curriculum guide 6th · pdf filecurriculum guide for: advanced m/j mathematics 1- 6th grade...

Curriculum Guide For: Advanced M/J Mathematics 1- 6th Grade AdvancedSCHOOL BOARD OF BROWARD COUNTY, FLORIDA

Textbook: Prentice Hall Course 2

New Benchmarks Transitional Benchmarks (2005) Chapter Skill Set

MA.6.A.5.3 Estimate the results of computations with fractions, decimals, and percents and judge the reasonableness of the results.

MA.A.4.3.1 uses estimation strategies to predict results and to check the reasonableness of results.

MA.B.3.3.1 solves real-world and mathematical problems involving estimates of measurements including length, time, weight/mass, temperature, money, perimeter, area, and volume, in either customary or metric units.

MA.6.A.1.1 Explain and justify procedures for multiplying and dividing fractions and decimals MA.7.A.3.1 Use and justify the rules for adding, subtracting, multiplying, dividing and finding the absolute value of integers.

MA.A.3.3.1 understands and explains the effects of addition, subtraction, multiplication, and division on whole numbers, fractions, including mixed numbers, and decimals, including the inverse relationships of positive and negative numbers.

MA.6.A.1.2 Multiply and divide fractions and decimals efficiently. MA.6.A.1.3 Solve real-world problems involving multiplication and division of fractions and decimals. MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems. MA.6.A.2.2 Interpret and compare ratios and rates.

MA.A.3.3.2 selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

Chapter 1 : Decimals And Integers

• Adding and subtracting decimals • Multiply and divide decimals • Using and changing metric units • Find opposite and absolute values • Graph and order integers • Add and subtract integers and find range • Multiply and divide integers • Use the order of operations and distributive properties

1.2: Adding and Subtracting Decimals 1.3: Multiplying and Dividing Decimals 1.4: Measuring in Metric Units 4.8: Changing units of length, capacity, and weight 1.6: Comparing and Ordering Integers 1.7: Adding and Subtracting Integers 1.8: Multiplying and Dividing Integers 1.9: Order of Operations and The Distributive Property

Textbook Alignment

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New Benchmarks Transitional Benchmarks (2005) Chapter Skill SetTextbook Alignment


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MA.7.A.5.2 Solve non-routine problems by working backwards.

MA.A.3.3.3 adds, subtracts, multiplies, and divides whole numbers, decimals, and fractions, including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

MA.7.A.5.1 Express rational numbers as terminating or repeating decimals.

MA.A.1.3.1 associates verbal names, written word names, and standard numerals with integers, fractions, decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios.

MA.6.A.5.2 Compare and order fractions, decimals, and percents, including finding their approximate location on a number line.

MA.A.1.3.2 understands the relative size of integers, fractions, and decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios.


MA.A.1.3.3 understands concrete and symbolic representations of rational numbers and irrational numbers in real-world situations.

MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems. MA.7.A.5.1 Express rational numbers as terminating or repeating decimals.

MA.A.1.3.4 understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, and absolute value.



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MA.7.A.3.2 Add, subtract, multiply, and divide integers, fractions, and terminating decimals, and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts.

MA.A.2.3.1 understands and uses exponential and scientific notation.









Chapter 2 : Algebra Equations and Inequalities

• Evaluate and write algebraic

expressions

• Solve one-step equations

using number sense

• Solve equations by adding

and subtracting

• Solve equations by

multiplying and dividing

• Write and evaluate

expressions with two

operations

• Solve two-step equations

using number sense

2.1: Evaluating and

Writing Algebraic

Expressions

2.2: Using Number Sense

to solve equations

2.3: Solve Equations by

Addition and Subtraction

2.4: Solving Equations by

Multiplication and Division

2.5: Exploring Two-Step

Problems

2.6: Solving Two-Step

Equations

4.6: Solving Equations

with Fractions

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MA.6.A.3.1 Write and evaluate mathematical expressions that correspond to given situations. MA.6.A.3.2 Write, solve and graph one- and two-step linear equations and inequalities. MA.6.A.3.6 Construct and analyze tables, graphs and equations to describe linear functions and other simple relations using both common language and algebraic notation. MA.7.A.3.3 Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.

MA.D.1.3.2 creates and interprets tables, graphs, equations, and verbal descriptions to explain cause-and-effect relationships.

MA.6.A.3.1 Write and evaluate mathematical expressions that correspond to given situations. MA.6.A.3.2 Write, solve and graph one- and two-step linear equations and inequalities. MA.6.A.3.4 Solve problems given a formula. MA.7.A.3.3 Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.

MA.D.2.3.1 represents and solves real-world problems graphically, with algebraic expressions, equations, and inequalities.

