Chapter 5 Lesson 51B Rates and Unit Rates · When I study for tests, I practice everything from the...

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Chapter 5Lesson 51B

Rates and Unit Rates

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Happy Thursday!!!!

Today we will take pretest

We will define: rate and unit rate

We will calculate unit rate by finding heartbeat

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Happy Friday!!!By the end of today you should be able to:

1) identify the difference between a rate and a unit rate

2) Convert a rate into a unit rate

***** If you haven't taken the Ch 4 test or the Ch 5 pre-test yet, please see me!

To Do:

1) Open Notebook to Notes Section and head it "UNIT RATES"

2) Write down HW

3) Wait quietly :)

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Name ______________________________________________

Rate Yourself: #15 for each item below (1 worst 5 best)

____I do my homework

____When we go over homework, I pay attention, check my work and correct my mistakes

____I ask questions in class, when I am confused

____I get extra help, when I'm really confused

____I study for tests

Check the appropriate response:

When I study for tests, I practice everything from the chapter either by:

____ using online tests ____ going back through the book ____ other (please explain)

This year in math, I feel like I have gotten:

____ better ____worse ___stayed the same

Answer with your own words:

I felt I was good at math when....

(give me a grade you were in, a topic you learned, or habits you had, etc. list as many as you can)

My plan for improving my understanding in math is...

It would help me if Mrs. Holland would:

These are the things Mrs. Holland does that really help me:

List the times that you know Mrs. Holland is available for extra help:

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How to Find a Unit Rate:Guided Practice

http://connected.mcgraw-hill.com/media/repository/protected_content/COMPOUND/50000037/42/61/topic_02_33/topic_02_33.swf

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What problems do you want to see from

last night's homework? Drag to green area!

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Happy Monday!!Make sure you have....

1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in plannerBellwork...Write fractions and find the cross-products 2 6 3 9Today's Goals:Can you tell the difference between a rate and a unit rate?Can you use what you know to find more rates?Can you define "proportion"?Can you use cross products to solve proportions?

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No clue how to do the hw...very confused!

25 26 2728 29 30 31 3233 34 35 36No clue how to do the hw...very confused!

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5

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Go over last night's homeworkP. 268 #124 even

Today's Goals:Can you tell the difference between a rate and a unit rate?Can you use what you know to find more rates?Can you define "proportion"?Can you use cross products to solve proportions?

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Guided Practice (Choose Use a Unit Rate on Lesson Menu)


http://connected.mcgraw-hill.com/media/repository/protected_content/COMPOUND/50000037/42/61/topic_02_33/topic_02_33.swf

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Happy Tuesday!!Make sure you have....

1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner


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HW 1) # 6 and #2024 even

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16 cupcakes for 8 tables

Rates Unit rates

$0.50 for 1 bacon strip$15 for 4 pizzas

4 cupcakes per table

$100 per window

$2 for 8 juice boxes

$10,000 for 1 car

$8 for 16 bacon strips10 books per shelf

3 laps in 7 minutes3 inches every 6 months

$300 for 1 Ipad

6 bballs per court

Drag rates to the correct column :)

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Happy Monday!!Welcome Back...Review Day!Make sure you have....

1) Pencil, notebook & CALCULATOR 2) Write homework in planner

Today's Goals:Can you tell the difference between a rate and a unit rate?Can you use what you know to find more rates?

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Happy Tuesday!!Make sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Proportions: Skills Practice Wkst~Quiz tomorrow over rates & unit rates

Today's Goals:Can you define "proportion"?Can you determine whether two or more ratios are in proportion?Can you use cross products to solve proportions?

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a ratio comparing two quantities with different units of measure.

When ratios are equal

(in proportion), their cross products are

equal!

2 54 10

A ratio comparing two quantities with different units of measure and having a

denominator of 1!

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Lesson 51C,DProportional Vs NonProportional

Relationshipsand Solving Proportions

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In other words...Equal ratios proprotionalNot Equal Rations nonproportional

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Two ways to check if ratios are proportional or nonproportional...1) simplify both ratios or convert to decimals 2) check the crossproducts (works if you are only comparing two ratios)!

Examples:A. B. C.2 54 10

3 9 4 15

5 1025 50

Do in Notes...

