Practice Test: Mathematics Flashcards
Which of the following is equivalent to 1/200?
1/2 or 1% (5% = 1/20, 2% = 4/200, 0.200 = 0.2 = 2/10)
Mr. G had 30 pencils for his students. Three students wanted two pencils each. Then, a new student came to school that day and he wanted three pencils. Then, one of the first three students gave their two pencils back. how many pencils did Mr. G have left to pass out? Which formula provides the correct solution to the problem?
30 - (3 x 2) - 3 + 2
*Which of the following illustrates the property of reciprocals?
the product of 31 and 1/31 equals 1 (property of reciprocals states that any number (a) multiplies by 1 divided by that number (1/2) equals 1)
Mr. R teaches 3rd grade. his students’ averages for last year are plotted on the graph. Which conclusion can be drawn from the data?
the greatest gains from 1st quarter to 4th quarter were made in history (see graph)
A school wants to create a vegetable garden for students as an applied science project. The school principal wants you to go see a supplier in order to order a fence for it. The garden is 30 feet wide and 44 feet long; however, there will be a gate which is 4 feet wide. How many feet of fending are needed?
144 feet
perimeter = 2(30) + 2(40) = 148
gate = 4 feet
148 - 4 = 144
*A certain kind of bacteria moves slowly, taking steps that have a distance of 0.0000002 feet each. If the bacteria take 4,250,000,000 steps, how far will it travel?
850 feet
Total distance = size of step x number of steps D = 0.0000002 x 4,250,000,000 D = (2 x 10^-7) x (4.25 x 10^9) D = (2 x 4.25) x (10^-7 x 10^9) D = (8.50) x (10^2) D = 8.5 x 100 D = 850 feet
Principal S passes Mr. C’s classroom and sees the following written on the board: PEMDAS and Please Excuse My Dear Aunt Sally. Principal S concludes that the focus of the lesson is _______.
order of operations
PEMDAS
(parentheses, exponents, multiplication, division, addition, subtraction)
Ms. B gives an exam to her class. The scores are as follows: 75, 80, 95, 90, 70, 65, 80, 100, 60, 80, 90, 70, 55, 50. Which of the following statements are true?
The median is 80; the mode is 80; the mean is 76
A principal is walking past a teacher’s classroom and overhears him say the following: “So the numbers in this set have exactly two whole-number factors-1 and the number itself.” When the principal peeks into the door, she sees the numbers 2, 3, 5, 7, 11, 13 , 17 written on the board. Which Sunshine State Math Standard is the teacher addressing?
determine the prime factorization of numbers (numbers w/exactly two whole-number factors that are 1 and the number itself is the definition of prime numbers)
*Six students at the Florida Virtual School sign up for a group project. Since they don’t know each other, the teacher suggests that each student call the other students individually to get to know each other. How many phone calls will there be?
15 (5 + 4 + 3 + 2 + 1 = 15)
*Absolute standard deviation is a measure of _________.
variability
Results showed that 31 students at West High School failed the FCAT test. If that represents about 5.5% of the students, what is the population of the school?
564 students
0.055x = 31 31/0.05 = 563.63
*Which is the correct sequence (largest to smallest) for the following measurement abbreviations?
km (kilometer), m (meter), dm (decimeter), cm (centimeter), mm (millimeter)
Which shape is smooth with no edges?
ovoid
*Ms. P’s students are at a pictorial level in terms of development. What is an example of something that her students might be using in math class?
drawings
Learner-centered instruction is based on ______ theories.
constructivist
Ms. F is teaching her students about volume. What would be a good manipulative for her to use?
capacity contrainers
What is a learning progression?
concepts and procedural steps in math that occur over time
*How many thousands are in a million?
1,000
1,000 = 10^3
1,000,000 = 10^6
10^6/10^3 is 10^3 or 1,000
A teacher wants to do small group projects in her class and needs to buy supplies. Each group will do the same project. What information does she need to determine the cost of the project supplies for the class?
total cost supplies for one project and number of groups
*A farmer picked twice as many oranges in the afternoon than he picked in the morning. During the whole day he picked 360 oranges. How many oranges did he pick in the morning and how many in the afternoon?
