Transcript Must Do's Notes

U2D6
Unit 2 – Day 6
Rearrange a multivariable equation to
highlight a variable.
Make sense of problems and persevere in
solving them.
Attend to precision.
Must Do:
Write an equation and solve.
1. Twelve less than one sixth of a number is the
same as fifteen. What is that number?
2. Rolex Smudgepot owns 17 ounces of gold. This is
one ounce more than two thirds of the amount
he owned last year. How much gold did he own
last year?
3. Gus needs to paint his house, which has a surface area
of x square feet. The brand of paint he buys (at a price
of p dollars a can) comes in cans that cover y square feet
each. Write an equation using variables to show how much
will it cost him to paint his house?
Must Do:
Write an equation and solve.
1. The sum of a number and 9 is multiplied by -2 and
the answer is -8. Find the number.
2. On an algebra test, the highest grade was 42
points higher than the lowest grade. The sum of the
two grades was 138. Find the lowest grade.
3. At the end of the day, a pharmacist counted and found she
has 4/3 as many prescriptions for antibiotics as she did for
tranquilizers. She had 84 prescriptions for the two types of
drugs. How many prescriptions did she have for
tranquilizers?
1.
The sum of a number and 9 is multiplied by -2 and the answer
is -8. Find the number.
2. On an algebra test, the highest grade was 42 points higher than
the lowest grade. The sum of the two grades was 138. Find the
lowest grade.
3. At the end of the day, a pharmacist counted and found she has 4/3
as many prescriptions for antibiotics as she did for tranquilizers. She
had 84 prescriptions for the two types of drugs. How many
prescriptions did she have for tranquilizers?
U2D6
Rearrange (highlight) a variable
• There are a lot of formulas that involve many
different values. It’s nice to be able to change
the formula around to highlight the variable
we’re interested in…
U2D6
For example
• The formula for converting Fahrenheit to
5
Celsius is 𝐶 = (𝐹 − 32)
9
• Solve for 𝑭
• Find 𝐹 when 𝐶 = 36
U2D6
Another Example
• The formula for the circumference of a circle is
𝐶 = 2𝜋𝑟
• Solve for 𝒓.
• Find 𝑟 when 𝐶 = 154 and 𝜋 =
22
7
U2D6
You Try!!!
• Solve 𝑄 =
𝑊𝐿
𝑇
+C for 𝑻.
• Find 𝑇 when 𝑄 = 250, 𝑊 = 125, 𝐶 = 200
and 𝐿 = 20
U2D6
Independent Practice
Finish the worksheet from Friday: “3-6 Practice”
Due today:)
Must Do:
Solve for c.
1. ac - t = x
3. 𝑎𝑐 − 𝑥 = 𝑏𝑐
𝑎
𝑐
2. + t = x
Must Do:
Solve for y.
1. ax – by = c
2.
1
𝑦
2
+
1 𝑦+6
=
4
8
Write an algebraic equation and solve:
3. Half of a number plus 5 is 11. What is the number?
Challenge!
4. A man took a trip in a car. He drove 70miles at a slower speed.
Then, he went the next 300 miles at a speed that was 40 mph faster
than earlier. The time he spent driving at the faster speed was twice
the time spent at the slower speed. Find the two speeds.
1. ax – by = c
2.
1
𝑦
2
+
1 𝑦+6
=
4
8
3. Half of a number plus 5 is 11. What is the
number?
Must Do:
Solve for y.
1. 𝑎 =
𝑦
(𝑏
2
− 𝑐)
2.
𝑎+𝑏
𝑦
=
𝑐
𝑑
Write an algebraic equation and solve:
3. Three consecutive even integers add up to fifty-four.
What are the integers?
Challenge!
4. Gloria’s washing machine is broken. Since her machine is
pretty old, she doesn’t want to spend more than $100 for
repairs. A service call will cost $35 and the labor will be an
additional $20 per hour. There are no other charges. What is
the maximum number of hours that the repair person can
work without the total cost exceeding $100?
Solve for y.
1. 𝑎 =
𝑦
(𝑏
2
− 𝑐)
2.
𝑎+𝑏
𝑦
=
𝑐
𝑑
Write an algebraic equation and solve:
3. Three consecutive even integers add up to fiftyfour. What are the integers?
Unit 2 – Day 7
A little more practice on isolating a variable
Then, a mini Quiz (FA) on solving for a specific
variable.
And then……
U2D7
Do these:
1. Solve 𝑄 = 0.000477𝐸𝐼𝑇 for 𝑻
- Find 𝑇 when 𝑄 = 954, 𝐸 = 1000 and 𝐼 = 20
2. Solve 𝑝 = 𝑎 + 𝑏 + 𝑐 for 𝒄.
- Find 𝑐 when 𝑝 = 100, 𝑎 = 21 and 𝑏 = 17.
U2D7
Now try these:
3. Solve 𝑖 = 𝑝𝑟𝑡 for 𝒓.
- Find 𝑟 when 𝑖 = $80, 𝑝 = $500 and 𝑡 = 2 𝑦𝑒𝑎𝑟𝑠
4. Solve 𝐿 =
𝜋𝑟𝐴
180
for 𝑨.
