|
Mathematics
An overview of the mathematics courses offered
Page Content 7th Grade Connected Math
CMP Textbooks |
Areas of focus |
|
|
Variables and Patterns |
An Introduction to Algebra: variables, tables, graphs and symbols as representations |
Bits and Pieces III |
Number Sense: make sense of, and find shortcuts for, computing with decimal numbers and develop strategies for working with percents in everyday situations |
Stretching and Shrinking |
Similarity: scale factor, ratio, and similar figures with congruence as a special case |
Comparing and Scaling |
Proportional Reasoning: rate, ratio, proportion, and percent |
What Do You Expect |
Probability: theoretical probability, experimental probability, and expected value |
Accentuate the Negative |
Integers: operations with positive and negative numbers |
Moving Straight Ahead |
Linear Relationships: expressed in words, tables, graphs and equations |
Data Distributions |
Statistics and Data analysis: describe the variability within a set of data and compare data sets |
8th Grade Connected Math
CMP Textbooks |
Areas of focus |
|
|
Thinking with Mathematical Models |
Functions: recognize and analyze linear relationships, compare linear patterns with nonlinear patterns (*inverse), and write equations that summarize, or model data patterns |
Looking for Pythagoras |
Pythagorean Theorem: explore side lengths and areas of right triangles and squares, discover the Pythagorean theorem, and use irrational numbers as representations of length |
Growing, Growing, Growing |
Exponential Growth & Decay: Graphing and writing exponential functions |
Frogs, Fleas, and Painted Cubes |
Quadratic Growth: Graphing, writing, and solving quadratic functions |
Samples and Populations |
Statistics: Gathering data from samples to make predictions about populations |
Say it With Symbols |
Symbolic expressions: Simplifying expressions and solving more complicated linear equations |
Shapes of Algebra |
Transformational geometry: Symmetries and their relationship to algebraic properties |
Algebra - Discovering Algebra
Chapter |
Areas of focus |
|
|
Data Exploration |
Measures of center, five-number summary, pictograph, bar graph, histogram, dot plot, stem-and-leaf plot, and box-plot |
Proportional Reasoning |
Ratios, proportions, percents, conversion factors, and dimensional analysis |
Variations and Graphs |
Rates, similar figures, direct and inverse relationships |
Linear Equations |
Recursive sequences, evaluating expressions, solving equations using the balancing method & by undoing operations, rate of change, linear plots |
Fitting a line to data |
Slope formula, linear equations & the intercept form, writing a linear equation to fit data, equivalent algebraic equations |
Systems of Equations & Inequalities |
Solving Systems of Equations (graphically, substitution method, elimination method), Inequalities in 1-variable & 2-variables, Solving Systems of Inequalities(graphically) |
Exponents and Exponential Models |
Recursive routines, exponential equations (growth & decay), positive, zero & negative exponents, scientific notation |
Functions |
Identifying functions (given table, graph or equation), function notation, absolute value function, basic quadratic function (b=0, c=0), square root |
Quadratic Models |
Solving quadratic equations, finding the roots & vertex, factored form, general form, quadratic formula |
Geometry - Discovering Geometry
Chapter |
Areas of focus |
|
|
Introducing Geometry |
Overview of content |
Reasoning in Geometry |
Inductive reasoning, deductive reasoning, finding the nth term, linear pair of angles, vertical angles, special angles on parallel lines |
Using Tools in Geometry |
Duplicating: segments & angles; Constructing: perpendicular bisectors, perpendiculars to a line, angle bisectors, parallel lines, circumcenter, incenter, orthocenter, & centroid; One point perspective drawings |
Discovering & Proving Triangle Properties |
Triangle sum conjecture, properties of isosceles triangles, congruency shortcuts, corresponding parts of congruent triangles, proving special triangle conjectures |
Discovering & Proving Polygon Properties |
Polygon sum conjecture, exterior angles of a polygon, properties of kites & trapezoids, properties of triangle mid-segments & trapezoid mid-segments, properties of special parallelograms, proving quadrilateral properties |
Discovering & Proving Circle Properties |
Tangent properties, chord properties, arcs and angles, pi, arc length, proving circle conjectures |
Area |
Solving problems using the area formulas for: rectangles, parallelograms, triangles, trapezoids, kites, regular polygons, & circles
