Download 8th grade assessment review

8th Grade Assessment Review
S1B1K5a-c
Standard 1: Number and Computation – The student uses numerical and
computational concepts and procedures in a variety of situations.
Benchmark 1: Number Sense – The student demonstrates number sense for real
numbers and simple algebraic expressions in a variety of situations
▲ knows and explains what happens to the product or quotient
when (2.4.K1a):
a. a positive number is multiplied or divided by a rational number
greater than zero and less than one, e.g., if 24 is divided by 1/3,
will the answer be larger than 24 or smaller than 24? Explain.
b. a positive number is multiplied or divided by a rational number
greater than one, C
c. a nonzero real number is multiplied or divided by zero
• a number multiplied by 0 equals 0
• you CANNOT divide by 0
• a positive number greater than 1 divided by a fraction between 0 and
1 results in a quotient GREATER THAN 1
• a number multiplied by it’s reciprocal equals 1
S1B2A1ab
Standard 1 continued
Benchmark 2: Number Systems and Their Properties – The student demonstrates an
understanding of the real number system; recognizes, applies, and explains their
properties; and extends these properties to algebraic expressions.
a.▲ commutative, associative, distributive, and substitution properties;
b. ▲ identity and inverse properties of addition and multiplication
Commutative Property of Multiplication and Addition – “flip-flop” the order
of numbers doesn’t make a difference 5+6=6+5 or ab=ba
Associative Property of Multiplication and Addition – grouping of numbers
doesn’t make a difference 5+(6+7)=(5+6)+7 or (a∙b) ∙c=a ∙(b ∙c)
the numbers inside parentheses are grouped differently
Distributive Property – what’s inside the parentheses gets multiplied by
what’s outside the parentheses 5(3-2)=15-10 or a(b + c) =ab + ac;
Substitution Property - if a = 2, then 3a = 3 x 2 = 6
Additive Identity Property – 0 added to any number equals that number
Additive Inverse Property – any number added to its inverse equals 0
-6+6=)
Multiplicative Property – any number multiplied by 1 is that number
Multiplicative Inverse Property – any number multiplied by its reciprocal is 1
Standard 1 continued
S1B2K2
Benchmark 2: Number Systems and Their Properties – The student demonstrates an
understanding of the real number system; recognizes, applies, and explains their
properties; and extends these properties to algebraic expressions.
2. ▲ identifies all the subsets of the real number system [natural (counting) numbers,
whole numbers, integers, rational numbers, irrational numbers] to which a given number
belongs (2.4.K1l). (For the purpose of assessment, irrational numbers will not be included.)
Natural (counting) numbers – positive whole numbers beginning with 1
DOES NOT INCLUDE 0
Whole numbers – positive numbers BEGINNING AT 0
Integers – whole numbers and their opposites (positive and negative numbers)
Rational numbers – fractions (including such as -7/1 or 23/1)
RATIONAL NUMBERS
THE REAL
INTEGERS
NUMBER
WHOLE NUMBERS
SYSTEM
NATURAL
NUMBERS
Standard 1 continued
S1B4A1a
Benchmark 4: Computation – The student models, performs, and explains computation
with rational numbers, the irrational number pi, and algebraic expressions in a variety of
situations.
1. ▲ generates and/or solves one- and two-step real-world problems
using computational procedures and mathematical concepts
S1B4K2ab
2. performs and explains these computational procedures with rational
numbers (2.4.K1a):
a. ▲ addition, subtraction, multiplication, and division of integers
b. ▲ order of operations (evaluates within grouping symbols, evaluates powers to the
second or third power, multiplies or divides in order from left to right, then adds or
subtracts in order from left to right)
These questions on the assessment are one and two step real world word problems using
the order of operations to solve:
Parentheses and other grouping symbols: brackets, division (fraction) bars
Exponents
Multiplication/Division from left to right
Addition/Subtraction from left to right
Please Excuse My Dear Aunt Sally
S1B4A1a and S1B4K2ab continued
These problems would include problems such as:
Given the area of a rectangular deck is 525 square feet and the length
of the deck is 20 feet, what is the width of the deck.
To Solve: work backwards Area=length ∙ width so 525÷20 = 26.25
feet; the width of the deck is 26.25 feet
Given a circular corral has an area of 624 square feet, what is the
diameter and what is the radius.
