# Pre-Algebra (7) Mathematics

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1 Course Overview In Grade 7, instructional time focuses on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. In addition students will be instructed in the areas of irrational numbers, solving more complex equations, interpreting graphs, congruence and similarity, and solving real world problems involving volume. 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) Materials and Resources Glencoe McGraw-Hill Pre-Algebra 2010 edition Studyisland.com connect-mcgraw-hil.com (student was given login and password) Prerequisites 6th Grade Math Rational Numbers and Equations Proportions and Similarity Linear and Nonlinear Functions Two- and Three-Dimensional Space Data Sets Looking Ahead to Algebra Unit: Rational Numbers and Equations Materials and Resources Glencoe Mc-Graw Hill Pre-Algebra book, 2010 copyright studyisland.com connected.mcgraw-hill.com Academic Vocabulary numerical expression evaluate order of operations algebra variable algebraic expression counterexample simplify y-axis coordinate plane origin x-axis ordered pair function function rule function table equation sum difference operations product quotient 1. Pre-paring for Pre-Algebra 2. The Tools of Algebra 3. Operations with Integers 4. 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. Stastic and Probability 1. Looking Ahead to Algebra Duration: 64 Day(s) Page 1

2 Topic: Pre-paring for Pre-Algebra Duration: 9 Day(s) Students will review several concepts, skills, and vocabulary terms as they study this chapter. 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 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 Topic: Duration: 9 Day(s) 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 comon multiple 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 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 Unit: Proportions and Similarity Duration: 26 Day(s) Topic: Duration: 13 Day(s) Ratio, Proportions, and Similar Figures 1) Compare and contrast proportional and nonproportional linear relationships 2) Use proportional relationships in similar two-deimnsional figures to find missing measurements Page 2

3 Topic: Percent Duration: 13 Day(s) 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 Fractions and Percents Fractions, Decimals, and Percents Using the Percent Proportion Find Percent of a Number Mentally Using Percent Equations Percent of Change Simple and Compound Interest Circle Graphs Unit: Linear and Nonlinear Functions Duration: 28 Day(s) Topic: Duration: 15 Day(s) Linear Functions and Graphing 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 Functions Rate of Change Constant Rate of Change and Direct Variation Slope Slope-Intercept Form 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 Powers and Exponents Prime Factorization Multiplying and Dividing Monomials Negative Exponents Scientific Notation Powers and Monomials Page 3

4 Unit: Two- and Three-Dimensional Space Duration: 42 Day(s) Topic: Duration: 12 Day(s) Real Numbers and Right Triangles 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 Squares and Square Roots The Real Number System Triangles The Pythagorean Theorem Special Right Triangles 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 Angle and Line Relationships Congruent Triangles Rotations Quadrilaterals Polygons Area of Parallelograms, Triangles, and Trapezoids Circles and Circumference Area if Circles 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 Three-Dimensional Figures Volume of Prisms Volume of Cylinders Volumes of Pyramids, Cones, and Spheres Surface Area of Prisms Surface Area of Cylinders Surface Area of Pyramids and Cones Similar Solids Page 4

5 Unit: Data Sets Duration: 16 Day(s) Topic: Duration: 16 Day(s) Stastic and Probability 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 Theoretical and Experimental Probability Using Sampling to Predict Counting Outcomes Probability of Compound Events Unit: Looking Ahead to Algebra Duration: 8 Day(s) Topic: Duration: 8 Day(s) Looking Ahead to Algebra These topics help students get ready for the next year by introducing key standards from algebra at a concrete level. Students will investigate opearations with polynomials. Polynomials Adding Polynomials Subtracting Polynomials Multiplying a Binomial by a Monomial Multiplying Two Binomials Dividing a Polynomial by a Monomial Using the GCF to Factor Polynomials Factoring Trinomials Page 5

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