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More guided practice...print page for students to work with me and keep in notes

Determining Proportionality:

Solving Proportions:

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Exit ticket:Match each term with the correct definition or example. Put the letter of the correct definition on example on the line in front of the term.

____ 1. set proportional ratios A.

____ 2. set of nonproportional ratios B. 1 3 2 4 4 10

____ 3. proportion C. 1 2 3 6

____ 4. cross products D. 1 3 6 2 6 12

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Happy Wednesday!!Quiz today over rates and unit ratesMake sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Problem Solving Practice Wkst on proportions

~Quiz tomorrow on proportions

Today's Goals:Can you apply what you know about proportions to solve problems involving scales?

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a statement that two ratios are

equal.



equal!

to be equal

2 54 10

Check their cross products

orsimplify them!


denominator of 1!

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Happy Thursday!!Quiz today over proportionsMake sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Scale Worksheet~Quiz tomorrow over proportions


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2

5

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36

35


45

6 78

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equal.



equal!

to be equal

2 54 10


orsimplify them!


denominator of 1!

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Guided Practice...provide copy for student notes

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Guided Practice Continued

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4 cm 2.5 cm

3 cm 1 cm

Name ___________________________________________________________ Period ________Scale Model Worksheet

1. 2.

3. 4.

5.6.

7. 8.

1.

Did you label the units on all your ratios?Did you label all your answers with units?


vb

vc

40

4 cm 2.5 cm

3 cm 1 cm

Name ___________________________________________________________ Period ________Scale Model Worksheet

1. 2.

3. 4.

5.6.

7. 8.

1.



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Happy Friday!!Make sure you have.... 1) Pencil, notebook& CALCULATOR 2) Write homework in planner ~Scale Problem Solving Wkst ~Quiz monday over Scale Drawing

3) Get this out...


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a ratio that compares the size on a model or map to the actual size or distance



equal.



equal!

to be equal

2 54 10


orsimplify them!

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More Practice with Scale...

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Happy Monday!!Quiz Today on Scale Models and DrawingsMake sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Complete Corresponding sides and angles wkst

Today's Goals:Can you apply what you know about proportions to similar figures?Can you identify corresponding sides and angles on a set of figures?

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equal.



equal!

to be equal

2 54 10


orsimplify them!

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matching same measure

equivalent ratios


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Today we will begin by simply learning to identify corresponding sides and angles.....


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Try it with me:Example 1: Example 2:

1) 2)

3) 4)

5) 6) TRICKY!

Try it yourself: Monday: Use colors or hash marks to identify the corresponding sides and angles in each set of figures.Tuesday: use ratios to determine if the pairs of figures are similar

A B

C D

W X

Y Z12 in

4 in

6 in

2 in

Name _________________________________________________________ Period ________Similar Figures

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Happy Tuesday!!Make sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Similar Figures Wkst. Follow "Tuesday" directions

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See me before leaving today about make-ups :)

1st:• Dominic• Kylie• Erin• Maya• Zach

4/5:• Jordan• Armon• Chris

6/7:• Bridget

12th:• Reagan• Bilal• Ethan

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matching sides on a set of figures



equal.



equal!

to be equal

2 54 10


orsimplify them!

same size/measure


a ratio comparing two quantities with different units of measure that has a

denominator of 1!


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matching same measure

equivalent ratios


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Try it with me:Example 1: Example 2:

1) 2)

3) 4)

5) 6) TRICKY!

Try it yourself: Monday: Use colors or hash marks to identify the corresponding sides and angles in each set of figures.Tuesday: use ratios to determine if the pairs of figures are similar

A B

C D

W X

Y Z12 in

4 in

6 in

2 in

Name _________________________________________________________ Period ________Similar Figures

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Step 1: Identify Corresponding Angles & decide if the angles have the same measure HINT: If you are not given the measures of the angles...just check to

see if the figures are the same shape. yes: move on no: you are done, they are NOT similar

Step 2: Identify and mark corresponding sides

Step 3: Make ratios out of the measurements of the corresponding sides

Step 4: Simplify the ratios and see if they match yes: they are similar figures no: they are NOT similar figures

How to Identify Similar Figures

Example to do for class:


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Name _________________________________ Period ____

Exit Ticket:

1.) Identify the corresponding sides in the following pair of figures

2.) Make ratios using the measures of the corresponding sides

3.) Check to see if those ratios are in proportion and mark one choice:

____ similar ____ not similar

A

B C

D

E F3 in.

