7A Classes

UNIT 1: RATIONAL NUMBERS/INTEGERS 

  • Define integers as a set of numbers (review counting & whole numbers), compare & order integers, and find the absolute value of a number
  • Adding Integers & the additive inverse property
  • Subtract integers
  • Applications of Adding & Subtracting
  • Multiply & Divide integers /Applications
  • Order of operations with integers
  • Evaluation with Integers 

UNIT 2: RATIONAL NUMBERS/FRACTIONS 

  • Intro to fractions, terminology (numerator, denominator, ratio), Convert between fractions and mixed numerals expressing negative quantities with fractions, equivalent fractions including reducing fractions to lowest terms. Introduce set of Rational Numbers.
  • Adding & subtracting fractions and mixed numerals (positives & negatives)  video
  • Multiply fractions & mixed numerals (including negatives)
  • Division of fractions & mixed numerals (including negatives)
  • Evaluate expressions with fractions & mixed numerals (Introduce calculators) 

Unit 3: RATIONAL NUMBERS/DECIMALS 

  • Convert fractions to decimals – all fractions are division problems, different types of decimals (terminating & repeating). Terminating & repeating decimals are Rational Numbers.  Undefined fractions.
  • Place value, rounding & terminating decimals to fractions
  • Repeating decimals & partially repeating decimals to fractions
  • Adding & Subtracting Decimals (including negatives)
  • Multiplying & Dividing Decimals (including negatives)
  • Word Problems involving decimal operations
  • Review/ Mixed Practice with Operations/Evaluate Expressions
  • Scientific Notation vs Standard Notation
  • Scientific Notation Operations 

Unit 3a: THE REAL NUMBER SYSTEM 

  • Sets of Numbers
  • Perfect Squares & Perfect Cubes
  • Non-perfect squares (approximating square roots, placement on the number line) 

UNIT 4: EXPRESSIONS    

  • Define an expression and its parts (coefficients, constants, terms and like terms)
  • Define and identify like terms, simplify expressions by combining like terms (use expressions with multiple variables ex: 2rs + 7rs)
  • Simplify expressions by combining like terms using the distributive property (including rationals & binomials)
  • Factoring out the GCF – Distributive Property Backwards
  • Laws of Exponents – Multiplying with coefficients & power to a power
  • Laws of Exponents – Dividing with coefficients
  • Writing expressions with positive exponents only 

UNIT 5: EQUATIONS 

  • Solve and check one step equations with addition and subtraction (with rationals)
  • Solve and check one step equations with multiplication and division (with rationals)
  • Translating expressions & solving one step equations
  • Solve and check two step equations (with rationals)
  • Using the algebraic process to solve word problems/two step equations
  • Solve and check multi-step equations by using the distributive property
  • Solve and check multi-step equations by combining like terms
  • Solve and check equations with variables on both sides
  • Solving Equations—Identities and Contradictions
  • Solving One & Two Step Literal Equations
  • Solving Multi-step Literal Equations 

UNIT 6: INEQUALITIES 

  • Intro to inequalities and graphing on a number line.  Working with inequalities (conceptual understanding of flipping the symbol)
  • Solve and graph one step inequalities (with rationals)
  • Solve and graph two step inequalities
  • Solve and graph multi-step inequalities
  • Using the algebraic process to solve word problems/one & two step inequalities. Interpreting the answer to an inequality. 

UNIT 7: RATIO & PROPORTION 

  • Review the definitions of ratio and rate and their 3 mathematical representations, find unit rate and unit price
  • Find unit rate with complex fractions
  • Use unit price to find the better buy
  • Intro to independent vs dependent variables
  • Examples of proportional versus non-proportional reasoning (given a chart/table is it proportional or not, find the constant of proportionality & writing equations)
  • Proportional versus non-proportional reasoning (with graphs – interpreting, drawing & writing equations)
  • Solve proportions algebraically
  • Word problems with proportions
  • Word problems (part to whole and part, part, whole) 

UNIT 7a: PROPORTIONAL GEOMETRY 

  • What are similar figures, name corresponding parts, find missing measures
  • Application of similar figures, indirect measures
  • Solve problems involving scale drawings (using a ruler to measure)
  • Reproduce scale drawings using a different scale 

UNIT 8: PERCENTS 

  • Define percent, write percents as fractions and decimals including percents less than one and greater than 100
  • Introduction to percent proportion, solve for missing parts
  • Real world applications
  • Sales tax, discount, commission, gratuity & mark up
  • Percent of change and percent error
  • Simple Interest 

UNIT 9: STATISTICS 

  • Random samples, fair or biased surveys
  • Intro to statistics, and measures of central tendency
  • Box & Whisker Plots (creating and interpreting)
  • Dot/Line Plots (creating and interpreting)
  • Histograms
  • Mean Absolute Deviation (M.A.D) 

UNIT 10: PROBABILITY 

  • Intro to probability, probability of a single event (theoretical), certain, impossible, likely, unlikely events
  • Probability of two or more events (independent & dependent)
  • Tree Diagrams, Sample Space and Basic Counting Principle
  • Theoretical versus experimental probability  
  • Use a sample set to make predictions about a population 

Unit 11: EXPLORING 2-D GEOMETRIC FIGURES 

  • Parts of a circle and estimate the value of Pi
  • Circumference (exact and approximate)
  • Area of a circle (exact and approximate)
  • Find the radius or diameter given the area or circumference
  • Review of 2-D shapes and find their areas
  • Area of irregular shapes/composite figures
  • Informal constructing of geometric shapes with given conditions 

UNIT 12: EXPLORING 3-D GEOMETRIC FIGURES 

  • Surface Area (prisms and pyramids)
  • Surface Area (cylinders, cones & spheres)
  • Volume (prisms and pyramids only)
  • Volume (cylinders, cones & spheres)
  • Real world applications with surface area and volume
  • Review 3-D shapes and find cross sections (right rectangular prisms, right rectangular pyramids) 

UNIT 13: ANGLE RELATIONSHIPS 

  • Complementary, supplementary & vertical angles, including algebraic examples
  • Parallel Lines cut by a transversal (corresponding, alternate interior, alternate exterior, vertical & supplementary, including algebraic examples 

UNIT 13a: ANGLE RELATIONSHIPS in 2-D GEOMETRIC FIGURES 

  • Classify triangles according to their sides and angles, triangle inequality (informal constructions), identify largest side/shortest side, largest angle/smallest angle
  • Solve for the missing angle algebraically in a triangle
  • Classify quadrilaterals and solve for the missing angle algebraically 

UNIT 14:  LINEAR EQUATIONS 

  • Review of Coordinate Plane
  • Graphing a Linear Equation using T-Charts
  • Intro to Slope (reading slope of a line as positive, negative, zero, undefined, define slope as a constant rate of change)
  • Finding the slope given two points
  • Slope-intercept Form of a Line
  • Rewriting an equation in slope intercept form
  • Systems of Equations
  • x & y intercepts 

UNIT 15:  TRANSFORMATIONAL GEOMETRY 

  • Reflections in the Coordinate Plane (x-axis, y-axis, y=x and line reflections)
  • Translations in the Coordinate Plane
  • Dilations in the Coordinate Plane, define Isometry
  • Rotations-90° and 180°-Rotational Symmetry
  • Composition of Transformation to Produce similar and congruent figures

 

 

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