students in grade 5 found the area of a rectangle with fractional or decimal sides. In grade 6, students find the surface area of right rectangular prisms and pyramids. In grade 7, students calculate the surface area of right circular cylinders. 

• Instruction includes constructing models and nets of three-dimensional figures and describing them by the number of edges, vertices and faces. Providing these opportunities will allow students to manipulate materials and connect to the symbolic and more abstract aspects of geometry.
• Instruction includes students using formulas and decomposition strategies to find the surface area of figures. Using the dimensions of the individual faces, students should calculate each rectangle or triangle area and add these values together to find the surface area of the figure.
• Instruction includes describing the types of faces needed to create a three-dimensional figure. Students can make and test conjectures by determining what is needed to create a specific three-dimensional figures.
• Students need to practice the language of the problems they are being asked to solve.
  • For instance, when being asked how much wrapping paper is needed to wrap a box, they know from experience that they are working with surface area. If they are being asked how many boxes will fit in a shipping container, then they are looking at volume.
• When using rational numbers, instruction should stay within the same form. Students should not be penalized though if they convert from one form to another when performing operations.
  • For example, if students are working with fractions, the side lengths will not include decimals. If students are working with decimals, the side lengths will not include fractions.
• Instruction includes representing measurements for surface area as square units, units squared or units².
• Problem types include having students measure lengths using a ruler to determine the surface area.

 

Common Misconceptions or Errors

• Students may not be able to determine the difference in the two-dimensional figures that compose three-dimensional figures.
• Students may invert the formulas for surface area and volume.

 

Strategies to Support Tiered Instruction

• Teacher provides nets of the three-dimensional figures and model color coding each similar shape. This will help students properly identify each shape to find the area to calculate surface area.
  • For example, a right rectangular prism can be modeled by the net shown below.
    
    
    
• Teacher reviews definitions of surface area and volume and co-creates an anchor chart to display in the room explaining the differences between them. Teacher models the use of manipulatives and geometric software to review the concept of area and surface area.
• Teacher breaks down formulas for area of a rectangle and volume of a rectangular prism to show when finding area, we are multiplying two sides which is why we use units², but with the rectangular prism, we are multiplying three sides, so we use units³ to label. Providing flash cards or cue cards with the formulas will help students in place of anchor charts when they are outside the classroom area.

 

Instructional Tasks

Instructional Task 1 (MTR.6.1)
The surface area of a rectangular prism is 115 square inches. The net of the prism is shown. What are the possible dimensions of the prism?

 

Instructional Items

Instructional Item 1
Carl is shipping a cardboard box that is a rectangular prism. The net of Carl’s box is shown. What is the area of cardboard, in square inches, required for Carl’s box?