Ftce k-6 FINAL EVERYTHING subject area MATH
Power of a Fraction Rule
(a/b)^x = a^x/b^x
power of a power rule (exponents)
(a^x)^y = a^x*y Multiply your exponents
Power of a Product Rule
(ab)^x a^x * b^x
Decagon
10 sided polygon
Simplify the expression (-9)(-3)-[4-(3-6)]
20
Estimate the length of a new pencil
20 cm
Hexagon
6 sided polygon
metric capacity liters
Beverages
Which of the following letters is an example of point rotational symmetry?
N
Select the perpendicular pair of lines
NM-KL
Two planes that do not intercept are called
Parallel
After teaching the concept of addition with addends with 4 addends, an appropriate application will be to have the students find what?
Perimeter of the classroom
Strategic Competency
ability to formulate, represent, and solve mathematical problems
Partioning
divide into parts
Find the 8th term of the geometric sequence: -9,36,-144
147465
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 3/16 = 7.5 * 2 =15
A student types 3750 words report in 1 hour & 15 min. Find his average words per minute?
50 wpm 3750/75 = 50
Identify parts of an Addition Sentence
In an addition equation, addends are the numbers that are added together to give a sum.
Dodecagon
12 sided polygon
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
Jamal's grandfather has written in his journal that the family had purchased a land for ten thousand one hundred and eleven. Write this amount in standard form
$10,111.00
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 -5-3 = -8
Section of this cake has been decorated with chocolate vanilla icing. What decimal best describes the area covered by chocolate icing?
.25
What is the total measure of the interior angles of the geometric shape?
180
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 shows the correct way to break apart to divide? A 248 ÷ 4 = (24 ÷ 4) + (8 ÷ 4) B. 248 ÷ 4 = (240 ÷ 4) + (8 ÷ 4) C. 248 ÷ 4 = (24 ÷ 4) - (8 ÷ 4)
248 ÷ 4 = (240 ÷ 4) + (8 ÷ 4)
Estimate the mass of a slice of bread
25 g
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of carpet needed for the living room is how many times greater than the amount of carpet needed for the bedroom?
3
Which equation illustrates the property of the identity element of addition?
3 + 0= 3
Triangle
3 sided polygon
Which of the following is NOT equivalent to 22 over 7?
3(7/ 1) + 1 1/ 7
Partitioning (Break-Apart)
369 ÷ 3= (300 ÷ 3) + (60 ÷ 3) + (9 ÷ 3) 243 - 132 = (200 - 100) + (40 - 30) + (3 - 2) 125 x 4 = (100 x 4) + (20 x 4) + (5 x 4)
Estimate the temperature of the human body Is it: 101 degrees F 37degrees F 101 degrees C 37 degrees C
37 degrees C
The probability of newlyweds honeymooning out of state is 40%. What are the odds in favor of the couple staying in state for their honeymoon?
3:2
Which of the following sets of numbers is ordered from least to greatest?
3^-2, 0.3, 33%, 1/3
Quadrilateral
4 sided polygon
A contractor is tilling a bathroom with an area of 36 sq ft. How many square yards of area is he working on?
4 sq. yds.
A rectangular prism has a length of 3 units, width of 4 units, and a height of 5 units. What is the volume of this prism?
60 units cubed
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
Octagon
8 sided polygon
Which of the following could be the height of a man? 3 m 80 in. 80 cm 3 yd.
80 in.
A school purchased computers for students to use at the cost of $824.06 each. The ratio of students available for each computer is 8.682 students. Which of the following would be the most appropriate mental computation?
800/9
Simplify the expression. 90 − 60 ÷ 30 + 10
98
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
98.5 degrees Fahrenheit
Scatter Plot Graph
A graph of plotted points that show the relationship between two sets of data that do not depend on each other where the line is not connected. (Ex. height versus weight)
Tiling
A pattern of shapes repeated to fill a plane. The shapes do not overlap and there are no gaps.
tiling
A pattern of shapes repeated to fill a plane. The shapes do not overlap and there are no gaps.
