Download END OF YEAR SUMMARY 6th Grade 2011 EXAMPLE PROBLEMS

END OF YEAR SUMMARY
6th Grade 2011
EXAMPLE PROBLEMS
(unedited student work)
How to evaluate:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
How to find the area, diameter,
radius, and circumference
C= 3.14*D
A=3.14*R*R
D=2*R
R=D/2
R= Radius
D=Diameter
A=Area
C=Circumference
3.14=Pi
Bench mark fractions
1/2=.5 2/2=1.0
1/3=.3 2/3=.6 3/3=1.0
1/4=.25 2/4=.5 3/4=.75 4/4=1.0
1/5=.2 2/5=.4 3/5=.6 4/5=.8 5/5=1.0
1/6=.16 2/6=.3 3/6=.5 4/6=.6 5/6=.83 6/6=1.0
1/7=.143 2/7=.29 3/7=.43 4/7=.57 5/7=.71 6/7=.86 7/7=1.0
1/8=.125 2/8=.25 3/8=.375 4/8=.5 5/8=.625 6/8=.75 7/8=.875 8/8=1.0
1/9=.1 2/9=.2 3/9=.3 4/9=.4 5/9=.5 6/9=.6 7/9=.7 8/9=.8 9/9=1.0
1/10=.10 2/10=.20 3/10=.30 4/10=.40 5/10=.50 6/10=.60 7/10=.70 8/10=.80 9/10=.90
10/10=1.0
Symmetry
Measures of Central Tendency
Mean-add all numbers together and divide
Mode-number that shows up the most
Range-max-min
Max- biggest number
Min-smallest number
Median-middle number
Multiplying Fractions- multiply straight
across the fractions
ex. 2/5 x 2/5=4/10
Dividing Fractions-invert and multiply
ex. 3/5 / 4/5 = then 3/5 x 5/4=15/20
Adding Fractions- to add fractions make
common denominators then add numerators
ex.3/10 + 2/5
2/5x2=4/10 then 4/10+3/10=7/10
Subtracting Fractions- to subtract fractions
make common denominators then subtract
numerators. Leave denominators the same!
ex.7/10 – 3/5=
3/5x2=6/10 then 7/10 - 6/10=1/10
Area of a Circle- RadiusxRadiusx3.14
ex. radius=2
2x2=4 then 4x3.14=12.56
Circumference of a circle- Radiusx2x3.14
ex. Radius=3
3x2=6 then 6x3.14=18.84
Geometry3 sides- triangle
4 sides- quadraleteral
5 sides- pentagon
6 sides- hexagon
7 sides- heptagon
8 sides- octagon
9 sides- nonagon
10 sides-decagon
12 sides- dodecagon
Parellelogram- shape with 2 sets of parallel
sides
Dalton Slater has 34 hits in 5 baseball games. What is his average of hits per game?
34 / 5 = 6.8
how many hits does he need to have an average of 7 after his next game?
42 / 6 = 7
Kayla has 6 apples. She gives 1 to the dog, 2 to her dad, 1 to her mom, and 1 for her
self. How many apples does she have left?
1 apple is left
2+1+1+1=5
6-5 = 1
Arrange from least to greatest 6.0 .56 .060
.056 .6
.056 .060 .56 .6 6.0
Write as a fraction decimal or percent
2/5 A.40% B.400% C.20% D.200%
AWNSER A !!!!!!!! is correct
.23 A.0.23% B.0.023% C.23% D.2.3%
AWNSER C is correct :)
Here is how you check if your fractions are
equivalent
( 4 / 12 = .3 ) ( 1 /3 = .3 ) it is ALMOST
equivalent
Factors of 20...........
1,2,4,5,10,20
Changing a fraction to a Decimal
Just divide!
88/100 = . 88
99/100 = . 99
50/100 = . 50
How to multiply mixed numbers:
2 3/5 * 6 1/2 = ?
2 * 6 = 12
Find common denominators of the 2 fractions.
5 * 2 = 10
Convert the numerators to match the
denominators.
3*2=6
1*5=5
Now put the fractions together.
6/10 * 5/10 = 30/10
The improper fraction becomes a mixed/whole
number.
30 / 10 = 3
12 + 3 = 15.
2 3/5 * 6 ½ = 15
7+2(n+2) + 11n=13n+13
6a2 + 11a + 3a2=9a2+11a
2a + 18=2(a+9)
three decreased by the number 3-n
e(m+n) m=6 and n=15 answer = 7
w=5 x =2 xw = 10
How to evaluate:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
Ella invited ¼ of her club to a social gathering
at her house Saturday. If Ella has 80 kids in
her club, how many kids were invited?
20 because 80 / = 20
Of the kids that came, ¾ brought pie. (WOO)
How many pies did she revive?
15 because 20 / 4 = 5*3 + 15
Which is a square number?
16 49 48
16 AND 49 cause 4*4=16 and 7*7=49
How many factors does 15 have?
