Math Math

February 16, 2015February 16, 2015

Tuesday: Bell Work Tuesday: Bell Work * *show workshow work

Use notebook Use notebook paper and create paper and create the bell work grid the bell work grid

Date Date WorkWork AnswerAnswer

2/22/244

2/22/255

2/22/266

2/22/277

**show work- do not just write down an show work- do not just write down an answeranswer

AgendaAgenda

• 1- bell work1- bell work• 2- Agenda-2- Agenda-

• *Vocabulary Quiz on Friday 2/27*Vocabulary Quiz on Friday 2/27• Benchmark on Monday 3/2Benchmark on Monday 3/2

• 3- Vocabulary3- Vocabulary• 4- Objective 4- Objective • 5- lesson *Area of Squares 5- lesson *Area of Squares • 6- exit ticket6- exit ticket

VocabularyVocabulary

Study and review the terms!! Study and review the terms!!

Objective Objective

7.G.1 Solve problems involving scale 7.G.1 Solve problems involving scale drawings of geometric figures, drawings of geometric figures, including computing actual lengths including computing actual lengths and areas from a scale drawing and and areas from a scale drawing and reproducing a scale drawing at a reproducing a scale drawing at a different scale. different scale.

AreaArea

Lesson: Lesson:

Since all sides of the square are the Since all sides of the square are the same you can “square” your numbersame you can “square” your number

4 ft

To find the area multiply length and width

4 x 4

Or you can square it

42

7 ft

72 = 49

49 ft2

Be sure to include units of measure!! Since it is area you need to square the units.

12 m

4.5 in

Now that you can find area- Now that you can find area- let’s undo it!! let’s undo it!!

Area is 25 ft 2

What is one side???

Now that you can find area- Now that you can find area- let’s undo it!! let’s undo it!!

Area is 25 ft 2

What is one side???

What operation would you use to undo a square- the square root!!!

The square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so a square root of 16 is 4.

The symbol is √

Another example: √36 = 6 (because 6 x 6 = 36)

Now that you can find area- Now that you can find area- let’s undo it!! let’s undo it!!

Area is 25 ft 2

What is one side???

√25 = 5

Therefore one side is 5 ft.

Area = 81 sq in

Area = 36 sq m

Area = 81 sq in

Now that you found the side

Length is 9 in.

What is the perimeter???

Area = 81 sq in

Now that you found the side

Length is 9 in.

What is the perimeter???

9 x 4 = 36 in

Try this oneTry this one

Step 1: find the side lengthStep 2: find the perimeter

Exit TicketExit Ticket

Discuss with your partner Discuss with your partner

What can you do to “undo” the area of a What can you do to “undo” the area of a square?square?

Wednesday: Bell Work Wednesday: Bell Work * *show workshow work

**show work- do show work- do not just write not just write down an down an answeranswer

AgendaAgenda

• 1- bell work1- bell work• 2- Agenda-2- Agenda-

• *Vocabulary Quiz on Friday 2/27*Vocabulary Quiz on Friday 2/27• Benchmark on Monday 3/2Benchmark on Monday 3/2

• 3- Vocabulary3- Vocabulary• 4- Objective 4- Objective • 5- lesson *Area of Squares HW – WB p. 835- lesson *Area of Squares HW – WB p. 83• 6- exit ticket6- exit ticket

VocabularyVocabulary

Study and review the terms!! Study and review the terms!!

Objective Objective

7.G.1 Solve problems involving scale 7.G.1 Solve problems involving scale drawings of geometric figures, drawings of geometric figures, including computing actual lengths including computing actual lengths and areas from a scale drawing and and areas from a scale drawing and reproducing a scale drawing at a reproducing a scale drawing at a different scale. different scale.

Lesson: Triangles Lesson: Triangles

TrapezoidsTrapezoids

Exit TicketExit Ticket

Discuss with your partner Discuss with your partner

Why does the triangle formula have a ½ in Why does the triangle formula have a ½ in it?it?

What is its purpose?What is its purpose?

Thursday: Bell Work Thursday: Bell Work * *show workshow work

**give a detailed explanation why-- do not just give a detailed explanation why-- do not just write down an answerwrite down an answer

AgendaAgenda

• 1- bell work1- bell work• 2- Agenda-2- Agenda-

• *Vocabulary Quiz on Friday 2/27*Vocabulary Quiz on Friday 2/27• Benchmark on Monday 3/2Benchmark on Monday 3/2

• 3- Vocabulary3- Vocabulary• 4- Objective 4- Objective • 5- lesson *Vocabulary “I have Who Has”, 5- lesson *Vocabulary “I have Who Has”,

Need to Know, Vocabulary CrosswordNeed to Know, Vocabulary Crossword• 6- exit ticket6- exit ticket

VocabularyVocabulary

Study and review the terms!! Study and review the terms!!

