Grade 8 Pre-Algebra

NUMBER SYSTEM including FRACTIONS: Students develop an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.

OPERATIONS and ALGEBRAIC THINKING : Students use basic and advanced procedures to understand the meaning of operations in relation to advanced properties of functions and algebra.

Geometry: Mathematics is helpful in describing the physical world and the patterns of God’s creation, students analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships and specify locations and describe spatial relationships using coordinate geometry and other representational systems.

Measurement: Students understand measurable attributes of objects and the units, systems, and processes of measurement

STATISTICS, PROBABILITY, AND DATA ANALYSIS: Design investigations, select, use and appropriate statistical methods to analyze data in order to make inferences and predictions based on data.

Work flexibly with integers to solve problems

Compare and order rational and irrational numbers efficiently and find their approximate location on a number line

Understand the classification of numbers

Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation

Understand relationships between numbers

Reason quantitatively and use units to solve problems

Analyze and interpret the structure of expressions

Precisely describe, classify, and understand relationships among types of two and three – dimensional objects using their defining properties

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationships.

Apply geometric concepts in modeling

Apply transformations and use symmetry to analyze mathematical situations

Examine the congruence, similarity , and line or rotational symmetry of objects using transformations

Determine and apply appropriate volume formulas in order to solve mathematical and real-world problems for the given shape

Define and explain key vocabulary

Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

Apply geometric measurement for angles, area, capacity, circles, conic sections

Solves problems with units

Applies scale factors using rates, ratios, proportions and percents

Formulate questions, design studies, and collect data about characteristics shared by two populations or different characteristics within one population

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots.

Interpret categorical and quantitative data 

Evaluate, analyze, interpret and make predictions based on data

Use sampling and probability to make decisions

Develop a deeper understanding of very large and very small numbers and of various representations of them

Define rational and irrational numbers

Convert a decimal expansion which repeats eventually into a rational number 

Generate and explain equivalencies of fractions, decimals, and percents

Order numbers from least to greatest – rational, irrational and integers

Show informally that every number has a decimal expansion

Compare the size of irrational numbers using rational approximations

Estimate the value of expressions involving irrational numbers using rational approximations

Approximate irrational numbers as rational numbers

Approximately locate irrational numbers on a number line

Describe relationships among subsets of real numbers

Examine absolute value as it relates to real numbers

Understand the real number system as a set of elements, operations and properties

Solve problems using exponents, raising to the power and extracting roots and scientific notation

Express numbers as a single digit times an integer power of 10

Use scientific calculators to show scientific notation

Use scientific calculators to compute exponents or roots

Express numbers as a single digit times an integer power of 10

Use scientific notation to estimate very large and/or very small quantities

Identify prime and composite numbers

Determine the least common multiple or greatest common factor for pairs of numbers

Use divisibility tests for 2, 3, 4, 5, 8, 9, and 10

Compute and apply operations with decimals, fractions, and integers including order of operation

Identify and apply ratios as proportions

Write ratios and proportions by using equivalent forms

Find the missing term in a proportion

Compute and apply percentages such as interest, discount, commission

Represent quantities in a circle graph

Use factoring to find common denominations in addition and subtraction of fractions

Explain the meaning of absolute value

Convert fractions to decimals and percents

Define dilations as a reduction or enlargement of a figure

Identify the scale factor of a dilation

Identify corresponding sides and corresponding angles

Apply the concept of congruency to write congruent statements

Define similar triangles

Identify angles created when a parallel line is cut by a transversal

Recall Pythagorean Theorem and its converse

Apply Pythagorean Theorem in solving real-world problems dealing with two and three dimensional shapes

Utilize ratios and proportions in reading and constructing scale drawings

Justify that the sum of interior angles equals 180

Use angle-angle criterion to prove similarity among triangles

Explain a proof of the Pythagorean Theorem

Determine how to create a right triangle from two pints on a coordinate graph

 Identify the legs and hypotenuse of a right triangle

Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint

Define and identify rotations, reflections and translations

Understand prime notation to describe an image after a translation, reflection, or rotation

Use physical models, transparencies or geometry software to verify the properties of rotations, reflections, and translations

Describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using coordinates

Solve basic mathematical Pythagorean Theorem problems and its converse to find missing lengths of sides of triangles in two or three dimensions

Identify symbols for congruency

Apply the concept of congruency to write congruent statements

Recognize the symbol for similar

Determine the coordinates of the vertices of a polygon after a translation or a series of translations

Apply the concept of similarity to write similarity statements

Determine the image of a polygon on a coordinate plane after a reflection or a series of reflections

Identify the degree of rotation that will map one figure onto another without the coordinate plane

Know formulas for volume of cones, cylinders and spheres

Compare the volume of cones, cylinders, and spheres

Given the volume of a cone, cylinder, or sphere, find the radii, height, or approximate using pi

square root; Pythagorean Theorem; right triangle; legs a&b; hypotenuse; sides; right angle;  converse; base; height; proof; cone; cylinder; sphere;  radius; diameter; circumference; area; volume; pi; base; height

Identify and estimate angle measures

Measure non-right angles using a protractor

Solve one-step word problems involving angles

Describe the effect on area when dimensions of a rectangle are changed

Determine the area of a polygon when the formula is given

Determine the area of a polygon when the formula is not given

Solve problems involving area and perimeter of rectangles within a real-world or mathematical context

Writes the equation of a circle given the center and radius

Solves elapsed time word problems

Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context

Solves problems involving volumes of rectangular prisms within a real-world or mathematical context

Applies scale factors to solve problems involving scale drawings of geometric figures.

Applies scale factors to solve problems involving scare drawings, maps, and models

Applies the concept of density to solve problems involving area and volume

Determines scale factors in problems involving scale drawings of geometric figures

Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association

Construct scatter plots for bivariate measurement data

Interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities

Read and interpret data from a histogram

Determine whether two quantitative variables have a positive linear, negative linear, or zero association

Diistinguish between linear and nonlinear relationships in scatter plots

Identify the median, quartiles, extreme values, and outliers from a box plot

Solve multi-step word problems using data from line or dot plots with fractional scales

Analyze data from samples to make inferences about populations

Identify a sampling method that produces the most representational sample

Describe the likelihood of compound events occurring

Determine marginal probabilities using a two- way frequency table

Make predictions based on theoretical probabilities of simple events

Make predictions based on experimental probabilities of simple events

Understand the concept of independence in situations

Use the Fundamental Counting Principle to determine the number of possible outcomes