1
Q
- 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?
A
18 + 2 🔑20 X 3 = 60
Compensation
2
Q
- 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
A
The student does not have mastery of the basic subtraction facts.
3
Q
- Which of the following structured experiences would promote students understanding of place value?
A
Students gather a large number of objects and count by making groups of ten.
4
Q
- Which of the following is the LEAST effective strategy to develop conceptual understanding of multiplication?
A
Memorizing
5
Q
- A 2nd grade class is solving the expression 53 +7 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?
A
Flexibility
6
Q
- 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 col1ected 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?
Weeks 1 2 3 6 5 6
Sodas Cans 23 65 107 149 191 233
A
Chart C
7
Q
- 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
Double
Quadruple
Stay the same
Drop by half
A
Drop by half
8
Q
- A student working as sales clerk at a local store earns $12per hour and 3 percent commission of all sales made. If the student works for h hours and makes s dollars of sa1eswhich of the following expressions represents the total amount of money the student earns?
A
12h + 0.03s
9
Q
- A jar contains five more quarters than dimes. If it contains a total of $2.30, which of the following equations can be used to determine the number of quarters in the jar?
A
0.10x + 0.25(x + 5) = $2.30
10
Q
- A student used centimeter 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?
A
Commutative property of multiplication ab=ba
11
Q
- Which of the following illustrates the associative property of addition?
A
(a + b) + c = a + (b+ c)
12
Q
- Simplify 4 + 3 (5-2) + 3 X 2² =
A
25
13
Q
- 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?
A
The student used a correct compensation strategy.
14
Q
- Find the greatest common factor of 34, 102, and 170
A
34
15
Q
- Find the least common multiple of 8, 15, 60
A
120
16
Q
- Which of the following set of numbers is ordered from least to greatest? 3
A
3-², 0.3, 33%, 1/3
17
Q
- Which of the following expressions has the greatest value?
A
2.0 ÷ 0.6
18
Q
- A pair of baseball team completed 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?
A
126 minutes
19
Q
- Which of the following expressions is the correct way to use exponents to write one hundred thousand?
A
10^5
20
Q
- A person who weighs 168 pounds on earth would weigh 28 on the moon. How many pounds would a 30-pound person on earth weigh on the moon?
A
5 (Divide)
21
Q
- Identify the pattern in the following sequence? 1, 4, 2, 8, 4, 16, 8
A
Multiple one term by 4 and divide the next term by 2
22
Q
The entire figure represents one unit. The shaded portion of the figure illustrates which of the following? ? [This grid is a 10 X 10 grid with 3 vertical by 4 horizontal squares shaded]
A
0.12
23
Q
- The following stem and leaf plot shows the body temperature of 25 healthy adults. What is the median temperature of the adults in this data set?
96 :9
97 :0 0 1 2 9
98 :0 0 1 1 1 4 6 6 6 6 6 7 8 9 9
99 :0 0 1 1
A
98.6
24
Q
- The following measurements show the rainfall in Center City over the course of a week. 4cm, 5cm, 4cm, 0.1cm, 0.25cm, 0cm, 2cm. If the chamber of commerce would like to portray the Center City as a city of low rainfall, the best statistical measure to advertise would be
A
median
25
16. A student used a compensation strategy to successfully computes 500 - 203. The student's 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
26
26. 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
27
27. Identify the coordinates of the vertices of a polygon ABCD
The answer is option D [a (-3, -4), b (-2,3), c (1,5), d (1, -3)]
28
28. Which of the following figures is not a quadrilateral?
Pentagon
29
29. Which of the following figures is considered an octagon?
(8 sides any figure that has 8 sides is an octagon) 1080*
30
```
Step 1: 3² + 4 - 5 x 2 = 9 + 4 - 5 x 2
Step 2: = (9 + 4 -5) x 2
Step3: _ = (13 - 5) x 2
Step 4: = 8 x 2
Step 5: = 16
```
At what step did the student make the error?
Step 2
31
2. 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?
b. Equal groups, partition division
32
3. A student was given two plates of counters and asked to determine which group has a greater number of counters.
Which of the following could result in an error in student reasoning?
The students draws ten frames to represent each number
33
4. 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
34
A student solved a subtraction problem incorrectly and arrived at this answer.
63- 26 = 47
The student did not regroup property.
35
6. 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?
d. Using realistic examples in a familiar context
36
7. A student answers immediately that 10 + 5 = 15: The student 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?
a. Explain to the student that the same principle applies to 20 + 5 as 10+ 5.
37
8. 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?
a. Decompose fractions into sums of smaller fractions.
38
9. Which of the following levels of thinking is in a sequence from developing to more proficient in the learning trajectory for counting?
