Download Name - Butler Area School District

(Revised 10/26/01)
Name ________________________________________
6th – Everyday Math
Unit 3
Date ________________________
Page 1
Study Guide for Unit 3 Assessment
1)
Numerator in a fraction is the top number or the number of equal parts you are talking about.
2)
Denominator in a fraction is the bottom number or the number of equal parts in all.
Example:
3)
5
8
5 is the numerator
8 is the denominator
Improper or Top-heavy Fractions
A fraction that names a number greater than or equal to 1 ; a
fraction whose numerator is greater than or equal to its denominator.
Examples are: 7/3,
5/4,
9/9,
16/4.
To change an improper fraction or top heavy fraction into a mixed number divide the numerator by the
denominator. Then place the remainder over the denominator.
Example:
To change 35/8 back to a mixed number, 35 divided by 8 equals 4 with 3 left over.
Place the 3 over the denominator 8, so your answer is
35/8 = 4 3/8.
4)
Practice by converting each improper (top heavy) fraction to a mixed number.
a.
17/4 = __________
b.
12/5 = ___________
c.
35/6 = __________
d.
18/7 = ___________
e.
24/4 = __________
f.
139/10 = ___________
To change a mixed number to an improper (top heavy) fraction – You need to do three steps
Change
2 1/2 to a fraction.
1/2
2
+
1) Multiply the whole number by the denominator,
= 5/2
(2 * 2 = 4)
2) Add on the numerator to that answer. (1 + 4 = 5).
3) Then, place that number over the denominator. (5 over 2 = 5/2).
*
So,
2 1/2 = 5/2
5)
Practice by converting each mixed (top-heavy) number into an improper fraction.
a.
2 2/5 = _________
b.
1 3/10 = _________
c.
4 4/5 = _________
d.
6 5/12 = _________
e.
2 2/3 = _________
f.
1 2/9 = _________
Name ___________________________________
6th – Everyday Math
Date __________________
Unit 3
Page 2
The Greatest Common Factor of two numbers is the largest number that is a factor of both numbers.
Ex.
1)
2)
Find the greatest common factor of 12 and 8.
List all of the factors of 12: 1 x 12, 2 x 6, 3 x 4
In order, 1, 2, 3, 4, 6 and 12 are factors.
List all of the factors of 8: 1 x 8, 2 x 4
In order, 1, 2, 4, and 8 are factors.
1, 2, and 4 are on both lists. They are common factors.
4 is the largest. It is the greatest common factor.
6)
Find the greatest common factors.
a
4:
7:
GCF: _______
b)
3:
21:
GCF: _______
c)
6:
4:
2:
GCF: ________
d)
9:
12:
GCF: _______
e)
3:
15:
GCF: _______
f)
5:
6:
GCF: ________
The Least Common Multiple of two whole numbers is the smallest number that is a multiple of both numbers.
Ex.
1)
2)
Find the least common multiple of 12 and 8.
List a few multiples of 12:
12, 24, 36, 48, 60, 72
List a few multiples of 8
8, 16, 24, 32, 40, 48, 56, 64, 72
24, 48, and 72 are on both lists. They are common multiples.
24 is the smallest. It is the least common multiple of 12 and 8.
7)
Find the least common multiples.
a)
4:
7:
LCM: _______
b)
3:
21:
LCM: _______
c)
6:
4:
2:
LCM: ________
d)
9:
12:
LCM: _______
e)
3:
15:
LCM: _______
f)
5:
6:
LCM: ________
Adding and Subtracting Negative Numbers When adding two numbers, think of the first addend as a starting point
on a number line, the second addend as a move away from that starting point to the sum or difference.
(Start at 1, Add –5)
Example:
-6 –5 –4 –3 –2 –1
0 1
2 3
4 5 6
1 + (-5) = -4
8)
Solve:
a)
-3 + 5 = _____
b)
5 + (-3) = _____
c)
-8 – (-3) = _____
d)
(the two minuses make a plus)
9 – (-3) = _____
Name ___________________________________
6th – Everyday Math
9)
perimeter
Date __________________
Page 3
Unit 3
The distance around a two-dimensional shape.
A formula for a parallelogram is
2"
P = 2 * (length + width).
3"
Ex. This parallelogram is 2" by 3" .
Either add all sides: 2 + 3 + 2 + 3 = 10" or 2 * ( 2" + 3") = 10"
2"
10)
area
The measure of a surface inside a boundary.
