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Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
ANSWER KEY
Question 1: Correct Response C
The associative property of multiplication is the grouping property. In this problem, there are three
factors, 4, 8, and 7. On the left side of the equals sign, the numbers inside the parentheses are 7 and 8.
On the right side of the equals sign, the numbers inside the parentheses are 4 and 8. The numbers 4, 8,
7 and have stayed in the same order, but the grouping of pairs of factors is different.
Incorrect Response A
This answer is incorrect because it is an example of the commutative property of multiplication.
Incorrect Response B
This answer is incorrect because it is an example of the commutative property of addition.
Incorrect Response D
This answer is incorrect because it is an example of the associative property of addition, not of
multiplication.
6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.3 - Apply the properties of operations to generate equivalent expressions. Example For
example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent
expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the
equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the
equivalent expression 3y.
Question 2: Correct Response C
According to the chart, the relationship between the number of people and the number of tables is that
the number of tables is one less than one-half the number of people. As an equation, if t represents the
number of tables and p represents the number of people, this relationship could be written as t = ½p – 1
Therefore, for 20 people, the number of tables is t = ½(20) – 1 = 10 – 1 = 9.
Another way to see that 9 tables are needed for 20 people is that starting with 4 people at one table, the
number of tables increases by 1 each time the number of people increases by 2.
Incorrect Response A
There are more than 7 tables needed for 20 people because there would be room for only 16 people
at 7 tables.
Incorrect Response B
There are more than 8 tables needed for 20 people because there would be room for only 18 people
at 8 tables.
Incorrect Response D
There would be room for 22 people at 10 tables while 9 tables would have room for 20 people, so
10 is not the smallest number of tables that would seat 20 people.
6.EE - Expressions and Equations
Reason about and solve one-variable equations and inequalities.
6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or, depending
on the purpose at hand, any number in a specified set.
Page 1 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9 - Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the dependent
variable, in terms of the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using graphs and tables, and relate
these to the equation. Example For example, in a problem involving motion at constant speed, list
and graph ordered pairs of distances and times, and write the equation d = 65t to represent the
relationship between distance and time.
Question 3: Correct Response D
Each y-value in the table is 1 more than 3 times the corresponding x-value. Therefore, the correct
equation is y = 3x + 1.
6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2.a - Write expressions that record operations with numbers and with letters standing for
numbers. Example For example, express the calculation “Subtract y from 5” as 5 - y.
Question 4: Correct Response B
Each y-value in the table is 1 more than 4 times the corresponding x-value. Therefore, the correct
equation is y = 4x + 1.
Incorrect Response A
If this answer were correct, each y-value in the table would be 4 more than the corresponding xvalue. However, 9 is not 4 more than 2.
Incorrect Response C
If this answer were correct, each y -value in the table would be 3 more than 2 times the
corresponding x-value. However, 13 is not 3 more than 2 x 2.
Incorrect Response D
If this answer were correct, each y -value in the table would be 2 more than 3 times the
corresponding x-value. However, 13 is not 2 more than 3 x 3.
6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2.a - Write expressions that record operations with numbers and with letters standing for
numbers. Example For example, express the calculation “Subtract y from 5” as 5 - y.
Reason about and solve one-variable equations and inequalities.
6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or, depending
on the purpose at hand, any number in a specified set.
Page 2 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Question 5: Correct Response D
The total amount for skating is represented by the expression 6.5h which is the rate per hour multiplied
by the number of hours, h. he words ‘less than’ indicate that the less than (<) symbol should be used.
Therefore, the inequality 6.5h < 20 can be used to find h the number of hours Edward can skate if he
wants the total amount for skating to be less than $20.
Incorrect Response A
The inequality symbol means ‘greater than or equal to’. The solution set for the inequality 6.5h >
20 includes values of h that result in a total amount for skating greater than or equal to $20. Since
Edward wants the total amount for skating to be less than $20 this inequality is incorrect.
Incorrect Response B
The inequality symbol > means ‘greater than’. The solution set for the inequality 6.5h > 50
includes values of h that result in a total amount for skating to be greater than $20. Since Edward
wants the total amount for skating to be less than $20 this inequality is incorrect.
Incorrect Response C
The inequality symbol < means ‘less than or equal to’. The solution set for the inequality 6.5h < 20
includes the value of h that results in a total of $20. Since Edward wants the total amount for
skating to be less than $20 this inequality is incorrect.