Counter, producer, recite
39
10. 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
40
11. 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 a multiplication problem. Teacher B believes the students should
explore various multiplication strategies and decide which is best for each problem.
What component of math fluency is Teacher B promoting?
Flexibility
41
12. Which of the following is an appropriate translation for 12(x - 3)?
12 times the quantity X minus 3
42
Step 1 : 1 , Step 2 : 3, Step 3 : 5, Step 4 : 7, Step 5 : 9, Step 6 : 11, Step 7 : 13,
Step 8 : ?
15
43
14. 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
44
15. Which of the following expressions does not represent the value for the phrase provided
Three less than twice a number 3 – 2X
45
16. In general multiplication can be defined by the equation ab = c, if and only if b = c – a
d. b = c/a, a ≠0
46
17. A student is attempting to solve the following expression 4 X (3 - 1) + 24 ÷ 2. He states that the answer is 5 and shows the steps below in his notebook.
```
Result after step 1 4 X 4 + 24 ÷2ᶾ
Result after step 2 4 X 4 + 24 ÷ 8
Result after step 3 16 + 24 ÷ 8
Result after step 4 40 ÷ 8
The student's incorrect answer results from an error in which of the following steps?
```
a. Solving the expression in parenthesis in Step 1
47
18. Simplify the given expression.
8X – 4(2X – 5) – 2
18
48
19. Which equation illustrates the distributive property?
c. X (Y + Z) = XY + XZ
49
20. What is the value of X that makes the equation true?
| X + 7 ÷ 6 + (2X – 8) ÷ 2 = -4
-1
50
21. 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 50 fish and 25 of those had been tagged. What would be a reasonable estimate for the fish population in the lake?
800
51
22. 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 feet. How many square feet are left for the walkway?
94
52
23. Find the greatest common factor of 36, 135, 144.
9
53
24. Which of the following is true about the number 1,103,211?
It is divisible by 3 and 9
54
25. Which of the following strategies for computing 3.8+ 27 illustrates compensation?
38 + 2 = 40 40 + 27 = 67 67 – 2 = 65
55
26. A shorebird researcher recorded a 0.0033 increase in the number of piping plovers from one year to the next. Which percentage represents this increase.
.33%
56
27. 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
57
28. A pitcher of water starts with 38,96 milliliters of water. During lunch, 1.50 liters of water poured from the pitcher. How many milliliters of water are still in the pitcher?
2396 mL
58
29. At an all school event, the teachers want to demonstrate how long a kilometer is by having children make a human chain. If arm span of an average child is about 100 cm approximately how many children are needed to stretch the length of playing field that is about 0.5 kilometer long?
500
59
30. The temperature in northern Minnesota at 6.00pm was 5° below zero. By 7.00pm., the temperature had dropped another 3°. What was the temperature at 7.00pm?
-8°
60
31. What is the value of 1 ¾ ÷ 2/3?
c. 2 5/8
61
32. A teacher wants to show an example of the equivalent of2/3 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 an example of teaching using which of the following types of representation?
a. Set model
62
33. A 3/16 section of a 40-acre garden is planted with green beans. Twice as much of the garden is planted with carrots. How many acres of the garden are planted with carrots?
15 acres
63
34. A student is building a skateboard ramp to do tricks. For every 4 inches of height, the ramp needs to be 2-foot long. If he wants the ramp to be ½ feet high, how many feet long does the ramp need to be?
9
64
35. Which of the following is the next term in the sequence? 1, 3, 7, 15, ___
31
65
36. Which of the following statements is true about this set of numbers?
(4, 16, 12, 8, 14, 6)
The mean is the same as the median
66
37. The total distance covered by 2 bikers during the first 21 minutes of a race are shown in the following graph. How long after the start of the race did one biker pass the other?
11 minutes
67
38. The smallest state in the United States is Rhode Island. Which measurement is closest to the area of Rhode Island?
3000 square kilometers
68
39. A shoe manufacturer is analyzing data showing the annual sales of different sizes of one type of sandal. Which of the following measures of center would be most useful in planning production so that more of the most popular size is being manufactured?
mode
69
40. A family drove their car on a vacation last summer. In the first 8 hours, they traveled 500 miles. Due to traffic and construction, they were only able to drive 300 miles in the next 6 hours. How much greater was their average speed .in the first part of the trip than the second part of the trip?
12.5 miles per hour
70
41. An individual working for a certain company earns an hourly rate of $18.50 for the first 40 hours of work per week plus 1.5 times the hourly rate for each hour more than 40 hours. How much money will the individual earn for working 48 hours in a week?
$962
71
To complete a quilt design, Dehlia needs two sets of right triangles. The first set has sides with lengths of 3 inches, 4 inches, and 5 inches. If the length of each side of the larger pieces is double the length of the shorter pieces, how much greater will the area of the larger pieces be than the area of the smaller pieces?
