### Clarifications

*Clarification 1:*Instruction focuses on representing a right rectangular prism and right rectangular pyramid with its net and on the connection between the surface area of a figure and its net.

*Clarification 2: *Within this benchmark, the expectation is to find the surface area when given a net or when given a three-dimensional figure.

*Clarification 3:* Problems involving right rectangular pyramids are limited to cases where the heights of triangles are given.

*Clarification 4:* Dimensions are limited to positive rational numbers.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**6

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Area
- Net
- Rectangular Prism
- Rectangular Prism

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### 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.

- 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?

*Instructional Item 2*

Maxwell is making a replica of the Egyptian pyramids. The figures’ dimensions have a square base with a side length of 7.7 cm and a slant height of 6.2 cm. Maxwell wants to cover the model with gold paper. How much paper, in square centimeters, is needed to cover the pyramid?

**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

## Problem-Solving Tasks

## Tutorials

## Unit/Lesson Sequence

## STEM Lessons - Model Eliciting Activity

This MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

In this Model Eliciting Activity, MEA, students are asked to develop a procedure to fit the most amount of rectangular prism plant packages on one sheet of cardboard, using nets and surface area.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

Students are asked to calculate the volume and surface area of a cube.

## Student Resources

## Problem-Solving Task

Students are asked to use the given information to determine the cost of painting a barn.

Type: Problem-Solving Task

## Tutorials

This video demonstrates how to construct nets for 3-D shapes.

Type: Tutorial

This video demonstrates using a net to find surface area.

Type: Tutorial

## Parent Resources

## Problem-Solving Task

Students are asked to use the given information to determine the cost of painting a barn.

Type: Problem-Solving Task