• Evaluate and write algebraic

expressions

• Solve one-step equations

using number sense

• Solve equations by adding

and subtracting

• Solve equations by

multiplying and dividing

• Write and evaluate

expressions with two

operations

• Solve two-step equations

using number sense

2.1: Evaluating and

Writing Algebraic

Expressions

2.2: Using Number Sense

to solve equations

2.3: Solve Equations by

Addition and Subtraction

2.4: Solving Equations by

Multiplication and Division

2.5: Exploring Two-Step

Problems

2.6: Solving Two-Step

Equations

4.6: Solving Equations

with Fractions

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MA.6.A.3.3 Works backward with two-step function rules to undo expressions. MA.7.A.3.3 Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients. MA.7.A.3.4 Use the properties of equality to represent an equation in a different way and to show that two equations are equivalent in a given context.

MA.D.2.3.2 uses algebraic problem-solving strategies to solve real-world problems involving linear equations and inequalities.

• Solve problems by writing equations • Graph and write Inequalities

• Solving inequalities by adding and subtracting • Solving inequalities by multiplying or dividing

2.7: Write an Equation

2.8: Graphing and

Writing Inequalities

2.9: Solving

Inequalities by Adding or

Subtracting

2.10: Solving Inequalities

by Multiplying or Dividing







Chapter 3: Exponents, Factors, and Fractions

• Writing numbers with exponents • Write numbers in scientific notation and in standard form • Using divisibility tests • Finding multiples and factors • Writing equivalent fractions • Comparing and ordering fractions • Writing mixed numbers as improper fractions and vice versa • Relating fractions and decimals • Comparing and ordering rational numbers

3.1: Exponents and Order of Operations 3.2: Scientific Notation 3.3: Divisibility Tests 3.4: Prime Factorization 3.5: Simplifying Fractions 3.6: Comparing and Ordering Fractions 3.8: Mixed Numbers and Improper Fractions 3.9 Fractions and Decimals3.10 Rational Numbers

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MA.5.A.2.4 Determine the prime factorization of numbers.

MA.A.5.3.1 uses concepts about numbers, including primes, factors, and multiples, to build number sequences.





• Writing numbers with exponents • Write numbers in scientific notation and in standard form • Using divisibility tests • Finding multiples and factors • Writing equivalent fractions • Comparing and ordering fractions • Writing mixed numbers as improper fractions and vice versa • Relating fractions and decimals • Comparing and ordering rational numbers

3.1: Exponents and Order of Operations 3.2: Scientific Notation 3.3: Divisibility Tests 3.4: Prime Factorization 3.5: Simplifying Fractions 3.6: Comparing and Ordering Fractions 3.8: Mixed Numbers and Improper Fractions 3.9 Fractions and Decimals3.10 Rational Numbers

Chapter 4 : Operations with Fractions

• Add and subtract fractions • Add and subtract mixed numbers • Multiply fractions and multiply mixed numbers • Divide fractions

4.2: Adding and Subtracting Fractions4.3: Adding and Subtracting Mixed Numbers 4.4: Multiplying Fractions and Mixed Numbers 4.5: Dividing Fractions and Mixed Numbers

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MA.7.G.4.4 Compare, contrast, and convert units of measure between different measurement systems (US customary or metric (SI)), dimensions, and derived units to solve problems.

MA.B.2.3.2 solves problems involving units of measure and converts answers to a larger or smaller unit within either the metric or customary system.




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• Writing and finding equal ratios • Finding unit rates and using unit process • Solve a problem in two different ways • Test ratios and using cross products • Solve proportions using unit rates and variables • Solve problems involving scale

5.1: Ratios 5.2: Unit Rates and Proportional Reasoning 5.3: Draw a Diagram and Solve a Simpler Problem 5.4: Proportions 5.5: Solving Proportions 5.7: Maps and Scale Drawings



Chapter 5: Ratio, Rates, and Proportions

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MA.B.2.3.1 uses direct (measured) and indirect (not measured) measures to compare a given characteristic in either metric or customary units.





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MA.6.A.3.2 Write, solve and graph one- and two-step linear equations and inequalities. MA.6.A.3.6 Construct and analyze tables, graphs and equations to describe linear functions and other simple relations using both common language and algebraic notation. MA.7.A.1.4 Graph proportional relationships and identify the unit rate as the slope of the related linear function. MA.7.A.1.5 Distinguish direct variation from other relationships, including inverse variation

MA.D.1.3.1 describes a wide variety of patterns, relationships, and functions through models, such as manipulatives, tables, graphs, expressions, equations, and inequalities.





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MA.7.A.1.6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed.

MA.B.1.3.4 constructs, interprets, and uses scale drawings such as those based on number lines and maps to solve real-world problems.