120 morning, 240 afternoon
x + 2x = 360
3x = 360
x = 120
2x = 240
((6^{2})^{4} = )
(6^{8})
exponent outside of parenthesis indicates multiplication, 2 x 4 = 8
Ms. G is using a strategy that involves a “teaching pint.” What strategy is Ms. Green using?
math workshop (modeled on the reading workshop model which includes a teaching point)
What’s the difference between collaborative and cooperative learning?
Cooperative learning is more structured than collaborative learning (cooperative learning, assigns roles and responsibilities)
What is the relationship between ‘subtilize’ and ‘iterations’?
subitize is an estimate and iteration is repeated estimations
*Mr. Sanders wrote the following on the board: A^2 + B^2 = C^2
This is an example of
thinking at an abstract level.
abstract thinking involves symbols, expressions, and formulas
Ellie has been asked to estimate how many items she sees. There are 3 groups of 5 cubes. What process is she most likely to be using?
subitizing
skill to see and estimate the number of items
Students in a fifth-grade class need to buy a protractor and a compass for math class. The combined cost for both items is $7.59 (without tax). The cost of the compass is $3.99 more than the protractor. Which of the following equations can a student use to determine the cost of the protractor?
$7.59 = x + (x + $3.99)
Mr. Gleason is answering a question in math class. His answer is “You do so by dividing the numerator by the denominator.” What was the question?
How do you change a fraction into a decimal?
*Ms. Johnson's students have been learning about metric and customary units. Which of the following is correct? A. A meter is longer than a yard. B. A kilometer is longer than a mile. C. A kilogram is less than a pound. D. A liter is less than a quart.
A. A meter is longer than a yard.
*Susan brought a water bottle from home. She wants to measure its capacity. What unit of measurement should she use? A. kilogram B. millimeter C. liter D. pound
C. liter
Mr. Wood’s class averaged 84 points on the last exam. What can be said about the class?
The class mean is 84.
Which math prefix and amount are correctly matched?
Kilo = 10^?
Kilo = 10^3
*Which figure has the fewest number of parallel lines?
trapezium
*Which description best describes a scatter plot?
points on an x-axis and y-axis showing correlations
Mr. Anthony is using the following manipulative in his classroom: An oblong frame with rows of wires or grooves along which beads are moved. What is Mr. Anthony likely to be teaching?
operations on whole numbers
In terms of developmental skills, Mrs. Camp’s students are developing reasoning skills in concrete and real-life situations. What is most likely to be the age of students in Mrs. Camp’s class?
8 years
Casey is learning about the property of reciprocals. Which of the following notations would exemplify what she is learning?
5 x 1/5 = 1
Which of the following is a composite number? A. 9 B. 11 C. 13 D. 7
A. 9
composite number is one that can be expressed as several whole-number factors. 9 can be expressed as 3 x 3 or 9 x 1
Which of the following concepts are correctly paired?
A. hands-on math and scientific notation
B. composite numbers and exponential notation
C. integers and decimals
D. ratio notation and fractions
D. ratio notation and fractions
*Which of the following is a customary unit? A. liter B. ton C. meter D. gram
B. ton
all other are metric terms
Ms. Carlisle gave her students a spelling test that had a maximum of 20 points. Students had the following scores: 5, 5, 5, 5, 5, 11, 12, 12, 13, 20. What measure of central tendency would be best to use?
median
Kristin is solving a problem. She wants to cover the outside of her locker with an adhesive fabric. Which estimation strategy would be best to try?
make a sketch
What is true of the following figures? (see picture)
They are similar
What is true of a coordinate plane?
ti has 4 quadrants
*Mrs. Castleberry uses a constructivist approach for teaching math in her second-grade classroom. What would you expect to see in the classroom?
an interactive whiteboard
allows the teacher and students to work with and manipulate math concepts
Mr. Marco has a large box of color tiles. He is using them to help students understand successive estimations as a problem-solving approach for larger groups of items. This reflects the concept of
iterations
(3^2)3^3=
3^5
when multiplying two numbers that consist of the same base and exponents the exponents are are added
*Convert .875 to a fraction
7/8
Convert .233 to a percentage.
