Download Q1studyguide

6th Grade Math 1st Quarter - Study Guide
1. (6.NS.4) Which of the following represents the prime factorization of 355?
a. 5 x 5 x 5
b. 5 x 71
c. 3 x 5 x 6
d. 56
It takes Carlos 10 minutes to complete one section in his History workbook or complete one page in his science
book.
2. (6.EE.2) Write an expression using a variable that shows how long it takes Carlos to complete some sections in his
History workbook and some pages in his Science book. Identify what the variable represents.
a. 10x + 10y x = number of sections in history workbook
y = number of science pages
b. 10x + 12y x = number of sections in history workbook
y = number of science pages
c. 6x +6y
x = number of sections in history workbook
y = number of science pages
d. 15x+9y
x= number of sections in history workbook
y = number of science pages
3. (6.EE.2) For homework one night, Carlos has 5 sections of History and 6 pages of Science to complete. Evaluate the
expression in number 2 to find out how long it will take Carlos to finish his homework.
a. 218 mins
b. 240 mins
c. 110 mins
d. 216 mins
4. (6.EE.3) Translate the algebraic expression into word form: 7y - 5.
a. The difference of 7 times y plus 5
b. Seven times y minus 5
c. Seven y and 5
d. Seven times the sum of y and 5
5. (6.EE.1) Simplify: 23 – 5 + 10 / 2
a. 9
b. 27
c. 8
d. 6
6. (6.EE.5) Which inequality does the graph, to the right, show?
a. m ≥ -1
b. n < -3
c. 1 > p > 10
d. x < 1
7. (6.EE.8) The sleeping bag will keep a person warm for temperatures down to (but not including) -20 degrees
Farenheit.
a. x > -20
b. x < 20
c. x > 20
d. x < -20
6th Grade Math 1st Quarter - Study Guide
8. (6.NS.4) Two radio stations are playing the #1 hit song “2 Nice to be True” by Anita and the Goody-2-Shoes. WMTH
plays the song every 24 minutes. WMSU plays the song every 12 minutes. Both stations play the song at 3:00PM.
When is the next time the stations will play the song at the same time?
a. 4:00
b. 3:12
c. 3:24
d. 3:59
9. (6.NS.4) Judy is planning a party for her younger brother. She has 30 prizes and 20 balloons. How many children can
she have at the party so that each child gets an equal number of prizes and an equal number of balloons? Explain your
answer.
a. 5
b. 6
c. 9
d. 12
10. (6.NS.4) Michael’s Craft store wants to rent between 25 and 30 square yards of space for a big craft show. The space
must be rectangular, and the side lengths must be whole numbers. Which number between 25 and 30 has the most
factor pairs that will give the greatest number of rectangular arrangements to choose from?
a. 29
b. 30
c. 26
d. 25
11. (6.EE.5) Solve the equation 10g – 5 = 15
a. g = 22
b. g = 20
c. g = 12
d. g = 2
12. (6.EE.3) Which expression shows the distributive property for 2 ∙ (x – 6)
a. 3+ x - 6
b. 3x - 18
c. 2x - 12
d. 3x - 6
13. (6.EE.3) Which expression shows the associative property for 19 + (6x + 15)
a. 19 + 6x + 15
b. (19) + 6x + 15
c. (19 + 6x) + 15
d. 5+ 6x + 19
14. (6.EE.4) Simplify (Combine like terms) 2y + 5 – y + 7 + y2
a. y2 +5y + 19
b. y2 + y + 12
c. y2 + 3y + 19
d. 3y2 + 19
6th Grade Math 1st Quarter - Study Guide
ANSWER GUIDE
1. (6.NS.4) Which of the following represents the prime factorization of 355?
a. 5 x 5 x 5
Multiply each answer choice to see if it equals 355
b. 5 x 71
a. 5x5x5 = 125
c. 3 x 5 x 6
b. 5x71 = 355
d. 56
c. 6 is not a prime number
d. The first answer was 53 and that was wrong, so 56 is probably wrong too.
It takes Carlos 10 minutes to complete one section in his History workbook or complete one pg. in his science book.
2. (6.EE.2) Write an expression using a variable that shows how long it takes Carlos to complete some sections in his
History workbook and some pages in his Science book. Identify what the variable represents.
e. 10x + 10y x Start
= number
of sections in history workbook
y = number of science pages
simple: What’s the homework? History and Science. Same as History + Science.
f. 10x + 12y x (Use
= number
of
sections
in
history
workbook
number
a variable for each type of homework.) H +y S= or
X + Y.of science pages
g. 6x +6y
x Add
= number
of sections
workbook
y = +number
of(10mins)
science pages
how long
it takes in
to history
do each:
History (10mins)
Science
h. 15x+9y
x=That’s
number
sections in history workbook
y = number of science pages
the of
answer!
3. (6.EE.2) For homework one night, Carlos has 5 sections of History and 6 pages of Science to complete. Evaluate the
expression in number 2 to find out how long it will take Carlos to finish his homework.
e. 218 mins
Use the expression you wrote in the last problem.
f. 240 mins
History + Science
g. 110 mins
10mins for each history + 10 mins for each Science
h. 216 mins
10*5 + 10*6 = 50 + 60 = (remember they asked how long so your answer has to be in Mins.)
