Mathematics Curriculum Map

* The asterisk next to a document represents an adapted document.

MATHEMATICS CURRICULUM MAP Sixth Grade

2011

Table of Contents

Overview:

I. Best Practices

II. Assessment

III. Sixth Grade Vocabulary

IV. Timeline

V. Appendix A - Websites

Units by Standard:

Unit 1: Whole Numbers Operations

Unit 2: Decimals Operations

Unit 3: Number Theory

Unit 4: Fraction Concepts

Unit 5: Add and Subtract Fractions

Unit 6: Multiplying and Divide Fractions and Mixed Numbers

Unit 7: Statistics, Probability, and Graphing

Unit 8: Integers

Unit 9: Rational Numbers

Unit 10: Expressions and Equations

Unit 11: Equations, Inequalities, and Variables

Unit 12: Patterns

Unit 13: Geometric Figures

Unit 14: Plane Figures

Unit 15: Congruence and Motion Geometry

Unit 16: Solid Figures

Unit 17: Unit of Measurement

Unit 18: Perimeter

Unit 19: Area Unit 20: Volume Unit 21: Ratios and Proportions Unit 22: Percent and Change


Best Practices

Small Group

Modeling

Guided Practice

Independent Practice

Plans and teaches lessons to support full implementation of

mathematics core standards.

Establishes physical classroom environment to support mathematics learning

Establishes classroom climate or culture focused on student‐centered learning

Supports mathematical communication (student’s ability to explain mathematical process)

Common Math vocabulary

Uses assessment to support student learning and to guide planning.

Relating Concepts to real life situations

Incorporate word problems within units

Use concrete examples and have students draw representations of concepts


Assessment

Core Practice- Independent Worksheets

Activities- Showing understanding

Quizzes

Pre- Post Test

Common Assessment

Observations

MAP Assessment

ISAT Assessment


Sixth Grade VocabularyAcute angle

Acute triangle

Addend

Algebraic addition

Algorithm

Alternate exterior angles

Alternate interior angles

a.m.

Angle

Angle bisector

Area

Associative Property of Addition

Associative Property of Multiplication

Average

Base

Bimodal

Bisect

Capacity

Celsius scale

Center

Chance

Circle

Circle graph

Circumference

Closed-option survey

Common Denominator

Commutative Property of Addition

Commutative Property of Mult.

Compass

Complementary Angles

Composite Number

Compound Interest

Concentric Circles

Cone

Congruent

Construction

Coordinate plane

Corresponding angles

Corresponding parts

Counting numbers

Cross product

Cube

Cylinder

Decimal number

Decimal places

Decimal point

Degrees (C) (F)

Denominator

Diameter

Difference

Digit

Distributive Property

Dividend

Divisible

Divisor

Edge

Endpoint

Equation

Equilateral Triangle

Equivalent Fractions

Estimate

Evaluate

Even Numbers

Expanded Notation

Experimental Probability

Exponent

Exponential Expression

Exterior Angle

Exact

Face

Fact Family

Factor

Fahrenheit Scale

Fraction

Function

Geometric solid

Geometry

Graph

Greatest Common Factor

Height

Histogram

Horizontal

Identity Property of Addition

Identity Property of Mult.

Improper Fraction

Integers

Interest

Interest Rate

Interior Angle

International System

Intersect

Inverse Operations

Invert


Irrational Numbers

Isosceles Triangle

Least Common Multiple

Legend

Line

Line of Symmetry

Line Plot

Lowest Terms

Mass

Mean (Average)

Median

Metric System

Minuend

Mixed Number

Mode

Multiple

Negative Numbers

Number Line

Numeral

Numerator

Oblique Lines

Obtuse Angle

Obtuse Triangle

Odd Numbers

Open-option survey

Operations of Arithmetic

Opposites

Ordered Pair

Origin

Outlier

Parallel lines

Parallelogram

Percent (%)

Perfect Square

Perimeter

Perpendicular bisector

Perpendicular lines

Pi

Pictograph

Pie Graph

Place value

Plane

Platonic solid

p.m.

point

polyhedron

Positive Numbers

Power

Prime Factorization

Prime Number

Principal

Prism

Probability

Product

Property of Zero for Mult.