1, 15, 3, 5 = 4 factors
5+5=10
10-5=5
5x5=25
4 over 10 =40%
. 2 = 20%
.75+.75 =1.5
multiples of 2 are 2,4,6,8,10
factors of 6 are 1,2,3,6
1 ¾ = 7/4 because 4 + 3= 7 = 7/4
Probability- If there is a gumball machine
with 10 gumballs and 2 are blue, 4 red, 2
yellow, whats the percentage of red?
4/10 = .4 = 40%
9/50 = 18% 9 / 50= .18
80/1 = 80
An equilateral triangle has a perimeter of 21.
Whats the length of each side?
21 / 3 = 7
Adding fractions- ½ + ¾ = 2/4 + ¾ = 5/4 or
1¼
Subtracting fractions- ¾ – 2/4= ¼
Multiplying fractions- 2/4 * ¾
2 * 3 = 6/4
Whats the aria of the rectangle?
Keep the denominator the same.
2*2=4 aria
Dividing fractions- 2/4 / ¾
Whats
the perimeter?
Flip the second fraction so that, in this case, ¾,
2+2+2+2= 8 perimeter
becomes 4/3 now change it to *. now its 2/4 *
¾ = 8/12
17t = 17 * t
20*2/4 = 80/4 = 40
How to add/subtract fractions with the same
denominator:
2/5 + 1/5 = 3/5 because if the denominator is
the same, then all there is to do is add/subtract
the numerators.
How to find the mean (average) of a group of
numbers:
Add them up, divide by how many numbers
there were.
7 + 6 + 8 + 9 + 10 = 40 / 5 = 8.
How to solve an algebra equasion:
3 + 5y + 7(y + 4) = ?
Only same terms can be used with others such
as; letters to letters, #s to #s, # and letters, #
and letters. When a letter or parentheses is
directly next to a number, that means to
multiply.
7 * y = 7y, 7 * 4 = 28. Now it would look like:
3 + 5y + 7y + 28 = ?
3 + 28 = 31, 5y + 7y = 12y
When doing algebra, it doesn't always get 1
final number for an answer. In this case the
best answer you can get is;
31 + 12y
How to multiply fractions:
When using fractions, * is the same as “of”.
2/5 * 7/10 = ?
2 * 7 = 14
5 * 10 = 50
2/5 * 7/10 = 14/50
How to find the volume of a cylinder:
Find the radius of the top or bottom and the
height of the side. Then use this formula;
∏r2h = volume
How to add/subtract fractions with different
denominators:
2/6 + 1/3 = ?
Find a way to get both denominators to be the
same. If one is a multiple of the other, divide
the multiple by the factor and divide the
numerator by the same number, then finally
do the addition/subtraction of the numerators.
If one is a factor of the other, divide the bigger
one by the smaller one and then the
numerator times the same number, then
finally . If they aren't multiples or factors of
each other, then find the LCM of the 2, and
multiply or divide the numerator by the same
number.
2/6 + 1/3
3*2=6
1*2=2
2/6 + 2/6 = 4/6 = 2/3.
How to find the least common multiple of 2
numbers:
List the multiples of each in order until you
find a pair that matches.
12
27
24
54
36
81
48
108
60
72
84
96
108
Sometimes the least common multiple is
gotten by multiplying the numbers together.
5 * 7 = 35
35 is the LCM of 5 and 7.
How to determine if a number is square:
Divide 225 by different numbers, and when
the divisor and quotient end up being the
same, the number that is both is the square
root of 225. In this case, 225 / 15 = 15.
Symmetry:
How to divide fractions:
3/7 / 4/5 = ?
Flip the divisor (dividend / divisor = quotient)
and then multiply the fractions straight across
to get the answer.
3/7 * 5/4 = 15/28
This shape has 1 line of symmetery.
Symmetry:
This shape has 4 lines of symmetery.
How to turn a mixed number into an
improper fraction:
2 1/5 = ?
Multiply the denominator of the fraction by
the whole number.
5 * 2 = 10
Add the product to the numerator of the
fraction.
10 + 1 = 11
Put the sum over the original denominator to
make an improper fraction.
11/5
5(a2+4)+2(a2+b2)
2
5* a + 5 * 4 + 2 * a2 + 2 * b2
5a2 + 20 + 2a2 + 2b2
If you were to guess at the 4 answers for the
true / false test,what is the probability of
getting at least two right?
1/2*1/2=1/4
1/4
add like term 5a2+2a2=7a2
so the final answer is
7a2 + 20 + 2a2 + 2b2
How to subtract fractions
1/2-1/3=?
you must create a common denom
2*3=6
/6 /6
now subtract the top, keep the denom
3/6-2/6=1/6
How to find the LEAST COMMON
MULTIPLE of 25 and 10
10
10,20,30,40,50,60,70,80,90,100
How to calculate a percentage:
Set up a fraction, PART / WHOLE
Johnny got a 13 out of 30 on his test.
