8.1 – Monomials & Factoring. Factoring Factoring – opposite of simplifying!
MATHEMATICS 7 ACCELERATED CURRICULUM GUIDE · Vocab – linear expression Session 8 Factoring...
Transcript of MATHEMATICS 7 ACCELERATED CURRICULUM GUIDE · Vocab – linear expression Session 8 Factoring...
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 Lisa Katz
JoAnn DeLauter Nina Lanci
Wendy Gargiulo Gina Piskin
CENTRAL ADMINISTRATION
John DeTommaso
Superintendent of Schools
Mara Bollettieri, Psy.D.
Deputy Superintendent
Kate Freeman
David Seinfeld
Assistant Superintendents
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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
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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
Drawings
15
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
Pythagorean Theorem
23
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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.
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Unit 1 – Integers
Big Ideas Chapter 1
Sessions 1-2 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
Sessions 3-4 Adding Integers
Vocab: additive inverse, commutative property
Sessions 5-6 Subtracting Integers
Session 7 Review
Session 8 Unit 1 Quiz
Sessions 9-10 Multiplying Integers
Including Exponents: ex -23 verse (-2)
3
Session 11 Dividing Integers
Session 12 Order of Operations
Session 13 Evaluating Expression (optional: see BI chapter 1, page 31, ex 3)
Session 14 Review
Session 15 Unit 1 Test
13 Sessions
1 Quiz
1 Test
5 extras
20 total
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Unit 2 – Rational Numbers
Big Ideas Chapter 2
Sessions 1-2 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
Sessions 3-4 Adding Rationals
Including evaluating expressions with rationals (BI chapter 2, page 53,
ex 3)
Session 5 Review
Session 6 Unit 2 Quiz
Sessions 7-8 Subtracting Rationals
Including distance between (BI chapter 2, page 61, ex 3)
Sessions 9-10 Multiplying and Dividing Rationals
Vocab: Multiplicative Inverse
Session 11 Review
Session 12 Unit 2 Test
10 Sessions
1 Quiz
1 Test
3 Extras
15 total
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Unit 3 – Expressions and Equations
Big Ideas Chapter 3
Session 1 Evaluating Algebraic Expressions (optional in Unit 1)
Session 2 Translating Algebraic Expressions
Sessions 3-5 Identifying Like Terms and Simplifying Algebraic Expressions
Vocab – simplest form, like terms, distributive property
Sessions 6-7 Adding and Subtracting Linear Expressions
Vocab – linear expression
Session 8 Factoring Algebraic Expressions
Vocab – greatest common factor, factoring
Session 9 Multiplying Expressions and Distributing
Vocab – distributive property
Session 10 Review
Session 11 Unit 3 Quiz
Sessions 12-13 One-Step Equations
Sessions 14-15 Two-Step Equations
Session 16 Multi-Step Equations – Combining Like Terms
Session 17 Multi-Step Equations – Distributive
Session 18 Multi-Step Equations – Variables on Both Sides
Session 19 Review
Session 20 Unit 3 Test
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18 Sessions
1 Quiz
1 Test
3 Extras
----------------------------------------------
23 total
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Unit 4 –Inequalities
Big Ideas Chapter 4
Session 1-2 Intro to Inequalities:
Writing an Inequality, Graphing an Inequality, Checking Solutions
Vocab- inequality, solution set, graph of an inequality
Sessions 3-5 Solving One-Step Inequalities
Session 6 Unit 4 Quiz
Session 7-8 Solving Two-Step Inequalities
Session 9 Solving Multi-Step Inequalities
Session 10 Review
Session 11 Unit 4 Test
9 Sessions
1 Quiz
1 Test
3 Extras
----------------------------------------------
14 total
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Unit 5 – Ratios and Proportions
Big Ideas Chapter 5
Session 1 Simplifying Fractions and Finding Equivalent Fractions
Sessions 2-3 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
Sessions 4-5 Proportions:
Determining if ratios forms a proportion; determine if two quantities form
a proportion; identify a proportional relationship
Vocab – proportion, proportional relationship, cross products
Sessions 6-7 Graphing Proportional Relationships:
Determine if two quantities are proportional; interpreting the graph of a
proportional relationship
Session 8 Review
Session 9 Unit 5 Quiz
Sessions 10-11 Writing and Solving Proportions
Sessions 12-13 Slope:
Finding slope of a line; interpreting slope
Vocab - slope
Sessions 14-15 Direct Variation:
Identifying direct variation; writing an equation to represent a line
Vocab – direct variation, constant of proportionality
Session 16 Review
Session 17 Unit 5 Test
12
15 Sessions
1 Quiz
1 Test
3 Extras
----------------------------------------
20 total
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Unit 6 – Percent
Big Ideas Chapter 6
Sessions 1-2 Percent Conversions:
Percent to fraction; fraction to percent; percent to decimal; decimal to
percent; fraction to percent and decimal
Sessions 3-4 Comparing and Ordering Fractions, Decimals and Percents
Sessions 5-6 Percent Proportion:
Solving for percent, part and whole
Session 7-8 Percent Equation:
Solving for percent, part and whole
Session 9 Review
Session 10 Unit 6 Quiz