Which of the following skills is in the correct order according to mathematical fluency? A. Understanding Whole Numbers, Understanding parts of numbers, classifying even and odd numbers, on using numbers to produce equations B. Understanding parts of numbers, understanding whole numbers, classifying evens and odd numbers, on using numbers to produce equations C. Understanding whole numbers, classifying even And odd numbers, understanding parts of numbers, on using numbers to produce equations
A. Understanding Whole Numbers, Understanding parts of numbers, classifying even and odd numbers, on using numbers to produce equations
There are 22 kids on a bus between two classes. The first class on the bus has 11 kids. How many kids are in the second class? What type of problem is this? Hint: (set up problems written out like : __________ ⬜️ ___________ = ___________ Start. Change. Result )
Add to, change unknown
The best instruction methods most appropriate in 3rd grade for learning and creating graphs will be to:
Allow the students to tally their math scores and graphs using these scores
How would you translate this number sentence to an actual phrase? 12(x-3) A. Twelve times x less than three B. Twelve times three less than x C. Twelve times the quantity of 3 less than x D. Twelve times the quantity of x less than three
C. Twelve times the quantity of 3 less than x
A teacher is teaching students different mathematical methods on the board. Problem: 54+66= ____ 60+60= ____ 50+70= ____ Which of the following mathematical methods is the teacher showing his students? Partition Compensation Additive Inverse Property Add and subtract property
Compensation
____________________ angles are two angles whose sum is 90 degrees.
Complementary
Conceptual Understanding
Comprehension of mathematical concepts, operations, and relations
Tiling
Covering an area or shape with repeated shapes as in tessellations. Can be used to determine the area of a figure by "covering" it with tiles of a standard area such as square centimeters or square inches.
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
Which of the following sequences is the most appropriate learning progression through the levels of geometric thinking?
Descriptive, analytic, abstract
In a 4thfourth -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 strategy is best for each problem. What component of math fluency is Teacher B promoting?
Flexibility
Jenny has some coins. Jake gives her 3 more. Now jenny has 10 coins what problem structure is here? Hint: (set up problems written out like : __________ ⬜️ ___________ = ___________ Start. Change. Result )
Join, Start Unknown
What is the accurate weight unit of a 6ft male?
Kilogram
number line
Remember that numbers increase in value as you move right, and decrease as you move left. The MAGNITUDE of negative numbers increase as you move left, but the value increases!
Which of the following concepts is recommended to be taught first in the development of fractional understanding for students?
Representing fractions with area models
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
The diagonals of a quadrilateral are congruent perpendicular bisectors of each other. Identify the polygons
Rhombus
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
A 4thfourth -student is experiencing difficulty in understanding the concept of place value. Which of the following is the best strategy for reteaching the concept?
Using counters and a chart to display numbers
Composite Number
a number that has more than two factors
Commutative Property of Addition
a+b=b+a 4+7 = 7+4
zero exponent
a^0 = 1, a≠0 if a number is raised to the 0 power it will always be 1 NOT 0
Metric: Length milimeter
Width of a dime
Which of the following is the LEAST effective strategy to develop conceptual understanding of multiplication?
Memorizing
Mr. Singh sells ground cinnamon. He has a 1.5 lbs bag. How many 8 oz. bags does he have?
3 1.5oz = 24lb/8 =3
Which is not a quadrilateral? A rectangle A rhombus A pentagon A trapezoid
A pentagon
A sweater sells for $28. If it is on sale for 35% off, how much will be taken off the original price?
$9.80
A family's annual income is 25,000. If the family spends 30% on food and 10% on clothing, how much of the annual income was spent on food and clothing?
10,000
A student brought a small apple for lunch. Which measurement would best describe the mass of the small apple?
100 grams
A regular polygon has 5 sides. Find the measure of an interior angle of the polugon.
108
Find the sum of the angle measures of the interior angle of the octagon below
1080 n-8 * 180 = 1080
What is the correct way to write the scientific notation for 1,000,000?
10x10^6
Company XYZ has a total monthly payment of 6894of which 1447.74 is for employee fringe benefit. What percent of the total pay roll goes for fringe benefits?
21%
A teacher went to the store to buy treats for her classroom. At the store, she found the following deals. Which deal is the best buy?