23.30%
Which of the following is factually correct?
A. Integers can be expressed as fractions.
B. There are more fractions than whole numbers.
C. Not all fractions can be expressed as integers.
D. All of the above are factually correct.
D. All of the above are factually correct.
A truck container is 10 feet high, 10 feet wide, and 25 feet long. What is the volume of the container?
C. 2500 ft^3
volume is in cubic feet
Kendra is plotting data on a coordinate plane. In which quadrant should she place (3, -2)?
Quadrant 4
Mr. Fuqua wants to know if there is a relationship between the day of the week and the number of absences. He tracks this data over the course of a year. What should he use to present the data?
a frequency chart
Given the following shapes, what is the relationship between them? (see figure)
The second figure is a rotated version of the first figure
Principal Fitzmorris has put together a presentation. He wants to show the number of students in each grade as a proportion of the total number of students at the school. What should he use?
pie chart
Cassie is solving the following math problem.
The number of people going to a movie on Monday is 95. If increased by a factor of 5 on Saturday night, what is the attendance at the movie on Saturday night?
What process should Cassie use?
multiply 5 by 95
Mrs. Foret told her class that the distance from the Earth to the sun is approximately 1.4959826 x 10^8 km. The number is equal to which of the following?
149,598,260 km
In terms of number theory, which of the following is true?
A. Parity describes a number that only has 2 factors - the number itself and 1.
B. Factors, when divided, result in a product.
C. Only whole numbers ending in 0, 2, 4, 6, and 8 are divisible by 2.
D. 0 is a prime number because it is divisible by itself.
Only whole numbers ending in 0, 2, 4, 6, and 8 are divisible by 2
*Which of the following statements about numbers is true?
A. Multiplication is repeated subtraction
B. Whole numbers are the same as counting numbers.
C. A fraction is the same as a rational number
D. In the number 32, 3 is the exponent and 2 is the base.
A fraction is the same as a rational number
Ms. Wood is using a contextual approach to teaching math to her first-grade class.
What would you expect to see in her classroom?
students learning about measurements by making recipes
*Kaitlyn is using tans in her class. What mathematical concept is Kaitlyn most likely to be learning?
spatial reasoning
tans are flat shapes in a dissection puzzle which facilitates the development of visual, spatial thinking
*Measures of central tendency
describe data as a single number
measures of central tendency include mean, median, and mode that can be reported as a single number
In the following data set, 9 is which of the following?
1, 4, 6, 7, 9, 13, 14, 14, 21
median
In a data set, what is the average distance from each data point in the set to the average?
the absolute standard deviation
*Mr. Green is teaching his third-grade students about money and money management using “Green Bucks.” Just as workers get paid to come to work, his students get “paid” to come to class and get there on time. His students also get paid for their “work” in class or for homework. Higher grades get more money; however, students can get paid “overtime” by correcting their work. He has a variety of ways in which students can spend their money. They can buy small items at the “Green Store” each week, purchase recess or free time, or save for monthly “Big Green Deals.” What method is Mr. Green using?
simulation
created situation modeled on a workplace
*Each day, Mr. Varnado has a “problem of the day” as bellwork for his 5th grade class. In today’s problem, he shows them how to use 8 toothpicks to make the shape of a fish. Then he challenges them to move 3 of the toothpicks so that the fish is going in the opposite direction. This type of problem would be classified as a
puzzle
situation that require ingenuity for the solution
Which of the following is equal to 16?
16^1
*Ms. Cane’s fifth-grade math class has been learning about expressions. Which student made the correct comment about expressions?
A. Greg: 3x + 12 is an example of a number sentence.
B. Collier: Verbal expressions use the language of math.
C. Luke: Expressions and equations are the same things.
D. Lola: Variables are used in expression but not in equations.
B. Collier: Verbal expressions use the language of math.
Jennifer is sorting beads. She has made several groups. One group contains beads that are both red and round. One group contains beads that are both blue and round. One group contains beads that are both blue and square. One group contains beads that are both red and square. In Piagetian terms, Jennifer’s ability to sort beads is at the
concrete level
Mr. Morehouse is grading papers. He sees that Elsa incorrectly solved the following 4 problems:
18 95 73 22 88
23 18 27 29 66
__ __ __ __ __
311 1013 910 411 ?