To Solve: work backwards Area of a circle =π r2 so 624÷3.14 =198.7
feet (rounded to the tenths) then take the square root of that answer.
√198.7≈14.1
Given a triangular window has an area of 315 square inches and a
base of 14 inches, what is the height of the window?
To Solve: work backwards A=1/2(b ∙ h) so (315 ∙ 2) ÷ 14=45 inches
S2B2A1a
Standard 2: Algebra – The student uses algebraic concepts and procedures in a variety of
situations.
Benchmark 2: Variable, Equations, and Inequalities – The student uses variables, symbols,
real numbers, and algebraic expressions to solve equations and inequalities in a variety of
situations.
1. represents real-world problems using:
a. ▲ ■ variables, symbols, expressions, one- or two-step equations with rational number
coefficients and constants, e.g., today John is 3.25 inches more than half his sister’s
height. If J = John’s height, and S = his sister’s height, then J = 0.5S + 3.25.
The student must be able to choose the correct algebraic expression or equation based on
the real world problem and be able to solve.
Examples:
A garage charged Mr. Tilton $48 for parts and $36/hour for labor. How many hours did
the garage work on Mr. Tilton's car if the total bill was $156?
Lindsay is 2.5 years older than Mikayla. Mikayla is 8 years old. How old is Lindsay?
S2B2K3
Standard 2 continued
Benchmark 2: Variable, Equations, and Inequalities – The student uses variables, symbols,
real numbers, and algebraic expressions to solve equations and inequalities in a variety of
situations.
3. solves:
a. ▲ one- and two-step linear equations in one variable with rational number
coefficients and constants intuitively and/or analytically
Examples:
4x + 7 = 23
6x + 1 = 19
2x – 5 = 13
S2B3A3
Standard 2 continued
Benchmark 3: Functions – The student recognizes, describes, and analyzes constant, linear,
and nonlinear relationships in a variety of situations.
3. ▲ translates between the numerical, tabular, graphical, and symbolic representations of
linear relationships with integer coefficients and constants (2.4.A1a), e.g., a fish tank is
being filled with water with a 2-liter jug. There are already 5 liters of water in the
fish tank. Therefore, you are showing how full the tank is as you empty 2-liter jugs of water
into it. Y = 2x + 5 (symbolic) can be represented in a table (tabular) –
X0123
Y 5 7 9 11
The student must be able to recognize
and create function tables and graphs.
x
y
1
8
2
6
3
4
S2B4A2
Standard 2 continued
Benchmark 4: Models – The student generates and uses mathematical models to
represent and justify mathematical relationships found in a variety of situations.
2. ▲ determines if a given graphical, algebraic, or geometric model is an accurate
representation of a given real-world situation
EXAMPLE:
The community is building a new swimming pool with varying depths. Choose the diagram
that shows depths of 3 ft, 6 ft, and 12 ft, with a sloped incline between each area.
A
B
C
Correct answer is a – only graph with BOTH 12 ft depth and SLOPED INCLINE
D
S3B1A1a
Standard 3: Geometry – The student uses geometric concepts and procedures in a variety
of situations.
Benchmark 1: Geometric Figures and Their Properties – The student recognizes geometric
figures and compares their properties in a variety of situations.
1. solves real-world problems by (2.4.A1a):
a. ▲ ■ using the properties of corresponding parts of similar and congruent
figures, e.g., scale drawings, map reading, proportions, or indirect
measurements.
Examples:
Marshall County is a rectangular shape that is 28 miles wide and 30 miles long. On the
map, the width is 3 cm. What is the length of the county on the map?
28 mi (width) = 3 cm (width)
30 mi (length) x cm (length)
28x=90 x≈3.21 cm
The distance on a map from Kansas City to Topeka is 6.1 cm, and the distance from
Topeka to Wichita is 14 cm. If the scale is 1cm = 10 miles, what is the distance from
Kansas City to Wichita?
1 cm = 20.1cm (total distance from KC to Wichita)
10 mi x mi
1x=201 miles x = 201 miles
S3B1K6
Standard 3 continued
6. ▲ uses the Pythagorean theorem to (2.4.K1h):
a. determine if a triangle is a right triangle,
b. find a missing side of a right triangle where the lengths of all three sides are
whole numbers.
a and b are both LEGS
c is the HYPOTENUSE (always opposite right angle)
c
FORMULA: a2 + b2 = c2
a
b
The student must be able to use the formula to:
find the hypotenuse when given the two legs
find an unknown leg when given the other leg and hypotenuse
determine if a triangle is a right triangle
The legs of a right triangle measure 10 and 24 inches. What is the length of the
hypotenuse?