26 treats for 4 dollars
A teacher wants to make a model of 0.5 Km. The arm son of her students is approx 100cm. How many students would she need to put finger tip to finger tip to reach .5km? (Hint Solve with Proportions and use Conversion sheet provided)
500
Estimate the weight (mass) of an adult female.
55 kg
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
Calculators can be used most effectively in an elementary school for what?
Introducing mathematical concpets
What is the accurate weight unit of a lion?
Kilograms
Metric Capacity Milliliters
Measuring Drops
The teacher wants to teach her students fraction equivalence using two fractions 2 over 6 and 3 over 9. She arranged counters to represent the numerators and denominators. What method is she using: Area model Set model Pattern blocks
Set model
Which equation illustrates the distributive property?
X(Y+Z)=XY+XZ
Unit of Capacity
liter
Which unit will be most appropriate for measuring a prescribed dose of medicine?
mL
Which of the following numbers represents 75 thousandths?
0.075
Sections of this cake hve been decorated either with chocoloate or vanilla icing. Which of the following best describes the area covered by the icing?
0.25
An 8800 square foot of a highway is supposed to be resurfaces. Which of the following is an appropriate conversion into miles?
1 2/3 miles
The outside edge of the deck in which a 16' x 40' rectangular pool is centered measures 32' x 56'. To purchase the right amount of sealant for the dark area, Ms. Santia wants to determine the are of the decking. What is the are of the deck?
1,152 sq st. 16*40 - 32*56
Gold mining in the US Dakota 29% Nevada 32% Utah 18% Colorado 5% Arizona 8% Other 8% During a time period 2,000,000 ounces of gold are produced in the U.S. Use the above graph to determine the amount of gold produced in Arizona and Colorado
260,000 oz
A pharmacist has 14 gm of aspirin he needs to add 50 mg of each capsule of a cold medicine. How many capsules can he make?
280
Calculator using scientific notation will display 3,200,000 as which of the following?
3.2 x 10^6
To complete a quit 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
Which step should be done first to simplify the expression? 8a − 4a ÷ 2a − 16a • 8a + a
4a ÷ 2a
Which of the following expressions represents: 3 less than 4 times a number A. 4 (x-3) B. 4x - 3 C. 3 - 4x D. 3 - 4 (x-3)
4x-3
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
The expression (5^2)^2 is equivalent to
625
Heptagon
7 sided polygon
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
Which of the following figures is an obtuse triangle?
A triangle with one angle greater than 90 degrees
Which statement is true about a triangular pyramid?
A triangular pyramid has 4 faces.
Prime Number
A whole number that has exactly two factors, 1 and itself.
Which of the following statements is true?
A+B=C if and only if B=C-A
A student is working out the problem 6x8. He/she rewrites the problem 6x4 + 6x4. This is an example of? A. Distributive Multiplicative Property B. Commutative Multiplicative Property C. Distributive Addition Property D. Commutative Addition Property
A. Distributive Multiplicative Property
If a = b and b = c then: A. a = c B. ab = c C. ac = b D. cb = a
A=C (Transitive Property )
A local school district requires all 5thfifth graders to complete an untimed test containing 50 multiple choice mathematics problems. The tests are scored and the results are compared throughout the district. What component of mathematics fluency is most likely the goal of this type of assessment?
Accuracy
(-10a) + 10a = 0
Additive Inverse
Which of the following sequences is the most appropriate learning progression through the levels of geometric thinking? A. Analytic, abstract, descriptive B. Analytic, descriptive, abstract C. Descriptive, abstract, analytic D. Descriptive, analytic, abstract
Analytic, descriptive, abstract
Adaptive Reasoning
Capacity for logical thought, reflection, explanation, and justification
Subitizing happens before?
Counting
Which of the following is a polyhedral with 6 congruent faces, 12 edges and 8 vertexes?
Cube
Pairity
Determining Even or Odd
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
The teacher is showing students how to divide 169 inches of paper into thirteen 13-inch pieces. The teacher is using: A. Array strategy B. Base ten strategy C. Equal parts strategy D. Tiling strategy
Equal Parts Strategy Why? Because she is showing two equal parts
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
Two match boxes can be stacked in two different ways as shown in the diagram. The boxes are identical. Which of the following statements are true about the boxes? Figure A Figure B
Figure A has more surface area than Figure B
The Ramirez Family panned for gold on thier recent vacation to California then recorded their findings in this chart with family member and his/her corresponding number of counces of gold Luis: 14/10 Maria: 1.87 Norma: 6.24 Gabriela: 16/6 Which of the family members recieved the second largest ounces of gold?
