Measurement & Modeling

Modules 18, 19, and 20

QOD # 51

35 Minute Movie!!!!

FLAT LAND

Adapted from a book

by: Edwin A. Abbott

Nets,Cross Sections, Rotations

module 19

GOALS:

**I can draw and identify nets & cross sections of 3D solid figures

→ I can:

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Identify the most precise name for each pictured solid:

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Euler’s Formula

Nets of Solids

Cube

Rectangular Prism

Triangular prism

Square pyramid

Cone

Cylinder

What is a net?

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A net is a two-dimensional pattern of a three-dimensional solid

Match the solid to the correct Net on the right.

https://www.youtube.com/watch?v=7uAbGoGYLcc

Nets start @ 4:52 minutes in

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Sphere Nets

Net of a Cube:

optional Project - Nets

Visit

http://www.cubeecraft.com/

Pick a character, (more than a single cube) and print out the net. card stock works best….but is not required. If you don’t have color print as an option, color your character before you cut it out and put it together. Difficulty level will be taken into account.

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• Imagine a light has been placed perpendicular to each of the figures. Sketch the Shadow that each 3D figure would make on a wall. What shape would be made?

Cross Sections (Cylinder):

Cross Sections (Square Pyramid)

CONE

Cross Sections of a Cone

Triangle

Cross Section of a Sphere

Which letter represents the cross section of a sphere?

Rotation of 2D figure in the 3D plane:

Rotating Simple Figures Video

Khan Academy Video

Rotation Questions

a

b

c

d

optional Project - Nets

Visit

http://www.cubeecraft.com/

Pick a character, (more than a single cube) and print out the net. card stock works best….but is not required. If you don’t have color print as an option, color your character before you cut it out and put it together. Difficulty level will be taken into account.

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Evaluate the total volume of the compound figure:

QOD #52

VOLUME

Module 18

The amount of space measured in cubic units that an object or substance occupies

GOALS:

→ I can:

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Volume of �Prisms, Cylinders, Pyramids, Cones, and Spheres.

Prisms and Cylinders

Module 18.1

Volume of a Prism

V = Bh

B = area of Base

h = height of prism

rectangular prism

Example:

Finding Volume of Non-rectangular Prisms

V = Bh

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Evaluate Volume

Evaluate Volume

Evaluate Volume

Evaluate Volume

Reminder: Area of Regular Polygons

• The area (A) of a regular polygon equals one half the product of the apothem and the perimeter

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(Perimeter of a regular polygon equals a side length times the number of sides, by the way)

8 cm

Evaluate Volume

Evaluate Volume

Volume of a Right Cylinder

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V=Bh

r = radius

B = Area of circle base

h = height

Circle Formulas you need to know:

Evaluate the circumference and area of the circle to the right if the diameter is 14cm.

Evaluate Volume

5

3

2

6

20

5

4

Solve for Volume of each figure:

TNReady

Volume =

Volume of a Right Pyramid

B = area of base

h = height

h

Why ⅓ ?

Examples:

Volume of a Cone

h

Volume of Sphere

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r = radius

https://www.youtube.com/watch?v=YNutS8eIhEs

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Volume of hemisphere

Evaluate the volume of each figure

Evaluate the total volume

Go back to QOD #52 and solve what can!

QOD #53

Evaluate total volume:

4in

10in

10in

20 in

VOLUME

Module 18

The amount of space measured in cubic units that an object or substance occupies

GOALS:

→ I can:

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Volume of Sphere

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r = radius

https://www.youtube.com/watch?v=YNutS8eIhEs

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Volume of hemisphere

Evaluate the volume of each figure

Volume Problems

On a separate sheet of paper, show the work (steps a-e) on finding volume of each figure.

#7 requires some perseverance! - Honors Level

#7

Meatball Task

Half a sheet of paper with somebody

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Dan Meyer Video (meatballs)

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Will it overflow?

1. How many meatballs will it take to overflow?

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2. What is a number of meatballs you know is too high?

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3. What is a number of meatballs you know is too low?

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What information would be useful?

What does the math say?

The answer!

QOD #54

Evaluate the total volume; Leave answer in terms of pi.

VOLUME

Module 18

The amount of space measured in cubic units that an object or substance occupies

GOALS:

→ I can:

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TN Ready

Assignment:

• Volume of a Castle Worksheet (composite figures)

l

l

h

• Make sure you cell phones are put away & sit in your normal general area. (Be an active participant!)
• Take one block from the bucket (these are my son’s, please be considerate!)
• You will need a ruler
• You will probably want a calculator
• Be ready for you QOD Question to pop up. You will have 5 minutes to get it copied down.
• If you did not turn in your castle volume yesterday, have that out as well.

As you enter the classroom:

It’s going to be a good day :)

-Mrs. B

�QOD # 55

Evaluate total surface area of the composite figure.

Surface Area

module 19

GOALS:

**I can evaluate Surface Area of 3D solid figures

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→ I can:

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On a sheet of paper (that you will be turning in):

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• Sketch your chosen block
• Record the dimensions of the block on your sketch in centimeters.
• Evaluate the surface area of your block by finding the area of each side and totaling it up. Show all work on your paper. Persevere!

Evaluating Surface Area Task

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• Group up with others that have the same figure as you. Compare your work and make adjustments if needed.

Evaluating Surface Area Task

Surface Area Findings

Surface Area Findings

Surface Area Findings

QOD #56 Find Surface Area

Take out your volume and surface area problems 1-9

Surface Area

module 19

GOALS:

**I can evaluate Surface Area of 3D solid figures

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→ I can:

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Lateral Area of a Right Prism

• lateral area – the area of all the lateral faces of a prism (the area of all sides except the top and bottom bases)

P = perimeter

h= height

Surface Area of a Right Prism

You can find the surface area of a prism by adding the areas of each of the faces.

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LA = Lateral Area

P = perimeter, h = height,

B= area of base

LA=ph

S.A. = ph + 2B

S.A. = ph + 2B

Evaluate Surface Area

Lateral Area of a Right Cylinder

Surface Area of a Right Cylinder

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h = height, r = radius of base

Heights of a Pyramids & Cones

vertex

slant

height

slant height (l) – the height of each

lateral face

altitude (h) – the segment from the

vertex perpendicular to the base

Pyramids

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l = slant height

P = perimeter of base

Lateral Surface Area:

Total Surface

Area

B = area of base

Cones

Lateral Surface Area: Total Surface Area:

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r = radius, l = slant height

When a plane intersects a sphere so that it contains the center of the sphere, the intersection is called a great circle.

Each great circle separates a sphere into 2 congruent halves called hemispheres.

SPHERE

Surface Area of Sphere

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r = radius

Surface Area of hemisphere

Assignment:

• Surface Area Problems 1-9 With work
• Finish up Volume and add Surface Area to the Castle; (100 pts total with all work shown!)
• Check off totals with me! ☺

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Tutorial video

TURN IN CASTLE SHEETS

• 50 pts Surface Area
• 50 pts Volume

TNReady Type Question

• Quiz
• Volume and Surface Area of castle
• Module 18 homework (late)

QOD Quiz #9

• Take out a sheet of paper
• Put name, Date & Title on it
• Work each of the following problems presented. (must show work)
• Turn in before you leave!

Modeling

Module 20

Goals: I can

http://www.shmoop.com/common-core-standards/ccss-hs-g-mg-1.html

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TNReady Review

TNReady Warm-Up

Evaluate Volume & Surface Area of the figure below:

h

l=

TNReady Warm-up

Follow Directions:

Please put Chromebooks away responsibly.