FTCE Subject Area Math
Which point is closest to the point located at (3.4)
(3,7)
Which of the following illustrates the associative property of addition?
(a + b) + c= a + (b +c)
What is the value of X that makes the equation true? (X+7)/6+(2X-8)/2= -4
-1
Simplify the following: 96 / 4^2 + (4 x 2)- 15 - 3
-4
The temperature in northern Minnesota at 6.00 p.m. was 5 degrees below zero. By 7:00 p.m., the temperature had dropped another 3 degrees. What was the temperature at 7:00 p.m.?
-8 degrees
A jar contains five more quarters than dimes. If it contained a total of $2.30, which of the following equations can be used to determine the number of quarters in the jar?
0.10x + 0.25(x + 5)= 2.30
The entire figure represents one unit. The shaded portion of the figure illustrates which of the following? [This is a 10 x 10 grid with 3 vertical by 4 horizontal squares shaded]
0.12
Together, four students wrote a 60-page book. Sean wrote 1/4 of the book. Sara wrote 1/3 of the book, and Jermaine wrote 1/6 of the book. What fraction represents the portion of the book that Maria wrote?
1/4
Simplify the following: 90 - 60 - 30 + 10
10
Which of the following expressions is the correct way to use exponents to write one hundred thousand?
10^5
Find the least common multiple of 8, 15, & 60
120
A pair of baseball team competed 2 innings of a game in 28 minutes. If the game continues at the same pace, how many minutes will it take to complete a 9 inning game?
126 minutes
A student working as a sales clerk at a local store earns $12 per hour and 3 percent commission of all sales made. If the student works for h hours and makes s dollars of sales, which of the following expressions represents the total amount of money the student earns?
12h + 0.03s
Two students start at the same point and run in opposite directions. The first student runs 10 feet per second to the left for 8 seconds. The second student runs 8 feet per second to the right for 7 seconds. How many feet apart are the two students after they both stop?
136 feet
If the patter continues, which of the following patterns would represent how many there are in the 8th step? Step 1: 1 Step 2: 3 Step 3: 5 Step 4: 7 Step 8: ?
15
Estimate the length of a U.S. Dollar bill
15 cm
Simplify the given expression 8X-4(2X-5)-2
18
What is the value of 1 3/4 / 2/3?
2 5/8
What is the prime factorization of 30?
2 x 3 x 5
Which of the following expressions has the greatest value?
2.0/0.6
Simplify the expression (-9)(-3)-[4-(3-6)]
20
A 4th grade teacher is preparing a diagnostic test on multiplication for use in mathematics class. Which set of multiplication examples is presenting in order of increasing difficulty from left to right?
22 x 4;13 x 6;35 x 5;246 x 3
A pitcher of water starts with 3896 milliliters of water. During lunch, 1.50 liters of water is poured from the pitcher. How many mililiters of water are still in the pitcher?
2396 mL
Estimate the area of a teachers table cloth
24 ft^2
Simplify 4 + 3(5 - 2)+ 3 x 2^2
25
A group of volunteers are clearing brush away from an overgrown park. The park covers 3 1/4 acres. If the group clears 1/2 acre every 4 days, how many days will it take them to clear the entire park?
26.0
A student ran an average of 6 miles per hour for 30 minutes. How many miles did he run?
3 Miles
Which of the following expressions gives the solution to the statement below? A recipe for making 2 dozen cookies requires 3/4 cup of sugar. To make 6 dozen cookies, how much sugar is needed?
3 x 3/4
Find the greatest common factor of 34, 102, & 170
34
Which of the following strategies for computing 38 + 27 illustrates compensation?
38+2=40 -> 40+27=67 -> 67-2=65
Which of the following sets of numbers is ordered from least to greatest?
3^-2, 0.3, 33%, 1/3
A group of students are working on a project. They complete 30% of the project in 12 hours. If they continue to work at the same speed, how many hours will it take the group to finish the project?