Gabriela
Transitivity
General definition: Being about to transfer previously acquired skills to new situation. Math Specific: If a = b and b = c, then a = c If d1=r1t1 and d2 = r2t2 and d1= d2, then r1t1 = r2t2
Accuracy
Getting it Right!
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
Which unit is more appropriate to measure a person's weight?
Kilograms
Automaticity
Knowing math facts (addition, subtraction, multiplication, and division) with instant recall and being able to make mental math calculation (compensation, estimation) without hesitation
Which of the following would be most appropriate to measure in kilograms? A. Paper clip B. Cell phone C. Lion D. Car
Lion
If students are working in groups to unfold shapes to understand geometry What would be one of the best manipulative to use?
Nets-net is a two-dimensional figure that can be folded into a three-dimensional object.
Which of the following would be most appropriate to weigh in grams? A. Paper clip B. Elephant C. Lion D. Car
Paper clip
Which of the following mathematical methods is the student displaying? Problem: 434+261= ____ 400+200=600 30+60=90 4+1=5 Partition Compensation Scaffolding Adding by parts
Partition
What strategy did this student use to solve? Question: 546+261 Students Work: 500+200=700 40+60=100 6+1=7 = 700+100+7= 807 Check their work: 546+261=807
Partitioning
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
Which shape has the MOST vertices?
Rectangular Prism
If a = a is an example of: A. Reflexive property B. Transitive property C. Commutative property D. Symmetric property
Reflexive Property
Which quadrilateral is best described from the following descriptions below: • Opposite sides are parallel • All four sides are congruent • One set of opposite sides are acute A. Parallelogram B. Rhombus C. Square D. Trapezoid
Rhombus
Which quadrilateral is best described from the following descriptions below: • Opposite sides are parallel • All four sides are congruent • Diagonals are congruent A. Parallelogram B. Rhombus C. Square D. Trapezoid
Square
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
Kruti just purchased 3 shirts, 1 skirt, and 2 pairs of shoes. She would like to compute the change she would receive from a $100 bill. Which operation should she use last?
Subtraction
A 45º angle and a 135º angle are considered to be: A.Vertical B.Complementary C.Supplementary D.Shared E.Right
Supplementary
____________ angles are two angles whose sum is 180 degrees
Supplementary
metric capacity Kiloliters
Swimming Pool
If a = b, then b = a is an example of: A. Reflexive property B. Transitive property C. Communicative property D. Symmetric property
Symmetric Property
Which of the following figures is considered an octagon?
T-turned upside down
Which item below has a weight in about 1 kilogram?
Textbook
Which shape will have more surface area? The boxes stacked on top of each other, or side by side? The boxes stacked side by side. The boxes stacked next to each other. The surface area will be the same.
The boxes stacked side by side
Which of the following figures has at least online of symmetry?
The figure that be split evenly down the middle ________ |_______>
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
Identify Parts of a Subtractions Sentence
The part you start with is called the minuend. The part being taken away is called the subtrahend. The part that is left after subtraction is called the difference. In the problem 5 - 3 = 2, the number 5 is the minuend, the number 3 is the subtrahend, and the number 2 is the difference.
How can you tell is decimals will be larger or small in division? Ex: which of the following is the largest? A. 0.2/0.07 B. 0.2/0.17 C. 0.02/7 D. 0.02/ 7.7
The smaller the decimal the larger the result - A. 0.2/0.07
You have a box that is 5 cm x 7 cm x 10 cm. How does it affect the volume if you add a second box of the same size
The volume doubles.
Identify Parts a Multiplication Equation
There are two terms which describe the three numbers in a multiplication problem. The factors are the numbers that are being multiplied together. The product is the result or answer of multiplying the multiplicand by the multiplier. A multiplication problem may be written horizontally such as 6532 * 7 = 45724.
