Eighth Grade Math

• Students will be able to demonstrate an understanding of congruence and similarity through the following applications.

• • Verify that angle measure, collinearity, and distance are preserved under rigid transformations.

  • Prove that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image tot the image.

  • Describe a possible sequence of rigid transformations between two congruent figures

  • Describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates

  • Understand that two-dimensional figures are similar if a series of transformations(rotations, reflections, translations and dilations) can be performed to map the pre-image to the image.

  • Describe a possible sequence of transformations between two similar figures.

• Students will explore angle relationships to perform the following tasks.

• • Derive the sum of the interior angles of polygons

  • Explore the relationship between he interior and exterior angles of a polygon

  • Construct and explore the angles created when parallel lines are cut by a transversal

• Students will investigate bivariate data and demonstrate understanding of the following skills 

• • Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two qualities.

  • Generate a use a trend line for bivariate data and assess the line of best fit.

  • Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects

  • Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

• Students will demonstrate a preliminary understanding of functions and will master the concepts listed. 

  • Explain that a function assigns to each input exactly one output

  • Determine if a relation is a function

  • Recognize the graph of linear and non-linear functions

  • Determine the x-intercept and parameters of a linear function

  • Interpret the equation y = mx +  b as defining a linear function

  • Recognize that the graph of a linear function has a constant rate of change.      

• Students will be able to understand the connections between proportional relationships, lines and linear equations by completing the following.

  • Compare two different proportional relationships

  • Interpret and draw conclusions of the unit rate as slope and recognize slope as the change in y over the change in x

  • Explain why the slope is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane

  • Derive the equation y = mx  for a line through the origin and the equation 

 y = mx +  b for a line intersecting the vertical axis at b 

• • Write a linear equation in point-slope form and standard form using points and slope in the Cartesian coordinate plane.     

• Students will extend their knowledge of linear equations through the following skills.

  • Create and identify linear equations with one solution, infinitely many solutions or not solutions

  • Apply linear equations and inequalities with rational number coefficients including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms

  • Graph systems of linear equations and recognize the intersection as the solution of the system

  • Explain why solution(s) to a system of two linear equations in two variables correspond to point(s0 of intersection of the graphs

  • Explain why systems of linear equations can have one solution no solution, or infinitely many solutions

  • Solve systems of simultaneous equations

• Students will explore the real number system and be able to

  • Generate equivalent representations of rational numbers, including converting decimals which repeat into fractions and fractions into repeating decimals.

  • Estimate the value and compare the size of irrational numbers and approximate their locations on a number line.

• Students will understand and apply the Pythagorean Theorem

  •  Use models to demonstrate a proof of the Pythagorean Theorem

  • Use the Pythagorean Theorem to determine the unknown side lengths in right triangles in problems in two and three dimensional contexts

  • Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate plane.

• Students will use integer exponents to accomplish the following

  •  Express very large and very small quantities in scientific notation

  • Perform operations with numbers expressed in scientific notation

  • Apply the properties of exponents to generate equivalent expressions