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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