What is the accurate weight unit of a car
Tons
Which quadrilateral is best described from the following descriptions below: • Has a pair of parallel lines • Diagonals are congruent A. Parallelogram B. Rhombus C. Square D. Trapezoid
Trapezoid
What would be of these choices the BEST way to teach 3rd grade students about Place Value? -
Unit Cubes
Flexibility
Use of a variety of strategies in various situations
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
The best way to teach her 3rd grade students about PLACE VALUE: Learning to name the ones, tens, and hundred places. (What Manuiulative for 3rd graders? think of their age and cognative level?)
Using unit cubes
metric length centimeter
Width of a pinky
Which graph represents a solution set of this inequality? 2x-5>13
X>9
Which of the following figures is a trapezoid?
_____ |_____\
Fractional Exponent Rule
a^x/y = ^y√a^x
Which of the following shapes can be classified as a regular?
all sides equal and all angles equal
Concrete models are critical for
deep understanding
Solve real-world problems involving ratios and proportions
most ratio problems can be solved by either setting up equivalent fractions or calculating the PART you are looking at over the WHOLE. For instance, If a dozen assorted donuts has two chocolate, the ratio of chocolate donuts to donuts is 2/12
Which equation illustrates the associative property of multiplication?
( a • b)c = a( b • c)
A giant coordinate grid is painted on the playgroup 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)
Which polyhedron has the most vertices
Rectangular prism
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
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
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
associatve property of addition
a + (b+c) = (a+b) +c 3 + (7+29) = (3+7)+29
Identity Property of Addition
a + 0 = a 1 + 0 = 1
Which of the following shows the transitive property of equality? a(b x c) = ab + ac a = b and b = c, then a = c ab + cd = abcd a(b x c) = ab + c
a = b and b = c, then a = c
Geoboards
a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons. It consists of a physical board with a certain number of nails half driven in, around which are wrapped rubber bands.
Arrays Strategy
a pictorial representation of a multiplication problem
3-4-5 triangle
a triangle in which the sides are 3, 4, and 5 units long. A 3-4-5 triangle is always a right triangle.
Base Ten Strategy
a way students can use to learn addition, subtraction, number sense, place value and counting. this can be with manuipulatives or pictorals
Inverse Property of Multiplication (Hint: think opposite)
a(1/a)= 1 2(1/2) =1
Which of the following demonstrates the distributive property of multiplication? a(b x c) = ab + ac a = b and b = c, then a = c ab + cd = abcd a(b x c) = ab + c
a(b x c) = ab + ac
Inverse Properties of Addition (Hint: think opposite)
a+(-a)= 0 3+(-3) = 0
Negative Exponent
a^-x = 1/a^x Negative is the opposite of positive and division is the opposite of multiplication, so a number with a negative exponent should be moved to the denominator of a fraction and the exponent switched to positive.
Multiplication Rule for Exponents
a^x * a^y = a ^x+y (add exponents)
Division Rule for Exponents
a^x / a^y = a ^x-y (subtract exponents)
Early elementary students are not ready for
abstract reasoning
What is the order in which students progress through mathematics?
concrete manipualtives, semi-concrete drawings, abstract thinking with standard algorithms
Group students with
diverse mathematical approaches when solving cognitively complex problems.
A farmer purchased approximately 4.8 hacres of Property for 144,000 if an acre is approximately 0.4hacres how much does an acre cost? *hint do not stress about the hacres! Look at the information you have three solid point of information, so it much a proportion to solve!
$12,000
Determine which choice best shows the distributive property of multiplication. A. 9 × 5 = 5 × 9 B. 9 × 1 = 9 C. (9 × 5) × 7 = 9 × (5 × 7) D. (9 × 5) + (9 × 7) = 9 × (5 + 7)
(9 × 5) + (9 × 7) = 9 × (5 + 7)
Which of the following illustrates the associative property of addition?
(a + b) + c= a + (b +c)
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 min
The perimeter of an isosceles triangle is 32 units. The length of the base is 8 units. What is the length of one of the equal sides?
