MATHEMATICS 7 ACCELERATED CURRICULUM GUIDE: Mathematics 7 Accelerated SPRING 2017
BELLMORE-MERRICK CENTRAL HIGH SCHOOL DISTRICT BOARD OF EDUCATION 2016-2017 Janet Goller, President Nancy Kaplan, Ed.D., Vice President Marion Blane JoAnn DeLauter Wendy Gargiulo Lisa Katz Nina Lanci Gina Piskin CENTRAL ADMINISTRATION John DeTommaso Superintendent of Schools Mara Bollettieri, Psy.D. Deputy Superintendent Kate Freeman David Seinfeld Assistant Superintendents
MATHEMATICS 7 ACCELERATED CURRICULUM GUIDE: Mathematics 7 Accelerated Authored by: Anna Aprilakis (Merrick Avenue Middle School) Katie Zaikowski (Grand Avenue Middle School) Project Administrator: David T. Gunder District Chairperson - Mathematics 3
TABLE OF CONTENTS UNIT PAGE NUMBERS Introduction 5 Unit 1 - Integers 6 Unit 2 - Rational Numbers 7 Unit 3 - Expressions and Equations 8 Unit 4 - Inequalities 10 Unit 5 - Ratios and Proportions 11 Unit 6 - Percents 13 Unit 7 Similarity and Scale 15 Drawings Unit 8 Circles and Area 16 Unit 9 Surface Area/Volume 18 Unit 10 Probability 20 Unit 11 Statistics 21 Unit 12 Angles and Triangles 22 Unit 13 Square Roots and 23 Pythagorean Theorem 4
INTRODUCTION This curriculum guide was created in response to the restructuring of the Mathematics 7 Accelerated Course. In order to create more opportunities for students in the subject of mathematics, this course provides an alternate day block schedule which allows for additional instruction in mathematics. This curriculum guide contains a yearly overview of the course, divided by unit of study. The course has been aligned to the Big Ideas textbook series and has sequenced out each unit, allowing for additional days of instruction/remediation at the discretion of the teacher. Key vocabulary terms are indicated for each unit in which to emphasize during instruction. With the introduction of the blocked scheduling, units are divided into sessions rather than lessons as each day will vary with a single or double period for students. 5
Unit 1 Integers Big Ideas Chapter 1 Sessions 1-2 Sessions 3-4 Sessions 5-6 Session 7 Session 8 Sessions 9-10 Session 11 Session 12 Intro to Integers: Vocab, Positive vs Negative, Integer Concepts, Absolute Value, Comparing Integers (with and without a number line) Vocab: rational, integer, absolute value, additive inverse Adding Integers Vocab: additive inverse, commutative property Subtracting Integers Unit 1 Quiz Multiplying Integers Including Exponents: ex -2 3 verse (-2) 3 Dividing Integers Order of Operations Session 13 Evaluating Expression (optional: see BI chapter 1, page 31, ex 3) Session 14 Session 15 Unit 13 Sessions 1 Quiz 5 extras 20 total 6
Unit 2 Rational Numbers Big Ideas Chapter 2 Sessions 1-2 Sessions 3-4 Session 5 Session 6 Sessions 7-8 Sessions 9-10 Session 11 Session 12 Intro to Rationals: Ordering Rationals (with and without a number line), Converting Fractions to Decimals, Converting Decimals to Fractions Vocab: rational number, terminating decimal, repeating decimal Adding Rationals Including evaluating expressions with rationals (BI chapter 2, page 53, ex 3) Unit 2 Quiz Subtracting Rationals Including distance between (BI chapter 2, page 61, ex 3) Multiplying and Dividing Rationals Vocab: Multiplicative Inverse Unit 2 Test 10 Sessions 1 Quiz 3 Extras 15 total 7
Unit 3 Expressions and Equations Big Ideas Chapter 3 Session 1 Evaluating Algebraic Expressions (optional in Unit 1) Session 2 Sessions 3-5 Sessions 6-7 Session 8 Session 9 Session 10 Session 11 Sessions 12-13 Sessions 14-15 Session 16 Session 17 Session 18 Session 19 Session 20 Translating Algebraic Expressions Identifying Like Terms and Simplifying Algebraic Expressions Vocab simplest form, like terms, distributive property Adding and Subtracting Linear Expressions Vocab linear expression Factoring Algebraic Expressions Vocab greatest common factor, factoring Multiplying Expressions and Distributing Vocab distributive property Unit 3 Quiz One-Step Equations Two-Step Equations Multi-Step Equations Combining Like Terms Multi-Step Equations Distributive Multi-Step Equations Variables on Both Sides Unit 3 Test 8