Finding the surface area of regular circles & cones |
Pythagorean Theorem |
Pythagorean Theorem, Converse of Pythagorean Theorem properties of isosceles right and 30°-60°-90° triangles, the distance formula |
Volume |
Euler’s formula for polyhedrons, volume formula for prisms, cylinders, pyramids, and cones, density and displacement, volume and surface area of spheres |
Probability |
Geometric probability, counting outcomes, tree diagrams, mutually exclusive events, Venn diagrams, expected value, permutations, and combinations |
Similarity |
Similar Polygons, similar triangles (similarity shortcuts, indirect measurement, & corresponding parts), solving proportions with area, surface area, & volume, proportional segments between parallel lines |
Advanced Algebra - Discovering Advanced Algebra
Chapter |
Areas of focus |
Patterns & Recursion |
Uses recursive formulas to model growth and explores them in tables, formulas, and graphs |
Describing Data |
Reviews and goes deeper into topics introduced in Algebra I. Presents methods of analyzing and describing one-variable data sets. Topics include measures of central tendency, standard deviation, and percentiles. |
Linear Models & Systems |
Explores lines first as mathematical objects that can model two-variable data, and then as graphical representations of linear equations. The recursive formulas for arithmetic growth from Chapter 1 are developed into explicit linear formulas. Students find lines of fit for data, learn the median-median line of fit, and evaluate quality of fit using residuals. Students solve systems graphically and using substitution and elimination. |
Functions, Relations, & Transformations |
Distinguishes between functions and relations, explores translations, and investigates different families of functions, including quadratic, absolute value, and circles and ellipses. |
Exponential, Power, & Logarithmic Functions |
Introduces exponential functions to model growth and decay, and explores real-world applications. Students learn about inverses and the logarithmic function, and study properties of exponents and logarithms. |
Matrices & Linear Systems |
Explores the value of matrices to organize data and solve systems and covers operations on matrices and inverse matrices. Real-world applications of linear systems and inequalities and linear programming including optimum combinations are explored. |
Quadratic & Other Polynomial Functions |
Explores applications of quadratic models, various forms of quadratic functions, and solving quadratic functions. Methods of solving polynomial functions are covered, and complex numbers arise as non-real solutions to polynomial functions. |
Introduction Trigonometry |
Covers parametric equations to model motion and introduces trigonometric ratios and their properties, vectors, and real world navigation |
Rational Functions |
Extends earlier coverage of circles and ellipses. Students also explore the rational functions and apply to real world motion, rate of work and other situations. |
Algebra – Cognitive Tutor Algebra I
Chapter |
Areas of focus |
|
|
Patterns & Multiple Representations |
Finding the 10th term of a sequence, finding the nth term of a sequence, representing a problem situation using a table, graph & equation |
Proportional Reasoning, Percents & Direct Variation |
Sampling, ratios (part-to-whole relationships & part-to-part relationships), rates, proportions, mixture problems, indirect measurement, direct variation & percents |
Solving Linear Equations |
Solving 1-step equations, solving 2-step equations, using the percent equation, algebraic check of a solution & graphical check of a solution |
Linear Functions & Inequalities |
The distributive property |
Writing & Graphing Linear Equations |
Finding intercepts of graphs, finding the slope of a line, writing equations of lines in intercept form & solving literal equations |
Lines of Best Fit |
Using lines of best fit |
Systems of Equations |
Solving Linear Systems: graphically, using substitution & using linear combinations |
Systems of Inequalities |
Writing and Graphing an inequality in 2 variables |
Quadratic Functions |
Square roots & radicals |
Properties of Exponents |
Scientific notation |
Polynomial Functions & Rational Expressions |
Multiplying binomials & factoring polynomials |
Statistical Analysis |
Collecting & analyzing date, box plots |
Students spend 3 days a week in the classroom & 2 days a week in the computer lab using the Cognitive Tutor Software
|
|
|
|
|
SuperKidsPractice worksheet generator with answers
|
|
|
|