Mathematics: Reasoning and Problem
Solving With complete solutions
2025/2026
A first-grade student is asked to find the total value of the following coins: 3 dimes, 1 nickel, and
4 pennies.
The student's response is that the coins are worth $0.12.
Based on this response, what concept does this student likely need help with?
A
how to correctly write the value of a set of coins
B
recognizing different coins and their respective values
C
understanding that different coins have different values
D
remembering to check their work - correct answer ✔✔recognizing different coins and their
respective values
Sarah wants to buy a sandwich, chips, and a drink for lunch. The sandwich cost $3, the chips
cost $1.50 and the drink costs $1.25. What information is needed to determine if Sarah has
enough money to cover the cost of her lunch?
A
The total amount of money she has to spend on lunch.
B
The number of coins she has.
C
,The number of ounces in her drink.
D
The total cost of her lunch. - correct answer ✔✔The total amount of money she has to spend on
lunch.
Mallory has $2.16 in her pocket to buy an apple and a bag of chips. What information is needed
to determine how much money Mallory will have left after she makes her purchase?
A
how many apples Mallory has in all
B
the cost of the apple and the chips
C
how many coins she used to make her purchase
D
how many coins she has remaining - correct answer ✔✔the cost of the apple and the chips
Mrs. Dobbs is teaching students to skip-count by 2s, 5s, and 10s in her second-grade class.
Earlier in the year, she evaluated her students learning style and assigns them one task based on
this evaluation. Visual learners have been given a number line and they are to draw the hops
across the top. Auditory learners have been given a list of the even number to 20, numbers
divisible by 5 to 50 and numbers ending in 0 up to 100. They are told to say them over and over
aloud to memorize the skips. Kinesthetic learners have been given a large number line on the
floor. They are jumping to the next number as they skip-count. What can Mrs. Dobbs do to
improve her teaching?
A
Allow all students to participate in all three activities by rotating through them.
B
Allow for more creativity by letting students make an art project out of drawing or write a song
as they recite numbers.
,C
Require them to participate in the jumping ac - correct answer ✔✔Allow all students to
participate in all three activities by rotating through them.
Mr. Romeo wants his students to understand that math is very important and used in the real
world all the time. He wants them to understand that math is used outside of school on a
regular basis. Which of the following is the best way to have students learn about this?
A
Make students do a hands on project that uses math.
B
Have students interview two adults about how they use math in their everyday life.
C
Have students teach their younger siblings to use math to solve problems.
D
Make students read a book about famous mathematicians. - correct answer ✔✔Have students
interview two adults about how they use math in their everyday life.
Does the following given statement: "a rectangle is a square" apply to all problems?
A
No, because this rectangle is not a square.
B
Yes, because all squares are rectangles.
C
No, because not all rectangles are squares.
D
Yes, because all rectangles are squares. - correct answer ✔✔No, because not all rectangles are
squares.
, A student asks a teacher when calculating percentages of numbers will be useful in real life.
Which of the following examples would be the most appropriate response for the student?
A
a builder cutting materials for a house
B
a architect designing a building
C
a pharmacist measuring the correct amount of medication
D
a mother going shopping at a store sale - correct answer ✔✔a mother going shopping at a store
sale
A sixth-grade student asked his teacher the value for 0 ÷ 0. What is the answer to this student's
question?
A
It is infinity.
B
It is equal to 0.
C
It is indeterminate.
D
It is equal to 1. - correct answer ✔✔It is indeterminate.
In division, 6 ÷ 3 = 2 because 3 • 2 = 6; and any number divided by itself is equal to 1. In general,
a ÷ b is asking the question, "how many groups of size b are there in a?" So, it is pretty well
understood that 0 ÷ n = 0, where n is any number. There are 0 groups of size n in 0, and n • 0 =
0. It is also pretty well understood that division by 0 is not allowed; the mathematical term used
is "undefined". But the problem of 0 ÷ 0 is rather different. It is a number divided by itself, so it
seems that we could say that 0 ÷ 0 = 1. It also follows that 0 • 1 = 0. So, what is the problem?