4 times
72
43. Estimate the normal temperature of the human body?
37°C
73
44. A giant coordinate grid is painted on the playground at an elementary school. A student starts a point (-9, 8). She walks in a straight horizontal line and then stops. Which point could she be at now?
(9, 8)
74
45. Which of the following is a polyhedral with 6 congruent faces, 12 edges and 8 vertexes?
Cube
75
46. Which of the following is an isosceles triangle?
[ two equal sides]
76
48. Analyze the sample scenario to answer the following question. A student saved money from her babysitting business. This month she saves 3 times as much as she did last month. This month she saved $15. How much did she save last month?
$5
77
49. Which of the following describes the problem structure?
c. Equal groups, division
78
The seven salespeople at Rosbud Realty earned the following Commission on sales last year: 12811,17750,27092,32253,37354,49584, and 98583 Find the mean Commission for this company.
39346.7 or 39346
79
Which equation illustrates the additive inverse of property?
-10a+10a=0 a+(-a)=0
80
Which of the following numbers is the smallest.0.09783x13 After teaching the concept of addition with four addends, inappropriate application would be to have students find what?
Perimeter of the classroom.
81
Find the vertexes of triangle P,Q,R shown in the diagram.
(4,1)(0,-4)(-3,-1)
82
In general division can be defined by which equation, assuming b(does not equal) 0 a/b=c if and only if
(c)(b)=a
83
Which graph represents a solution set of this inequality 2x-5>13?
x>9 -->
84
A sweater is marked 25% off the original price. Which expression represents the cost of the sweater after the markdown?
-0.25P
85
Which equation illustrates the property of identity element of addition?
3+0=3 a+0=a
86
Triangle Equal Sides
```
1= Scalene
2= Isosceles
3= Equilateral
```
87
The probability of newlyweds honeymooning out of state in 40%. What are the odds in favor of the couple staying in state for the honeymoon?
3:2
88
Select the perpendicular pair of lines:
LN (Lines that intersect at 90 degrees)
89
A prism has a height of 10cm and base of 3cm and 4cm. Find the total surface area?
132cm
90
The Springfield city council voted to lengthen each side of the cities new stop signs. Each side would be 2 inches longer than the old sign 8 inches. What will be the perimeter of the new stop sign?
80 inches
91
Ms. Gomez has a small 5ft^3 refrigerator. What is the value of the refrigerator in cubic inches?
8640^3
92
. Estimate the capacity of a family swimming pool (10mL, 10L, 10kL, 10 gallons)?
10 kL
93
The distance between two cities is 175 miles. If a trip one way took 3.5 hours, and the return trip along the same route took 4 hours, what was the average rate of travel?
46.7 MPH
94
In a multiple-choice test, the probability of getting the correct answer by guessing alone is 20%. What are the odds against getting the correct answer by pure guessing?
4:1
95
How much pure anti-freeze must be added to 10 gal of a 40% anti-freeze solution to increase it's concentration to a 60% anti-freeze solution? If X represents the number of gallons appear anti-freeze solution to be added, what is the correct statement of the problem?
.4(10)+x= .6(x+10)
96
570. Two guys are biking at different rates. Determine from the graph when both bikers will cross each other (they crossed at a point between 9 and 12?)
11
97
Ms. Michaels has installed a new and more powerful sprinkler system, but the new system will go 20 meters further than the old system pictured below. What is the circumference of the spring area of the new system?
439.6 meters
98
John wants to cover his bench with 10-centimeter square vinyl tiles. The surface of the bench is 3.4 meter. How many tiles are needed to cover the bench?
3,400
99
A regular Polygon has eight sides. Find the measure of the exterior angle of the Polygon:
45
100
. Compare the two triangles:
Rotation
101
. A customer decides to give a tip to a waiter of only one coin randomly selected from 8 coins from his pocket. What are the odds of his giving the waiter a quarter if he has 3 quarters, 2 half dollars 1 dime, and 2 pennies?
3:5
102
The graph shows actual and predicted rainfall. Determine the month with the largest difference between the actual and predicted rainfall?
August
103
A pharmacist has 14 GM of aspirin add 50MG. How many capsules can he make?
280 capsules
104
A teacher writes this on the board 3 (2x-5) – 6(x-2) 6x-15 -6x-12
The teacher reminds the students that the first step of parenthesis?
Distributive Property
105
. A recipe 24 hamburger will make 8 servings of chili. How many the oz of hamburgers will be needed to make 28 servings of chili?
84ozs
106
Which of the following expressions give the solution to this problem: a recipe for making 2 dozen cookies requires ¾ Cup of sugar to make 6 dozen cookies, how much sugar is needed?
3x ¾
K-6 Teaching
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