# Using the State Curriculum: Mathematics, Grade 8

## State Curriculum Toolkit

Tools aligned to State Curriculum indicators and/or objectives.

• Clarification of Indicator and/or Objective
Explanation and/or examples of indicator and/or objective
• Lesson Seeds
Ideas/seeds for an objective-aligned activity
• Higher Order
Thinking Skills

Examples of questions at various levels of cognitive demand
• Sample Assessments
Items and annotated student responses as appropriate
• Public Release Items
Actual MSA items and annotated student responses as appropriate
 Algebra Geometry Measurement Statistics Probability Number Processes

## Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

### Topic

A. Patterns and Functions

#### Indicator

• 1. Identify, describe, extend, and create patterns, functions and sequences
##### Objectives
1. Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph
###### Assessment limit: Provide the nth term no more than 10 terms beyond the last given term using common differences no more than 10 with integers (-100 to 5000)
2. Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph
###### Assessment limit: Provide the nth term no more than 5 terms beyond the last given term using the recursive relationship of geometric sequences with whole numbers and a common ratio of no more than 5:1 (0 – 10,000)
3. Determine whether relationships are linear or nonlinear when represented in words, in a table, symbolically, or in a graph
###### Assessment limit: Use a graph to determine if a relationsip is linear or nonlinear
4. Determine whether relationships are linear or nonlinear when represented symbolically

### Topic

B. Expressions, Equations, and Inequalities

#### Indicator

• 1. Write, simplify, and evaluate expressions
##### Objectives
1. Write an algebraic expression to represent unknown quantities
###### Assessment limit: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)
2. Evaluate an algebraic expression
###### Assessment limit: Use one or two unknowns and up to three operations and rational numbers (-100 to 100)
3. Evaluate numeric expressions using the order of operations
###### Assessment limit: Use no more than 5 operations including exponents of no more than 3 and 2 sets of parentheses, brackets, a division bar, or absolute value with rational numbers (-100 to 100)
4. Simplify algebraic expressions by combining like terms
###### Assessment limit: Use no more than 3 variables with integers (-50 to 50), or proper fractions with denominators as factors of 20 (-20 to 20)
5. Describe a real-world situation represented by an algebraic expression

#### Indicator

• 2. Identify, write, solve, and apply equations and inequalities
##### Objectives
1. Write equations or inequalities to represent relationships
###### Assessment limit: Use a variable, the appropriate relational symbols (>, ≥, <, ≤, =) and no more than 3 operational symbols (+, -, ×, ÷) on either side and rational numbers (-1000 to 1000)
2. Solve for the unknown in a linear equation
###### Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and rational numbers (-2000 to 2000)
3. Solve for the unknown in an inequality
###### Assessment limit: Use a one- or two-operation inequality with one variable on one side no more than 3 times whose result after combining coefficients is a positive whole number coefficient with integers (-100 to 100)
4. Identify or graph solutions of inequalities on a number line
###### Assessment limit: Use one variable once with a positive whole number coefficient and integers (-100 to 100)
5. Identify equivalent equations
###### Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and integers (-2000 to 2000)
6. Apply given formulas to a problem-solving situation
###### Assessment limit: Use no more than four variables and up to three operations with rational numbers (-500 to 500)
7. Write equations and inequalities that describe real-world problems

### Topic

C. Numeric and Graphic Representations of Relationships

#### Indicator

##### Objective
1. Graph linear equations in a coordinate plane

#### Indicator

• 2. Analyze linear relationships
##### Objectives
1. Determine the slope of a graph in a linear relationship
###### Assessment limit: Use an equation with integer coefficients (-9 to 9) and integer constants (-20 to 20) and a given graph of the relationship
2. Determine the slope of a linear relationship represented numerically or algebraically

Note: Highlighted assessment limits will be tested in the no calculator section of MSA. In the assessment limit, (0-10) or (-10 to 10) means all numbers in the problem or the answer will fall within the range of 0 to 10 (including endpoints) or -10 to 10 (including endpoints), respectively. All content standards are tested in MSA but not all objectives. Objectives that have an assessment limit are tested on MSA. Objectives without an assessment limit are not tested on MSA.

June 2004