Transcript Final Exam II, PPT Review

Final Exam Review:
Part II (Chapters 9+)
5th Grade Advanced Math
First topic!
Chapter 9
Integers
Definition
 Positive
integer – a number
greater than zero.
0 1 2 3 4 5 6
Definition
 Negative
number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Place the following integers
in order from least to
greatest:
297
-56
39
-125
78
0
Place the following integers
in order from least to
greatest:
297
-125
-56
-56
39
0
-125
39
78
78
0
297
Definition
 Absolute
Value – The distance a
number is from zero on the
number line
The absolute value of
9 or of –9 is 9.
Hint
 If
you don’t see a negative
or positive sign in front of a
number, it is ALWAYS
positive.
+9
Integer Addition Rules

Rule #1 – When adding two integers
with the same sign, ADD the numbers
and keep the sign.
9 + 5 = 14
-9 + -5 = -14
Solve the Following
Problems:
 -3 + -5 =
4 + 7 =
 (+3) + (+4) =
 -6 + -7 =
5 + 9 =
 -9 + -9 =
Check Your Answers:
 -3
+ -5 =
-8
+11
4 + 7 =
 (+3) + (+4) = +7
-13
 -6 + -7 =
14
5 + 9 =
-18
 -9 + -9 =
Solve the following:
1.
2.
3.
4.
8 + 13 =
–22 + -11 =
55 + 17 =
–14 + -35 =
Check Your Answers
1.
2.
3.
4.
8 + 13 =
–22 + -11 =
55 + 17 =
–14 + -35 =
+21
-33
+72
-49
Integer Addition Rules

Rule #2 – When adding two integers
with different signs, find the difference
(SUBTRACT) and take the sign of the
larger number.
-9 + +5 =
9 - 5 = 4 Answer = - 4
Larger absolute value:
Solve These Problems
+ -5 = 5 – 3 = 2 -2
 -4 + 7 = 7 – 4 = 3 +3
 (+3) + (-4) =
4 – 3 = 1 -1
7 – 6 = 1 +1
 -6 + 7 =
 5 + -9 = 9 – 5 = 4
-4
0
9–9=0
 -9 + 9 =
3
Solve the following:
1.
2.
3.
4.
–12 + 22 =
–20 + 5 =
14 + (-7) =
–70 + 15 =
Check Your Answers
1.
2.
3.
4.
–12 + 22 =
–20 + 5 =
14 + (-7) =
–70 + 15 =
+10
-15
+7
-55
Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive one.
Change the sign and add.
“Keep, change, change.”
is the same as
2 – (-7)
2 + (+7)
2 + 7 = 9
Here are some more examples.
12 – (-8)
-3 – (-11)
12 + (+8)
-3 + (+11)
12 + 8 = 20
-3 + 11 = 8
Solve the following:
1. 8 – (-12) =
2. 22 – (-30) =
3. – 17 – (-3) =
4. –52 – 5 =
Check Your Answers
1. 8 – (-12) = 8 + 12 =
+20
2. 22 – (-30) = 22 + 30 = +52
3. – 17 – (-3) = -17 + 3 =
-14
4. –52 – 5 = -52 + (-5) =
-57
Integer Multiplication
Rules

Rule #1
When multiplying two integers with the same sign,
the product is always positive.

Rule #2
When multiplying two integers with different signs,
the product is always negative.

Rule #3
If the number of negative signs is even,
the product is always positive.

Rule #4
If the number of negative signs is odd,
the product is always negative.
Solve the following:
1. +8 x (-12) =
2. -20 x +30 =
3. – 17 x (-3) =
4. +50 x +5 =
Check Your Answers:
1. +8 x (-12) = -96
2. -20 x +30 = -600
3. – 17 x (-3) = +51
4. +50 x +5 = +250
Integer Division Rules

Rule #1
When dividing two integers with the same sign,
the quotient is always positive.