40 Hours
Students were asked to solve the following problem using the distributive property 42 x 8. Which of the following does not involve a correct application of the distributive property?
40 x 16 - 2 x 2
A person who weighs 168 pounds on Earth would weigh 28 on the moon. How many pounds would a 30-pound on Earth weigh on the Moon?
5
A student starts walking on a large grid at the point (5,-1) and moves in a vertical direction exactly 5 unite up. At what point will the student be 5 unites above the starting point?
5,4
At an all school event, the teachers want to demonstrate how long a kilometer is by having children make a human chain. If the arm span of a average child is about 100 cm, approximately how many children are needed to stretch the length of a playing field that is about 0.5 kilometers long?
500
The following amounts are the weekly wages of 7 employees of a company. $180, $240, $360, $714, $300, $250 Determine the ranges of the wages
534
A homeowner decides to install a swimming pool in her backyard. The pool has a volume of 1000 cubic feet. Given that one cubic foot has a capacity of about 7.48 gallons, how many gallons of water does the pool hold?
7,480 gallons
An individual leaves home for work at 7:52 a.m. and arrives home from work at 4:31 p.m. How much time elapsed before the individual returned home?
8 hours 39 minutes
To estimate the fish population in a lake, a game warden caught and tagged 200 fish. After several months, the game warden caught a sample of 80 fish and 25 of those had been tagged. What would be a reasonable estimate for the fish population in the lake?
800
A recipe for 24 oz hamburger will make 8 oz serving of chili. How many ounces of hamburgers will be needed to make 28 servings of chili?
84
Find the greatest common factor of 36, 135, 144
9
A shorebird researcher recorded a 0.0933 increase in the number of piping plovers from one year to the next. Which percentage represents this increase
9 1/3%
A family is adding a walkway around their 12 foot by 8 foot rectangular swimming pool. Because of existing shrubbery, the total area of the project including the pool cannot exceed 190 square feet. How many square feet are left for the walkway?
94 ft^2
The following stem and leaf plots shows the best temperatures of 25 healthy adults. What is the median temperature of the adults in this data set? 96: 9 97: 00129 98: 001114566667899 99: 0011
98.6 degrees Fahrenheit 98.5 degrees Fahrenheit
Which of the following figures is an obtuse triangle?
A triangle with one angle greater than 90 degrees
Which of the following statements is true?
A+B=C if and only if B=C-A
A teacher uses a chart in his classroom to track the progress of students as they learn their addition facts. A volunteer asks students a fact and records how many facts the student recalled without apparent calculation. As students master the fact, they are moved up on the chart. What component of mathematics fluency is the teacher assessing?
Automaticity
An elementary school is collecting soda cans to raise money for a school project. The students collected 23 cans the first week. In the second week, they collected 42 more cans than the first week. For the remaining weeks they collected 42 more cans each week than the previous week. Which of the following charts shows the data they recorded?
Chart C
The 5th grade classes at an elementary school set a goal to read 250 books by the end of the school year. According to the following table. Which class is closest to the goal after 3 months?
Class D
A student uses square tiles to create an array for the multiplication problem, 6 x 8. She states that she can find the product by adding the products of 6 x 4 and 6 x 4. What property is she demonstrating understanding of?
Commutative property of addition
A student used centimetres grid paper to draw an array. Then the student drew the same array rotated 90 degrees as shown: What property is being illustrated by the arrays on the grid?
Commutative property of multiplication
The following is a student solution method 18 x 3 18 + 2 -> 20 x 3 -> 60 2 x 3 = 6 60 - 6= 54 What method did the student use to solve the multiplication problem?
Comprehension
Which of the following levels of thinking is in a sequence from developing to more proficient in the learning trajectory for counting?
Counter, producer, reciter
The table below shows the reading goals for a group of students who read a total of 250 books a year. Which of the following classes has performed best in terms of reaching the 3 month goal? Class Portion of Goal Met at 3 Months A 33% B 3/8 C 0.3 D 2/5
D
A 3rd grade teacher wishes to help her class develop fraction sense. Which of the following activities describes a high complexity task that has the best potential for developing fraction sense?
