# Pre-Algebra (7) B Mathematics

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1 Course Overview Students will develop skills in using variables, evaluating algebraic expressions by the use of the order of operations, solving equations and inequalities, graphing linear equations, functions and linear and linear inequalities, writing linear equations, and using functions. Problem solving skills will be emphasized and developed. Scope And Sequence Timeframe Unit Instructional Topics 64 Day(s) 26 Day(s) 28 Day(s) 42 Day(s) 16 Day(s) 8 Day(s) Unit 1: Rational Numbers and Equations Unit 2: Proportions and Similarity Unit 3: Linear and Nonlinear Functions Unit 4: Two- and Three-Dimensional Space Unit 5: Data Sets Unit 6: Looking Ahead to Algebra Unit: Unit 1: Rational Numbers and Equations 1. Preparing for Pre-Algebra 2. The Tools of Algebra 3. Operations with Integers 4. Operations with Rational Numbers 5. Expressions and Equations 6. Multi-Step Equations and Inequalities 1. Ratio, Proportions, and Similar Figures 2. Percent 1. Linear Functions and Graphing 2. Powers and Nonlinear Functions 1. Real Numbers and Right Triangles 2. Distance and Angle 3. Surface Area and Volume Course Details 1. Statistics and Probability 1. Looking Ahead to Algebra Duration: 64 Day(s) Page 1

2 Students will understand how to add, subtract, multiply, and divide integers and other rational numbers. They will also learn to solve equations and inequalities. Numerical Expression Evaluate Order of Operations Variable Algebraic Expression Properties Simplify Coordinate System Coordinate Plane Origin Ordered Pair Relation Domain, Range Function Function table Function Rule Equation Scatter Plot Negative Number Positive Number Integers Coordinate Inequality Absolute Value Zero Pair Opposites Additive Inverse Mean Quadrants Translation Reflection Terminating Decimal Repeating Decimal Bar Notation Rational Numbers Multiplicative Inverse Reciprocal Like Fractions Unlike Fraction Equivalent Expressions Distributive Property Term Coefficient Constant Equation Solution Inverse Operation Two-Step Equation Formula Perimeter Area Inequality Null/ Empty Set Identify Topic: Preparing for Pre-Algebra Duration: 9 Day(s) Students will review several concepts, skills, and vocabulary terms as they study this chapter. A Plan for Problem Solving Problem-Solving Strategies Number and Operations Page 2

3 Algebra Geometry Measurement Data Analysis Topic: Duration: 14 Day(s) The Tools of Algebra 1) Use variables, expressions, and equations to model real-world problems 2) Predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations 3) Locate and name points on a coordinate graph 4) Draw conclusions and make predictions using scatter plots Variables and Expressions Spreadsheet Lab: Expressions and Spreadsheets Properties Words, Equations, Tables, and Graphs Algebra Lab: Scatter Plots Scatter Plots Graphing Technology Lab: Scatter Plots Topic: Duration: 13 Day(s) Operations with Integers 1) Compare and Order Integers 2) Select appropriate operations to solve problems involving integers 3) Locate and name points on a coordinate plane using ordered pairs of integers 4) Graph reflections and translations on a coordinate plane Algebra Lab: Adding Integers Adding Integers Algebra Lab: Subtracting Integers Subtracting Integers Multiplying Integers Dividing Integers Translations and Reflections on the Coordinate Plane Topic: Duration: 9 Day(s) Operations with Rational Numbers 1) Explore rational numbers 2) Multiply and divide fractions 3) Add and subtract like fractions and unlike fractions 4) Convert fractions to decimals 5) Factor numbers 6) Determine least common multiple Fractions and Decimals Rational Numbers Multiplying Rational Numbers Dividing Rational Numbers Page 3

4 Adding and Subtracting Like Fractions Adding and Subtracting Unlike Fractions Topic: Duration: 10 Day(s) Expressions and Equations 1) Communicate mathematical ideas using algebraic mathematical models 2) Use inverse operations to solve equations 3) Predict, find, and justify solutions to application problems using algebraic equations Distributive Property Simplifying Algebraic Expressions Solving Equations by Adding or Subtracting Solving Equations by Multiplying or Dividing Solving Two-Step Equations Writing Equations Topic: Duration: 9 Day(s) Multi-Step Equations and Inequalities 1) Predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations 2) Use formulas to solve problems 3) Translate verbal phrases into inequalities Perimeter and Area Solving Equations with Variables on Each Side Inequalities Solving Inequalities Solving Multi-Step Equations and Inequalities Unit: Unit 2: Proportions and Similarity Duration: 26 Day(s) Page 4