Rule #2
When dividing two integers with different signs,
the quotient is always negative.
Solve the following:
1. (-36) ÷ 4 =
2. 200 ÷ -5 =
3. – 18 ÷ (-9) =
4. +50 ÷ +5 =
Check Your Work:
1. (-36) ÷ 4 = -9
2. 200 ÷ -5 = -40
3. – 18 ÷ (-9) = +2
4. +50 ÷ +5 = +10
Evaluate the following:
1. -45 + 10
3² - 2
2. 7 + -4(9 – 4) =
3. -50 ÷ 5² + (3 - 6) =
Check Your Work:
1. -45 + 10
3² - 2
-35 = -5
7
2. 7 + -4(9 – 4) =
3. -50 ÷ 5² + (3 - 7) =
-13
-6
Evaluate the following if n = -2 :
1. -5 (2n – 2)²
2. -48
n-6
Check Your Work:
1. -5 (2n – 2)²
2. -48
n-6
-180
6
Next chapter…
Chapter 11
Expressions & Equations
Write an algebraic expression for the
following. Tell what the variable
represents.
Ben has 12 pencils. He lost 3
and bought some more.
Write an algebraic expression for the
following. Tell what the variable
represents.
Ben has 12 pencils. He lost 3
and bought some more.
12 – 3 + p
(p = pencils that Ben bought)
Write each algebraic expression in words
s - 47
Write each algebraic expression in
words
s - 47
47 less than some number
Write each algebraic equation in
words
½ n = 16
Write each algebraic equation in
words
½ n = 16
one half of some number is 16
Evaluate the following
algebraic expressions for the
given value of the variable:
(n = 11)
(n + 25)
9
Evaluate the following
algebraic expressions for the
given value of the variable:
(n = 11)
(n + 25)
9
4
Simplify the following expressions
(combine like terms). Then evaluate
the expression for the given value of
the variable: (if a = 3)
3a + 10 - a
Simplify the following expressions (combine like
terms). Then evaluate the expression for the
given value of the variable: (if a = 3)
3a + 10 - a
2a + 10
2(3) + 10
16
Write an algebraic equation for the
following and evaluate. Tell what
the variable represents.
Sam had fish in his fish tank. 6 of
them died. There were 12 left
swimming in the tank.
How many fish did Sam have
originally?
Sam had fish in his fish tank. 6 of them
died. There were 12 left swimming in
the tank.
How many fish did Sam have originally?
f – 6 = 12
f = 18
f is the number of fish Sam had
originally in his tank.
Evaluate the following algebraic
equations.
Show your work.
30 = 5y
8 = x ÷ 9
t - 12 = 23
¼n = 7
3 = 18 + s
y ÷ 6 = 7
Evaluate the following algebraic
equations.
Show your work.
30 = 5y 6
8 = x ÷ 9 72
t - 12 = 23 35
¼n = 7 28
3 = 18 + s -15
y ÷ 6 = 7 42
For word problem practice,
review textbook pages
331, 340 and 341.
Next topic…
Chapter 12:
Patterns
Guess What’s Next
A. What is the Rule?
B. What are the next 3 numbers in the
sequence?
44
36
28
_______
_______ _______
20
30
45
_______
_______ _______
A. What is the Rule?
B. What are the next 3 numbers in the
sequence?
Rule is: Subtract 8
20
12
4
Rule is: Multiply by 1.5
67.5
101.25
151.875
A. What equation shows the function?
B. Find the missing term.
x
y
1
1
2
8
3
27
4
5
125
A. What equation shows the function?
B. Find the missing term.
x
y
1
2
3
4
5
1
8
27
64
125
Equation: x³ = y
Missing Term: 64
A. What equation shows the function?
B. Find the missing terms.
w
30
35
t
6
7
40
45
50
10
A. What equation shows the function?
B. Find the missing terms.
Equation: w ÷ 5 = t
Missing Term: 8, 9
w
30
35
t
6
7
40
45
50
10
Draw the seventh possible figure in the pattern.
How many squares will it have?
Draw the seventh possible figure in the pattern.
How many squares will it have? 7 x 7
49 small squares
Find the 9th term in the sequence.
20, 40, 60, 80…………
What is the rule?
Write the rule as an algebraic
expression.
Find the 9th term in the sequence:
180
20, 40, 60, 80…………
What is the rule?
Multiply the position of the term by 20.
Write the rule as an algebraic expression: 20n
Next chapter…
Chapter 13
Graph Relationships
Inequalities
Inequality: is an algebraic sentence that
contains the symbol:
> (greater than)
< (less than)
≥ (greater than or equal to)
≤ (less than or equal to)
≠ (not equal to)
***Inequalities can be graphed on a number
line***

