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Test Specifications
Contents
Mathematics

GEPA - p. 35-36

        Grade 8 Cluster IV:  Patterns, Functions, and Algebra

Macro A:  Recognize, create, and extend a variety of patterns and use inductive reasoning to understand and represent mathematical and other real-world phenomena.
CPIs:
4.6.3 4.11.9
4.6.16 4.11.12
4.11.1 4.11.13
4.11.2 4.13.2
4.11.5 4.13.6
4.11.6 4.13.8
4.11.7 4.15.1
4.11.8 4.15.5

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:
Graph Paper

KNOWLEDGE:
The student should have a conceptual understanding of:

  1. Patterns and sequences
    1. Finite
    2. Infinite
  2. Variables
  3. Expressions
  4. Rules or formulas
  5. Tables

The student should be able to:

  1. Form generalizations based on observations of patterns and sequences
  2. Identify patterns and relationships from tables and graphs
  3. Represent and describe mathematical patterns and relationships with tables, rules, simple equations, graphs, and concrete materials
  4. Recognize describe, and extend patterns in both finite and infinite number sequences involving whole numbers, rational numbers, and integers

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

  1. Use patterns and relationships to model mathematical situations and real-world phenomena
 Sample SC Item
In a rectangular array, 144 seats can be arranged with 6 rows and 24 seats in each row. Give two other rectangular arrays that are possible for 144 seats.
Possible answers include: 12 x 12
18 x 8
72 x 2
48 x 3

Sample MC Item
Sam Smart made a deal with his parents.  He agreed to do chores for one hour every day, if they would pay him in the following way.  He wanted to receive 1 cent on the first day, 2 cents on the second day, 4 cents on the third day, 8 cents on the fourth day, and so on.  Which of the following expressions represents how much he would receive (in cents) on the twentieth day?

a.  20       b.  2²¹      c.  2²º     * d.  2¹9

Sample OE Item
The sequence; 5, 25, 125, 625, . . . continues indefinitely. Analyze it in order to answer the following questions.

  • What is the 7th term of the sequence?
  • Describe the pattern you see in the sequence.
  • What algebraic expression represents the nth term?

Sample OE Item
Assume that the pattern of dots shown below continues infinitely, with more dots being added at each step.

Ginger wants to determine the number of dots in the 20th step, but she does not want to actually draw all 20 steps and then count the dots.

  • Explain how Ginger could find the number of dots in step 20 without actually drawing them.
  • What would be the number of dots in the 20th Step?

Sample OE Item
The Lucas sequence, shown below, is generated by taking two consecutive terms and adding them together to get the next term.

1, 3, 4, 7, 11, 18, 29, 47, 76, . . .

If you choose any three consecutive terms and add the numbers together, the result will be even.

  • Pick two sets of three consecutive terms and show that this is true.
  • Explain why the sum of three consecutive terms will always be even in this sequence.
  • Is it possible to generate a similar sequence (by taking two consecutive terms and adding them together to get the next term), starting with numbers other than 1 and 3, in which the sum of 3 consecutive terms is always odd? Explain your answer.