Proportion

Protractor

Pyramid

Quadrilateral

Qualitative

Quotient

Radius

Range

Ratio

Ray

Reciprocals

Rectangle

Reduce

Reflection

Regular Polygon

Remainder

Rhombus

Right Angle

Right Triangle

Rotation

Sales Tax

Scale

Scale Drawing

Scale Factor

Scale Model

Scalene Triangle

Sector

Segment

Sequence

Side

Similar

Simple Interest

Solid

Sphere

Square

Square Root

Stem-and-leaf plot

Straight angle

Subtrahend

Sum

Supplementary angles


Surface Area

Survey

Term

Theoretical Probability

Transformation

Translation

Transversal

Trapezium

Trapezoid

Unit Multiplier

U.S. Customary System

Vertex

Volume

Weight

Whole Numbers

X-axis

Y-axis


Sixth Grade- Concepts

CCS Unit Title Skill(s) Duration 5.NBT.1 5.NBT.2 5.NBT.5 5.NF.5A 6.NS.2

1 Whole Numbers Operations (review)

1. Whole Numbers and Place Value 2. Estimate with Whole Numbers 3. Add and Subtract Whole Numbers 4. Multiply and Divide Whole Numbers 5. Exponents 6. Order of Operations 7. Properties 8. Mental Math Strategies

1-2 wks

6.NS.3

2 Decimal Operations 1. Decimals and Place Value 2. Estimate with Decimals 3. Add and Subtract Decimals 4. Multiply Decimals 5. Divide Decimals by Whole Numbers

3-4 wks

6.NS.4 3 Number Theory 1. Divisibility 2. Prime and Composite Numbers 3. Prime Factorization 4. LCM and GCF

1-2 wks

5.NF.1 5.NF.2

4 Fraction Concepts 1. Understand Fractions 2. Equivalent Fractions and Simplest Form 3. Fractions and Decimals 4. Fractions, Decimals, and Percents 5. Compare and Order

2 wks

5.NF.1 5.NF.2

5 Add and Subtract Fractions and Mixed Numbers

1. Estimate Sums and Differences 2. Add and Subtract Fractions 3. Add and Subtract Mixed Numbers 4. Subtracting Equivalent Fractions

2 wks

5.NF.4a 5.NF.5b 5.NF.6 6.NS.1

6 Multiply and Divide Fractions and Mixed Numbers

1. Estimate Products and Quotients 2. Multiply Fractions 3. Multiply Mixed Numbers 4. Divide Fractions and Mixed Numbers

1-2 wks


6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5 6.EE.9

7 Statistics, Probability, and Graphing

1. Mean, Median, Mode and Range 2. Frequency Tables and Line Plots 3. Samples and Surveys 4. Make and Analyze Graphs 5. Stem-and-Leaf Plots and Histograms 6. Compare Graphs 7. Choose and Appropriate Graph 8. Box-and-Whisker Plots 9. Graph Functions 10. Graph Linear Equations 11. Graph Relationships 12. Theoretical Probability 13. Experimental Probability 14. Make Predictions 15. Outcomes of Compound Events 16. Independent and Dependent Events 17. Permutations and Combinations

4 wks

6.NS.5 8 Integers 1. Understand Integers 2. Add Integers 3. Subtract Integers 4. Multiply Integers 5. Divide Integers 6. Operations with Integers

2 wks

6.NS.6a 6.NS.6b 6.NS.6c 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.8

9 Rational Numbers 1. Rational Numbers 2. Compare and Order 3. Properties of Rational Numbers 4. Inequalities on a Number Line 5. Graph on a Coordinate Plane

2 wks

6.EE.1 6.EE.2 6.EE.3 6.EE.4

10 Expressions and Equations

1. Write Algebraic Expressions 2. Evaluate Algebraic Expressions 3. Words and Equations 4. Solve Addition Equations 5. Solve Subtraction Equations 6. Solve Multiplication and Division Equations

2-3 wks


6.EE.5 6.EE.6 6.EE.7 6.EE.8 6.EE.9

11 Equations, Inequalities and Variables

1. Understand Solving and Equation or Inequality 2. Use Substitution to Make an Equation True 3. Use Variables to Represent Numbers 4. Understand that a Variable can represent an

Unknown Number 5. Solve Word Problems with Equations 6. Inequalities 7. Dependent and Independent Variables

2-3 wks

5.OA.3

12 Patterns 1. Patterns in Sequences 2. Number Patterns and Functions 3. Geometric Patterns

1 wk

5.G.3 5.G.4

13 Geometric Figures 1. Points, Lines, and Planes 2. Angle Relationships 3. Congruent Line Segments and Angles 4. Classify Lines and Planes 5. Bisect Line Segments and Angles

1 wk

6.G.3 14 Plane Figures 1. Polygons 2. Triangles 3. Quadrilaterals 4. Draw Plane Figures 5. Circles

2-3 wks

5.G.3 5.G.4

15 Congruence and Motion Geometry

1. Similar and Congruent Figures 2. Transformations 3. Transformations on the Coordinate Plane 4. Symmetry

1 wk

6.G.4 16 Solid Figures 1. Types of Solid Figures 2. Views of Solid Figures 3. Nets of Solid Figures

1 wk

6.RP.3d 17 Units of Measure 1. Elapsed Time 2. Customary Measurements 3. Metric Measurements 4. Fahrenheit and Celsius 5. Appropriate Tools and Units

1-2 wks


Review 18 Perimeter 1. Find Perimeter 2. Perimeter Formulas 3. Estimate and Measure Perimeter 4. Circumference 5. Polygon Sides 6. Compare Perimeters