If Elsa continues to make the same mistake, what would her answer be for the last problem?
1414
student was not carrying from the ones place to the tens place
Becky is learning about place value. Given the number, 1345.29, which of the following is correctly matched with its place value?
5, ones place
Mr. Ellis is teaching his first-grade students subtraction and wants them to understand the correct vocabulary for each part of a problem. Given the problem 12 – 3 = 9, which word would be used to label the 3?
subtrahend
subtrahend is the number that is being subtracted. 12 is the minuend. 9 is the difference
6(5 + 3) = (6 x 5) + (6 x 3) exemplifies
the distributive property of multiplication over addition
PEMDAS is an acronym for remembering
the order of operations
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- Ms. R shows a student the following and asks, “without counting, what do you think is the best answer for the number of items? Two, Five, or Ten?” What is the focus of this question?
* *
*
* *
subitizing
Mr. H will be using Cuisenaire rods today with his class. The content of the lesson is most likely to be
basic mathematical operations
What operation does the phrase “decreased by a factor of” signal?
division
In terms of number theory concepts and properties, which of the following is true?
“a number is divisible by 6 if…”
a number is divisible by 6 if it is divisible by both 2 and 3
Mr. F has written the following on the board: 3.6 x 10^5. Mr. F’s lesson is most likely on the subject of
scientific notation
*What is true systems and units of measurement?
capacity is another name for volume
What is true of central tendency?
to determine the range, subtract the smallest number in the set from the highest number
A team of 3 students is working on a science project. They need to compare the distance from the sun to the earth and the earth to the moon in metric units. What unit would b best for them to use?
Kilometer
What is true of ordered pairs in the four quadrants of a rectangular coordinate system?
the center of the coordinate plane is called the origin
*Which of the following statements are true regarding the ability to interpret tables, graphs, equations, and verbal descriptions of real world situations?
I. A bar graph is used to track one or more subjects, usually over time.
II. A line graph depicts percentages of a particular subject
III. All of the slices within a circle graph show the totality of a quantity
IV. A table organized large amounts of information
C. III and IV
III. All of the slices within a circle graph show the totality of a quantity
IV. A table organized large amounts of information
Mrs. Larkin wants to use hands-on experiences to help her kindergarten students learn number concepts. Which material will help her achieve that goal?
using toy cars to practice addition facts
real objects
Mr. Kennedy often pairs students in his algebra class so that knowledgeable students can help their partners gain mastery. What grouping strategy is Mr. Kennedy using?
peer tutoring
one student helping another student master a concept
n terms of scientific notation, 349000000=3.49×_
10^8
Which of the following is sequenced correctly from smallest to largest?
A. meter, centimeter, decimeter, millimeter, kilometer
B. millimeter, centimeter, decimeter, meter, kilometer
C. decimeter, centimeter, meter, kilometer, millimeter
D. kilometer, meter, millimeter, decimeter, centimeter
B. millimeter, centimeter, decimeter, meter, kilometer
What operation is needed to solve the following problem?
The width of a classroom was increased by a factor of 2 to determine the length of the classroom. What is the length of the classroom?
multiplication
In which equation does Y stand for the addend? A. Y 3 = 12 B. Y + 5 = 17 C. Y - 5 = 25 D. Y x 5 = 3
B. Y + 5 = 17
Which of the following is a measure of variability? A. range B. mean C. mode D. median
A. range
Ms. Gleason has the following written on her board: a×b=b×a. What is the focus of her lesson?
