5 Minute Check
Simplify. Complete on the back of your
homework. (1st and last name on homework)
6
1. 16
45
2. 63
90
3. 120
6
4. 24
5 Minute Check
Simplify. Complete on the back of your
homework.
6
3∙2
3
1. 16
2∙ 2∙ 2∙ 2
8
=
=
5 Minute Check
Simplify. Complete on the back of your
homework.
45
2. 63
5 Minute Check
Simplify. Complete on the back of your
homework.
45
3∙3∙5
5
2. 63
3∙ 3∙ 7
7
=
=
5 Minute Check
Simplify. Complete on the back of your
homework.
90
3. 120
5 Minute Check
Simplify. Complete on the back of your
homework.
90
2∙3∙3∙5
3
3. 120
2∙ 2∙ 2∙3∙5
4
=
=
5 Minute Check
Simplify. Complete on the back of your
homework.
6
4. 24
5 Minute Check
Simplify. Complete on the back of your
homework.
6
2∙3
1
4. 24
2∙ 2∙ 2∙3
4
=
=
Inquiry Lab
Open your book to page 27
Inquiry Lab
Inquiry Lab
Inquiry Lab
Inquiry Lab
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Inquiry Lab
Inquiry Lab
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Inquiry Lab
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Inquiry Lab
Inquiry Lab
Inquiry Lab
Inquiry Lab
Inquiry Lab
Inquiry Lab
Inquiry Lab
Work with a partner to complete questions #16 on page 29 and 30. You have 15 minutes.
Inquiry Lab
Inquiry Lab
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Inquiry Lab
Inquiry Lab
Tuesday, Aug 26
Lesson 6.1.3
Rates
Rates
Objective: To understand and determine unit
rates.
Rates
A rate is a ratio (fraction) comparing
quantities of different kinds of units.
Example s
15 dollars
3 pounds
40 miles
4 hours
120 students
3 buses
Rates
A unit rate is a rate with a denominator of 1
when the rate is written as a fraction.
Examples5 dollars
1 pound
10 miles
1 hour
40 students
1 bus
Rates
Samantha picked 45 oranges in 5 minutes.
How many oranges did she pick per minute
(unit rate).
How to find a unit rate.
Step 1 – Find the rate (fraction).
Rates
Samantha picked 45 oranges in 5 minutes.
How many oranges did she pick per minute
(unit rate).
Step 1 – Find the rate (fraction).
45 oranges
5 minutes
Write this down with units
Rates
Samantha picked 45 oranges in 5 minutes.
How many oranges did she pick per minute
(unit rate).
Step 2 – Simplify.
45 oranges
5 minutes
Rates
Samantha picked 45 oranges in 5 minutes.
How many oranges did she pick per minute
(unit rate).
Step 2 – Simplify.
45 oranges
5 minutes
=
9 oranges
1minute
Rates
Samantha picked 45 oranges in 5 minutes. How
many oranges did she pick per minute (unit rate).
Step 3 – Divide the fraction by the number in the
denominator, if needed.
9 oranges
1 minute
What does this mean?
Rates
Samantha picked 45 oranges in 5 minutes. How
many oranges did she pick per minute (unit rate).
Step 3 – Divide the fraction by the number in the
denominator, if needed.
9 oranges
1 minute
Samantha picked 9 oranges per minute.
Step 3 reminder –
3
3÷7=
7
Rates
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
Step 1?
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
Step 1?
24 dollars
4 plants
How do we know to put the “plant” unit in the
denominator?
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
Step 1?
24 dollars
4 plants
Because we are looking for the “price per
plant”.
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
Step 2?
24 dollars
4 plants
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
Step 3 - ?
24 dollars
4 plants
=
6 dollars
1 plant
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
6 dollars
1 plant
What does this mean?
Rates
Four potted plants cost $24. What is the
price per plant (unit price)?
6 dollars
1 plant
6 dollars per plant.
Rates
David earned $28 last night working 4 hours.
How much did he earn per hour?
Do this on your own.
Rates
David earned $28 last night working 4 hours.
How much did he earn per hour?
28 dollars
4 hours
=
7 dollars
1 hours
What does this mean?
Rates
David earned $28 last night working 4 hours.