4 in

9 in.

12 in

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Happy Wednesday!!Make sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

...See Board


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Guided Practice

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HW: P. 296 #1, 5, 6

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Happy Thursday!!Make sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Similar Figures: Practice Wkst

Today's Goals:Can you apply what you know about proportions to similar figures?Can you apply what you know about similar figures, ratios and proportions to solve for the missing measure in a pair of similar figures?

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Finding Missing Measures on Similar Figures1) Identify and mark Corresponding Sides

2) Set up a proportion: *One ratio should include the missing side

3) Cross Multiply to Solve for the missing measure

Example:

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Guided Practice...students do with me ontheir note sheet.

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Guided Practice...students do with you ontheir note sheet.

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Tell if Figures are Similar Find Missing Measure on

Similar Figures

Find Scale FactorOnce you know the figures are similar...

simplify one of the ratios of the corresponding sides and you've found your scale factor.

*Make ratios of corresponding sides*simplify *see if the ratios are in proportion

if yes, similar if no, not similar

*Make proportion using ratios of corresponding sides*solve proportion using cross products

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HW: All Problems53A

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Challenge Page

Then, find the scale factor, if similar.

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Happy Friday!!Make sure you have.... 1) Pencil, notebook & CALCULATOR 2) HW Out 3) Write homework in planner

~Similar Figures Wkst

Today's Goals:Can you apply what you know about proportions to similar figures?Can you apply what you know about similar figures, ratios and proportions to solve for the missing measure in a pair of similar figures?Can you use ratios to find scale factor?

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Finding Scale FactorWhen figures are similar, there will be a scale factor that tells you how much larger or smaller the sides on one figure are, compared to the similar figure

It's easy to find...just find the ratio of corresponding sides!A

B C

D

E F

A B

C D

E F

G H

D E

F

2 CM3 CM

2.5 CM

3 FT

6 FT

9 FT1 FT.

2 FT.

3 FT.

2 IN.

3 IN.

8 IN.

12 IN.

4 CM

5 CM

6 CM

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53A

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A B

C D

E F

G H

D E

F

2 IN.

3 IN.

10 IN.

15 IN.

4 CM

5 CM

6 CM

2 CM3 CM

2.5 CM

Find the Scale Factor for each pair of similar figures and explain in your own words what the scale factor represents.

1)

2)

3)A

B

C

D

E

F

G

H

A

B C

D

EF

3 FT

6 FT

9 FT1 FT.

2 FT.

3 FT.4)

NAME __________________________________________ CLASS PERIOD _________

4 YARDS

2 YARDS 2.5 YARDS

3 YARDS

24 YARDS

20 YARDS

32 YARDS

16 YARDS

4 CM

5 CM

6 CM

5)

Scale Factor:

How do you know?

Scale Factor:

How do you know?

Scale Factor:

How do you know?

Scale Factor:

How do you know?

Scale Factor:

How do you know?

30 CM

D E

F

25 CM

20 CM

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See Similar FigureGroup Stations Activity

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Name _______________________________________________________ Period _____ Study Guide

1. You go to Target to buy pencils for math class. 1. _______________ When you get there you find several choices, shown below. Find each unit rate and use that information to determine which is a better deal?

2. Tell whether the following set of ratios is proportional 2. ________________ or non proportional. Show work or explain how you know:

3 12 48 9 4 16 54 12

3. Use cross products to prove that the following 3. No Answer Needed on the line ratios are in proportion:

4 = 6 5 7.5

4. Write and solve a proportion for the following word problem. SHOW ALL WORK!!!

Mrs. Holland bought 10 candy bars for $5.99. 4. ______________ At this same rate, how much would she pay for 28 candy bars? Round to the nearest cent, if necessary.