Chapter 6: Percents

• Model percents • Write percents using equal ratios • Learn percents, decimals and fractions • Use percents greater than 100 or less than 1 • Use a percent to find part of a whole • Use mental math and estimation with percents • Find the percent and whole using proportions • Find tax and tips • Find commissions

6.1:Understanding Percents 6.2: Percent, Fractions, and Decimals 6.3: Percents >100, < 1 6.4: Percent of a Number 6.5: Solving Percent Problems Using Proportions 6.7: Applications of Percent 6.8: Finding Percent of Change

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MA.6.G.4.2 Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies. MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane. MA.7.G.4.3 Identify and plot ordered pairs in all four quadrants of the coordinate plane.

MA.C.3.3.1 represents and applies geometric properties and relationships to solve real-world and mathematical problems.



Chapter 7: Geometry

• Identify segments, rays, and lines • Measure and describe angle • Work with pairs of angles • Construct segment and angle bisectors • Classify triangles • Find measures of angles in a triangle• Classify polygons • Identify special quadrilaterals• Identifying similar figures and finding missing lengths• Identify and work with congruent figures • Identify parts of a circle

7.1: Lines and Planes 7.2: Measuring and Classifying Angles 7.3: Constructing Bisectors 7.4: Triangles 7.5: Quadrilaterals 7.7: Congruent Figures 7.8: Circles

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MA.7.A.1.3 Solve problems involving similar figures.

MA.C.2.3.1 understands the geometric concepts of symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations, including flips (reflections), slides (translations), turns (rotations), and enlargements.


MA.B.2.3.1 uses direct (measured) and indirect (not measured) measures to compare a given characteristic in either metric or customary units.


• Identify segments, rays, and lines • Measure and describe angle • Work with pairs of angles • Construct segment and angle bisectors • Classify triangles • Find measures of angles in a triangle• Classify polygons • Identify special quadrilaterals• Identifying similar figures and finding missing lengths• Identify and work with congruent figures • Identify parts of a circle

7.1: Lines and Planes 7.2: Measuring and Classifying Angles 7.3: Constructing Bisectors 7.4: Triangles 7.5: Quadrilaterals 7.7: Congruent Figures 7.8: Circles

Chapter 8: Geometry and Measurement

• Find the area of a trapezoid and irregular figures • Find the area and circumference of a circle • Identify and draw three-dimensional figures • Find the volume of a prism • Find the volume of a cylinder

8.2: Areas of Parallelograms and Triangles 8.3: Areas of Other Figures 8.4: Circumference and Area of Circles 8.7: Three-Dimensional Figures 8.8: Surface Areas of Prisms and Cylinders 8.9: Volumes of Rectangular Prisms and Cylinders

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MA.6.A.3.4 Solve problems given a formula. MA.6.G.4.1 Understand the concept of π, know common estimates of π (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles. MA.6.G.4.2 Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies. MA.6.G.4.3 Determine a missing dimension of a plane figure or prism, given its area or volume and some of the dimensions, or determine the area or volume given the dimensions. MA.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three dimensional composite shapes.

MA.B.1.3.1 uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of two-and three-dimensional shapes, including rectangular solids and cylinders.


8.2: Areas of Parallelograms and Triangles 8.3: Areas of Other Figures 8.4: Circumference and Area of Circles 8.7: Three-Dimensional Figures 8.8: Surface Areas of Prisms and Cylinders 8.9: Volumes of Rectangular Prisms and Cylinders






Month

MA.6.G.4.2 Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies. MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane. MA.7.G.4.3 Identify and plot ordered pairs in all four quadrants of the coordinate plane.

MA.C.3.3.1 represents and applies geometric properties and relationships to solve real-world and mathematical problems.






Chapter 9: Algebra, Patterns and Rules

• Make graphs • Use graphs to make estimates • Use arithmetic sequences • Use geometric and other sequences • Represent patterns in tables • Write rules using tables • Write function rules • Evaluate functions

9.1: Patterns and Graphs

9.2: Number Sequences

9.3: Patterns and Tables

9.4: Function Rules

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MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems. MA.6.A.2.2 Interpret and compare ratios and rates. MA.7.A.1.6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed.

MA.B.1.3.2 uses concrete and graphic models to derive formulas for finding rates, distance, time, and angle measures.



• Make graphs • Use graphs to make estimates • Use arithmetic sequences • Use geometric and other sequences • Represent patterns in tables • Write rules using tables • Write function rules • Evaluate functions

9.1: Patterns and Graphs

9.2: Number Sequences

9.3: Patterns and Tables

9.4: Function Rules

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MA.7.G.4.3 Identify and plot ordered pairs in all four quadrants of the coordinate plane.

MA.C.3.3.2 identifies and plots ordered pairs in all four quadrants of a rectangular coordinate system (graph) and applies simple properties of lines.