Decompose fractions into sums of smaller fractions
A teacher presents to the class the following problem. The United States Pentagon is in the shape of a regular pentagon. What is the sum of the measures of the angles of a pentagon? The problem is an example of which of the following strategies?
Decomposing a shape
A teacher wrote the following problem on the board for her students to analyze. 3(2x-5)-6(x-2) 6x-15-6x+12 The teacher then reminds the students that the first step to take is to remember that parenthesis involve which of the following properties?
Distributive
The number of loaves of bread sold is inversely related to the cost of a loaf of bread. if the cost doubles, the number of loaves of bread sold will...
Drop by half
Analyze the sample scenario to answer the following question: "A student is making belts for some shorts. The student bought 66 inches of fabric which will be cut into 22 inch pieces. How many belts can be made with the fabric purchased?" Which of the following describes the problem structure?
Equal groups, Division
A student answers immediately that 10+5=15. The students says that this is a pattern that always works when adding 10 and a smaller whole number. When asked to find 20+5 the student counts 20,21,22,23,24,25. Which of the following would be the most appropriate for the teacher to do next to encourage the student to move beyond counting when adding to 20?
Explain to the student that the same principal applies to 20+5 as 10+5
Two match boxes can be stacked in two different ways as shown in figures A and B. The bases are identical. Which of the following statements is correct?
Figure A has more outer surface area than figure B
A 2nd grade class is solving the expression 53 + 27. A teacher is reviewing a students work and sees the following: Strategy 1: 53 + 27 = (50 + 20)+(3 + 7) =70 + 10 80 Strategy 2: 53 + 27 =(53 - 3)+(27 + 3) =50 + 30 =80 Which component of mathematics fluency has the student displayed in her work?
Flexibility
In a 4th grade mathematics meeting, two teachers are discussing ways to teach multiplication. Teacher A believes the class should be taught the standard algorithm as the best way to solve multiplication problem. Teacher B believes the students should explore various multiplication strategies and decide which is the best for each problem. What component of math fluency is Teacher B promoting?
Flexibility
Which of the following is true about the number 1103211
It is divisible by 3 and 9
Analyze the sample scenario to answer the following question. There were 4 frogs in the pool. Some more frogs hopped in the pool with them. Then there were 12 frogs. How many frogs joined the 4 frogs in the pool? Which of the following describes the problem structure?
Join, result unknown
Four students were shopping at a mall. Lisa purchases a $20.00 shirt at 10% off. Tim purchases a $20.00 shirt at 20% off. Tina purchases a $25.00 at 40% off. Joe purchases a $25.00 shirt at 30% off. Who paid the most for the shirt?
Lisa
Which of the following measures of central tendency is affected by one or two extremely large or extremely small values outside of the range of the rest of the data?
Mean
The following measurements show the rainfall in Center City over the course of a week 4 cm, 5 cm, 4 cm, 0.1 cm, 0.25 cm, 0 cm, 2 cm If the chamber of commerce would like to portray Center City as a city of low rainfall, the best statistical measure to advertise would be
Median
Which of the following is the LEAST effective strategy to develop conceptual understanding of multiplication?
Memorizing
Identify the pattern in the following sequence 1,4,2,8,4,16,8
Multiply one term by 4 and divide the next term by 2
Identify the coordinates of the verticies of polygon ABCD
Option D (1, -3)
Which of the following figures is NOT a quadrilateral?
Pentagon
A students work sheet is showing below: 48+26=614;97+24=1111;146+237=3713. To remediate the students errors, the teacher should....
Provide remedial conceptual instruction
Which of the polygons listed has the most vertexes?
Rectangular Prism
In the progression of mathematical knowledge and understanding, which of the following critical areas are students expected to gain mastery of last?