Objective Objective

7.G.1 Solve problems involving scale 7.G.1 Solve problems involving scale drawings of geometric figures, drawings of geometric figures, including computing actual lengths including computing actual lengths and areas from a scale drawing and and areas from a scale drawing and reproducing a scale drawing at a reproducing a scale drawing at a different scale. different scale.

Area practice: Area practice:

Complete the practice problems on the Complete the practice problems on the worksheet.worksheet.

Area formulas:Area formulas:

Square: sSquare: s2 2 (s=side) (s=side)

Triangle: 1/2bhTriangle: 1/2bh

Trapezoid: 1/2h (bTrapezoid: 1/2h (b11 + b + b22))

Exit TicketExit Ticket

Discuss with your partner Discuss with your partner

Why are the area formulas different for Why are the area formulas different for different shapes?different shapes?

Friday: Bell Work Friday: Bell Work * *show workshow work

**show work- do show work- do not just write not just write down an down an answeranswer

AgendaAgenda

• 1- bell work1- bell work• 2- Agenda-2- Agenda-

• *Vocabulary Quiz on Friday 2/27*Vocabulary Quiz on Friday 2/27• Benchmark on Monday 3/2Benchmark on Monday 3/2

• 3- Vocabulary3- Vocabulary• 4- Objective 4- Objective • 5- lesson *Area of Triangles and 5- lesson *Area of Triangles and

TrapezoidsTrapezoids• 6- exit ticket6- exit ticket

VocabularyVocabulary

Study and review the terms!! Study and review the terms!!

Objective Objective

7.G.1 Solve problems involving scale 7.G.1 Solve problems involving scale drawings of geometric figures, drawings of geometric figures, including computing actual lengths including computing actual lengths and areas from a scale drawing and and areas from a scale drawing and reproducing a scale drawing at a reproducing a scale drawing at a different scale. different scale.

Learn to find the volume and surface area of similar three-dimensional figures.

Recall that similar figures have proportional side lengths. The surface areas of similar three-dimensional figures are also proportional. To see this relationship, you can compare the areas of corresponding faces of similar rectangular prisms.

Area of front ofsmaller prism

Area of front of larger prism

3 · 5 6 · 10

15 (3 · 2) · (5 · 2)

(3 · 5) · (2 · 2)

15 · 22

Each dimension has a scale factor of 2.

A scale factor is a number that every dimension of a figure is multiplied by to make a similar figure.

Remember!

l · w l · w

The area of the front face of the larger prism is 22 times the area of the front face of the smaller prism. This is true for the entire surface area of the prisms.

The surface area of a box is 35 in2. What is the surface area of a similar box that is larger by a scale factor of 7?

Additional Example 1A: Finding the Surface Area of a Similar Figure

S = 35 · 72 Multiply by the square of the scale factor.

S = 35 · 49 Evaluate the power.

S = 1,715 Multiply.

The surface area of the larger box is 1,715 in2.

The surface area of a box is 1,300 in2. Find the surface area of a similar box that is

smaller by a scale factor of .

Additional Example 1B: Finding the Surface Area of a Similar Figure

12

S = 1,300 · 12

2

S = 1,300 · 14

S = 325

The surface area of the smaller box is 325 in2.

Multiply by the square of the scale factor.

Evaluate the power.

Multiply.

Check It Out: Example 1A

S = 50 · 32 Multiply by the square of the scale factor.

S = 50 · 9 Evaluate the power.

S = 450 Multiply.

The surface area of the larger box is 450 in2.

The surface area of a box is 50 in2. What is the surface area of a similar box that is larger by a scale factor of 3?

13

S = 1,800 · 13

2

S = 1,800 · 19

S = 200

The surface area of the smaller box is 200 in2.

Multiply by the square of the scale factor.

Evaluate the power.

Multiply.

Check It Out: Example 1B

The surface area of a box is 1,800 in2. Find the surface area of a similar box that is smaller

by a scale factor of .

The volumes of similar three-dimensional figures are also related.

3 ft

2 ft

1 ft2 ft

6 ft

4 ft

Volume of smaller box

Volume oflarger box

2 · 3 · 1

64 · 6 · 2

(2 · 2) · (3 · 2) · (1 · 2)

(2 · 3 · 1) · (2 · 2 · 2)

6 · 23

Each dimensionhas a scale factor of 2.

The volume of the larger box is 23 times the volume of the smaller box.

The volume of a child’s swimming pool is 28 ft3. What is the volume of a similar pool that is larger by a scale factor of 4?

Additional Example 2: Finding Volume Using Similar Figures

V = 28 · 43 Multiply by the cube of the scale factor.

V = 28 · 64 Evaluate the power.

V = 1,792 ft3 Multiply.

Estimate V ≈ 30 · 60 Round the measurements.

= 1,800 The answer is reasonable.

Check It Out: Example 2

The volume of a small hot tube is 48 ft3. What is the volume of a similar hot tub that is larger by a scale factor of 2?

V = 48 · 23 Use the volume of the smaller prismand the cube of the scale factor.

V = 48 · 8 Evaluate the power.

