Transcript Document

Materials
Reminders
Get out your agenda if you see
your name below. I would like
to have you in my FLEX
Wednesday.
Period 2
Period 7
Draw the following relationships on
separate graphs.
1. Non-linear relationship
2. Proportional linear relationship
3. Non-proportional linear relationship
4-5 Solving Proportions
How do I use proportions to solve
problems?
Important
Vocabulary
Equivalent ratio – any ratios that simplify to the
same ratio
Proportion – an equation showing two ratios or
rates are equal
Example:
10 𝑚𝑖𝑙𝑒𝑠 20 𝑚𝑖𝑙𝑒𝑠
=
1 ℎ𝑜𝑢𝑟
2 ℎ𝑜𝑢𝑟𝑠
Important
Vocabulary
Cross products – the cross products of any
proportion are equal
Example:
3
6
=
5 10
3(10) = 5(6)
30 = 30
Important
Vocabulary
Constant of Proportionality – a constant that
shows the relationship between two proportional
quantities
Example:
𝑎 = 2𝑏
2 is the constant of proportionality
Questions:
How do I solve
a proportion?
Notes:
Steps
1. Set the two equivalent ratios equal to each other so
that the numerators correspond and the denominators
correspond
2. Find the cross products
3. Solve for the variable
Example:
5
7
=
6 𝑥
5𝑥 = 6 7
5𝑥 = 42
𝑥=
42
5
𝑥 = 8.4
Concept Check
1. Get into groups of 2 and get one WHITE
BOARD and a DE marker
2. Teach each other how you would set up a
proportion for the following scenario AND
how you would solve the proportion for the
variable.
• For every 10 shrimp caught there are
always 3 minnows. If Bubba caught 379
shrimp , how many minnows did he catch?
• Bubba earns $0.20 for 2 shrimp. If he sold
372 shrimp, how much money would he
make?
3.
Be prepared to share with the class.
Questions:
How do I write
and use an
equation?
Notes:
Steps
1. Set up a proportion with numbers on one side and
equals variables on the other side
2. Solve the equation for whichever variable you want
using cross products
Example:
Frodo bought 5 mushrooms for 25 silver coins. Write an
equation that relates cost, c, and the number of
mushrooms, m, he bought.
5 𝑚𝑢𝑠ℎ𝑟𝑜𝑜𝑚𝑠
𝑚
=
25 𝑠𝑖𝑙𝑣𝑒𝑟 𝑐𝑜𝑖𝑛𝑠
𝑐
5𝑐 = 25𝑚
𝑐 = 5𝑚
Questions:
How do I write
and use an
equation?
Notes:
Steps
1. Find the proportionality constant that relates two
variables
2. Write an equation using the constant in a form that
would be useful for answering the question
Example:
Frodo bought 5 mushrooms for 25 silver coins. Write an
equation that relates cost, c, and the number of
mushrooms, m, he bought.
Find the Proportionality Constant
25 𝑐𝑜𝑖𝑛𝑠
5 𝑐𝑜𝑖𝑛𝑠
=
5 𝑚𝑢𝑠ℎ𝑟𝑜𝑜𝑚𝑠 1 𝑚𝑢𝑠ℎ𝑟𝑜𝑜𝑚
=5
Write the equation
𝑐𝑜𝑠𝑡 = 5 × # 𝑜𝑓 𝑚𝑢𝑠ℎ𝑟𝑜𝑜𝑚𝑠
𝑐 = 5𝑚
Concept Check
1. Get into groups of 2 and get one WHITE
BOARD and a DE marker
2. Teach each other how you would write an
equation for the following situations.
• For every 20 miles Samwise walks he loses
2 pounds. Write an equation that relates the
number of pounds lost to the number of
miles walked.
• For every 10 arrows Legolas shoots at the
orcs, 9 killed an orc. Write an equation that
relates the number of arrows shot to the
number orcs killed.
3.
Be prepared to share with the class.
Homework
Page 212-214; 1-17 and
33-35
AND Cornell Notes
Summary