18 Sessions 1 Quiz 3 Extras ---------------------------------------------- 23 total 9
Unit 4 Inequalities Big Ideas Chapter 4 Session 1-2 Sessions 3-5 Session 6 Session 7-8 Session 9 Session 10 Session 11 Intro to Inequalities: Writing an Inequality, Graphing an Inequality, Checking Solutions Vocab- inequality, solution set, graph of an inequality Solving One-Step Inequalities Unit 4 Quiz Solving Two-Step Inequalities Solving Multi-Step Inequalities Unit 4 Test 9 Sessions 1 Quiz 3 Extras ---------------------------------------------- 14 total 10
Unit 5 Ratios and Proportions Big Ideas Chapter 5 Session 1 Sessions 2-3 Sessions 4-5 Sessions 6-7 Session 8 Session 9 Sessions 10-11 Sessions 12-13 Sessions 14-15 Session 16 Session 17 Simplifying Fractions and Finding Equivalent Fractions Ratios, Rates and Unit Rates: Finding ratios and rates; finding a rate from a ratio table; finding a rate from a graph; solving ratio problems Vocab ratio, rate, unit rate and complex fraction Proportions: Determining if ratios forms a proportion; determine if two quantities form a proportion; identify a proportional relationship Vocab proportion, proportional relationship, cross products Graphing Proportional Relationships: Determine if two quantities are proportional; interpreting the graph of a proportional relationship Unit 5 Quiz Writing and Solving Proportions Slope: Finding slope of a line; interpreting slope Vocab - slope Direct Variation: Identifying direct variation; writing an equation to represent a line Vocab direct variation, constant of proportionality Unit 5 Test 11
15 Sessions 1 Quiz 3 Extras ---------------------------------------- 20 total 12
Unit 6 Percent Big Ideas Chapter 6 Sessions 1-2 Sessions 3-4 Sessions 5-6 Session 7-8 Session 9 Session 10 Session 11-12 Sessions 13-14 Session 15 Session 16-17 Session 18 Session 19 Percent Conversions: Percent to fraction; fraction to percent; percent to decimal; decimal to percent; fraction to percent and decimal Comparing and Ordering Fractions, Decimals and Percents Percent Proportion: Solving for percent, part and whole Percent Equation: Solving for percent, part and whole Unit 6 Quiz Percent Increase and Decrease: Vocab percent change, percent increase, percent decrease, percent error Discount and Markup Vocab discount, markup Commission and Gratuity Vocab commission, gratuity Simple Interest Vocab simple interest, principal Unit 6 Test 13
17 Sessions 1 Quiz 3 Extras --------------------------------------- 22 total 14
Unit 7 Similarity, Scale Drawings Big Ideas Chapter 7 Session 1 Session 2 Sessions 3-4 Sessions 5-6 Identifying Similar Figures Similar Figures, Corresponding Angles, Corresponding Sides, Proportion Perimeters and Areas of Similar Figures Finding Unknown Measures in Similar Figures (Include word problems such as shadow problems) Indirect Measurement Scale Drawings Scale Drawing, Scale Model, Scale, Scale Factor Study Tip: Scales are written so that the drawing distance comes first in the ratio Session 7 Session 8 Unit 7 Test 7 Sessions 3 Extras ---------------------- 11 total 15
Unit 8 Circles and Area Big Ideas Chapter 8 Sessions 1-3 Parts Of The Circle, Arc, Center, Chord, Circumference, Diameter, Radius, π Circumference of a Circle - include solving to a given place value and/or leaving answers in terms of π - include solving for the radius or diameter when given the circumference Sessions 4-5 Sessions 6-8 Area of A Circle - include solving to a given place value and/or leaving answers in terms of π - include solving for the radius or diameter when given the area Applications of Circles - include word problems, tire rotation questions (circumference) - include questions when given circumference you have to find area or when given area you have to find the circumference - include problems such as when the radius is multiplied by a given factor what happens to the circumference, area of the circle Session 9 Unit 8 Quiz 1 Sessions 10-12 Sessions 13-16 Session 16 Session 17 Vertical Angles, Supplementary Angles, Complementary Angles with Algebra Parallel Lines Cut By A Transversal Transversal, Interior Angles, Exterior Angles, Alternate Interior Angles, Alternate Exterior Angles, Corresponding Angles, Same Side Interior Angles Unit 8 Test review Unit 8 Test 16
