Seventh Grade



Pittsford Central School District

HONORS Seventh Grade Mathematics Topical Outline

The topics listed below summarize the major content pieces of the grade 7 mathematics program reflecting the common core learning standards. A common final exam will be given to all seventh grade students. Instructional strategies are targeted to develop the following in our students:

Mathematical Practices

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Number Systems

Complex Fractions [pic]

Categories of Numbers (whole-W, counting/natural-N, integers-Z, rational-R, irrational-Q)

Ordering Positive & Negative Integers, Fractions, Decimals

Operations with Integers

Operations with Rationals and Negative Decimals *

Word Problems with Integers and Rational Numbers

Absolute Value

Exponents (positive, zero power)

Square Roots (perfect squares up to 15 & [pic] lie between which 2 integers)

Order of Operations (including integers, clearing parenthesis, absolute value, exponents & [pic]s )

Expressions and Equations (Rational numbers should be used when appropriate)

Number Properties (commutative, associative, distributive, identity, inverse)

Review variable substitution (use formulas)

Distributing and Combining Like Terms in Expressions and Equations

Using the Distributive property to expand and factor Expressions p(x + q) where p & q are numbers

One step Equations with Integers and Rational Numbers

Solving Two Step Equations

Checking answers

Solving Equations such as p(x + q) = r by Distributing or by Dividing by p first

Solving Equations with Variables on Both Sides

Word problems (one step, two step, rate, p(x + q) = r, multiple Let statements, consecutive integers, perimeter)

Inequalities - solve & graph on a number line

Translating verbal expressions, equations, and Inequalities (2-step)

Inequality Word problems (two-step)

Geometry (Algebra should be used when appropriate)

Basic Vocabulary& Notation

Angles - complementary, supplementary, vertical, & adjacent with Algebra

Triangles - types by sides & angles, 180(

Triangular inequality

Constructing Triangles given the measures of sides & angles

Quadrilaterals – types of quadrilaterals, 360(

Parallel Lines and Angle Relationships (alternate interior, alternate exterior, and corresponding vertical)

Area and Circumference of a Circle in Terms of π, using 3.14, or π key

Ratios & Proportional Relationships

Rates and Ratios

Unit Rates (complex fractions)

Constant of Proportionality (k) in tables, graphs, diagrams, equations, word problems y = kx

Solving Proportions and real life problems

Proportional Relationship –testing for equivalent ratios in a table or graph in a coordinate plane

Proportional Relationship in a Graph (unit rate(r) (1,r) and the meaning of (0,0))

Similar Figures - scale drawings & compute missing sides

Scale Drawing -finding lengths & areas of geometric figures, reproducing a scale drawing at a different scale

Percent - meaning, greater than 100% & less than 1%

Percent ( Fractions ( Decimals (Encourage memorization of thirds, fourths, fifths & eighths)

Mental Percent of a Number (10%, 15%, 20%, 25%, 50%)

Real life problems involving percent ([pic]) (for example: gratuities & fees)

Discount & Tax (and “given total, find original price” problem)

Markups & Markdowns

Commission

Percent of Increase & Decrease

Percent Error

Simple Interest

Statistics and Probability

Range of Probability - Probability of Certain Events P(E) = 1 and Impossible Events P(E) = 0

Theoretical Probability (making a prediction, how many times do you expect an event to occur?)

Probability of a single event with equally likely outcomes

Probability of a single event with unequal outcomes (ex. toss a cup in the air, dart board)

Probability of compound events using lists, tables, tree diagrams, and simulation

Probability with and without replacement

Counting Principle

Statistics and Probability

Sampling from population -representative sample, random sample, biased/valid sample

Use data from a random sample to draw inferences (use survey data for predictions)

Interpret mean absolute deviation with numerical data which informs spread/variability

Central Tendency-mean, median, mode, and range

Compare numerical details of 2 data sets including measures of central tendency, center, and spread

(Interpret data sets which can be lists, tables, dot plots, box & whisker plot …)

Linear Equations

Graphing lines using a table

Meaning of Slope (classify as positive, negative, zero, or undefined)

Finding slope from a graph

Finding the slope given two points

Recognizing slope as the Rate of Change in real word problems

Interpret the slope and y-intercept in a real world model

Find the slope and y-intercept given an equation

Graphing lines using Slope-intercept form

Monomials

Exponent Rules with Numerical Bases

Adding, Subtracting, Multiplying, & Dividing Monomials

Raising Monomials to a Power

Negative Exponents

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