Solving With complete solutions
2025/2026
A first-grade student is asked to find the total value of the following coins: 3 dimes, 1 nickel, and
4 pennies.
The student's response is that the coins are worth $0.12.
Based on this response, what concept does this student likely need help with?
A
how to correctly write the value of a set of coins
B
recognizing different coins and their respective values
C
understanding that different coins have different values
D
remembering to check their work - correct answer ✔✔recognizing different coins and their
respective values
Sarah wants to buy a sandwich, chips, and a drink for lunch. The sandwich cost $3, the chips
cost $1.50 and the drink costs $1.25. What information is needed to determine if Sarah has
enough money to cover the cost of her lunch?
A
The total amount of money she has to spend on lunch.
B
The number of coins she has.
C
,The number of ounces in her drink.
D
The total cost of her lunch. - correct answer ✔✔The total amount of money she has to spend on
lunch.
Mallory has $2.16 in her pocket to buy an apple and a bag of chips. What information is needed
to determine how much money Mallory will have left after she makes her purchase?
A
how many apples Mallory has in all
B
the cost of the apple and the chips
C
how many coins she used to make her purchase
D
how many coins she has remaining - correct answer ✔✔the cost of the apple and the chips
Mrs. Dobbs is teaching students to skip-count by 2s, 5s, and 10s in her second-grade class.
Earlier in the year, she evaluated her students learning style and assigns them one task based on
this evaluation. Visual learners have been given a number line and they are to draw the hops
across the top. Auditory learners have been given a list of the even number to 20, numbers
divisible by 5 to 50 and numbers ending in 0 up to 100. They are told to say them over and over
aloud to memorize the skips. Kinesthetic learners have been given a large number line on the
floor. They are jumping to the next number as they skip-count. What can Mrs. Dobbs do to
improve her teaching?
A
Allow all students to participate in all three activities by rotating through them.
B
Allow for more creativity by letting students make an art project out of drawing or write a song
as they recite numbers.
,C
Require them to participate in the jumping ac - correct answer ✔✔Allow all students to
participate in all three activities by rotating through them.
Mr. Romeo wants his students to understand that math is very important and used in the real
world all the time. He wants them to understand that math is used outside of school on a
regular basis. Which of the following is the best way to have students learn about this?
A
Make students do a hands on project that uses math.
B
Have students interview two adults about how they use math in their everyday life.
C
Have students teach their younger siblings to use math to solve problems.
D
Make students read a book about famous mathematicians. - correct answer ✔✔Have students
interview two adults about how they use math in their everyday life.
Does the following given statement: "a rectangle is a square" apply to all problems?
A
No, because this rectangle is not a square.
B
Yes, because all squares are rectangles.
C
No, because not all rectangles are squares.
D
Yes, because all rectangles are squares. - correct answer ✔✔No, because not all rectangles are
squares.
, A student asks a teacher when calculating percentages of numbers will be useful in real life.
Which of the following examples would be the most appropriate response for the student?
A
a builder cutting materials for a house
B
a architect designing a building
C
a pharmacist measuring the correct amount of medication
D
a mother going shopping at a store sale - correct answer ✔✔a mother going shopping at a store
sale
A sixth-grade student asked his teacher the value for 0 ÷ 0. What is the answer to this student's
question?
A
It is infinity.
B
It is equal to 0.
C
It is indeterminate.
D
It is equal to 1. - correct answer ✔✔It is indeterminate.
In division, 6 ÷ 3 = 2 because 3 • 2 = 6; and any number divided by itself is equal to 1. In general,
a ÷ b is asking the question, "how many groups of size b are there in a?" So, it is pretty well
understood that 0 ÷ n = 0, where n is any number. There are 0 groups of size n in 0, and n • 0 =
0. It is also pretty well understood that division by 0 is not allowed; the mathematical term used
is "undefined". But the problem of 0 ÷ 0 is rather different. It is a number divided by itself, so it
seems that we could say that 0 ÷ 0 = 1. It also follows that 0 • 1 = 0. So, what is the problem?