- Find 𝐴 when 𝐿 = 314, 𝑟 = 60 and 𝜋 = 3.14
Quiz Time!
U2D7
Copy down each problem. Show all your work. Leave answers as improper fractions.
Solve for x.
1
1. 2 12 − 𝑥 = 𝑥 − 10
Write an algebraic equation and solve.
2. On an algebra test, the highest grade was 32 points higher than the lowest grade. The sum
of the two grades was 138. Find the highest grade.
Solve for y.
1
3. 3 𝑥𝑦 + 𝑧 = 𝑎
4. Self-Assess: In complete sentences, describe how you think you did on this formative.
What did you do to do well, or what could you do different to do better in the future?
U2D7
Next Up:
Inequalities!!!
Standards Addressed:
 Solve inequalities using algebraic manipulation
 Solve inequalities arising from a context
 Make sense of problems and persevere in solving them
 Model with mathematics
Must do:
Review: Tell whether each statement is true, false, or
unable to tell.
1. 43 − 6 3 − 8 ≥ 3 2 − 3 + 26
2.
1 2
3
−
3. 5𝑥 ≤ 3
3
4
<
1 7
2 8
−
1
9
U2D7
Inequalities!
• Vocab: An Inequality is a comparison of two
values that may or may not be equal.
U2D7
Inequalities!
Symbol
Meaning
a>b
a is greater than b
a≥b
a is greater than or equal to b
a<b
a is less than b
a≤b
a is less than or equal to b
Hand out properties ws
U2D7
Properties of Inequalities
What does it all mean!?
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We can solve inequalities the same way we solve equations, but
we need to be careful about a couple things…
Examples!
Solve each inequality and graph on a number line.
1. x  5
2. 2  x
3. x  2  1
4. 12  3x
U2D7
You Try!
Solve each inequality and graph on a number line
1. 3x  9
2. 3  2 x 1
U2D7
Here comes the tricky part…
• Multiplying or dividing by negative numbers
does funky stuff to our inequality sign.
• Complete Questions 1-4 of your handout.
• After you have answered questions 1-4,
discuss with your table what you found for
question 4.
Do Consider 4>1
U2D7
Solve each Inequality and graph the solution
1.
y
6
4
2.  21  1.4 p
x  2.5
3. 7 
 1.5
4.
 5(3  2 x)  5
U2D7
You Try!!
Solve each inequality and graph the solution
1.  4 y  7  5 y  2
y
2.
 5  19
2
3.
3
x 1  4
5
U2D7
Independent Practice
U2D7 – ICP
Due at the end of the period:)
Unit 2 – Day 8
Model with mathematics
Formulate a model by creating a
representation that accurately describes
relationships between variables
Quick Check
• Solve each inequality and then graph the
solution.
•
3𝑥 ≤ 21
•
6 − 2𝑦 > 26
•
𝑤
−5
<4
U2D8
Today we will practice writing inequalities given
a context.
• Define a variable and write an inequality to
represent each situation:
– The temperature outside today will be no warmer
than 65 degrees.
U2D8
Define a variable and write an inequality to
represent the situation:
• Example
– My bank account balance is at least $3.
U2D8
Define a variable and write an inequality to
represent the situation
• Example
• There are between 12 and 28 people on the bus.
U2D8
You Try!
• You have a maximum of $6 in change in your
couch.
U2D8
You Try!!
• The temperature tonight should warmer than
32 degrees.
U2D8
Write an inequality and solve!
• Examples
– A number decreased by ten is no more than −5
– A number increased by 4 is at least −9
U2D8
You Try!
• Write and inequality to represent the
situation. Then solve it.
– A number decreased by 1 is less than −10
– A number increased by 2 is at most 6
U2D7
Independent Practice
U2D8 - ICP
U2D9
Unit 2 – Day 9
Learning Targets
Solve inequalities arising from a context.
Solve inequalities using algebraic
manipulation.
U2D9
Write an inequality and solve
• Yellow Cab charges a $1.75 flat fee and a rate
of $0.65 per mile. Katie has only $10 to spend
on her fare. How far can Katie afford to go?
U2D9
Write an inequality and solve
• You want to go on a road trip to Lagoon in
Utah. Woohoo! The car you are taking gets 30
miles per gallon and the trip is 325 miles, one
way. What is the minimum number of gallons
of gas you need to buy to make the whole
trip?
U2D9
Write an inequality and solve
• Ike’s age is three years more than twice his
younger brother’s age. The sum of their ages
is no more than 18.
– What is the maximum age that Ike’s brother could
be?
U2D9
You Try!
• Write an inequality and solve
– You have $5.75 to spend on skittles. Taste the
rainbow!!! If one giant bag of skittles costs $1.15,
what is the maximum number of bags you can
buy?
U2D9
You Try!
• Write an inequality and solve
– There are 40 children and 12 adults going on a trip
to New York City by car. Each car can hold a
maximum of 5 people. What is the least number
of cars needed for the trip?
U2D9
Independent Practice
U2D9 – ICP
Remember, Inequalities Summative tomorrow!
I will post the answers to the review tonight so you
can check your answers. However, you will get an
NP on the review worksheet if all I see are answers
and no work.