how can you show that two objects are...

HOW can you show that two objects are proportional?

Course 2, Lesson 1-1

7th Quick Check page 6

•  1. 2/15 •  2. 45/1 •  3. 1/51 •  4. Yes, 4/1 •  5. 1/2

Course 3, Lesson 5-‐1 Common Core State Standards © Copyright 2010. NaFonal Governors AssociaFon Center for Best PracFces and Council of Chief State School Officers. All rights reserved.

•  MAFS.7.RP.1.2 Recognize and represent proportional relationships between quantities.

•  MAFS.7.RP.1.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Mathematical Practices MP1 Make sense of problems and persevere in solving them. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. Course 2, Lesson 1-1

Mathematics Florida Standards – Mathematics, numbering and wording from www.cpalms.org.

To •  find a unit rate • determine the lowest price


•  rate

•  unit rate


Explain how to find a unit rate.


• What does it mean to be proportional?

• What does it mean to be non-proportional?


Proportional?

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ProporFonal?

Propor%on in art. Golden rectangle in art.

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hPp://www.wingsdailynews.com/wp-‐content/uploads/2015/04/mona-‐lisa-‐golden-‐raFo.png

ProporFonal PaPerns

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ARE THERE OTHER TERMS FOR THIS?

Looking at the definition on page 34, we see that two quantities must have a constant ratio or unit rate.

All rights reserved.

Equivalent FracFons

Equivalent raFos

Constant unit rate ProporFonal

Is the relationship proportional?

Example 1

Example 2

Answers

Since the raFos are the same, the total cost is proporFonal to the number of CDs purchased.

Since the raFos are not the same, the total cost is nonproporFonal to the number of hours rented with shoes.

Think, Pair, Share

Now do problem 3b at the boPom of page 35.

In the blank next to each exercise number, write whether the columns are propor%onal or

nonpropor%onal.

Column A Column B 1. _________________ 100 T-shirts printed for

$428.00

3,000 T-shirts printed for

$12,180.00 2. _________________ 3 compact discs for

$23.34 10,000 compact discs for

$32,900.00 3. _________________

8 books for $43.20 250 books for $1,350.00

4. _________________ $546.00 earned in 42 hours

$31,200.00 earned in 2,400 hours

5. _________________

36 photos printed for $7.20


6. _________________

1 bus token for $1.75 20 bus tokens for $34.00

In the blank next to each exercise number, write whether the columns are propor%onal or

nonpropor%onal.

Column A Column B 1. non-porportional 100 T-shirts printed for

$428.00 3,000 T-shirts printed for$12,180.00

2. non-porportional 3 compact discs for $23.34

10,000 compact discs for$32,900.00

3. porportional 8 books for $43.20

250 books for $1,350.00

4. porportional $546.00 earned in 42 hours

$31,200.00 earned in 2,400 hours

5. non-porportional 36 photos printed for $7.20


6. non-porportional 1 bus token for $1.75 20 bus tokens for $34.00

Wrap-Up

Explain what makes two quantities proportional.


Essential Question

How does graphing relationships help you determine whether the

relationship is proportional or not?

How can we tell on a graph if 2 quantities are proportional?

How can we tell on a graph if 2 quantities are proportional?

It’s a straight line

Passes through the origin (0,0)

hPps://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Geom_lines_axiom_2.png/300px-‐Geom_lines_axiom_2.png hPp://www.proprofs.com/sat/study-‐guide/Topic3/geometryM5_S3/_images/course/M5L1S16_1.jpg

Turn to page 48

•  Let’s do #1 together. Is it proportional?


Turn to page 48

•  Let’s do #1 together. Is it proportional? – Yes, the cost is proportional and the graph

forms a straight line through the origin. •  Analyze #2, which is proportional?

Turn to page 48

•  Let’s do #1 together. Is it proportional? – Yes, the cost is proportional and the graph

forms a straight line through the origin. •  Analyze #2, which is proportional?

– The Book Palace because it is a straight line through the origin.

Is there another way we could have determined if the

quantities were proportional?

Wrap-Up

How can you determine whether the relationship between quantities

are proportional or not?

Essential Question

How do you solve a proportion?


What is a proporFon?

•  It is an equaFon staFng that two raFos or rates are equivalent. (see page 56)

•  The cross products of any proporFon are equal.

•  hPps://www.youtube.com/watch?v=fDty_2CjYhE

Think, Pair, Share Why do you think cross

multiplying with proportions works mathematically?

Let’s pracFceJ

•  Go to page 58. •  Let’s work #1 together. K= ?


Let’s practiceJ

•  Go to page 58. •  Let’s work #1 together. K= 4

•  Now, work #2 & 3.

Let’s practiceJ

•  Go to page 58. •  Let’s work #1 together. K= 4

•  Now, work #2 & 3. 2.  n = 12.8 3.  x = 16.4

Looking back…

Remember – some ratios are written part compared to part part compared to whole

See example #2 on page 57. Now work 2d on page 57

How many are in 7th grade?

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Looking back…

Now work 2d on page 57

How many are in 7th grade? 85 Set up like 17 = x 17+23 200 (This is a part to whole scenario.)

hPp://images.clipartpanda.com/clipart-‐eyes-‐Anime-‐Eyes-‐Clip-‐Art.jpg

Essential Question

How do you solve a proportion?


Essential Question

How do use unit rate to write an equation?


To write an equation using unit rate:

1.  Find the unit rate. 2.  Write in the format y=kx

where k is the unit rate. See examples 3 & 4 on pages 57 & 58. Now, let’s work #4 together on page 58.

Work problems 6, 7, and 8 on page 59.

Work problems 6, 7, and 8 on page 59. 6.   d=34g ; 17 gallons 7.   c=0.50p ; $4.00 8.   h=4w ; 74in. >>>What do the numbers in blue represent?

Inquiry Lab

Complete the Inquiry Lab on page 63-‐64 with your face partner. How is a unit rate related to rate of change?

Key Ideas

•  Rate of change is a rate that describes how one quanFty changes in relaFon to another.

•  Linear relaFonships have a constant rate of change.

•  In linear relaFonships, the rate of change between any two quanFFes is the same.

What is proporFonal?

•  hPps://www.youtube.com/watch?v=HwJPkXOboBk

ProporFonal RelaFonships

1. • Have a constant raFo or • Constant rate

2. • Line graph • Passes through the origin

3. • One step equaFon • Example: y=0.3x or y=1/2x

Wrap-‐up

How is a unit rate related to rate of change?

how can you show that two objects are...

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