Download Algebra 1 Unit Assessment

Algebra 1-2 Unit 1
Algebra 1-2 Real Numbers Unit
Learning Goal 1: Classify and order real numbers
Advanced
Score
4.0
In addition to score 3.0 performance, in-depth inferences and applications that go beyond what was
targeted for all students (Proficient).
 Justify why there are infinitely many numbers between any two numbers on a number line
 Justify why a number is irrational
 Classify the sum (product, difference, or quotient) of two natural (whole, rational, etc..)
numbers into appropriate number set(s). Predict and explain if this will always be true.
Score 3.5 In addition to score 3.0 performance, partial success at inferences and applications that go
beyond what was targeted for all atudents.
Proficient
Score
3.0
No major errors or omissions regarding any of the information and/or processes (simple or complex)
that were explicitly taught.
 Estimate the square root of non-perfect square numbers
Place real numbers on a number line, including irrational numbers ( 5 ,  )
Classify numbers into all appropriate number sets
Identify non-benchmark numbers (numbers other than halves and quarters) between any two
numbers
Score 2.5 No major errors or omissions regarding the simpler details and/or processes and partial
knowledge of the more complex ideas and processes.



Basic
Score
2.0
No major errors or omissions regarding the simpler details and processes, but major errors or
omissions regarding the more complex ideas and processes.
 Recognize and recall specific vocabulary
 Find the absolute value of a number
 Find the opposite of a number
 Find the square root of perfect squares
 Order rational numbers
 Classify numbers as rational or irrational
 Identify the benchmark numbers (halves and quarters) between any two numbers
Score 1.5 Partial knowledge of the simpler details and processes, but major errors or omissions
regarding the more complex ideas and processes.
Below
Basic
Score
1.0
With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Score .5
Score
0.0
With help, a partial understanding of some of the simpler details and processes but not
more complex ideas and processes.
There is no evidence or demonstration of student learning.
Adapted from: Marzano (2004) Workshop materials. Centennial, CO: Marzano & Associates.
Algebra 1-2 Real Numbers Unit
Learning Goal 2: Compute with Real Numbers
Advanced
Score
4.0
In addition to score 3.0 performance, in-depth inferences and applications that go beyond what was
targeted for all students (Proficient).
 Analyze a problem and solution and determine the errors.
 Create expressions using real numbers and operations given specific criteria
 Create a word problem that can be solved using a given computation problem in its
numerical form.
Score 3.5 In addition to score 3.0 performance, partial success at inferences and applications that
go beyond what was targeted for all students.
Proficient
Score
3.0
No major errors or omissions regarding any of the information and/or processes (simple or complex)
that were explicitly taught.
 Solve word problems requiring accurate computation of real numbers.
 Explain the affect of operations on the magnitude of quantities
 Apply and explain the methods of computation when problem solving using real numbers.
 Check reasonableness of computation using estimation.
Score 2.5 No major errors or omissions regarding the simpler details and/or processes and partial
knowledge of the more complex ideas and processes.
Basic
Score
2.0
No major errors or omissions regarding the simpler details and processes, but major errors or
omissions regarding the more complex ideas and processes.
 Recognize and recall specific vocabulary
 Compute with real numbers in their numerical form, including order of operations
Score 1.5
Below
Basic
Score
1.0
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Score .5
Score
0.0
Partial knowledge of the simpler details and processes, but major errors or omissions
regarding the more complex ideas and processes.
With help, a partial understanding of some of the simpler details and processes but not
more complex ideas and processes.
There is no evidence or demonstration of student learning.
Adapted from: Marzano (2004) Workshop materials. Centennial, CO: Marzano & Associates.
Name:____________________________
Date:_________________
Algebra Real Numbers Unit 1 Assessment
Learning Goal 1: Classify and Order Real Numbers
Level 2/Basic
1) Find the opposite and the absolute value of 23.
Opposite: ______ Absolute Value: _______
2) What is the definition of a rational number?
3) Classify the following as rational or irrational:
a. 2/3
b. -3.5
c.
9
d. -12
e.