6.EE - Expressions and Equations
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9 - Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the dependent
variable, in terms of the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using graphs and tables, and relate
these to the equation. Example For example, in a problem involving motion at constant speed, list
and graph ordered pairs of distances and times, and write the equation d = 65t to represent the
relationship between distance and time.
Question 6: Correct Response A
2n + 0.50(n – 50) = 2n + 0.5n – 0.5(50) = 2.50n – 25
Incorrect Response B.
The expression 2.50n + 25 is 50 greater than the correct expression.
Incorrect Response C.
The expression 2.50n – 50 is 25less than the correct expression.
Incorrect Response D.
The expression 2.50n + 50 is 75 greater than the correct expression.
6.EE - Expressions and Equations
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9 - Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the dependent
variable, in terms of the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using graphs and tables, and relate
these to the equation. Example For example, in a problem involving motion at constant speed, list
and graph ordered pairs of distances and times, and write the equation d = 65t to represent the
relationship between distance and time.
Page 3 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Question 7: Correct Response A
This situation can be described using the formula rx = d where r is the rate of speed in miles per hour,
x is time in hours, and d is distance in miles. In this situation, the rate, or average speed, is 48 mph, and
the distance is 278 miles. Substituting these values into the formula results in the equation 48x = 278.
So, the number of hours that Mary drove is x hours
Incorrect Response B
The equation that describes this situation is 278(48) = x, where x represents the total number of
crayons.
Incorrect Response C
The equation that describes this situation is 278 + 48 = x, where x represents the total amount of
money Franz made at his garage sale.
Incorrect Response D
The equation that describes this situation is 278 – 48 = x, where x represents the number of e-mail
messages left in Gino’s inbox.
6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2.a - Write expressions that record operations with numbers and with letters standing for
numbers. For example, express the calculation “Subtract y from 5” as 5 - y.
Reason about and solve one-variable equations and inequalities.
6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or, depending
on the purpose at hand, any number in a specified set.
Represent and analyze quantitative relationships between dependent and independent variables.
Question 8: Correct Response C
To find the number of servings, divide 5.7 by 0.05. Find an upper estimate and a lower estimate. Since
0.005 = 1 / 20, there are 20 portions in each ounce. Hot pepper sauce can be added to more than 20 x 5
= 100 servings and less than 20 x 6 = 120 servings. Thus, of the choices, 110 is closest to the number
of servings that can be made.
Incorrect Response A
0.05 ≠ ½, so there are not 2 portions in each ounce, or between 2 x 5 = 10 and 2 x 6 = 12 servings.
Incorrect Response B
Since 5.7 > 0.05, more than one serving can be made. Therefore,0.11 could not be the closest
number.
Incorrect Response D
0.05 ≠ 1 / 200, so there are not 200 portions in each ounce, or between 200 x 5 = 1,000 and 200 x 6
= 1,200 servings.
6.NS - The Number System
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2 - Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 - Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
Page 4 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Question 9: Correct Response B
This is correct, because addition is the correct operation to find the total amount of two quantities.
Therefore, 3⅓ + 2¼ is an appropriate model for this situation.
Incorrect Response A
This is incorrect, because division should be used to model this situation. Dividing 3⅓ by 2¼ and
increasing the result to the next whole number tells you how many trips Greyson will have to
make.
Incorrect Response C
This is incorrect, because multiplication should be used to model this situation. $2.25can be written
as 2¼ dollars, and therefore, 3⅓ x 2¼ represents this situation.
Incorrect Response D
6.NS - The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by
fractions.
6.NS.1 - Interpret and compute quotients of fractions, and solve word problems involving division
of fractions by fractions, e.g., by using visual fraction models and equations to represent the
problem. Example For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction
model to show the quotient; use the relationship between multiplication and division to explain that
(2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup
servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi
and area 1/2 square mi?
Question 10: Correct Response C
The mosquito’s original length is 0.2 inch. Each day, the mosquito grows 0.08 inch. To find the
mosquito’s length 4 days from now, we must add the amount of growth (0.08 inch) for each of the 4
days to its original length: 0.2 + 0.08 + 0.08 + 0.08 + 0.08 = 0.52 inch.
