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    Course Description

    Unit 1: Equivalent Forms of Fractions, Decimals, and Percents

    This unit introduces students to percentages.  They will practice converting between fractions, decimals, and percents and work to memorize the benchmark percents/fractions/decimals that are frequently used.  Those being 1/2, the thirds, fourths, fifths, eighths, and tenths.  Students will also solve real-world problems involving part, whole, and percent relationships.  The three types of percent problems are finding the whole given a part and the percent, finding the part given the whole and the percent, and finding the percent given the part and the whole, including the use of concrete and pictorial models. 

     

    Unit 2:  Comparing and Ordering Rational Numbers

    During this Unit students will…

    • Generate equivalent forms of fractions, decimals, & percent using real-world problems
    • Order a set of rational numbers (whole numbers, decimals, fractions, integers, percent) arising from mathematical & real-world contexts
    • Classify whole numbers, integers, & rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers
    • Locate, compare, & order integers & rational numbers using a number line
    • Understand the closer a negative number is to zero on the number line, the larger the number (i.e  -.5 is greater than -1)
    • Use inequality symbols (comparison symbols) to expression written comparison of integers & rational numbers

    In addiiton to the above, Pre-AP students will . . . 

    • Extend previous knowledge of sets & subsets using a visual representation to describe relationships between sets of rational numbers

    .Review Resources

    Learnzillion - Comparing & Ordering Integers

    Song - Classifying Rational Numbers

     

     

    Unit 3:  Operations with Positive Rational Numbers

    During this Unit students will…

    • Recall that decimals are another way to write a fractional part of a whole
    • Recognize multiplying a rational number by its reciprocal gives a value of one whole - 23 & its reciprocal 32
    • Recognize that a number multiplied by a fraction (less than one whole) will decrease in value
    • Recognize that a number multiplied by a rational number greater than one (improper fractions & mixed numbers) will increase in value
    • Explain ways to pay for college: savings, grant, scholarships, student loans and work study
    • Compare annual salaries of different jobs requiring different levels of education
    • Calculate the effects of the different annual salaries on lifetime income

    In addition to the above, Pre-AP students will . . . 

    • Add, subtract, multiply, & divide rational numbers fluently
    • Apply & extend previous understandings of operations to solve problems using addition, subtraction, multiplication, & division of rational numbers
    • Calculate the sales tax for a given purchase & calculate income tax for earned wages

    Review Resources

     

    Song - Dividing Decimals 'Swoop'

    Song - Dividing Decimals - 'Long Division Style'

    Video - Forms of Fractions

    Song - Multiplying Fractions

    Song - Dividing Fractions (Flocabulary)

    Song - Dividing Fractions (NumberRock)

     

    Unit 4:  Operations with Integers

    What an exciting unit!!!  The students will be learning how to add, subtract, multiply, and divide integers.  Integers, of course, being positive and negative whole numbers.  We begin the unit by reviewing the definition of integer and differentiating between opposites and absolute value.  We will look extensively at number lines and 2-sided counters to model operations and connect the models with the standard algorithms.  Once the process for integer operations is learned, we practice, practice, practice!

    Review Resources

     

    Song - Integer Introduction

    Song - Adding Integers

    Video - Subtracting Integers (Khan Academy)

    Video - Subtracting Integers (Math Club)

    Video - Multiplying Integers (Khan Academy)

    Song - Multiplying and Dividing Integers

    Song - Multiplying and Dividing Integers (I Love Rock 'N Roll)

     

     

    Unit 5:  Proportional Reasoning with Ratios & Rates

     In this unit students will . . . 

    • Understand proportional reasoning with the building blocks of ratios, rates, & proportions.
    • examine & distinguish between ratios & rates, giving examples of ratios as multiplicative comparisons of two quantities & examples of rates as the comparison by division of two quantities having different attributes.
    • extend previous work with representing percents using concrete models & fractions.
    • generate equivalent forms of fractions, decimals, & percents using ratios, including problems that involve money.
    • solve & represent problem situations involving ratios & rates with scale factors, tables, graphs, & proportions & represent real-world problems including unit rates & converting within a measurement system.
    • make predictions & comparisons in problem situations involving ratios & rates.
    • revisit solving real-world problems to find the whole given a part & the percent, to find the part given the whole & the percent, & to find the percent given the part & the whole

    Pre-AP will extend the 6th grade concepts to include . . . 

