June 4, 2012

This course was designed to align with the "Traditional Pathway" as defined and outlined in the Common Core State Standards Appendix A.

- Mathematics > Algebra
- Mathematics > General
- Mathematics > Number Sense & Operations
- Mathematics > Problem Solving

- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10

All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

All decimals

Recognize the decimal nature of United States currency and compute with money.

Demonstrate a sense of the relative magnitudes of numbers.

Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.

Primes, factors, multiples

Compare and order numbers.

Recognize the appropriate use of each arithmetic operation in problem situations.

Pencil-and-paper

Mental math

Calculator

Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.

Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

Check the reasonableness of results of computations.

Understand and use the various relationships among operations and properties of operations.

Use a variety of estimation strategies for both number and computation.

Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

Determine the reasonableness of an answer by estimating the result of operations.

Determine whether a given estimate is an overestimate or an underestimate.

Notation for line, ray, angle, line segment

Properties of parallel, perpendicular, and intersecting lines

Sum of the measures of the interior angles of a triangle is 180°

Triangles by angles and sides

Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

Polygons by number of sides.

Equilateral, equiangular, regular

All points equidistant from a given point form a circle

Identify similar figures.

Understand and apply the concepts of congruence and symmetry (line and rotational).

Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.

Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

Create geometric shapes with specified properties in the first quadrant on a coordinate grid.

Select and use appropriate units to measure angles and area.

Convert measurement units within a system (e.g., 3 feet = ___ inches).

Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).

Use measurements and estimates to describe and compare phenomena.

Use a protractor to measure angles.

Square

Rectangle

Recognize that rectangles with the same perimeter do not necessarily have the same area and vice versa.

Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).

Descriptions using tables, verbal rules, simple equations, and graphs

Describe arithmetic operations as functions, including combining operations and reversing them.

Graph points satisfying a function from T-charts, from verbal rules, and from simple equations.

Using variables to represent unknown quantities

Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations

Changes over time

Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

Whole-number coefficients only, answers also whole numbers

Variables on one side of equation

Data generated from surveys

Bar graph, line graph, circle graph, table

Range, median, and mean

Respond to questions about data and generate their own questions and hypotheses.

Event, probability of an event

Probability of certain event is 1 and of impossible event is 0

Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked

Given data obtained experimentally, what is the likely distribution of items in the bag

Model situations involving probability using simulations (with spinners, dice) and theoretical models.

Organized lists, charts, tree diagrams, tables

Explore the multiplication principle of counting in simple situations by representing all possibilities in an organized way (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).

Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.

Learn mathematics through problem solving, inquiry, and discovery.

Open-ended problems

Non-routine problems

Problems with multiple solutions

Problems that can be solved in several ways

Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.

Pose problems of various types and levels of difficulty.

Monitor their progress and reflect on the process of their problem solving activity.

Distinguish relevant from irrelevant information, and identify missing information.

Reading and writing

Discussion, listening, and questioning

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.

Analyze and evaluate the mathematical thinking and strategies of others.

Use the language of mathematics to express mathematical ideas precisely.

Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).

Recognize that mathematics is used in a variety of contexts outside of mathematics.

Apply mathematics in practical situations and in other disciplines.

Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).

Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

Recognize that mathematical facts, procedures, and claims must be justified.

Use reasoning to support their mathematical conclusions and problem solutions.

Select and use various types of reasoning and methods of proof.

Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.

Counterexamples as a means of disproving conjectures

Verifying conjectures using informal reasoning or proofs.

Evaluate examples of mathematical reasoning and determine whether they are valid.

Concrete representations (e.g., base-ten blocks or algebra tiles)

Pictorial representations (e.g., diagrams, charts, or tables)

Symbolic representations (e.g., a formula)

Graphical representations (e.g., a line graph)

Select, apply, and translate among mathematical representations to solve problems.

Use representations to model and interpret physical, social, and mathematical phenomena.

Use technology to gather, analyze, and communicate mathematical information.

Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.

Use graphing calculators and computer software to investigate properties of functions and their graphs.

Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

Use computer software to make and verify conjectures about geometric objects.

Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).