What percent is this?
13 / 30 = 0.43 which is 43%
Give the dimensions(length&width)of a
rectangle with an area of 100 sq. units and
whole number side lengths that has:
largest perimeter.
DIMENSION:
smallest perimeter.
DIMENSION:
largest:1by100
25
12,50,75,100
smallest:10by10
Therefore the LCM is 50!
Cross multiplication: 1/6+1/4
6*4= 24
1*4=4 4/24
3
4*6= 24
1*6=6 6/24
6+4=10
10/24
10/ 2=5
24/2=12 5/12
Final answer: 5/12
All rectangles are parallelograms.
True or false
True
Because a rectangle has both opposite sides
the same length.
To get multiples and factors you must:
Multiples- you must multiply an number by
and number and get another number and
that's a multiple of both of those numbers
Ex. 4*5= 20
so 20 is a multiple of 5 and 4
Factor- you must divide a number by another
number and if its whole it a factor
Ex. factors of 6- 1,2,3,6(:
To be a regular polygon means the polygon
has all side lengths the same, but the angles
can be different.
True or false
False
Because the side lengths and the angles have
to be the same.
How to evaluate:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
How To Multiply a Fraction:you multiply
across the equation
5/12X4/3=20/36
2/7X 7/8 =14/56
9/8X4/7=36/56
How to evaluate:
Y = 2X + 8 for X = 4
Y = 2(4) + 8
Y=8+8
Y = 16
done!
Algebra problems:using letters in place of
numbers in a number sentence
7x+6+2x+5=9+11
7+2(3+n)+11n=13n+13
4(6t+5)+9t+3(4t+7)=45t+41
5x+5y+x+8y=6x+13y
How to turn a fraction into a percent:
divide the numerator by the denominator, move
the decimal two places right
¼ = .75= 75%
1/4=.75
This problem goes with simplifying fractions.
Write 53% as a fraction in simplest form.
A fraction is simplest form is a fraction that can't
get smaller.
Correct answer: 53/100. Show your work to
prove your right!
This problem goes with adding fractions:
What does 4/32+12/64 equal?
Remember when adding fractions you need the
denominator the same.
Correct answer:20/64. Show your work to
prove your right!
How to: Take 4/32, multiply it by 2, and you
end up with 8/32+12/64=20/64.
This problem is based off of probability.
There are 25 gumballs in a machine, 2 are
orange, 5 are yellow, 6 are purple, and 12 are
green. What is the probability of pulling a
yellow?
When dealing with probability make it out of
100, to easily make it a out of a percent.
The correct answer is 20%! Show your work
to prove your right!
2/4= . 5
2/4_____ ½
The sum of the measures of the angles of any
triangle is 90 degrees.
True or false
1/2= . 5
False
2/4 =
½
This problem deals with the bigger number.
Which is bigger? -4_2 ?
Remember, when having to pick the biggest
number use either < or this > or =, to show
what it is.
The correct answer is <(for the 2)
Because the sum of all triangle angles is 180
degrees.
This problem deals with improper fractions:
Do this problem: turn 8 3/7 into a improper
fraction.
When you turn a fraction in to a improper
fraction you can't have any whole numbers
there.
You take 8 x 7=56+3=59/7
Correct answer:59/7. Show you work to prove
your right!
An equilateral triangle has a perimeter of
21.What is the length of each side? Explain.
This problem is connected to shapes and
designs. Which ones are acute angles?
An equilateral has 3 sides, and they have the
same length in sides.
Correct Answer: 7, because 21 divided 3=7.
A. l/ B. l_ C. l/ Remember an acute angle is
an angle that is less than 90 degrees.
How to: Measure the three angles, and which
ones that are less than 90 degrees is an acute
angle.
Correct answer is A and C.
Are all rectangles parallelograms?
Mike tosses a coin 50 times and the coin lands
on heads 28 times. What fraction of the 50
tosses is heads? What percent is this?
Remember: Parallelograms must have both
sides parallel.
Answer: Yes, all rectangles are
parallelograms. Draw rectangles to prove it.
To get the percent make the fraction out of
100 so you can get the percent easily.
The answer is 56%, and the fraction is 56/100.
Find five fractions between 8/10 and 5/4.
You need to find the decimal of both of these
numbers to make it easy to find a number
between it. 8/10=.80 5/4 =1.25
Answer anything between .80 and 1.25.
Two quadrilaterals are congruent.
Which statement is correct?
F They have the same area, but may have
different perimeters. G They have the same
perimeters but have different areas. H They
have different perimeters/area. J. They have
the same area and perimeter.
Answer: F, because they have the same
angles, but not the same side length.
A sugarless gum company says that four out
of five dentist surveyed recommend sugarless
gum for their patients who chew gum.
Do you think this statement means that 80%
of the dentist believe patients should chew
sugarless gum?
Answer: No, because 80% of the ones they
surveyed said people should chew that type of
gum.