12 inches
Which of the following is an appropriate translation for 12(x - 3)
12 times the quantity, x - 3
A family drove their car on a vacation last summer. In the first 8 hours, they traveled 500 miles. Due to the 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 500/8 - 300/6 = 12.5
Find the least common multiple of 8, 15, & 60
120
A baseball game lasts 9 innings. If the first two innings last a total of 28 minutes, how long will the entire game be? a. 126 minutes b. 252 c. 504 min d. 224
126 minutes
Compensation (Borrowing Between Numbers)
134 + 36 = 140 + 30 (the six was borrowed from the 36 and added to the 134) 35 - 18 35 - 20 = 15 15 + 2 = 17 (18 was rounded to 20 and they subtracted 2 too many, then the 2 was added back to the 15)
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
Estimate the length of a U.S. Dollar bill
15 cm
The altitude to the base of an isosceles triangle is 6. If each of the equal sides measures 10, find the length of the base.
16
Estimate the average height of an adult male
180 cm
Which of the following could be the height of a man? 180 cm 180 mm 180 m 180 inches
180 cm
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 = 2.25
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 = 2.25 OR 2 1/4
Find the greatest common factor of 34, 102, & 170
34
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
You get $18.50 an hour for the first 40 hours you work, then you are paid for 1.5 (time and a half) hours for every hour you work after that. How much is your pay before taxes and deductions for a 48-hour work week? a. 48 × 18.50 × 1.5 b. 40 × $18.50 + 8 × $18.50 × 1.5 c. 40 × $18.50 + 8 × $18.50 × 0.5 d. 48 × $18.50 + 8 × $18.50 × 1.5
40 × $18.50 + 8 × $18.50 × 1.5
Pentagon
5 sided polygon
An athelete swam 100 yards in 52 seconds. To the nearest 10th, what was the average number of feet per second traveled?
5.8 feet per second
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
Nonagon
9 sided polygon
24 oz hamburger meat is needed to make 8 servings of chili. If the meat can only be purchased in 24 oz packages, how many oz are needed to serve 28 people?
96 oz
bar graph
A graph that uses horizontal or vertical bars to display data, addtionally used to compare data. The histogram compares data in ranges and has no spaces between the bars.
A local district requires all 5th graders to complete an untimed test containing 50 multiple choice mathematics problems. The tests are scores and the results are compared throughout the district. What component of mathematics fluency is most likely the goal of this type of assessment? A. Rate B. Flexibility C. Automaticity D. Accuracy
Accuracy
unit of mass
grams
Which graph can students display data of variable information : bar graph line graph pictograph circle graph
line graph
Teacher asked to demonstrate the solution process for solving word problems involving 2-digit numbers and different operations using base-ten blocks. Which skill is being assessed? Use of speed accuracy when solving word problems. Appropriate conceptualization of the knowledge of the operations. Appropriate procedural understanding of computational algorithm. Appropriate flexibility with computational algorithms.
Appropriate conceptualization of the knowledge of the operations.
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
Which instructional aid would be most appropriate to introduce the concept of "place values of 3 digits numbers" to a 2nd grade class?
Base-ten blocks
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
Sandy made 20 bracelets in one week. That was four times as many as she made the week before. What is the problem structure? Partitive Multiplication Quotitive Division Comparison Multiplication Put-Together
Comparison Multiplication
Sue sells fruit and vegetables at the local farmers market. She sold 4 times as much today as she did yesterday. She made $56 today. What type of problem is this? A. Comparison division B. Comparison multiplication C. Put-together D. Take-apart
Comparison multiplication
A teacher is explaining a mental mathematics strategy to the class and says: Suppose we wanted to add 76 + 9. One way to do this addition problem is to think: 76 + 9 is the same as 76 plus 10 minus 1, because 10 minus 1 is 9. By adding 76 and 10, we get 86, then subtracting 1 gives the answer 85. This kind of thinking is also called "making 10." What type of strategy is being taught?
Compensation
What is the order in which students progress through mathematics?
Concrete manipulatives , semi concrete drawings, abstract thinking with standard algorithms
What is the formula for calculating distance?
D=rt
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
Which of the following sequences is the most appropriate learning progression through the levels of geometric thinking? -analytic, abstract, descriptive -analytic, descriptive, abstract -descriptive, analytic, abstract -descriptive, abstract, analytic
Descriptive, Analytic, Abstract
When students are using calculators to find the answer to a division problem, which of the following should they enter first?