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Name ________________________________________________________ Period ______________

Attachments

5.2B scale drawings powerpoint.ppt

Lesson Menu

Main Idea and New Vocabulary

Example 1:Use a Map Scale

Example 2:Use a Scale Model

Main Idea/Vocabulary

Solve problems involving scale drawings.

scale drawing

scale model

scale

scale factor

Example 1 CYP

A.21 miles

B.28 miles

C.42 miles

D.56 miles

MAPS The distance on a map has a scale of

0.5 inch = 14 miles. The measured distance between West Palm Beach and Ft. Lauderdale on the map is 1.5 inches. What is the actual distance between these two cities?

Example 2

Use a Scale Model

MURALS An artist is painting a large mural of flowers on the side of a school. If she uses the scale 4 inches = 1 inch, how large will the mural painting of a rose bloom be if it is inches high?

Example 2 CYP

A.40 in.

B.55 in.

C.60 in.

D.80 in.

FURNITURE A full-size model is being created from a child-size rocking chair which has a height of 15 inches. If the scale to be used is

4 inches = 1 inch, what is the height of the model?

SMART Notebook

Page 1: Dec 20-11:14 AMPage 2: Nov 21-8:15 AMPage 3: Nov 21-2:06 PMPage 4: Dec 20-11:10 AMPage 5: Nov 21-11:11 AMPage 6: Nov 21-11:06 AMPage 7: Nov 21-11:45 AMPage 8: Nov 21-2:11 PMPage 9: Nov 21-1:09 PMPage 10: Dec 20-11:14 AMPage 11: Jan 29-10:29 AMPage 12: Jan 29-10:30 AMPage 13: Jan 29-10:30 AMPage 14: Feb 17-9:15 AMPage 15: Dec 20-11:26 AMPage 16: Dec 20-11:14 AMPage 17: Feb 17-9:15 AMPage 18: Jan 4-3:12 PMPage 19: Dec 20-11:25 AMPage 20: Feb 17-9:15 AMPage 21: Nov 26-2:22 PMPage 22: Feb 17-9:15 AMPage 23: Nov 27-2:25 PMPage 24: Jan 4-2:53 PMPage 25: Dec 2-10:06 AMPage 26: Dec 20-11:21 AMPage 27: Dec 20-11:31 AMPage 28: Dec 20-11:40 AMPage 29: Dec 2-10:29 AMPage 30: Feb 17-9:15 AMPage 31: Dec 4-11:42 AMPage 32: Nov 27-2:25 PMPage 33: Feb 5-10:43 AMPage 34: Feb 17-9:15 AMPage 35: Nov 27-2:25 PMPage 36: Jan 4-3:44 PMPage 37: Jan 4-3:44 PMPage 38: Jan 4-3:44 PMPage 39: Jan 12-9:17 AMPage 40: Jan 12-9:17 AMPage 41: Feb 17-9:15 AMPage 42: Nov 27-2:25 PMPage 43: Dec 2-11:51 AMPage 44: Feb 17-9:15 AMPage 45: Nov 27-2:25 PMPage 46: Jan 13-10:51 AMPage 47: Dec 2-12:24 PMPage 48: Dec 2-12:27 PMPage 49: Feb 17-9:15 AMPage 50: Nov 27-2:25 PMPage 51: Jan 13-10:51 AMPage 52: Dec 2-12:27 PMPage 53: Jan 13-10:54 AMPage 54: Dec 2-1:15 PMPage 55: Feb 17-9:15 AMPage 56: Jan 13-11:01 AMPage 57: Jan 13-11:05 AMPage 58: Feb 17-9:15 AMPage 59: Jan 17-11:02 AMPage 60: Jan 17-10:53 AMPage 61: Jan 17-10:53 AMPage 62: Feb 11-11:43 AMPage 63: Jan 17-11:08 AMPage 64: Dec 12-10:11 AMPage 65: Dec 4-1:41 PMPage 66: Feb 17-9:15 AMPage 67: Jan 17-11:26 AMPage 68: Jan 17-10:53 AMPage 69: Jan 19-10:44 AMPage 70: Dec 16-8:41 AMPage 71: Dec 2-5:08 PMPage 72: Feb 5-2:37 PMPage 73: Jan 17-11:21 AMPage 74: Dec 2-12:07 PMAttachments Page 1

Chapter 5 Lesson 51B Rates and Unit Rates · When I study for tests, I practice everything from the...

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Transcript of Chapter 5 Lesson 51B Rates and Unit Rates · When I study for tests, I practice everything from the...