20
4) Write the following rational numbers in order from least to greatest:
4.7,
 12
13
4
,  1.8, 26, , 0,  7 and
2
5
5
Level 3/Proficient
5) Plot the following numbers on the number line: 5,
3
, 3.2,  16,  1
2
6) Identify at least two numbers between 3 and 3.2 on the number line.
7) Estimate the square root of 10 and explain your reasoning.
8) Check which number set(s) each real numbers belongs to in the table.
Irrational
Rational
Natural #
Whole #
Integer
0
13
-12
7
Level 4/Advanced
9) When you multiply an irrational number times another irrational number, is the product always
irrational? If yes, explain and if no, give a counterexample.
10) Justify why there are infinitely many numbers between 1 and 1.25 on the number line.
Learning Goal 2 Compute with Real Numbers
Level 2/Basic
1) Compute the following problems:
a.
22 - 35
b.
2.35 (-1.7)
c.
3.4 ÷ -1.7
d.
1 3
2 1
5 4
e.
90 – 5 • 2 + 62
f.
-14 + |-17|
g.
8
3
- 15
4
h.
i.
40 ÷ 2 • 5 ÷ 4
16
81
Level 3/Proficient
2) In California Mt. Whitney raises to 14,495 feet above sea level. Nearby, Death Valley sinks to
282 feet below sea level. What is the difference in the sea level of the two locations?
3) Jeffery opened a savings account with a $30 deposit. He made 2 more deposits of $26 each and
2 withdrawals of $15 and $18.
a) What is the total amount currently in Jeffery’s account? ____________________
b) What is the difference between the starting balance and ending balance? ________
4) A recipe for strawberry shortcake calls for the egg, melted butter, and milk to add up to 1 ½ cups
of liquid. If the egg and butter equal 2/3 cups of liquid, how much milk should be added to the
mixture?
5) Explain the difference between -32 and (-3)2.
Level 4/Advanced Choose 2 of the following 3 problems
6) Use four 4’s to write expressions with values from 1 through 4. (Hint: 4÷4 - 4÷4 = 0)
7) The sum of any two real numbers is a real number. To mathematicians this means that the set
of real numbers is closed under addition. The set of real numbers is also closed under
subtraction. Is the set of whole numbers closed under addition? Is the set of whole numbers
closed under subtraction? Explain your conclusion in complete sentences. Be sure to include a
complete definition of whole numbers and examples that justify your conclusions.
8) Given the following numerical expression, 15 + 12.79(3),write a real life word problem this
expression could represent and solve the problem.
Learning Goal 3: Apply Properties
Level 2/Basic
Identify the property being illustrated. Choose from the word bank.
1) ( 5 + 12) + 18 = 5 + ( 12 + 18) _______________________
2) 17 + (-17) = 0 _____________________________
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Additive Inverse Property
Multiplicative Inverse Property
Identity Property of Multiplication
Distributive Property
Give an example of each of the following properties:
3) Commutative Property of Multiplication _________________
4) Multiplicative Inverse Property ________________________
Level 3/Proficient
5) Kenny used the distributive property to solve the following problem. His work is show below.
Circle his error(s) and on the line provided explain what he did wrong. Show the correct
solution.
-8( -10 + 5)
(-8 x -10) + 5
80 + 5
85
___________
___________
___________
___________
Correct solution
6) Ryan earns $7.50 per hour working at Scheel’s. He worked 7.5 hours on Saturday and 4 hours
on Sunday. Use the Distributive Property to compute Ryan’s earnings for the weekend.
Remember to use correct order of operations and to check your answer.
Level 4/Advanced: Choose 2 of the 3.
7) Create a word problem that requires the use of one or more properties to solve. Identify the
specific properties used and show a detailed solution.
8) Compare/contrast the commutative and associative properties. Include a thorough explanation
of their similarities and differences and provide examples to support your explanations.
9) Is there a commutative property of subtraction? Why or why not? Provide clear examples to
support your answer.