How much did he earn per hour?
7 dollars
1 hours
David earned 7 dollars per hour.
Rates
You walked 15 miles in 2 hours last night.
How many miles per hour did you walk?
Do this on your own.
Rates
You walked 15 miles in 2 hours last night.
How many miles per hour did you walk?
15 miles ÷ 2 7.5 miles
2 hours ÷ 2 = 1 hours
You walked 7.5 miles per hour.
Rates
Tom sold 12 books for $9. How much did he
make per book?
Do this on your own.
Rates
Tom sold 12 books for $9. How much did he
make per book?
9 dollars
12 books
=
3 dollars ÷ 4
4 book ÷ 4
What does this mean?
=
dollars
1 book
3
4
Rates
Tom sold 12 books for $9. How much did he
make per book?
9 dollars
12 books
=
3 dollars ÷ 4
4 book ÷ 4
=
He made 3/4 dollars per book,
75 cents per book.
dollars
1 book
3
4
Rates
The Australian dragonfly can travel 18 miles
in 30 minutes. How far can it travel in 1
minute?
Do this on your own.
Rates
The Australian dragonfly can travel 18 miles
in 30 minutes. How far can it travel in 1
minute?
18 miles
30 minute
3
5
=
3 miles ÷ 5
5 minute ÷ 5
miles per minute
=
3
5
miles
1 minute
Write the unit rate.
34 miles in 2 hours.
Rates
Write the unit rate.
34 miles
2 hours
=
Rates
17 miles
1hour
Or 17 miles per hour
Rates
Anna downloaded 35 songs in 5 minutes.
How many songs does she download per
minute?
Do this on your own.
Rates
Anna downloaded 35 songs in 5 minutes.
How many songs does she download per
minute?
35 songs ÷ 5
5 minutes ÷ 5
=
7 songs
1 minute
How many songs can she download in 8
minutes?
Rates
Anna downloaded 35 songs in 5 minutes.
How many songs does she download per
minute?
How many songs can she download in 8
minutes?
7 songs x 8 minutes
1 minute x 8 minutes
=
56 songs
8 minutes
Rates
Molly shot 20 baskets in 4 minutes. Nino shot
42 baskets in 6 minutes. Who shot the most
baskets per minute?
(Do this on your own)
Rates
Molly shot 20 baskets in 4 minutes. Nino shot 42
baskets in 6 minutes. Who shot the most baskets
per minute?
Molly
Nino
20 baskets ÷ 4
4 minutes ÷ 4
42 baskets ÷ 6
6 minutes ÷ 6
5 baskets
1 minute
7 baskets
1 minute
5 baskets per minute
7 baskets per minute
Rates
Marcella divided 40.8 gallons of paint among 8
containers. How much paint is in each
container?
(Do this on your own)
Rates
Marcella divided 40.8 gallons of paint among 8
containers. How much paint is in each
container?
40.8 gallons ÷ 8
8 containers ÷ 8 =
5.1 gallons
1 container
5.1 gallons per container
Rates
Julia wrote the rate $108 in 6 weeks as a unit
rate. Find her mistake and correct it.
Rates
Julia wrote the rate $108 in 6 weeks as a unit
rate. Find her mistake and correct it.
A unit rate has a denominator of 1.
$108
6 𝑤𝑒𝑒𝑘𝑠
$18
= 1 𝑤𝑒𝑒𝑘
Rates
The ratio of red jelly beans to yellow jelly
beans in a dish is 3:4. If Greg eats 3 red jelly
beans and 6 yellow one, the ratio is 4:5. How
many yellow jelly beans were originally in the
dish?
Rates
As, the ratio of red jelly beans to yellow jelly beans in a dish
is 3:4. If Greg eats 3 red jelly beans and 6 yellow one, the
ratio is 4:5. How many yellow jelly beans were originally in
the dish?
3 𝑟𝑒𝑑
4 𝑦𝑒𝑙𝑙𝑜𝑤
= =
6
8
9
12
=
12
16
=
15
20
=
18
24
=
21
28
=
24
32
=
27
36
= ……
30
40
Rates
As, the ratio of red jelly beans to yellow jelly beans in a dish
is 3:4. If Greg eats 3 red jelly beans and 6 yellow one, the
ratio is 4:5. How many yellow jelly beans were originally in
the dish?