C. commutative property of addition
Which of the following can be used to measure mass?
gram
Ms. Penny is teaching her third-grade students how to handle money and make change. She has a created a “play store” in her classroom in which students practice selling objects and making change. This approach is best described as
a simulation
Mrs. Bell’s algebra class is learning the formula for solving quadratic equations. In terms of teaching, this would be at the ____________ level.
abstract
Mr. Leo’s class is learning about graphics. Mr. Leo said, “For this type of graphic, remember that it shows how one unit is divided into parts.” What type of graphic is the focus of the lesson?
circle graph
Which number is a prime number? A. 27 B. 39 C. 127 D. 143
127
Mrs. Lake is teaching her class a math lesson. She just said, “. . . .and to do so, you will divide numerator by denominator.” What is the focus of the lesson?
converting a fraction to a decimal
Solve: 100–(2^2)^3×1/2+(18÷2)
27
*Kevin is solving the following problem: How many hours will a car traveling at 75 miles per hour take to catch up to a car traveling 55 miles per hour if the slower car starts one hour before the faster car? Kevin decides to create a frequency table with 3 rows (hours, slower car distance, faster car distance) to organize the data. What numbers should Kevin write in row 3?
1 Hour 1 2 3 4
2 Slower
Car 55 110 165 220
3 Faster
Car0, 75, 150, 225
A third-grade class is getting an aquarium. The aquarium measures 23 inches by 16 inches by 12 inches. If the aquarium is filled to the top, which formula would be used to determine the capacity of the aquarium?
length×width×height
The following shape Image can be described as a _____________. (see image) 4 sided figure with no parallel lines
trapezium
4 sided figure, no parallel lines
Angelina has some marbles. As she plays with them and without counting them specifically, she sees that she has 5 marbles. This realization involves _________________.
subitizing
Tim is walking to school and sees a school crossing sign. He realizes that the sign is in the shape of a ____________________. (see image) 5 sided figure
pentagon
*Ms. Brandt’s class is learning about odd and even numbers. Another name for this content is _________________.
parity
Solve: 8^0+8^1–8^2
-55
1 + 8 - 64 = 55
Simplify 15–3(8–3)^2÷5.
answer: 0 15-3(8-3)^2 ÷ 5 15-3(5)^2 ÷ 5 15-3(25) ÷ 5 15-75 ÷ 5 15 - 15 = 0
5 x 10^0
5
*What is an example of educational scaffolding?
A. First grade students use flashcards to review math addition facts.
B. A teacher uses think-alouds to model thought processes in solving a word problem.
C. Kindergarten students use capacity containers of varying sizes to fill containers.
D. A teacher works with other teachers to create common activities for seventh-grade math students.
B. A teacher uses think-alouds to model thought processes in solving a word problem.
Kacy is solving the following problem:
Mr. Thomas and Mr. Smith are planning trips. Mr. Thomas will travel 150 miles on day 1. On days 2-5 he will travel 50 miles farther than the preceding day. Mr. Smith will travel 100 miles on day 1. On days 2-5 he will travel 100 miles farther than the preceding day. Which person traveled the greatest distance on his trip?
Kacy has created a table to help her solve the problem. Will she get the correct answer? (see chart)
No. The numbers for day 1 are correct for both Mr. Thomas and Mr. Smith; however, the numbers of days 2-5 for Mr. Smith should be 200, 300, 400 and 500.
Christopher is learning about the meanings of metric prefixes. Which prefix and meaning are correctly matched? A. hecto, 10^2 B. deka, 10^0 C. centi, 10^–1 illi, 10^3
A. hecto, 10^2
Given the ordered pair (3, -1), in what quadrant would it fall on a coordinate plane?
Quadrant 4
The perimeter of a rectangle is 16. What is the length and width?
The length is 5 and the width is 3
Ms. Jamison’s class is learning about patterns. Ms. Jamison provides them with the following pattern of numbers: 14, 15, 17, 20, 24, 29, 35. . . . What is the next number in the pattern?
42
Ms. Van Pelt asked students to explain the process they used to solve a problem. Which student used an invented strategy?
A. Phil: In adding 33 + 44, I added the 3 and 4 in the ones column to get 7. I added the 3 and 4 in the tens column to get 7. The answer is 77.
B. Katherine: In adding 92 + 98, I added the 2 and 8 in the ones column to get 10. I wrote the 0 in the ones column and added the one to the sum of 9 and 9 in the tens column to get 19. The answer is 190.