V = 384 ft3 Multiply.

Estimate V ≈ 50 · 8 Round the measurements.

= 400 The answer is reasonable.

The sink in Kevin’s workshop measures 16 in. by 15 in. by 6 in. Another sink with a similar shape is larger by a scale factor of 2. There are 231 in3 in 1 gallon. Estimate how many more gallons the larger sink holds.

Additional Example 3: Problem Solving Application

Additional Example 3 Continued

11 Understand the Problem

Rewrite the question as a statement.

• Compare the capacities of two similar sinks, and estimate how much more water the larger sink holds.

List the important information:• The smaller sink is 16 in. x 15 in. x 6 in.

• The large sink is similar to the small sink by a scale factor of 2.

• 231 in3 = 1 gal

Additional Example 3 Continued

22 Make a Plan

You can write an equation that relates the volume of the large sink to the volume of the small sink. Then convert cubic inches to gallons to compare the capacities of the sinks.

Volume of large sink = Volume of small sink · (a scale factor)3

Additional Example 3 Continued

Solve33Volume of small sink = 16 x 15 x 6 = 1,440 in3

Convert each volume into gallons:

Volume of large sink = 1,440 x 23 = 11,520 in3

1,440 in3 x ≈ 6 gallons1 gal 231 in3

11,520 in3 x ≈ 50 gallons1 gal 231 in3

Subtract the capacities: 50 gal – 6 gal = 44 gal

The large sink holds about 44 gallons more than the small sink.

Look Back44

Double the dimensions of the small sink and find the volume:32 x 30 x 12 = 11,520 in3. Subtract the volumes of the two sinks:11,520 – 1,440 = 10,080 in3. Convert this measurement to gallons:

10,080 x ≈ 44 gal

Additional Example 3 Continued

1 gal 231 in3

The bath tub in Ravina’s house measures 46 in. by 36 in. by 24 in. Another bath tub with a similar shape is

smaller by a scale factor of . There are

231 in3 in 1 gallon. Estimate how many more gallons the larger bath tub holds.

Check It Out: Example 3

1 2

Check It Out: Example 3 Continued

11 Understand the Problem

Rewrite the question as a statement.

• Compare the capacities of two similar tubs, and estimate how much more water the larger tub holds.

List the important information:• The larger tub is 46 in. x 36 in. x 24 in.

• 231 in3 = 1 gal

• The smaller tub is similar to the larger tub by a scale factor of . 1

2

Check It Out: Example 3 Continued

22 Make a Plan

You can write an equation that relates the volume of the small tub to the volume of the large tub. The convert cubic inches to gallons to compare the capacities of the tubs.

Volume of small tub = Volume of large tub · (a scale factor)3

Check It Out: Example 3 Continued

Solve33Volume of large tub = 46 x 36 x 24 = 39,744 in3

Convert each volume into gallons:

Volume of small tub = 39,744 x 0.53 = 4,968 in3

39,744 in3 x ≈ 172 gallons1 gal 231 in3

4,968 in3 x ≈ 22 gallons1 gal 231 in3

Subtract the capacities: 172 gal – 22 gal = 150 gal

The large tub holds about 150 gallons more than the small tub.

Look Back44

Halve the dimensions of the large tub and find the volume:23 x 18 x 12 = 4,968 in3. Subtract the volumes of the two tubs:39,744 – 4,968 = 34,776 in3. Convert this measurement to gallons:

34,776 x ≈ 150 gal.

Check It Out: Example 3 Continued

1 gal 231 in3

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Lesson Quiz: Part I

Given the scale factor, find the surface area to the nearest tenths of the similar prism.

1. The scale factor of the larger of two similar

triangular prisms is 8. The surface area of the

smaller prism is 18 ft2.

2. The scale factor of the smaller of two similar

triangular prisms is . The surface area of the

larger prism is 600 ft2.

66.7 ft2

1,152 ft2

13

Lesson Quiz: Part II

Given the scale factor, find the volume of the similar prism.

3. The scale factor of the larger of two similar

rectangular prisms is 3. The volume of the

smaller prism is 12 cm3.

4. A food storage container measures 6 in. by 10

in. by 2 in. A similar container is reduced by a

scale factor of . Estimate how many more

gallons the larger container holds.

324 cm3

about 0.5 gal

12

1. A fish storage aquariumcontainer measures 15 in. by 17 in. by 7 in. A similar container aquarium is larger by a scale factor of 4. Estimate how many more gallons the larger container aquarium holds.

A. about 494 gal

B. about 490 gal

C. about 487 gal

D. about 486 gal

Lesson Quiz for Student Response Systems

2. The volume of a prism is 28 cm3. What is the volume of a similar prism that is larger by a scale factor 4?

A. 32 cm3

B. 112 cm3

C. 448 cm3

D. 1,792 cm3

Lesson Quiz for Student Response Systems

Exit TicketExit Ticket

Discuss with your partner Discuss with your partner

What skills did you need for the need to What skills did you need for the need to know?know?