Incorrect Response A
This incorrect choice may result from adding 0.2 + 0.8 + 0.8 + 0.8 + 0.8 = 3.4 inches. But eight
hundredths of an inch is 0.08 inch, not 0.8 inches.
Incorrect Response B
This incorrect choice may result from adding the mosquito’s growth for 5 days. The correct answer
adds the insect’s growth for 4 days.
Incorrect Response D
This incorrect choice may result from adding 0.2 + 0.008 + 0.008 + 0.008 + 0.008 = 0.232 inch.
But eight hundredths of an inch is 0.08 inch, not 0.008 inches.
6.NS - The Number System
Apply and extend previous understandings of numbers to the system of rational numbers
6.NS.5 - Understand that positive and negative numbers are used together to describe quantities
having opposite directions or values (e.g., temperature above/below zero, elevation above/below
sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to
represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Page 5 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Question 11: Correct Response A
The pictorial representation of (–7) – (–2) = –5 shows an arrow of length 7 from 0 to –7 and then an
arrow of length 2 from –7 to –5.
Incorrect Response B
This represents (7) – (–2) = 9, not (–7) – (–2).
Incorrect Response C
This represents (–7) + (–2) = –9, not (–7) – (–2).
Incorrect Response D
This representation is not correct, the arrow for –(–2) should start where the arrow representing –7
ends.
6.NS - The Number System
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.5 - Understand that positive and negative numbers are used together to describe quantities
having opposite directions or values (e.g., temperature above/below zero, elevation above/below
sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to
represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.6 - Understand a rational number as a point on the number line. Extend number line diagrams
and coordinate axes familiar from previous grades to represent points on the line and in the plane
with negative number coordinates.
6.NS.6.a - Recognize opposite signs of numbers as indicating locations on opposite sides of 0
on the number line; recognize that the opposite of the opposite of a number is the number itself,
e.g., -(-3) = 3, and that 0 is its own opposite.
6.NS.6.c - Find and position integers and other rational numbers on a horizontal or vertical
number line diagram; find and position pairs of integers and other rational numbers on a
coordinate plane.
Question 12: Correct Response A
There are two rates in the chart. One rate is the cost for the first minute, and the remaining minutes are
charged at a different rate. A 9-minute phone call will cost $0.15 for the first minute and $0.10 for each
of the remaining 8 minutes. Therefore, the total cost of the phone call is given by the expression 0.15 +
(8)(0.10).
Incorrect Response B
In this expression, each minute is charged the same rate of $0.15. But after the first minute, each
minute of the phone call costs $0.10.
Incorrect Response C
In this expression, each minute is charged the same rate of $0.10. But the first minute of the call
costs $0.15.
Incorrect Response D
This expression gives the cost for the first minute of a call plus 9 additional minutes. Therefore,
this is the cost of a call that lasts a total of 10 minutes, not 9 minutes.
6.NS - The Number System
Apply and extend previous understandings of numbers to the system of rational numbers.
Page 6 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
6.NS.5 - Understand that positive and negative numbers are used together to describe quantities
having opposite directions or values (e.g., temperature above/below zero, elevation above/below
sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to
represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Question 13: Correct Response B
The greatest common factor is the largest number that divides both 10 and 40 with remainder zero. 10
divides both 10 and 40, and it is the largest number that divides 10 Therefore, 10 is the greatest
common factor of 10 and 40.
Incorrect Response A
10 is not divisible by 40, so 40 is not a common factor of both 10 and 40. (40 is the least common
multiple of 10 and 40.)
Incorrect Response C
5 is a common factor of 10 and 40, but it is not the greatest common factor.
Incorrect Response D
2 is a common factor of 10 and 40, but it is not the greatest common factor.
6.NS - The Number System
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2 - Fluently divide multi-digit numbers using the standard algorithm.
Question 14: Correct Response C
Since 48  5 9 3/5 is not a whole number, 5 is not a factor of 48.
Incorrect Response A
Since 48  3 = 16 is a whole number, 3 is a factor of 48.
Incorrect Response B
Since 48  4 = 12 is a whole number, 4 is a factor of 48.
Incorrect Response D
Since 48  6 = 8 is a whole number, 6 is a factor of 48.
6.NS - The Number System
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2 - Fluently divide multi-digit numbers using the standard algorithm.
Page 7 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Question 15: Correct Response A
The divisions between each whole number are in eighths. Point A lies six-eighths of the way between 7
and 8. Since 6/8 = 3/4, point A represents 7 ¾ .