Name:____________________________
Date:_________________
Algebra Real Numbers Unit 1 Assessment ANSWER KEY
Learning Goal 1: Classify and Order Real Numbers
1. Opposite: -23, Absolute Value: 23
2. A rational number is any number written as an integer divided by a non-zero integer.
3. A. Rational B. Rational C. Rational D Rational E Irrational
4. 7, 
12
4
13
,  1.8, 0, , 4.7,
, 26
5
5
2
5. Sample answer: 3.1, 3.15
6. Sample answer: The square root of 10 is about 3.2. I know that 3 squared is 9, so the square root of
10 has to be greater than 3. Since 4 squared is 16, the square root of 10 has to be less than 4. Since 10 is
closer to 9 than it is to 16, then the square root of 10 has to be closer to 3 than to 4.
7.
Irrational
0
13
-12
7
Rational
x
Natural #
Whole #
x
Integer
x
x
x
x
x
x
x
x
8. Sample answer: No, the product of two irrational numbers is not always irrational. For example,
5  5  5 . The square root of 5 is irrational, and when you multiply it by itself, you get 5 which is a
rational number.
9. Sample answer: If you went half-way between 1 and 1.25 on the number line, you would be at 1.125.
Then if you went half-way between 1 and 1.125, you’d be at 1.0625. You could go half-way between
the numbers an infinite number of times. That’s why there are infinitely many numbers between 1 and
1.25.
Learning Goal 2 Compute with Real Numbers
1. A. -13
D. 3
19
20
G. 6
1
4
B. -3.995
C. -2
E. 116
F. 3
H.
4
9
I . 25
2. Sample answer: The difference in the sea levels of the two locations is 14,777 feet.
3. a. The total amount currently in the account is $49.00.
b. The difference between the starting and ending balance is $19.00.
4.
5
cups
6
5. Sample answer: The difference between 32 and (3)2 is the placement of the parentheses. In 32
, the negative sign is not part of what is being squared. So, the answer is the opposite of 32 or -9. In
(3)2 , the negative sign is being squared, so the answer is just 9.
6. Sample answer: 4  4  4  4  1 , (4  4)  (4  4)  2 , (4  4  4)  4  3 , 4(4  4)  4  4
7. Sample answer: The set of whole numbers is closed under addition. Whole numbers are defined as
0, 1, 2, 3,… They are never negative and never include decimal parts like 0.5. When you group together
wholes and more wholes, you will always end up with a whole. But, they are not closed under
subtraction. If you start with a smaller group and take away a larger group, like 2 - 5, then you end up
with a negative number. Negative numbers are not whole numbers. This means that whole numbers
are not closed under subtraction.
8. Sample answer: I have 3 ropes that are each 12.79 feet long. The other is 15 ft. How many feet of
rope do I have altogether?
Learning Goal 3: Apply Properties
1. Associative Property of Addition
2. Additive Inverse Property
3. Sample answer: 2(3)  3(2)
1
2
4. Sample answer: 2( )
5. Sample answer:
-8( -10 + 5)
(-8 x -10) + 5
80 + 5
85
Correct solution: 40
6. Sample answer:
___________
On this line, they did not multiply -8 by the 5.
___________
___________
7.4(7.50)  4(7.50)
He earns $86.25 for the weekend.
7.50(7.5  4)
7.50(11.50)
86.25
7. Sample answer: I have a garden that is 5 feet long and 6 feet wide. I am going to add a 2 foot by 6
foot section this year. What will the total area of my new garden be?
6(5)  6(2) 
6(5  2) 
9(7)
42
My garden will be 42 square feet.
8. Sample answer: The commutative and associate properties are similar because both addition and
multiplication have these properties. For example, (2  3  4)  2  (3  4) and 2(3  4)  (2  3)  4 .
They are different because the commutative property always is about the order of the numbers in the
expression, while the associate property has to do with the grouping of the numbers.
9. Sample answer: No, there is no Commutative Property of Subtraction. This property means you can
change the order of numbers in an expression and will then have two equivalent expressions. This
works for addition. But, if you change the order of numbers in an expression with subtraction, then the
expressions are no longer equal to the same number. For example, 2  7  9 and 7  2  9 . But,
2  7  5 and 7  2  5 . 5 and -5 are not the same number, so the commutative property does not
work with subtraction.