Dividend
Identify the parts of a division equation
Division has 4 parts: divisor, dividend, quotient and remainder. The dividend is the number that is being divided. The divisor is the number that the dividend will be divided by.
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
Unit of Length
meter
Given a rectangular solid as shown in the diagram, which formula is a correct representation for its total surface area?
s = 2xz + 2yz +2xy
Area Model
students divide shapes into the appropriate number of equal sections given by the denominator, then shade in the appropriate number of sections, given by the numerator to create a picture of the fraction. Equivalent fractions are also developed using this area model. Teachers may use any of these manipulatives to develop the area model: `Pattern Blocks `Circular fraction regions `Pizzas `Geoboards `Spinners
Set Model
students use individual shapes to match the fraction. I have 4 cubes in my bag and 1/2 of them are blue or John brought 6 toy cars to school. 1/3 of them are red. Teachers may use any of these manipulatives to develop the set model: -Two-color counters -Colored counters or bingo chips -Centimeter or rainbow cubes -Foam shapes
Measurement or Linear Model
students use the number line model found on rulers or divide fraction strips into the appropriate sections by length. Teachers may use any of these manipulatives to develop the measurement or linear model: -Number line -Rulers -Linking cube trains -Cuisenaire rods -Fraction bars -Fraction strips
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, measurement 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
Students in the 3rdthird grade study multiplication in terms of equal groups, arrays, and area. What should students in the 4thfourth grade be expected to do as the next step in this learning progression?
Extend their concept of multiplication to make multiplicative comparisons
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
Front End Rounding
Front end rounding is rounding a number to the highest possible place, so all the digits become 0 except the first digit.
Productive Disposition
Habitual inclination to see mathematics and sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy.
Which type of activity is appropriate to introduce geometric shapes to a first grade class?
Have students draw various geometric shapes on graph papers
In which quadrant is the point (-2,-2) ?
III
Measurement Division Ex: I have 20 pounds of taffy. I want to put ½ pound in each bag. How many bags can I fill? Quotitive Division
In a measurement division problem, you know how many should go in each group, and you have to figure out how many groups there will be. It is also called Quotitive Division
Partitive Division
In a partitive division, you know how many groups to split it into, and you need to figure out how many in each group. Ex: A piñata has 210 pieces of candy. If 30 children at a party share the candy equally, how many does each child get? Four children share 12 apple slices evenly. How many apple slices does each child get?
You have two boxes that are 50 cm x 200 cm x 100 cm. You stack the boxes on top of each other, then tape them together to make one large box. How does that affect the surface area of the new figure?
It increase, but does not double due to the shared side.
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
A show 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?
Median
What is the most INEFFECTIVE way for a child to learn and meet certain objectives Ex: a student is struggling to learn her multiplication tables
Memorization
The math supervisor polled the teachers in the school district concerning which day of the week to hold a staff development workshop. The results showed that 20% of the teachers preferred Monday, 15% preferred Tuesday, 10% preferred Wednesday, 25% preferred Thursday, and 30% preferred Friday. To decide which day to hold the workshop, which statistic should the supervisor use?
Mode
What is the problem structure? A boy has a 66 inch length of ribbon and needs to divide it into 22 pieces. How big is each piece? (Remember, in quotition (measurement) division one asks how many parts there are; in partition division one asks what the size of each part is!) Partition, set size unknown Quotition, set size unknown Join, start unknown Join, change unknown
Partition, set size unknown
Which of the following figures is NOT a quadrilateral?
Pentagon
The teacher watches the student perform the math problem 34 + 17. The student adds 34 + 20 and gets the answer 54. The student subtracts 3 from the first answer to have a total of 51. Which of the following is true? A. Performed compensation correctly, incorrect answer B. Performed compensation incorrectly, correct answer C. Performed compensation incorrectly, incorrect answer D. Performed compensation correctly, correct answer
Performed compensation incorrectly, correct answer
You have a piece of fabric that is 30 cm long and 10 cm wide. You cut it into equal pieces that 10 cm long and 10 cm wide. How many pieces did you divide it into? (In quotation (measurement) division one asks how many parts there are; in partition division one asks what the size of each part is.) Quotion (Measurement Division), change (or number of sets) unknown Partition, result unknown Join, start unknown Join, result unknown
Quotion (Measurement Division), change (or number of sets) unknown
Which is the order in which children develop a numerical sense? Hint: ReCiPe
Recite, Count, Produce
A student is struggling to progress through the descriptive level of geometric thinking. Which of the following skills is considered the most basic in the levels of geometric thinking?