Incorrect Response B
This point represents 8 3/8
Incorrect Response C
This point represents 8 6/8 = 8¾
Incorrect Response D
This point represents. 9 6/8 = 9¾
6.NS - The Number System
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.6 - Understand a rational number as a point on the number line. Extend number line diagrams
and coordinate axes familiar from previous grades to represent points on the line and in the plane
with negative number coordinates.
6.NS.6.c - Find and position integers and other rational numbers on a horizontal or vertical
number line diagram; find and position pairs of integers and other rational numbers on a
coordinate plane.
Question 16: Correct Response A
If Katie gets $3 per hour, then she earns
dollars for h hours of work. If she gets paid $2 in addition
to the 3h dollars, she receives a total of 3h + 2 dollars.
Incorrect Response B
If Katie were to get paid $3to babysit for 2 hours, plus an additional $2, then for h hours of work,
she would get 3h/2 + 2 dollars.
Incorrect Response C
If Katie were to get paid $2 per hour to babysit for the first hour and $3 for each additional hour
then for h hours of work, she would get 2 + 3(h – 1) dollars.
Incorrect Response D
If Katie were to get paid $2 for the first hour of babysitting and 3 times as much for each additional
hour, then for h hours of work, she would get 2 + 6(h – 1) dollars.
6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2.a - Write expressions that record operations with numbers and with letters standing for
numbers. Example For example, express the calculation “Subtract y from 5” as 5 - y.
Reason about and solve one-variable equations and inequalities.
6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or,
depending on the purpose at hand, any number in a specified set.
Represent and analyze quantitative relationships between dependent and independent variables.
Page 8 of 9
Grade 6 Mid-Year Check In: Math
Teacher Instructions & Answer Key
SY: 2013-14
Question 17: Correct Response C
The solution to the equation 36 = 2a + 6 is 15. So, Rachael’s age, a is 15 years. Working backward, we
can find that 15 times 2 plus 6 is equal to 36 years, the age of Rachael’s sister. So, the equation 36 = 2a
+ 6 best represents Rachael’s age.
Incorrect Response A
This choice may be the result of a misunderstanding of the process of translating words into an
equation. The solution to the equation ½a = 36 – 6 is 60 which would mean that Rachael’s age, a is
60 years. However, working backwards, we would then find that the age of Rachael’s sister is 60
multiplied by 2 plus 6, which is equal to 126 years. But Rachael’s sister is 36 years old. Therefore,
the equation ½a = 36 – 6 cannot be used to find Rachael’s age.
Incorrect Response B
This choice may be the result of a misunderstanding of the process of translating words into an
equation. The solution to the equation a = 36 – 2(6) is 24 which means that Rachael’s age, a,is 24
years. However, Rachael’s sister is 6 years older than twice Rachael’s age, which would make
Rachael’s sister 6 + 2(24) = 54 years old, instead of 36 years old.
Incorrect Response D
This choice may be the result of a misunderstanding of the process of translating words into an
equation. The solution to the equation 36 = 2a – 6 is 21, which means that Rachael’s age, a, is 21
years. However, Rachael’s sister is 6 years older than twice Rachael’s age, which would make
Rachael’s sister 6 + 2(21) = 48 years old, instead of 36years old.
6.EE - Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.2 - Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2.a - Write expressions that record operations with numbers and with letters standing for
numbers. Example For example, express the calculation “Subtract y from 5” as 5 - y.
Reason about and solve one-variable equations and inequalities.
6.EE.6 - Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or, depending
on the purpose at hand, any number in a specified set.
Represent and analyze quantitative relationships between dependent and independent variables.
Question 18: (2pts)
Correct Response: 4 suits; no fabric left over
Question 19: (2pts)
Correct Response: 8 is a composite number because it has more than 2 factors: 1, 2, 4, and 8
Question 20: (4 points)
a. Students should set up a verbal model that includes the following:
Newspaper recycled + Newspaper to be recycled = Goal OR
Goal - Newspaper recycled = Newspaper to be recycled
b. Verbal model should include:
Newspaper recycled = 1585; Newspaper to be recycled = n; Goal = 2000
c. 1585 + n = 2000 or 2000 - 1585 = n
d. They still have 415 pounds of newspaper to recycle.
Page 9 of 9