3 𝑟𝑒𝑑
4 𝑦𝑒𝑙𝑙𝑜𝑤
= =
6
8
9
12
=
12
16
=
9
10
=
15
20
=
12
14
=
18
24
=
15
18
=
If he ate 3 red and 6 yellow,
0 𝑟𝑒𝑑
−2 𝑦𝑒𝑙𝑙𝑜𝑤
= = =
3
2
6
6
21
28
18
22
=
24
32
=
21
28
=
27
36
= ……
=
24
32
= …
30
40
27
36
Rates
As, the ratio of red jelly beans to yellow jelly beans in a dish
is 3:4. If Greg eats 3 red jelly beans and 6 yellow one, the
ratio is 4:5. How many yellow jelly beans were originally in
the dish?
0 𝑟𝑒𝑑
−2 𝑦𝑒𝑙𝑙𝑜𝑤
= = =
3
2
6
6
9
10
=
12
14
=
Do any of these simplify to 45 ?
15
18
=
18
22
=
21
26
=
24
30
= …
27
34
Rates
As, the ratio of red jelly beans to yellow jelly beans in a dish
is 3:4. If Greg eats 3 red jelly beans and 6 yellow one, the
ratio is 4:5. How many yellow jelly beans were originally in
the dish?
0 𝑟𝑒𝑑
−2 𝑦𝑒𝑙𝑙𝑜𝑤
= = =
3
2
6
6
9
10
=
12
14
=
15
18
=
18
22
=
21
26
=
24
30
= …
27
34
Do any of these simplify to 45 ?
0 𝑟𝑒𝑑
−2 𝑦𝑒𝑙𝑙𝑜𝑤
9
9
𝟒
3
= 32 = 1 = 10
= 67 = 56 = 11
= 21
=
=
…
26
𝟓
4
Rates
As, the ratio of red jelly beans to yellow jelly beans in a dish
is 3:4. If Greg eats 3 red jelly beans and 6 yellow one, the
ratio is 4:5. How many yellow jelly beans were originally in
the dish?
0 𝑟𝑒𝑑
−2 𝑦𝑒𝑙𝑙𝑜𝑤
= = =
3
2
6
6
9
10
=
12
14
=
15
18
=
18
22
=
21
26
=
24
30
= …
27
34
𝑟𝑒𝑑
There were 3024𝑦𝑒𝑙𝑙𝑜𝑤
after he ate the beans
0 𝑟𝑒𝑑
−2 𝑦𝑒𝑙𝑙𝑜𝑤
= =1=
3
2
9
10
= = =
6
7
5
6
9
11
=
21
26
= = …
𝟒
𝟓
3
4
Rates
As, the ratio of red jelly beans to yellow jelly beans in a dish
is 3:4. If Greg eats 3 red jelly beans and 6 yellow one, the
ratio is 4:5. How many yellow jelly beans were originally in
the dish?
Which means there were
24 𝑟𝑒𝑑+3 𝑟𝑒𝑑
30 𝑦𝑒𝑙𝑙𝑜𝑤+6 𝑦𝑒𝑙𝑙𝑜𝑤
before he ate the beans, or
27 𝑟𝑒𝑑
36 𝑦𝑒𝑙𝑙𝑜𝑤
Rates
What is the difference between a ratio and a
rate?
Rates
What is the difference between a ratio and a
rate?
A ratio generally does not have a unit (or if it
does, they are the same) and a rate has
different units.
For example,
Rates
Sarah has five chocolate bars, and she can
eat all of them in one minute. Joan has ten
chocolate bars, and she can eat all of them in
one minute.”
Rates
The rate by which Sarah eats her chocolate
bars is 5 bars/ 1minute; Joan’s rate is 10
bars/1 minute. The ratio between Sarah’s
chocolate bars to Joan’s is 5:10 or 1:2.
Rate
5 bars/ minute
Ratio
1:2
Rate
Agenda Notes
Homework –
Lesson 6.1.3 Homework Practice
Due Wednesday, Aug 27
Mid-Chapter Quiz
Friday, Aug 29