5 Students will learn the connection between ratios, proportions, and similar figures. They will also study percent and percent of change. Ratio Rate Unit Rate Dimensional Analysis Proportional Nonproportional Constant of Proportionality Proportion Cross Products Inverse Proportion Scale Drawing Scale Model Scale Scale Factor Similar Figures Corresponding Parts Dilation Indirect Measurement Percent Percent Proportion Percent Equation Percent of Change Percent of Increase Percent of Decrease Interest Principal Compound Interest Circle Graph Topic: Ratio, Proportions, and Similar Figures Duration: 13 Day(s) 1) Compare and contrast proportional and nonproportional linear relationships 2) Use proportional relationships in similar two-deimnsional figures to find missing measurements Ratios Unit Rates Proportional and Non-Proportional Relationships Solving Proportions Scale Drawings and Models Similar Figures Dilations Indirect Measurement Topic: Duration: 13 Day(s) Percent 1) Use ratios, proportions, and percent of change to solve problems 2) Evaluate a solution for reasonableness 3) Select and use appropriate representations for presenting and displyaing relationships among collected data Unit: Unit 3: Linear and Nonlinear Functions Duration: 28 Day(s) Page 5

6 Students will learn to identify functions and graph them using various forms of equations. They will also learn the rules of exponents. Independent Variable Dependent Variable Vertical Line Test Function Notation Sequence Term Arithmetic Sequence Common Difference Linear Equation X-intercept Y-intercept Rate of Change Linear Relationship Constant rate of change Direct Variation Constant of Variation Slope Slope-Intercept Form Point-Slope Form Line of Fit System of Equations Substitution Exponent Power Base Prime Number Composite Number Prime Factorization Factor Tree Monomial Factor Standard Form Scientific Notation Nonlinear Function Quadratic Function Parabola Cubic Function Exponential Function Topic: Linear Functions and Graphing Duration: 15 Day(s) 1) Generate a different representation of data given another representation of data 2) Predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations 3) Draw conclusions and make predictions by analyzing trends in scatter plots Topic: Duration: 13 Day(s) Powers and Nonlinear Functions 1) Examine factors and monomials 2) Evaluate expressions with powers and exponents 3) Multiply and divide monomials 4) Express numbers using positive and negative exponents 5) Use scientific notation 6) Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models Unit: Unit 4: Two- and Three-Dimensional Space Students will learn the characteristics of triangles, angles, and three-dimensional figures. Duration: 42 Day(s) Page 6

7 Perfect Square Square Root Radical Sign Irrational Numbers Real Numbers Vertex, Acute Angle Right Angle Obtuse Angle Straight Angle Congruent Acute Triangle Obtuse Triangle Right Triangle Scalene Triangle Isosceles Triangle Equilateral Triangle Legs Hypotenuse Pythagorean Theorem Solving a Right Triangle Converse Distance Formula Parallel Lines Transversal Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Perpendicular Lines Vertical Angles Adjacent Angles Complementary Angles Supplementary Angles Congruent Corresponding Parts Rotation Center of Rotation Rotational Symmetry Quadrilateral Polygon Diagonal Interior Angle Regular Polygon Tessellation Base Altitude Circle Center Radius Diameter Chord Circumference Pi Composite Figure Plane Solid Polyhedron Edge Vertex Face Prism Base Pyramid Cylinder Cone Cross Section Volume Page 7

8 Sphere Lateral Face Lateral Area Surface Area Regular Pyramid Slant Height Similar Solids Topic: Real Numbers and Right Triangles Duration: 12 Day(s) 1) Communicate mathematical ideas using algebraic mathematical models 2) Use geometric concepts and properties to solve problems in fields such as art and architecture 3) Use the Phthagorean Theorem to solve real-world problems Topic: Duration: 14 Day(s) Distance and Angle 1) Use geometric concepts and properties to solve problems in fields such as art and architecture 2) Graph rotations on a coordinate plane 3) Use properties to classify quadrilaterals and other polygons Topic: Duration: 16 Day(s) Surface Area and Volume 1) Draw three-dimensional figures from different perspectives 2) Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects 3) Estimate measurements and use formulas to solve application problems involving lateral and surface area 4) Use proportional relationships in similar three-dimensional figures to find missing measurements Unit: Unit 5: Data Sets Students will create graphs using specific data and find the probabilities of events. Duration: 16 Day(s) Measure of Central Tendency Mean Median Mode Stem-and-Leaf Plot Stems Leaves Measure of Variation Range Quartiles Outlier Box-and-Whisker Plot Histogram Outcomes Theoretical Probability Experimental Probability Sample Population Unbiased Sample Biased Sample Tree Diagram Fundamental Counting Principle Permutations Combinations Independent Events Dependent Events Mutually Exclusive Events Topic: Statistics and Probability Duration: 16 Day(s) Page 8

9 1) Select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem-and-leaf plots, circle graphs, bar graphs, box-and-whisker plots, histograms, and Venn diagrams, with and without the use of technology 2) Find the probabilites of dependent and independent events 3) Evaluate methods of sampling to determine validity of an inference made from a set of data Unit: Unit 6: Looking Ahead to Algebra Students will use this time to explore different types of polynomials and simplify expressions involving polynomials. Duration: 8 Day(s) Polynomial Binomial Monomial Trinomial Topic: Looking Ahead to Algebra Duration: 8 Day(s) These topics help students get ready for the next year by introducing key standards from algebra at a concrete level. Students will investigate operations with polynomials. Page 9

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