The formula for measuring the area of a rectangle is
6"
Area = Length * Width.
Ex. Area = 6" X 2" = 12 square inches or 12 in.2.
11)
Find the perimeter and area of each of the figures below.
6 ft.
4 in.
9m
4 ft.
8 in.
6m
a) Perimeter ________
c) Perimeter ________
e) Perimeter ________
b) Area ____________
d) Area ____________
f) Area ____________
12)
A rectangle has a length of 8 in. and a width of 6 in.
a)
What is its area?
____________
b)
What is its perimeter?
____________
Name ___________________________________
6th – Everyday Math
13)
Date __________________
Unit 3
Page 4
Complete the table for the given rule.
Plot the points and connect them to make a line graph.
Hint:
(To find the coordinates or plot a point on a graph with an X and Y axis always begin with x.)
Rule: x = (1/4 * y) + 5
x
y
y
0
20
4
18
________________________________________________________
________________________________________________________
16
7
12
9
20
*Remember to
plot the x axis first
then plot the y axis.
________________________________________________________
14
________________________________________________________
12
________________________________________________________
10
________________________________________________________
8
________________________________________________________
6
________________________________________________________
4
________________________________________________________
2
________________________________________________________
0
X
0
12
14)
2
14
4
16
6
8
18
10
20
A sixth grade teacher used the spreadsheet below to record the students' scores on 3 math tests.
A
B
C
D
E
1
STUDENT
Test 1
Test 2
Test 3
Mean
2
Joe
60%
80%
100%
80%
3
Mandy
70%
85%
100%
85%
4
Jonathan
90%
100%
86%
92%
5
Amanda
75%
85%
80%
a.
What score did Jonathan receive on Test 3? ________________________
b.
Calculate Amanda's mean score and write it in Cell E5.
c.
What is shown in Cell B4? _______________________________
d.
If Joe had received a 90% on Test 1 what would his mean average have been? ____________
Name ___________________________________
6th – Everyday Math
15)
Date __________________
Unit 3
Page 5
This formula can be used to find a length in centimeters when the length in inches is known. (or vice
versa) i is the number of inches, and C is the number of centimeters.
C = 2.54 * i
a.
How many centimeters are there in 2 inches? ____________________________
b.
How many centimeters are there in 5 inches? ________________
c.
Circle the best approximation for the number of cm in 1 yard.
100 cm
4 cm
40 cm
254 cm
16)
Equations – Number sentences that contain the relation symbol “=” are called equations.
Example: 7 * 5 = 35
17)
Variables A variable is a letter or symbol that represents a number.
Example 1:
7*5=x
Example 2:
7 * b = 35
x = 35
b=5
Algebraic expression An expression that contains a variable; much like writing a formula.
Ex. Maria is two inches taller than Joe, and if the variable M represents
Maria's height, then the expression M – 2 represents Joe's height.
Write an algebraic expression for this one.
Joe is 3 years younger than Maria. _________________________
18)
19)
Look at this general pattern.
(w * w * w) - z = w3 - z
(5 * 5 * 5) – 2
125
- 2
123
Give two more special cases for the general pattern above.
A special case for this problem would be:
= 53- 2
= 125 - 2
= 123
a) ________________________________________________________
b) ________________________________________________________
20)
Refer to the drawing at the right. Write an algebraic
Expression that describes each of the following.
a) The depth of the submarine if it dives 80 meters lower
__________
b) The depth of the submarine if it climbs 100 meters.
__________
c) The depth of another submarine b meters below this sub
__________
d meters
Name ___________________________________
6th – Everyday Math
Date __________________
Page 6
Unit 3
21) Circle all of the statements below that
describe the special cases at the right.
4+4+4=3*4
a)
x + y + z = 3 * xyz
1.5 + 1.5 + 1.5 = 3 * 1.5
b)
x+x+x=3*x
c)
2 + 2 + 2 = 23
d)
Adding a number to itself is the same as tripling it.
21)



The sixth graders in Butler School District did a survey to see what months of the year:
People play outdoor sports
People play indoor sports
People swim outdoors
7+7+7=3*7
They made graphs to show their results.
Label the graphs below with the most appropriate titles.
a) ________________________
Number
b) _____________________
of
People
Jan.
Apr.
July
Oct.
Dec.
Number
of
People
Jan.
c) _______________________
Number
of
People
Jan.
Apr.
July
Oct.
Dec.
Apr.
July
Oct.
Dec.