MA.5.GR.3.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.5.NSO.2.1 
• MA.5.NSO.2.2 
• MA.5.FR.1.1
• MA.5.AR.1.1 
• MA.5.M.1.1

Terms from the K-12 Glossary

• Composite Figure 
• Rectangular Prism

Vertical Alignment

Previous Benchmarks

• MA.4.GR.2.1

 

Next Benchmarks

• MA.6.GR.2.3

Purpose and Instructional Strategies

• Instruction of this benchmark can be combined with MA.5.GR.3.2 as students develop and apply understanding of calculating volume of right rectangular prisms using visual models and formulas (MTR.2.1). 
• While finding volume, teachers should have students communicate and justify their decisions while solving problems (MTR.4.1). 
• Instruction includes problems with the unknown side length being a fraction (MA.5.FR.1.1). 
  • For example, if a box has a base of 5 in × 3 in, and a volume of 20 in³ , what is the length of its missing side? 
• During instruction teachers should allow students the flexibility to use different equations for the same problem. 
  • For example, to find the height of a rectangular prism with volume 120 and base dimensions 3 and 10, students can use the any of the follow equations: 120 = 3 × 10 × h or 120 = 30h or 120 ÷ 30 = h.

Common Misconceptions or Errors

• Students may confuse the difference between b in the area formula A = b X h and B in the volume formula V = B × h. When building understanding of the volume formula for right rectangular prisms, teachers and students should include a visual model to use to justify their calculations. 
• Students may make computational errors when calculating volume. Encourage them to estimate reasonable solutions before calculating and justify their solutions after. Instruction can also encourage students to find efficient ways to use the formula.
  • For example, when calculating the volume of a rectangular prism using the formula, V = 45 × 12 × 2, students may find calculating easier if they first multiply 45 × 2 (which equals 90), instead of 45 × 12. During class discussions, teachers should encourage students to share their strategies so they can build efficiency.

Strategies to Support Tiered Instruction

• Instruction includes the use of visual models to justify calculations when using the volume formula for right rectangular prisms.
• Instruction includes differentiating between base in the area formula, Area = b × h and base in the volume formula, Volume = B × h. Teacher provides students with models of two-dimensional figures, and three-dimensional figures, and has them identify which formula they will use and what the base in each image is. Students highlight the lines included in the base measurement for each figure and use the base to calculate the area or volume. 
  • For example, the teacher provides students with a set of models like the one shown below. The teacher asks students which image they would use the area formula for and which image they would use the volume formula for. Students then highlight the measurements used for the base in the formula. For the first figure, students would use volume and the formula B × h with B = 16 × 4. For the second figure, students would find area and use the formula b × h with b = 16. 

• Instruction includes providing models of two-dimensional and three-dimensional figures with the area and volume formula labeled and color-coded with the measurements. 
  • For example, the teacher provides students with the following set of models and has students explain the difference in the base measurement in each formula. Students calculate the area or volume of each figure using the formula. 

• Instruction includes providing a graphic organizer that requires students to estimate the volume of real-world examples provided and then solve using any strategy they would like. Students then compare their strategy to the strategies used by other students. 
  • For example, the teacher provides students with a graphic organizer similar to the one shown below. Students use it to find the volume of the given example and then compare their strategy to others. 

• Instruction includes estimating reasonable solutions before calculating and justifying solutions after. Instruction can also encourage students to find efficient ways to use the formula. 
  • For example, when calculating the volume of a rectangular prism using the formula, V = 45 × 12 × 2, students may find calculating easier if they first multiply 45 × 2 (which equals 90), instead of 45 × 12. During class discussions, teachers should encourage students to share their strategies so they can build efficiency 
• Instruction includes providing worked examples of volume and having students determine which strategy is the better strategy to use and why. 
  • For example, the teacher provides students with the following image and two examples of how students solved for volume. Student A solved the area of the base first using the Distributive Property to help with the multiplication. Student B used the Associative Property of Multiplication and multiplied 20 × 5 first. Students discuss both strategies and explain which would be easier and why.

Instructional Tasks

Instructional Task 1 (MTR.6.1) 

• Part A. If the larger shipping box is a cube with edges that are each 30 inches, how many layers of graham cracker packages can the shipping box hold? Show your thinking using a visual model and equation(s). 
• Part B. Will the packages reach the top of the shipping box? If not, what will be the length of the gap from the top of the package to the top of the shipping box? 
• Part C. How many graham cracker packages will fit in the shipping box?

Instructional Items

Instructional Item 1 

• a. 2in × 4in
• b. 3in × 3in
• c. 1in × 8in
• d. 4in × 2in
• e. 56in × 56in 

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