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Test Specifications
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Mathematics

GEPA - p. 37-40

Grade 8 Cluster IV:  Patterns, Functions, and Algebra

Macro B: Use algebraic concepts and processes to concisely express, analyze, and model real-world situations.
CPIs:
4.11.3 4.13.5
4.11.4 4.13.7
4.11.7 4.13.9
4.11.8 4.13.8
4.11.9 4.13.10
4.11.10 4.13.11
4.11.11 4.13.12
4.11.12 4.13.13
4.13.1 4.15.2
4.13.2 4.15.4
4.13.3 4.15.7
4.13.4  

Power Base:
4.1  Problem Solving
4.2  Communication
4.3  Connections
4.4  Reasoning
4.5  Tools & Tech.
4.8  Numerical Oper.
4.9  Measurement
4.10 Estimation
4.16 Excel. & Equity

Question Types:
Multiple Choice (MC)
Short Constructed
    Response (SC)
Open Ended (OE)

Technology:
Calculator

Manipulatives:
Algebra tiles
Graph paper

KNOWLEDGE:
The student should have a conceptual understanding of:

  1. Variables, expressions, number sentences, and open sentences
  2. Linear equations and inequalities
  3. Algebraic order of operations
  4. Absolute value
  5. Number line
  6. Functions (linear and non-linear)
    1. Correspondence between two sets (domain & range)
    2. Graphs
    3. Input-output process
    4. Rules or formulas
    5. As models of phenomena
  7. Cartesian coordinate system
  8. Rates of change (ex: informal notion of slope)

The student should be able to:

  1. Use the number line and the rectangular coordinate system as representational tools
  2. Identify relationships from tables and graphs
  3. Solve equations using intuitive methods, manipulatives, paper-and-pencil techniques, tables, graphs, and calculators

PROBLEM-SOLVING SKILLS:
In problem settings, using abilities that comprise the power base, the student should be able to:

  1. Use inequalities to represent and describe mathematical situations and real-world phenomena
  2. Model and solve problems that involve varying quantities using variables, expressions, and equations
  3. Explain and compare how a change in one quantity can produce a corresponding change in another
  4. Describe how certain quantities change over given parameters (e.g. distance, time, etc.)
  5. Recognize and describe the difference between linear and exponential growth
  6. Use relations, graphs, and linear functions to model mathematical situations and real-world phenomena

Sample SC Item
The amount A that principal P will be worth after t years at interest rate r, compounded annually, is given by this formula:

A = P(1+ r)t

Suppose $4,000 principal is invested at 6% interest compounded annually for five years. How much money would the investment yield after 5 years?
(Answer: $5,352.90)

Sample MC Item
Each week, Tim and Andy earn $20 mowing Mrs. Leto's lawn. How they share $20 depends on who does the most work. Which of the graphs shown below could be used to represent the different ways that Tim and Andy can share the money?

Sample MC Item
The tiles on your reference sheet were used to construct the diagram below.

Which algebraic expression does this diagram represent?

a.  
 x + 2
* b.  
 x² + 3 x + 2
c.  
 x + 1
d.  
 x² + 2x+ 3



Sample MC Item
Which of the following problems can be solved by using the equation

x + 2 = 28?

a.  
A math class started with 28 students. Today, two more students enrolled in the class.  How many students does this class now have?
* b.  
 Erin added two more books to her collection of reference books. If she now has 28 books in this collection, how many books did she have in it before adding two more?
c.  
 Jim had $28.00 in his bank account. A week later, he deposited $2.00 in this account. Assuming Jim made no withdrawals from his account, how much money did Jim have in his account after making the deposit?
d.  
 Ann biked 28 miles at two miles per hour. How long did Ann bike?

Sample MC Item
Which equation describes the relationship shown in this table?
 

f
1
2
3
4
5
6
7
g
6
4
2
0
-2
-4
-6

a.  
 g = f + 5
b.  
 g = f - 2
c.  
 g = 2 + 4f
* d.  
 g = 8 - 2f

Sample MC Item
The Viking Hiking Club hikes a part of the Appalachian Trail once a year. On one occasion they hiked up the mountain at a constant rate until they reached Sunfish Pond. After a short rest, they hiked back down the mountain at a slightly faster constant rate. Which graph shows the relationship between the distance they traveled and the time it took them?