Session 11-12 Percent Increase and Decrease:
Vocab – percent change, percent increase, percent decrease, percent
error
Sessions 13-14 Discount and Markup
Vocab – discount, markup
Session 15 Commission and Gratuity
Vocab – commission, gratuity
Session 16-17 Simple Interest
Vocab – simple interest, principal
Session 18 Review
Session 19 Unit 6 Test
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17 Sessions
1 Quiz
1 Test
3 Extras
---------------------------------------
22 total
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Unit 7 – Similarity, Scale Drawings
Big Ideas Chapter 7
Session 1 Identifying Similar Figures
Similar Figures, Corresponding Angles, Corresponding Sides,
Proportion
Session 2 Perimeters and Areas of Similar Figures
Sessions 3-4 Finding Unknown Measures in Similar Figures
(Include word problems such as shadow problems)
Indirect Measurement
Sessions 5-6 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 Review
Session 8 Unit 7 Test
7 Sessions
1 Test
3 Extras
----------------------
11 total
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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 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
Sessions 6-8 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 Vertical Angles, Supplementary Angles, Complementary Angles with
Algebra
Sessions 13-16 Parallel Lines Cut By A Transversal
Transversal, Interior Angles, Exterior Angles, Alternate Interior
Angles, Alternate Exterior Angles, Corresponding Angles, Same Side
Interior Angles
Session 16 Unit 8 Test review
Session 17 Unit 8 Test
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15 Sessions
1 Quiz
1 Test
2 Extras
19 total
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Unit 9 – Surface Area/Volume
Big Ideas Chapter 9
Session 1 Review of Perimeter and Area
Apothem
Sessions 2-3 3-Dimensional Figures
(Drawing 3-D figures, Vocabulary, Cross Sections)
Edge, Vertex, Face, Base, Net, Cross Section, Solid, Polyhedron,
Lateral Face
Session 4 Surface Area of Prisms
Session 5 (OPTIONAL) Surface Areas of Cylinders
(you may want to start with a brief review of the circle)
Session 6 (OPTIONAL) Surface Areas of Pyramids
Regular Pyramid, Slant Height
Session 7 (OPTIONAL) Surface Areas of Cones
Slant Height
Sessions 8-9 Mixed Review, Real Life Applications, Surface Areas of Composite
Solids
Composite Solid
Session 10 Unit 9 Quiz
Session 11 Volumes of Prisms
B = Area of the base
Session 12 Volumes of Cylinders
Session 13 (OPTIONAL) Volumes of Pyramids
Session 14 Volumes of Cones
Session 15 Volumes of Spheres
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Sessions 16-17 Mixed Review, Real Life Applications, Volumes of Composite Solids
Session 18 Review
Session 19 Unit 9 Test
13 Sessions
4 Optional Sessions
1 Quiz
1 Test
2 Extras
----------------------
21 total (with optional topics) or 17 total
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Unit 10 - Probability
Big Ideas Chapter 10
Session 1 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
Session 2 Theoretical Probability
Session 3 Experimental Probability
Session 4 Making Predictions
Session 5 Applications and Activities
Session 6 Unit 10 Quiz
Session 7-8 Compound Probability
Independent Events, Dependent Events, Counting Principle
Session 9 Tree Diagrams, Sample Space
Session 10 Simulation (table of random digits)
Session 11 Review
Session 12 Unit 10 Test
10 Sessions
1 Quiz
1 Test
3 Extras
----------------------
15 Total
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Unit 11 – Statistics
Big Ideas Chapter 10
Session 1 Samples
Data, Survey, Population, Sample, Representative Sample, Random
Sample, Biased Sample
Session 2 Measures of Central Tendency
Mean, Median, Mode, Outlier
Session 3 Choosing The Best Measure
Session 4 Dot Plot and Range
Sessions 6-7 Measures of Variation, Box-and-Whisker Plot (Box Plot)
Range, Interquartile Range (IQR), 5 Number Summary – Minimum,
First Quartile, Median, Third Quartile, Maximum
Session 8 Mean Absolute Deviation (MAD)
Variability
Session 9 Compare Data Sets, Making Predictions
Session 10 Review
Session 11 Unit 11 Test
10 Sessions
1 Test
3 Extras
----------------------
14 Total
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Unit 12 – Angles and Triangles
Big Ideas Chapter 12
Sessions 1-2 Finding Measures of Angles When Parallel Lines Are Cut By A
Transversal (including algebra)
Sessions 3-4 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
Sessions 5-6 Exterior Angle of A Triangle Theorem
(Find missing angle measurements with exterior angles of a triangle
including algebra)
Session 7 Review
Session 8 Unit 12 Test
7 Sessions
1 Test
3 Extras
----------------------
11 Total
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Unit 13 – Square Roots and The Pythagorean Theorem
Big Ideas Chapter 14
Sessions 1-2 Finding Square Roots
Sessions 3-4 Finding Cube roots
Sessions 5-6 Approximating Square roots
Session 7 Unit 13 Quiz
Sessions 8-9 Pythagorean Theorem, Converse of Pythagorean Theorem, Pythagorean
Triples
Hypotenuse, Legs
Sessions 10-11 Word Problems with Pythagorean Theorem
Session 12 3D Pythagorean Theorem
Session 13 Review
Session 14 Unit 13 Test
12 Sessions
1 Quiz
1 Test
3 Extras
----------------------
17 Total