Chapter 10: Graphing in the Coordinate Plane

• Solve problems by writing equations• Graph and write Inequalities• Solving inequalities by adding and subtracting • Solving inequalities by multiplying or dividing• Find ordered pairs • Graph linear equations• Finding and using the slope of a line• Graphing nonlinear equations• Solving a problem by combining strategies

10.1: Graphing Points in Four Quadrants10.2: Graphing Linear Equations10.3: Finding the Slope of a Line10.4: Exploring Nonlinear Relationships 10.5: Make a Table/Graph10.6: Translations10.7: Symmetry and Reflections10.8: Rotations

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MA.6.S.6.1 Determine the measures of central tendency (mean, median, mode) and variability (range) for a given set of data. MA.7.S.6.2 Construct and analyze histograms, stem-and-leaf plots and circle graphs.

MA.E.1.3.2 understands and applies the concepts of range and central tendency (mean, median, and mode).



• Make a frequency table or line plot • Use a spreadsheet • Make stem-and–leaf plots. • Identifying a random sample • Write a survey question • Use the capture/recapture method • Identify misleading graphs and statistics • Draw and interpret scatter plots

11.1: Frequency 11.2: Data Display 11.3: Other Displays 11.5: Random Samples and Surveys 11.6: Estimate Population Size 11.7: Using data to persuade 11.8: Exploring Scatter Plots

Chapter 11: Displaying and Analyzing Data

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MA.6.S.6.1 Determine the measures of central tendency (mean, median, mode) and variability (range) for a given set of data. MA.7.S.6.2 Construct and analyze histograms, stem-and-leaf plots and circle graphs.

MA.E.1.3.3 analyzes real-world data by applying appropriate formulas for measures of central tendency and organizing data in a quality display, using appropriate technology, including calculators and computers.

MA.7.P.7.1 Determine the outcome of an experiment and predict which events are likely or unlikely, and if the experiment is fair or unfair. MA.7.P.7.2 Determine, compare, and make predictions based on experimental or theoretical probability of independent or dependent events.

MA.E.2.3.1 compares experimental results with mathematical expectations of probabilities.

MA.7.P.7.2 Determine, compare, and make predictions based on experimental or theoretical probability of independent or dependent events.

MA.E.2.3.2 determines odds for and odds against a given situation.

MA.7.S.6.1 Evaluate the reasonableness of a sample to determine the appopriateness of generalizations made about the population.

MA.E.3.3.1 formulates hypotheses, designs experiments, collects and interprets data, and evaluates hypotheses by making inferences and drawing conclusions based on statistics (range, mean, median, and mode) and tables, graphs, and charts.


MA.E.3.3.2 identifies the common uses and misuses of probability and statistical analysis in the everyday world.



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MA.7.P.7.2 Determine, compare, and make predictions based on experimental or theoretical probability of independent or dependent events.

MA.E.2.3.2 determines odds for and odds against a given situation.

• Find the probability, complements and odds of an event • Find experimental probability and using simulations • Solve a problem using two different methods • Find a sample space • Using the counting principle • Finding the probability of independent events • Finding the probability of dependent events • Finding permutations • Finding combinations

12.1: Probability 12.2: Experimental Probability 12.3: Make an Organized List 12.4: Sample Spaces 12.5: Compound Events 12.6: Permutations 12.7: Combinations



Chapter 12: Using Probability

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MA.7.P.7.1 Determine the outcome of an experiment and predict which events are likely or unlikely, and if the experiment is fair or unfair. MA.7.P.7.2 Determine, compare, and make predictions based on experimental or theoretical probability of independent or dependent events.

MA.E.2.3.1 compares experimental results with mathematical expectations of probabilities.


MA.E.3.3.2 identifies the common uses and misuses of probability and statistical analysis in the everyday world.


MA.E.3.3.1 formulates hypotheses, designs experiments, collects and interprets data, and evaluates hypotheses by making inferences and drawing conclusions based on statistics (range, mean, median, and mode) and tables, graphs, and charts.

MA.7.S.6.2 Construct and analyze histograms, stem-and-leaf plots and circle graphs.

MA.E.1.3.1 collects, organizes, and displays data in a variety of forms, including tables, line graphs, charts, bar graphs, to determine how different ways of presenting data can lead to different interpretations.



• Find the probability, complements and odds of an event • Find experimental probability and using simulations • Solve a problem using two different methods • Find a sample space • Using the counting principle • Finding the probability of independent events • Finding the probability of dependent events • Finding permutations • Finding combinations

12.1: Probability 12.2: Experimental Probability 12.3: Make an Organized List 12.4: Sample Spaces 12.5: Compound Events 12.6: Permutations 12.7: Combinations

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curriculum guide 6th · pdf filecurriculum guide for: advanced m/j mathematics 1- 6th grade...

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