    • Calculating unit rates from real-world problems & solve problems including ratios, rates, & percent in multi-step problems
    • Calculate percent of increse & decrease
    • Convert between measurement systems
    • Apply knowledge to financial literacy problem

    Review Resources

    Ratio Intro. Video - Bad Date

    Unit Rate Video - Ratey the Math Cat

    Scale Factor Video - Scale Ella

     

    Unit 6:  Equivalent Expressions & One-Variable Equations

     In this unit students will . . . 

    • Include exponents, fractions & decimals in Order of Operations problems
    • Prime Factorization
    • Generate equivalent expressions by identifying properties of operations: inverse, identity, commutative, associative, & distributive properties, including combining of like terms
    • Define & identify expressions & equations verbally, numerically, & algebraically
    • First time representing one-variable, one-step equations on number lines & using concrete models

    Review Resources

     

    Video - Exponents

    Video - Exponents #2

    Video - Order of Operations

    Video - Prime Factorization

    Video - Properties Song

    Video - Distributive Property

    Video - Simplifying Expressions ('pronumeral' means 'variable')

     

     

    Unit 7:  Equivalent Expressions & One-Variable Equations

     In this unit students will be introduced to algebraic inequalities.  This includes . . . 

    • Defining and identifying inequalities verbally, numerically, and algebraically
    • Identifying inequalities on a number line as well as determine missing values in one step inequalities

    • In addition, Pre-AP students will use a family budget estimator to determine the minimum household budget & average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby.

    Review Resources

     

    Video - Solving & Graphing Inequalities

    Video - Khan Academy Solving 1-step Inequalities (Addition/Subtraction)

    Video - Khan Academy Solving 1-step Inequalities (Multiplying/Dividing)

     

     

    Unit 8:  Two-Variable Relationships

     In this unit students will . . .

    • Graph ordered pair in all four quadrants
    • Compare two rules algebraically, graphically, and symbolically to determine if the relationship is additive or multiplicative
    • Recognize additive and multiplicative relationships when represented verbally,  by an equation, graph, or table
    • Identify independent or dependent relationships and quantities

     

     

    Unit 9: Geometry & Measurement  

     In this unit students will . . .

    • extend their knowledge of triangles and their properties to include . . . 
      • the sum of the angles of a triangle, and how those angle measurements are related to the three side lengths of the triangle and 
      • the Triangle Inequality Theorem:  examine and analyze the relationship between the three side lengths of a triangle and determine whether three side lengths will form a triangle
    • decompose and rearrange parts of parallelograms, rectangles, trapezoids, and triangles for modeling area formulas
    • write equations and determine solutions to problems to find the area of rectangles, parallelograms, trapezoids, and triangles.
    • extend writing equations and determining solutions to volume of right rectangular prisms  
    • expand previous knowledge of converting units within the same measurement system to determine solutions to problems involving length.

     Pre-AP students will also . . . 

    • use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas.
    • determine the circumference and area of circles and semi-circles
    • determine the area of composite figures containing combinations of shapes

     

     

    Unit 10: Data Anlysis

    In this unit students will . . .

    • Revisit dot plots and stem-and-leaf plots.
    • Create and analyze histograms, box plots, and percent bar graphs.
    • Describe the shape, center, and spread of the data distribution graphically.
    • Use skewed right, skewed left, symmetric, mean, median, mode, range, and interquartile range to describe the shape, center, and spread of a data set.
    • Summarize numeric data with numerical summaries, including the measures of center and the measures of spread.
    • Summarize categorical data numerically with the mode and the percent of values in each category and graphically with a percent bar graph.
    • Compare situations that yield data with and without variability.

    Review Resources

     

    Video - Mean, Median, Mode