21st Century Lessons

Mrs. ThompsonLevel 1

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Volume of Right, Rectangular Prisms

6.G.2.

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Lesson Objective Lesson Objective: SWBAT calculate the volume of right, rectangular prisms using unit-cube, spatial analysis and volume formulas: V = lwh and V = Bh

Student- Friendly Objective:I will be able to develop and utilize the formula for the volume of right, rectangular prisms.

Lesson Description This lesson was designed to teach volume within the confines of an engaging, relatable scenario. As it is an introduction into the most basic of volume formulae, the lesson is structured to be broadly accessible. Future lessons or problems involving the volume of right, rectangular prisms may necessitate more focused bands of differentiation, especially on the advanced end.

One option is choosing to arrange student groups and pairings by diversifying skill levels. This spectrum within each group may allow the teacher to circulate among groups more equally in terms of time assistance.

Again, future lessons on this concept might lend themselves better to homogenous skill set groupings.

Lesson Overview (1 of 3)

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Materials Classwork handout (double-sided), Homework handout (double-sided), Key To Leave page, Powerpoint does include sound clips… speakers optional

Scaffolding This lesson was crafted to proceed in a deliberate, concrete fashion. The classwork work-sheets that accompany it are procedural in nature. Diverse student groupings should also assist in access. Student-specific scaffolds would be up to teacher discretion.

Enrichment The homework offers some levels of enrichment in terms of unit pricing etc. A subsequent volume lesson would lend itself better to having advanced students really stretch the concept of volume. Again, this is a concept-intro lesson.

Online Resources for Absent Students

olume formula explained:http://mathvillage.info/node/111http://www.mathsisfun.com/fractions_multiplication.htmllyinghttp://www.mathsisfun.com/multiplying-decimals.html

Lesson Overview (2 of 3)

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Lesson Overview (3 of 3)

Common Core State Standard

6.G.2. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Before and After This lesson logically falls after skills in perimeter and area have been taught. It introduces students to the concept of volume and associated formulas. I would follow up this lesson with a class focused on students applying the formula to both concrete and theoretical problems. Then it would make sense to have lessons that really tie all the geometric measures together…perhaps in a project.

Topic Background The concept of volume was utilized by ancient Greeks and Babylonians for many purposes. While specific formulas can be attributed to individuals (Euclid is often linked to volume of a sphere although it is believed to have existed much earlier), it is nearly impossible to identify the ancient individual to first calculate the volume of rectangular prisms.

Perhaps the most famous account of volume discovery involved Archimedes of Syracuse who determined how to calculate the volume of irregular shapes.

Lean more about it…

http://en.wikipedia.org/wiki/Archimedes

Prism A solid object that has two identical ends and all flat sides. The cross section is the same all along its length. The shape of the ends give the prism a name

Right, Rectangular Prism A solid (3-dimensional) object which has six faces that are rectangles.

Volume The amount of 3-dimensional space an object occupies. Capacity.

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Lesson Vocabulary

Warm Up/Do NowOBJECTIVE: SWBAT develop and utilize the formula for the

volume of right, rectangular prisms.

Agenda

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A) Explain why the figure at left happens to be called a Right, Rectangular Prism.

B) Think of 3 examples of these prisms that you encounter in everyday life.

C) What geometric term do we use to describe the space inside 3-dimensional figures?

D) Why is such space measured in cubic units rather than square units like when measuring Area?

Agenda

1) Warm Up: Independent (10 Min) 2) Launch: Teacher Guided Problem (15 Min)

3) Explore: Partner/Group Investigation (30 Min)

4) Summary: Independent (5 Min)

5) Practice: Homework

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OBJECTIVE: SWBAT develop and utilize the formula for the volume of right, rectangular prisms.

Problem Launch

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Jamal started a Boston business, City Crave, selling chocolate bars made using his grandmother’s recipe. He wants to ship the bars to a candy store in Los Angeles.

Agenda

Jamal has 3 shipping box options.

What are some important things for Jamal to consider?

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No vertical stacking or bars will break.

First, he needs to know how much space is inside each box !

Agenda

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Remember that when we wanted to find the space inside a 2-dimensional, flat shape, we determined how many 1 x 1 squares fit into that shape.

Area of rectangle is 18 units2

Well, to find the space inside of Jamal’s boxes (3-dimensional prisms), we will use 1 x 1 x 1 cubes instead of flat squares. Don’t worry yet about the fact that his candy bars are not cubes…focus on box space.

Agenda

Measuring Area Vs. Measuring Volume

3units

6 units

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How many cubes will fill each box ? (these boxes are on CW page #1)

Agenda

1 X 1 X 1 cube

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Agenda

Click on the timer!

CW Page #1 1 Problem – Many Brains

6 minutes on the clock!

• Work with your partner(s) on problem #1.

• Pencils down when you reach the sign.

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CW Page #2 1 Problem – Many Brains

2 minutes on the clock!Click on the timer!

Work with your partner(s) on problem #2.

• Discuss why the formula is followed by units3

. • Pencils down when you

reach the sign.

Agenda

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CW Page #2 1 Problem – Many Brains

7 minutes on the clock!

Click on the timer!

Work with your partner(s) on problem #3.

• Make sure to assist one another if needed. • Pencils down when you reach the sign.

Agenda

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Agenda

Name:

Summary, Key to Leave, HW

1) Provide a definition for volume. How is it different than area and perimeter? (think units)

2) What is the formula for the volume of Right, Rectangular Prisms?

3) Calculate the volume of the prism. Show all work. Measured in cm.

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Challenge - Given a right, rectangular prism with a volume of 120 cm3, length of 12 cm, and width of 5 cm, determine the prism's height.