• This year's seventh-graders (regular or advanced) will be working on the Districts Essential Outcomes for 7th and 8th grade.  We enhance in as many areas as we can to provide a deeper and more concrete understanding of the materials.  Please also remember that there is overlap on many of the topics which strengthen the knowledge base.  If you have further questions about these Outcomes, please call and chat.
John Chaplin

## 1. Algebra, Patterns, & Functions

- Understand and distinguish between proportional relationships including inverse relationships.

- Using multiple representations, students will use proportional relationships to investigate the rate of change (slope).

- Represent, solve, and assess real-world or mathematical situations with multi-step equations or inequalities involving variables and all rational numbers symbolically, graphically and numerically.

- Demonstrate an understanding of the order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing all rational numbers.

- Apply technology for the order of operations and grouping.

- Students will simplify expressions by combining like terms.

## 2. Data and Statistics

-Use central tendencies to make conclusions, comparisons, and predictions.

- Describe the impact that inserting or deleting a data point has on the mean and the median of the data set.

-Interpret circle graphs and histograms.

-Choose and construct the most appropriate display for any data set.

## 3. Geometry and Spatial Sense

- Analyze the transformations of two-dimensional figures on a coordinate grid.

## 4. Measurement

-Explore and determine the proportionality between the diameter, radius, and circumference of circles.

-Develop and understand the calculations of circumference and area of circles and sectors of circles, volume and surface area of cylinders.

Measurement cont…

- Determine and apply scale factors, length ratios, and area ratios to find side lengths and areas of similar geometric figures.

- Use proportions and ratios to solve problems involving scale drawings and conversion of measurement units.

## 5. Number Sense

- Write rational numbers as ratios and decimals.

- Interpret the decimal result of a division problem when using a calculator.

- Understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

- Compare positive and negative rational numbers using inequality symbols.

- Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.

- Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line.

## 6. Operations and Computation

- Calculate with positive and negative rational numbers and rational numbers with whole numbers exponents, to solve real-world and mathematical problems.

## 7. Probability

- Use probabilities to solve real-world and mathematical problems, represent probabilities using fractions, decimals, and percents.

- Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.

- Simulate situations involving randomness (calculator, spreadsheet, etc.) display and compare results.

## 8th Grade Math Essential Outcomes

1.     Algebra, Patterns, & Functions

-Understand and use function notation (input/output, independent/dependent, linear/non-linear, F(x) = mx + b, F(x) = abˆx).

-Identify graphical properties of linear functions including slopes and intercepts.

-Know that the slope equals the rate of change and that the y-intercept is zero when the function represents a proportional relationship

-Use linear and nonlinear functions, linear and non-linear equations, and systems of linear equations to represent (tables, verbal descriptions, symbols, and graphs), analyze, and solve a variety of problems.

-Generate equivalent numerical and algebraic expressions (radicals, absolute value, etc…) and use algebraic properties to evaluate expressions.

-Represent and solve real-world and mathematical situations using equations and inequalities involving linear expressions.

-Express linear equations and convert between slope-intercept, point-slope, and standard forms.

-Using technology, identify how coefficient changes in the equation f(x)= mx+b affect the graphs of linear functions.

-Represent relationships in various contexts using the systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically, and numerically, and interpret solutions in the original context.

-Represent geometric and arithmetic sequences using equations, tables, graphs, and verbal descriptions.

2. Data and Statistics

- Represent geometric and arithmetic sequences using equations, tables, graphs, and verbal descriptions.

- Estimate and determine the equation for the line of best fit on a scatterplot.

Data and Statistics cont…

- Use the line of best fit to make predictions.

- Determine if a prediction for the line of best fit is reasonable

3. Geometry and Spatial Sense

- Know and apply the Pythagorean Theorem and its converse.

-  Understand and apply relationships between parallel and perpendicular lines and their equations (slope).

4. Measurement

- Explore relationships and solve problems involving rates such as motion at a constant speed, velocity, and rates of change (slope).

- Explore, understand, and apply the rates of change (slope) of lines and line segments to polygons.

- Solve a variety of problems involving parallel and perpendicular lines on a coordinate system.

5. Number Sense

- Classify real numbers as rational or irrational.

- Compare and locate real numbers on a number line.

- Determine rational approximations for real numbers.

## - Represent numbers using positive and negative integer exponents.

- Express numbers in scientific notation by hand and calculator.

## - Know and apply the properties of positive & negative integer exponents to generate equivalent numerical expressions, including scientific notation.

7. Probability