15 Sessions 1 Quiz 2 Extras 19 total 17
Unit 9 Surface Area/Volume Big Ideas Chapter 9 Session 1 Sessions 2-3 Session 4 Session 5 Session 6 Session 7 Sessions 8-9 Session 10 Session 11 Session 12 Session 13 Session 14 Session 15 of Perimeter and Area Apothem 3-Dimensional Figures (Drawing 3-D figures, Vocabulary, Cross Sections) Edge, Vertex, Face, Base, Net, Cross Section, Solid, Polyhedron, Lateral Face Surface Area of Prisms (OPTIONAL) Surface Areas of Cylinders (you may want to start with a brief review of the circle) (OPTIONAL) Surface Areas of Pyramids Regular Pyramid, Slant Height (OPTIONAL) Surface Areas of Cones Slant Height Mixed, Real Life Applications, Surface Areas of Composite Solids Composite Solid Unit 9 Quiz Volumes of Prisms B = Area of the base Volumes of Cylinders (OPTIONAL) Volumes of Pyramids Volumes of Cones Volumes of Spheres 18
Sessions 16-17 Session 18 Session 19 Mixed, Real Life Applications, Volumes of Composite Solids Unit 9 Test 13 Sessions 4 Optional Sessions 1 Quiz 2 Extras ---------------------- 21 total (with optional topics) or 17 total 19
Unit 10 - Probability Big Ideas Chapter 10 Session 1 Session 2 Session 3 Session 4 Session 5 Session 6 Session 7-8 Session 9 Session 10 Session 11 Session 12 Introduction To Probability Experiment, Outcomes, Favorable Outcomes, Event, Impossible Unlikely - As Likely As Not Likely - Certain), Theoretical Probability, Experimental Probability, Fair Experiment, Independent Events, Dependent Events Theoretical Probability Experimental Probability Making Predictions Applications and Activities Unit 10 Quiz Compound Probability Independent Events, Dependent Events, Counting Principle Tree Diagrams, Sample Space Simulation (table of random digits) Unit 10 Test 10 Sessions 1 Quiz 3 Extras ---------------------- 15 Total 20
Unit 11 Statistics Big Ideas Chapter 10 Session 1 Session 2 Session 3 Session 4 Sessions 6-7 Session 8 Session 9 Session 10 Session 11 Samples Data, Survey, Population, Sample, Representative Sample, Random Sample, Biased Sample Measures of Central Tendency Mean, Median, Mode, Outlier Choosing The Best Measure Dot Plot and Range Measures of Variation, Box-and-Whisker Plot (Box Plot) Range, Interquartile Range (IQR), 5 Number Summary Minimum, First Quartile, Median, Third Quartile, Maximum Mean Absolute Deviation (MAD) Variability Compare Data Sets, Making Predictions Unit 1 10 Sessions 3 Extras ---------------------- 14 Total 21
Unit 12 Angles and Triangles Big Ideas Chapter 12 Sessions 1-2 Sessions 3-4 Sessions 5-6 Session 7 Session 8 Finding Measures of Angles When Parallel Lines Are Cut By A Transversal (including algebra) Angles and Sides of A Triangle, Sum of Interior Angles of a Triangle (Find missing angle measurements in a triangle including algebra) Equiangular, Equilateral Triangle, Isosceles Triangle, Scalene Triangle, Acute Triangle, Obtuse Triangle, Right Triangle Exterior Angle of A Triangle Theorem (Find missing angle measurements with exterior angles of a triangle including algebra) Unit 12 Test 7 Sessions 3 Extras ---------------------- 11 Total 22
Unit 13 Square Roots and The Pythagorean Theorem Big Ideas Chapter 14 Sessions 1-2 Sessions 3-4 Sessions 5-6 Session 7 Sessions 8-9 Sessions 10-11 Session 12 Session 13 Session 14 Finding Square Roots Finding Cube roots Approximating Square roots Unit 13 Quiz Pythagorean Theorem, Converse of Pythagorean Theorem, Pythagorean Triples Hypotenuse, Legs Word Problems with Pythagorean Theorem 3D Pythagorean Theorem Unit 13 Test 12 Sessions 1 Quiz 3 Extras ---------------------- 17 Total 23