Graphing Inequalities on
a Number Line
Graphing Functions

Function: a relationship between two
numbers or variables. One quantity
depends uniquely on the other
Remember your Quadrants!
Plotting Coordinates



(x,y)
Find the point on the x-axis first
(horizontal / left to right)
Then find the point on the y-axis and
graph (vertical / up and down)
Linear Equations
When graphing a function, some
functions form a straight line
 Equations that
are straight lines
when graphed are
called linear
equations

Next topic…
Chapter 22:
Ratio and Proportion
Ratios, rates, unit rates,
maps & scales,
solving proportions


Use the picture to write the ratios.
Tell whether the ratio compares
part to part, part to whole, or whole to part.
All shapes to triangles.
Rectangles to ovals.
Ovals to all shapes.


Use the picture to write the ratios.
Tell whether the ratio compares
part to part, part to whole, or whole to part.
All shapes to triangles.
18 : 9
whole to part
Rectangles to ovals.
3:6
part to part
Ovals to all shapes.
6 : 18
part to whole

Which of the following shows
two equivalent ratios?
a. 7 : 9 and 14 : 16
b. 7 : 9 and 14 : 18

Which of the following shows
two equivalent ratios?
b.
7 : 9 and 14 : 18
7
= 14
9
18

Write two equivalent ratios for each of
the following.
a. 12 : 15
b.
1
3

Write two equivalent ratios for each of
the following.
a. 12 : 15
b.
24 : 30
4:5
1
2
3
3
6
9
*Note: There is more than 1 right answer.


Tell whether the ratios form a proportion.
Write yes or no.
4
10
and
26
24
65
6
and
27
9


Tell whether the ratios form a proportion.
Write yes or no.
4
and
10
Yes
26
24
65
6
and
27
9
No

Solve the following proportions using
Cross Products. Show your work!!
8
36
=
x
9
54
x
=
12
20

Solve the following proportions using
Cross Products. Show your work!!
8
=
36
x
9
54
x
=
12
20
36x = 8(54)
12x = 9(20)
36x = 432
12x = 180
36
36
x = 12
12
12
x = 15
Find the % of the number.
75% of 120
Find the % of the number.
75% of 120
.75 x 120 = 90
Find the % of the number.
30% of 50
Find the % of the number.
30% of 50
.30 x 50 = 15
Find the % of the number.
6% of 300
Find the % of the number.
6% of 300
.06 x 300 = 18
What is the unit rate ?
Show your work!!
a. Earn $56 for an 8 hour day
b. Score 120 points in 15 games
What is the unit rate ?
Show your work!!
a.
$$
hours
b.
points
games
$56 = x
8
1
x = $7 per hour
120 = x
15
1
x = 8 points per game
If the map scale is 1 in. = 15 miles,
what is the map distance if the
actual distance is 60 miles?
If the map scale is 1 in. = 15 miles,
what is the map distance if the
actual distance is 60 miles?
Inch
Miles
1 = x
15
60
15x = 1(60)
15x = 60
15
15
x = 4 inches
It takes Kenny 25 minutes to
inflate the tires of 50 bicycles.
How long will it take him to
inflate the tires of 120 bicycles?
It takes Kenny 25 minutes to
inflate the tires of 50 bicycles.
How long will it take him to
inflate the tires of 120 bicycles?
minutes
bicycles
25 = x
50
120
50x = 25 (120)
50x = 3,000
50
50
x = 60 minutes
How many pizzas do you need for
a party of 135 people
if at the last party,
90 people ate 52 pizzas?
How many pizzas do you need for a party of
135 people if at the last party, 90 people ate
52 pizzas?
pizzas
people
52 = x
90
135
90x = 52 (135)
90x = 7,020
90
90
x = 78 pizzas
Next chapter….
Chapter 18:
Measurement
Customary measurement of
length, mass and volume
Metric measurement of
length, mass and volume
Customary Measurements


