Download Slide 1 - Sage Middle School

Vocabulary from Quiz 1
• Define:
• Whole Numbers:
Whole numbers are the numbers beginning with
zero and moving to the right . They do not
include negative numbers. They are not
fractions.
• Fractions :
• The comparison of a part to a whole.
Vocabulary
• Complex Fractions
A fraction in which either the numerator,
denominator, or both contain fractions.
• Improper Fractions
A fraction in which the numerator is greater
than the denominator.
• Mixed Numbers
A mixed number is a whole number and a
fraction expressed together.
Solve
Study the next page to solve
4
3 /8 =
Convert 16/4 to a whole number
Convert 7 ½ to an improper fraction
Convert 32/5 to a mixed number
Divide 6/8
2/5
Traditional approach
• 4 bags of soil divided by 3/8 or the amount
needed to complete one garden.
•
•
•
•
•
Step 1:
4
3/8 =
Step 2
4 X 8/3 = 32/3
Step 3 divide 3 into 32 = 9 5/3 gardens.
Improper Fraction
• A fraction in which the numerator is greater
than the denominator.
16
4
Hint: 16/4 is equal to 4 wholes. The different
ways to express fractions are representing the
same amounts in different forms.
• Jill ordered 3 bags of soil for her raised flower
gardens. Each garden needs two thirds (2/3)
of a bag of soil. How many gardens can she fill
completely with soil?
•
•
•
•
Directions:
Build a model
Build a ratio table
Use the standard algorithm (invert and
multiply)
• Does the algorithm give the answer in terms
of soil or gardens?
Story problem
• Jill ordered 3 bags of soil for her raised flower
gardens. Each garden needs 2/3 of a bag of
soil. How many gardens can she fill completely
with soil?
½ of a
bag of
garden
2/3 of a
bag of
soil
Questions
• How do we divide by soil and end up
answering in gardens using the traditional
approach?
When we invert the fraction we are talking in
terms of gardens instead of in terms of soil.
• Why do we invert and multiply in the standard
algorithm?
We invert and multiply so that we can get an
answer in terms of what we want to know. It is
related to the above question.
To get you started
• Ratio Table
Garden
Soil
1
2/3
Practice Problems continued
Solve using the traditional method
5
6/8 =
2
7/3 =
8
6/8 =
7
3/6 =
14 2/3
1 6/3 =
Vocabulary from Quiz 2
Define
Coordinate Plane:
a plane formed by the intersection of a horizontal
number line with a vertical number line.
Ratio :
The comparison of one quantity to another. 3
lemons:4 apples
The horizontal axis is the X
axis.
The vertical axis is the
Y
axis.
Please put the x coordinate which is 3 and the y
coordinate which is 4 in parentheses
(3 , 4 )
Pizza Party
• You decide to have a Pizza Party to celebrate the
end of the trimester. You invite all of your friends
and receive conformation that 60 of them will be
attending your party. When you call the pizza
joint they tell you that one large pizza with two
toppings of your choice will cost $12.00 including
tax. There are 15 pieces of pizza in each pizza.
Each person eats an average of 5 pieces of pizza.
Directions
What is the ratio of people to pieces of pizza?
The ratio of people is 3:1. The reason is that if 3 people each eat 5 pieces of pizza then
that totals one pizza.
How many total pieces of pizza will you need to buy?
If one pizza feeds 3 people and 60 people are coming than divide 60 by three which is
20. You need 20 pizzas and there are 15 slices in each pizza therefore 15 and 20 is
300 slices of pizza.
How many total pizzas will you need to buy?
If one pizza feeds 3 people and 60 people are coming than divide 60 by three which is
20 pizzas.
How much is the total bill going to be?
If one pizza costs $12.00 and you need 20 pizzas then 20 times 12 is $240
What is the cost per person?
If 60 people are coming then take the total cost of $240.00 and divide that by 60. The
cost per person is $4.00
Build a ratio table that shows pizza, person/people and, cost all
the way from one person to 60 people.
Pizzas
1/3
2/3
1
People
1
2
3
Cost
Slices
$4.00
5
$8.00
10
10
30
20
60
$12.00 $120.00 $240.00
15
150
300
Build a Graph
People
• Using pizza has your x coordinate and people
as your y coordinate construct a graph
representing the line graph moving in only
whole pizzas. Hint: Use your ratio table to find
the information.
Pizzas
60
(20,60)
People
30
(10,30)
3
0
(1,3)
0 1
10
20
Pizza
The X and Y coordinates come right off of the ratio table to for a
linear line graph.