C. Luke: In adding 24 + 36, I added 20 plus 30 to get 50. I added 4 and 6 to get 10. I added 50 plus 10 to get 60.
D. Patrick: In adding 20 + 30, I knew that 0 + 0 equals 0, so I wrote 0 in the ones place. Then I added the 2 and the 3 to get five in the tens place. The answer is 50.
C. Luke: In adding 24 + 36, I added 20 plus 30 to get 50. I added 4 and 6 to get 10. I added 50 plus 10 to get 60.
Mr. Evans is grading Carl’s math test. He sees that when the problem is numerical, Carl’s answers are correct; however, if the same problem is presented as a word problem, Carl uses the incorrect formula for solving the problem. What comment should Mr. Evans write on Carl’s paper?
You understand the formulas, but cannot apply them to real-world situations.
Ms. Duncan’s students have the following scores on a math test. What is true of the scores?
100 50 65 90 95 85 75 100 100 90
The average is 85.
Based on the information in Question 33, what is the absolute standard deviation for the scores on Mrs. Duncan’s math test?
13
Alyssa is adding 37, 11, and 22. She thinks, “7 + 1 + 2 = 10 and 30 + 10 + 20 = 60 and 60 + 10 = 70 so the answer is 70.” What process is she using to solve the equation?
compensation
form of addition in which numbers are grouped by tens and ones
How would the following numbers be sequenced from smallest to largest on a number line? A. –.55, –.555, .05, .5, .505, 005 B. –.55, –.555, .005, .5, .05, .505 C. –555, –.55, .005, .05, .505, .5 D. –.555, –.55, .005, .05, .5, .505
D. –.555, –.55, .005, .05, .5, .505
Which sign makes the following statement true?
18?(50÷25)=9
÷
18 ÷ (50 ÷ 25) = 9
18 ÷ 2 = 9
Convert 1/8 to a decimal.
.125
Amanda is at the grocery store. She bought 2 loaves of bread for $1.39 each, 1 quart of milk for $2.83, a bag of apples for $3.29, and 2 jars of peanut butter for $2.89 each. As she puts items in her shopping cart, she mentally estimates how much the total will be. To the nearest dollar, Amanda estimates the cost to be approximately_____________.
15
Ms. Arton’s students are working in small groups on computers to conduct research for their math projects. As she walks around the room, she notices that some students have difficulty interacting in the groups and that others are having problems using the technology. This is an example of
behavioral assessment
In terms of cognitive complexity and depth of learning in the Florida Standards Depth of Knowledge Levels, which activity is at the Moderate: Basic Application of Skills & Concepts level?
A. Ms. Berry’s first-grade class celebrates the 100th day of school by bringing collections of 100 items.
B. Mrs. Ingram’s third-grade class uses computer software to review math vocabulary.
C. Mrs. Logan’s fifth-grade class determines how much food and supplies are needed for a class party.
D. Mr. Carpenter’s third-grade class records and graphs weather data.
D. Mr. Carpenter’s third-grade class records and graphs weather data.
Mr. Jeffries has ordered some new materials for his first-grade math class. One of the items he ordered is a set of ten different colored, rectangular pieces ranging in lengths from 1 cm to 10 cm. What material is this?
cuiseinaire rods
Which array best demonstrates the following problem?
A school serves four vegetables daily. How many vegetables are served each week?
∘∘∘∘ ∘∘∘∘ ∘∘∘∘ ∘∘∘∘ ∘∘∘∘
Which fraction converts to a repeating decimal?
1/3
In the equation 37 x 16 = 592, 592 is called the
product
What is true of fractions?
They can be written as decimals
The relationship between two variables is
a correlation
Which of the following is a summative assessment? A. screening assessment B. unit exam C. exit slip D. pre-test
B. unit exam
In the following figure, what point is (-2,4)?
see figure
left 2, up 4, quadrant II
Which of the following is an example of a customary unit? A. liter B. gram C. pint D. meter
Which of the following is an example of a customary unit?
pint
