MidSchoolMath 1

Math involving 3-D and 2-D figures is about as real as math can get, as pretty much everything in the world is made of shapes and solids. In Miracle Mural, Samira Faizan works for Marlon Hardaway at the Wayne County Urban Renewal Foundation in Detroit, Michigan. They find out that the Chamber of Commerce has approved their proposal to create a beautiful mural on a large wall of an old industrial bakery in the community. They need to get an of idea what materials will cost. Samira jumps to it, saying that she will start by calculating the total area of the wall. The data provided is the grid and scale that Samira created using the photo of the wall.

LESSON: MIRACLE MURALWhat is the total area of the mural wall?

Miracle Mural

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.

The Math SimulatorTM

ImmersionPlay Miracle Mural Immersion video, whole-class. Restate the question: What is the total area of the mural wall?Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay Miracle Mural Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

7.G.B.6Geometry

MidSchoolMath Miracle Mural

Clicker QuizLaunch the Clicker Quiz, whole-class.

7.G.B.6Geometry

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Gladys: When finding volume of less familiar shapes, like triangular prisms, students will need reminding that the bases are congruent and parallel.

Kevin: When finding surface area of prisms or pyramids, it may help to have students count the faces so they know how many sub-areas they need to find.

Megan: Refer to volume as area of the base times height, as this works for most figures without having to memorize formulas. Students need to identify the shape of the base, find its area, and multiply by the height of the figure.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #2Standard Math Procedures

Instruction at a Glance

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Determine the area of each face.

Calculate the volume of the cube.

864 sq. in. ÷ 6 equal faces = 144 sq. in. per face

12 in. • 12 in. • 12 in. = 1,728 cubic inches

√144 sq. in. = 12 in.2 Determine the dimensions of each square face.

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MIRACLE MURALWhat is the total area of the mural wall?

Samira Faizan and her boss, Marlon, loved the result of the last community mural they designed and painted. And so did the people in the community! Community members asked the Chamber of Commerce to fund a mural on another wall and to allow Samira and Marlon to create it.

The Chamber of Commerce provided Samira and Marlon a photo of the wall, and the wall has windows and doors that have to be worked around. Knowing the area of the wall will help Samira determine the cost of paint and materials, so she gridded out the wall to begin her calculations.

What is the total area of the mural wall, in square feet?

7.G.B.6

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.

About this standard

Date PeriodName

MidSchoolMath Miracle Mural 1 of 2

WINDOW

WINDOW

DOOR

DOOR

4 feet

APPLYING THE STANDARD

MidSchoolMath 2 of 2

Date PeriodName

How might this standard appear on a test?

Miracle Mural

A cube has a volume of 512 cubic units. What is the surface area of the cube?1)

Lauren’s grandma made her a birthday cake in the shape of an “L.” She put frosting on all sides of the cake except for the bottom.

2)

How many square inches of cake did Grandma cover with frosting?a)

What two-dimensional shape will each fl oor be?a)

What will be the vertical distance between each fl oor?b)

Floor 4 will be the personal residence of the CEO of the business. What is the square footage of the fl oor of her residence?

c)

How many cubic inches of space does Lauren’s cake take up?b)

Asher is painting a wall on a storage shed. He knows one can of paint covers an area of 24 square feet. Asher uses a meter stick to measure the wall, as shown. What is the fewest number of cans of paint Asher needs to paint the wall?

3)

An architect is designing a building in the shape of a pyramid for a new business. The building will have 4 fl oors, each parallel to the ground and equally spaced. The dimensions of each fl oor will be as long as the dimensions of the fl oor below.

4)

1 meter 1 meter 1 meter

1 m

eter

1 m

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1 m

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[1 meter ≈ 39 inches]

Floor 2 will have 30 offi ces of equal size, taking up 85% of the entire area on that fl oor. What could be the dimensions of the offi ces? Which dimensions are not realistic?

d)

34

9 in.

2 in.

4 in.

4 in.

8 in.

12 in.

Check out my worked example #1

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