Representing, relating, and operating for parts of a whole with sets of objects
In the progression of mathematical knowledge and understanding, Which of the following critical areas are students expected to gain master last?
Representing, relating, and operating of parts of a while with sets of objects
A student used a compensation strategy to successfully computes 500-203. The students strategy took the given numbers into account. Which of the following most likely describes what the student did first?
Rounding 203 to 200 before subtracting
A teacher wants to show an example of the equivalent of 2/3 and 6/9 to a small group of students. The teacher places 6 green and 3 red counters on the table. The teacher then arranges the counters in arrays to show that 2/3 or 6/9 are green. This is any example of teaching using which of the following types of representation?
Set Model
A student is attempting to solve the following expression 4x(3-1)+24/2^3 He states that the answer is 5 and shows the steps below in his notebook Results after Step 1..........4x4+24/2^3 Results after Step 2.........4x4+24/8 Results after Step 3.........16+24/8 Results after Step 4.........40/8 The students incorrect answer results from an error in which of the following steps?
Solving the expression in parenthesis in Step 1
+A student solved a mathematics problem using the following steps Step 1: 3^2+4-5x2= 9+4-5x2 Step 2: =(9+4-5)x2 Step 3: =(13-5)x2 Step 4: =8x2 Step 5: =16 At what step did the student make the error?
Step 2
A student solves the following problems and makes an error at one of the steps. Determine at which step did the student first make the error. 32+4-5x2=9+4-5x2........step 1 (9+4-5)x2......step 2 (13-5)x2.........step 3 8 x 2...............step 4
Step 2
Which of the following structured experiences would promote students' understanding of place value?
Students gather a large number of objects and count by making groups of ten
Which of the following structured experiences would best promote students' understanding of the place value?
Students work together to make buildings out of base blocks
Which of the following figures is considered an octagon?
T-turned upside down
Which item below has a weight in about 1 kilogram?
Textbook
A child calculated a subtraction problem incorrectly and arrived at this answer 373-189=216. Which of the following statements is the most valid assessment of this error?
The child does not have mastery of the basic facts
Which of the following figures has at least online of symmetry?
The figure that be split evenly down the middle ________ |_______>
A child calculated a subtraction problem incorrectly and arrives at the following answer. Which of these statements is the most valid assessment of this error? 782 -146 544
The student does not have master of the basic subtraction facts
A student was given two plates of counters and asked to determine which group has a greater number of counters [6 dots in port A; 7 dots in port B] Which of the following could result in an error in student reasoing?
The student draws ten frames to represent each number
To add 48 and 35, a student rounds 48 up to 50. The student knows that 50+35=85. The student then subtracted 2 from 85, arriving at an answer of 83. Which of the following best describes the students strategy?
The student used a correct compensation strategy
A student solved a subtraction problem incorrectly and arrived at this answer 63-26=47 A valid assessment of this error is that the student
The student's model does not show the correct number of groups
Students are asked to solve the following problem: "A student and his 3 friends want to share 12 pieces of gum. How many pieces of gum will each friend get?" One student solved the problem as shown: Diagram: 3-circle with 4 gums each What error does the student's response show?
The students model does not show the correct number of groups
Which of the following expressions does NOT represent the value for the phrase provided?
Three less than twice a number 3-2X
A kindergarten class is learning about addition without regrouping. Which of the following strategies would be most appropriate to begin teaching students how to add two digits?
Using realistic examples in a familiar context
Which equation illustrates the distributive property?
X(Y+Z)=XY+XZ
What is an appropriate interpretation of the multiplication expression 4x?
X+X+X+X
Which of the following figures is a trapezoid?
_____ |_____\
In general, multiplication can be defined by the equation ab-c, if and only if
b=c/a, a not equal to 0
A student travels m miles to visit a family member during a holiday vacation. If it takes the student 5 hours to arrive, which of the following expressions represents the average rate of speed, in miles per hour that the student traveled?
m/5