A system of measurement used in the
United States used to describe how
long, how heavy, or how big
something is
Examples:
inches, feet, yards, miles
Customary Measurement
of length
12 inches = 1 foot
3 feet = 1 yard
36 inches = 1 yard
5,280 feet = 1 mile
Customary Measurements
of weight/mass
16 ounces (0z) = 1 pound (lb)
2000 pounds (lbs) = 1 ton (T)
Customary Measurement
of Capacity/ Volume

Capacity/volume: how much a
container can hold
8 fl oz = 1 cup
2 cups = 1 pint
2 pints = 1 quart
2 quarts = 1/2 gallon
4 quarts = 1 gallon
Metric Measurements

A system of measurement used in
most other countries to measure how
long, how heavy, or how big
something is
Metric Measurements of
Length

10 millimeters (mm) = 1 centimeter
(cm)

100 centimeters = 1 meter (m)

1,000 meters = 1 kilometer (km)
Metric Measurements of
Weight/Mass

1,000 milligrams (mg) = 1 gram (g)

1,000 grams = 1 kilogram (kg)
Metric Measurements of
Capacity/ Volume


The milliliter (mL) is a metric unit used
to measure the capacities of small
containers. Example= a dropper
The liter (L) is equal to 1,000 mL, so it
is used to measure the capacities of
larger containers. Example= a bottle
of soda
Remember…
King Henry’s Daffy Uncle Drinks Choc Milk
*This can help you with conversions………
Next topic…
Geometry
Quadrilaterals,
Plotting coordinates on a grid
Perimeter and Area
Volume of rectangular prisms
Quadrilaterals


Quadrilaterals are any four-sided
shapes. They must have straight lines
and be two-dimensional.
Examples: squares, rectangles,
rhombuses, parallelograms,
trapezoids, kites
More about quadrilaterals
The Square


The square has four equal sides.
All angles of a square equal 90
degrees.
The Rectangle


The Rectangle has four right angles
and two sets of parallel lines.
Not all sides are equal to each other.
The Rhombus



A rhombus is a four-sided shape where all
sides have equal length.
Also opposite sides are
parallel and opposite angles are equal.
A rhombus is sometimes called a diamond.
The Parallelogram


A parallelogram has opposite sides
parallel and equal in length.
Also opposite angles are equal.
Plotting Coordinates
Plotting Coordinates
(continued)



(x,y)
Find the point on the x-axis first
(horizontal / left to right)
Then find the point on the y-axis and
graph (vertical / up and down)
Finding the Perimeter

To find the perimeter of most
two-dimensional shapes,
just add up the sides
Area


Area is the measurement of a shape’s
surface.
Remember that units are squared for
area!!
Finding the Area of a
Square




To find the area of a square,
multiply the length times the width
A= (l)(w)
A=2x2
A = 4 cm²
Finding the area of
rectangles


To find the area of a rectangle, just
multiply the length and the width.
A= (l)(w)
Volume


Volume is the amount of space that a
substance or object occupies, or that
is enclosed within a container
Remember that the units of volume
are cubed (example: inches^3)
because it measures the capacity of a
3-dimensional figure!
Finding the Volume of
Rectangular Prisms




To find the volume of a rectangular
prism, multiply the length by the width
and by the height of the figure
V = (l)(w)(h)
V=6x3x4
V = 72 cm³
Practice,
Practice,
Practice!