4. (6.EE.3) Translate the algebraic expression into word form: 7y - 5.
a. The difference of 7 times y plus 5
b. Seven times y minus 5
Take it step by step.
At the end we are taking away 5.
c. Seven y and 5
Which statement uses words that mean we will be subtracting 5?
d. Seven times the sum of y and 5
7y means 7*y. Which statement also has words showing this?
5. (6.EE.1) Simplify: 2 – 5 + 10 / 2
a. 9
Remember your order of operations: PEMDAS
b. 27
No parenthesis, so exponents are next: 23 = 2*2*2 = 8
c. 8
Multiply/Divide are next: so 10/2 means 10 ÷ 2 = 5
d. 6
Add/Subtract from side to side: 8-5+5
3
6. (6.EE.5) Which inequality does the graph, to the right, show?
e. m ≥ -1
f. n < -3
g. 1 > p > 10
First find the starting point on the graph: it starts at -1
h. x < 1
Next, cross out any answer choice that doesn’t have the starting point.
Next look at the numbers “shaded” by the arrow, are they bigger or smaller? That’s the sign.
Last, remember that a closes circle means “or equal to”
7. (6.EE.8) The sleeping bag will keep a person warm for temperatures down to (but not including) -20°Farenheit.
e. x > -20
We are comparing temperatures to -20°. Cross out any answer that doesn’t have that number.
f. x < 20
It says temperature “down to” that means the other temperatures will be above -20°F.
g. x > 20
If a temperature is above -20°F, then it will be bigger or more than. (>)
h. x < -20
“Not including” means that it cannot be equal to -20°F
6th Grade Math 1st Quarter - Study Guide
ANSWER GUIDE
8. (6.NS.4) Two radio stations are playing the #1 hit song “2 Nice to be True” by Anita and the Goody-2-Shoes. WMTH
plays the song every 24 minutes. WMSU plays the song every 12 minutes. Both stations play the song at 3:00PM.
When is the next time the stations will play the song at the same time?
e. 4:00
Look at the numbers used and decide it we will be going bigger or smaller?
f. 3:12
Every 24mins means I keep adding 24mins, so it’s getting bigger. Multiples get bigger.
This is a LCM problem. Break down each number to its Prime Factorization, then put the prime
g. 3:24
factors into a Venn Diagram. Multiply all the numbers and this will give the LCM in MINUTES.
h. 3:59
You need to add the number of minutes to the 3:00PM time to find the new time.
9. (6.NS.4) Judy is planning a party for her younger brother. She has 30 prizes and 20 balloons. How many children can
she have at the party so that each child gets an equal number of prizes and an equal number of balloons? Explain your
answer.
Look at the numbers used and decide if we will be going bigger or smaller?
e. 5
We only have 30 prizes and 20 balloons and we are not buying any more. So we are going
f. 6
smaller. Factors are smaller than the number.
g. 9
This is a GCF problem. Find the Prime Factorization of each number then put the prime factors
h. 12
into a Venn Diagram. The numbers they both have is the GCF.
10. (6.NS.4) Michael’s Craft store wants to rent between 25 and 30 square yards of space for a big craft show. The space
must be rectangular, and the side lengths must be whole numbers. Which number between 25 and 30 has the most
factor pairs that will give the greatest number of rectangular arrangements to choose from?
e. 29
We’re finding the factor pairs of the number between 25 and 30.
f. 30
Make a T-chart of each number (26, 27, 28, 29) and see which has the most factor pairs.
g. 26
**Remember the divisibility rules for our popular numbers 2, 3 & 5.**
h. 25
11. (6.EE.5) Solve the equation 10g – 5 = 15
e. g = 22
Solve means to find an answer to or get an answer for the variable.
f. g = 20
“g” is the variable, so I need to get it by itself. I will start with the item that is the farthest from it.
g. g = 12
Do the opposite of -5, which is +5 to both sides. Then I will get rid of the 10, by doing the
h. g = 2
opposite operation. 10g means 10*g, so I will divide both sides by 10.
**another way** plug in/substitute each number for ‘g’ and see which one is true.
12. (6.EE.3) Which expression shows the distributive property for 2 ∙ (x – 6)
e. 3+ x - 6
Distributive has the word distribute in it, so I know I will be giving out something fairly.
f. 3x - 18
2 is outside the parenthesis and right next to it. That tells me I am multiplying by 2.
g. 2x - 12
I will distribute a “multiply by 2” to every item inside the parenthesis.
h. 3x - 6
13. (6.EE.3) Which expression shows the associative property for 19 + (6x + 15)
e. 19 + 6x + 15
Associative has the word associate in it. Associates are like groups of people.
f. (19) + 6x + 15 I am looking at the grouping of the numbers.
g. (19 + 6x) + 15 Which answer choice has the same numbers but a different group?
h. 5+ 6x + 19
14. (6.EE.4) Simplify (Combine like terms) 2y + 5 – y + 7 + y2
a. y2 +5y + 19
Remember that different terms are like tuna, chocolate, and soup.
b. y2 + y + 12
You can put different shapes around the numbers AND their signs.
c. y2 + 3y + 19
They will be like this (2y & – y), (+5 & +7), (+y2). Combine the numbers to get your answer.
2
d. 3y + 19