Recognizing and identifying shapes
Which quadrilateral is best described from the following descriptions below: • Opposite sides are parallel • Opposite sides are congruent • Contains a 90 degree angle A. Parallelogram B. Rhombus C. Trapezoid D. Rectangle
Rectangle
A student is solving the following equation: 6(2x+10)-(x-15)÷5=0 At what step did the student make the INITIAL mistake: Step 1: 12x+60-x+15 ÷5=0 Step 2: 11x+75 ÷5=0 Step 3: 11x+15=0 Step 4: 11x= -15 Step 5: x= -15/11
STEP 2 ( did not follow PEMDAS) ( Completed step one P, however ignores D)
Procedural Fluency
Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
An 8 foot square floor is to be covered with square tiles measuring 8 inches on each side. If each tile costs 50 cents, how much will it cost to tile the floor?
$72
An individual working for a certain company earned 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
Which equation illustrates the additive inverse of property?
-10a + 10a = 0
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
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
During a certain time perios, 2,000,000 oz of gold was produced in the United States. Use the following graph to determine the amount of gold produced in Arizona and Colorado. [Arizona 8%, Colorado 5%]
260,000 8+5 = 13*2,000,000
The smallest state in the United States is Rhode Island, which measurement is closest to the area of Rhode Island?
3000 square kilometers
Ahmet is making a stem and leaf plot of the high temperatures for the past week. He recorded the temperatures as follows 4 0 5 25668 6 1144479 7 2 Which temperature would be considered an outlier for the data given?
40
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
A group of students are working on a project. They complete 30%percent 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
Mrs. Michaels has installed a new and more powerful sprinkler system, but the new system will go 20 meters farther than the old system with a radius of 50 meters as pictures below. What is the circumference of the spraying area of the new system?
439.6 meters 20+50= 70*3.14*2
A rectangular polygon has eight sides. Find the measure of an exterior angle of the polygon
45
Burritos are served with various choices of each of 3 layers of toppings. Customers may choose one of the following as the base: beans, beef, chicken. They may choose one vegetable topping: Lettuce, tomatoes, onions, or olives. They may also choose one condiment topping: sour cream, guacamole, cheese or salsa. How many different burritos can be made from all these choices?
48
A calculator using scientific notation would display 0.000507 as which
5.07 x 10^-4
A student types 3750 word report in 1 hour and 15 min. Find the average words per minute?
50 wpm
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism.
510cm2
The weekly wages of 7 employees are shown as follows: 180, 240, 360, 714, 300, 256, and 180. Find the range
534
Find the sum of the interior angles of the polygon shown in the figure (a pentagon that looks like a house)
540
A customer decides to give a tip to a waitor of only one coin randomly selected from 8 coins from his pocket. What are the odds of him giving the waiter a quarter is he has 3 quarters, 2 half dollars, 1 dime and 2 pennies?
5: 3
A teacher wants to build a scale model of the Earth and Pluto to compare their sizes. The Earth has a diameter of approximately 8000 miles and Pluto has a diameter of approximately 1500 miles. If the teacher builds a model of Earth with a diameter of 32 inches, what should be the diameter of her model of Pluto?
6 inches
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?
640
A bottle of children's cough syrup would most likely have a capacity of
8 Fluid ounces
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
A 6thsixth-grade teacher is plotting the vertices of a rectangle on a coordinate grid. The first 3 points he plots are (3, 1), (- 1, 1) and(-1, - 1). In what quadrant should the last vertex be plotted?
IV
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
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
Compare the twi triangles
Rotation
What is the 1st operation performed to simplify the following operation? 1/2 + 15/16 ------------/ 5/8 1-3/4
Subtract 3/4 from 1