102 + 242 = c2 100 + 576 = 676 √676 = 26
The hypotenuse of a right triangle measures 15 inches, and one of the legs measures 12
inches. What is the length of the other leg?
152 = 122 + b2
225 = 144 + b2 225-144 = 81 √81 = 9 b=9 inches
S3B4K1a-d
Standard 3 continued
Benchmark 4: Geometry from an Algebraic Perspective – The student uses an algebraic
perspective to examine the geometry of two-dimensional figures in a variety of situations.
1. uses the coordinate plane to (2.4.K1a):
a. ▲ list several ordered pairs on the graph of a line and find the slope of the line;
b. ▲ recognize that ordered pairs that lie on the graph of an equation are
solutions to that equation;
c. ▲ recognize that points that do not lie on the graph of an equation are not
solutions to that equation;
d. ▲ determine the length of a side of a figure drawn on a coordinate plane with
vertices having the same x- or y coordinates;
Continued on next slide
S3B4K6ab
Standard 3 continued
Negative slope – line goes down
Rise -4
Run 2
slope -4/2 = -2/1 slope = -2
-4
2
•Make a table of values
for five solutions and
graph. 3x + 2y = 4
X
3x + 2y = 4
Y
Coordinates
-2
3(-2) + 2(5)=4
5
(-2, 5)
-1
3(-1) + 2(3.5)=4
3.5
(-1, 3.5)
0
3(0)+2(2)=4
2
(0, 2)
1
3(1) +2(0.5)=4
0.5
(1, 0.5)
2
3(2)+2(-1)=4
-1
(2, -1)
S3B4Kcd
Standard 3 continued
What is the perimeter of the shape? Just count the
squares to determine the perimeter 2+4+2+4=12
Points located on the line
(-3, -2)
(-2, 0)
(-1, 2)
(0, 4)
If the point isn’t on the
line, it isn’t a solution to
the given linear equation.
S4B1A4a
Standard 4: Data – The student uses concepts and procedures of data analysis in a variety of
situations.
Benchmark 1: Probability – The student applies the concepts of probability to draw
conclusions, generate convincing arguments, and make predictions and decisions including
the use of concrete objects in a variety of situations.
4. makes predictions based on the theoretical probability of (2.4.A1a,i):
a. ▲ ■ a simple event in an experiment or simulation
Example:
There are thirteen balls in a bag of which six are black. If any taken ball from the bag is
replaced, what would you predict to be the number of black balls on 50 draws?
6÷13∙50 ≈ 23
Mr. Bill surveyed several students, asking them what their favorite ice cream was. 45%
of the class stated that they liked chocolate. Based on this information, what would be
a good prediction as to how many people in a school of 1,678 students like chocolate?
45% ∙ 1678 ≈ 755 students
S4B1K3
Standard 4 continued ****THIS INDICATOR IS DROPPED FOR 2012****
Benchmark 1: Probability – The student applies the concepts of probability to draw
conclusions, generate convincing arguments, and make predictions and decisions including
the use of objects in a variety of situations.
3. ▲ finds the probability of a compound event composed of two independent events in
an experiment, simulation, or situation e.g., what is the probability of getting two heads,
if you toss a dime and a quarter?
Example:
Your friend wants a new style. She tries on three shirts: white, red, and blue. Then she tries
on four pairs of pants: blue jeans, black jeans, brown jeans, and gray slacks. What is the
probability that your friend will pick the white shirt and blue jeans?
3 shirts ∙ 4 pants = 12 combinations so her probability is 1/12
A card is chosen at random from a set of 4 cards, of which 2 are red and 2 are black.
Another card is chosen without replacing the first. What is the probability that both are red
cards?
2/4 ∙ 1/3 (card not put back) = 2/12 reduces to 1/6
S4B2K3
Standard 4 continued
3. ▲ determines and explains the measures of central tendency
(mode, median, mean) for a rational number data set.
mean – the average; add up the numbers in the data set and divide by the
number of data
median – put the data in order from least to greatest, find the number in the
middle; if the median falls between 2 numbers, add them and divide
by 2
mode – the number that is used most often (can have more than 1 mode)