1 wk

6.G.1

19 Area 1. Estimate Area 2. Area of Squares, Rectangles, and Triangles 3. Area of Parallelograms and Trapezoids 4. Perimeter and Area 5. Area of Circles

2-3 wks

6.G.2 20 Volume

1. Surface Area 2. Volume of Prisms 3. Volume of Cylinders

2 wks

6.RP.1 6.RP.2 6.RP.3a 6.RP.3b

21 Ratio and Proportion 1. Ratios and Rates 2. Write and Solve Proportions 3. Distance, Rate, and Time 4. Ratios and Similar Figures 5. Scale Drawings 6. Proportional Reasoning 7. Golden Ratio

2 wks

6.RP.3c 22 Percent and Change 1. Percent 2. Percents, Decimals and Fractions 3. Percent of a Number 4. Discount and Sales Tax 5. Simple Interest

1-2 wks


Unit 1: Whole Number Operations Approximate Duration of Study: 1 - 2 weeks

CCS Essential Question

Concept Skills Assessments Helpful Strategies and Resources

5.NBT.1

How do we compare relationships between place values?

Place Value Relationship of digits in a multi-digit number The ones place is ten times as much as the place value to the right.

Pretest Pretest* Posttest Posttest* Quiz Quiz *

SMART Notebook- Place Value

5.NBT.2 How do I demonstrate the patterns between numbers, quantities and place value using the power of ten?

Multiplying by Power of Ten

Explain the patterns of zeros in whole numbers.

Explain the patterns of the placement of decimal points

SMART Notebook- Multiplying by Tens SMART Notebook- Multiplying by Tens GAME

5.NBT.5 How can we use the concept of multiplication to solve problems?

Whole Number Multiplying

Solve two digit multiplication.

Solve three digit multiplication.

SMART Notebook- Two and Three Digit Multiplication SMART Notebook- Two Digit Multiplication- Lattice Method SMART Notebook- Two Digit Multiplication

5.NF.5a How can we interpret multiplication as scaling (resizing)?

Comparing Sizes

Evaluate the factors to estimate the product (size), without multiplying

SMART Notebook- Estimate/Comparing Product Lesson/Activity

6.NS.2 What is the strategy to divide multi-digit numbers?

Divide multi-digit numbers

Fluently divide multi-digit numbers using the standard algorithm.

Vocabulary: addend, sum, subtrahend, minuend, difference, factor, product, divisor, dividend, quotient, estimation, operations, ordering, place value


Unit 2: Decimal Operations Approximate Duration of Study: 3 - 4 weeks



6.NS.3 What is the strategy to add, subtract, multiply, and divide multi-digit decimals?

Add, subtract, multiply and divide multi-digit decimals

Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.


Vocabulary: comparing, equivalent, algorithm


Unit 3: Number Theory Approximate Duration of Study: 1 - 2 weeks



6.NS.4 How do you find the greatest common factor of two whole numbers less than 100? How do you find the least common multiple of two whole numbers less than or equal to 12?

Greatest common factor and least common multiple

Find greatest common factor of two whole numbers less than or equal to 100.

Find least common multiple of two whole numbers less than or equal to 12.

Use distributive property to express an equation as a multiple of a sum of two whole numbers with no common factor.


SMART Notebook- Order of Operations SMART Notebook- Parentheses

BrainPOP- Order of Operations

Vocabulary: greatest common factor, least common multiple, composite, common multiple, factor, prime number, opposites, standard form, divisibility, expression

http://www.brainpop.com/search/search.weml?keyword=Parentheses


Unit 4: Fraction Concepts Approximate Duration of Study: 2 weeks



5.NF.1 How do we convert fractions to common denominators? How do we use fraction conversions in our daily life (cooking, slices, etc.)?

Unlike Denominators (changing to common denominators)

Add Fractions

Subtract Fractions


Unlike Denominators With Mixed Numbers

Add Mixed Numbers

Subtract Mixed Numbers

5.NF.2 How can we demonstrate fractions through story problems?

Story Problems (Addition/ Subtraction Common Denominators)

Use fraction models to represent the problem.

Use equations to represent the problem.

Estimate mentally using benchmark fractions and number sense to assess the reasonableness of an answer.

Story Problems (Addition/ Subtraction Unlike Denominators)




Vocabulary: Sum, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, and Factors. Benchmark Fraction: Benchmark fractions are common fractions that you can judge other numbers against. Normally, 1/4, 1/2, 3/4, and often 1/10 (because of its relationship with decimals) are referred to as benchmark fractions. Read more: http://wiki.answers.com/Q/What_is_benchmark_fraction#ixzz174UgbnsV

http://wiki.answers.com/Q/What_is_benchmark_fraction#ixzz174UgbnsV


Unit 5: Add/Subtract Fractions and Mixed Numbers Approximate Duration of Study: 2 weeks



5.NF.1 How do we convert fractions to common denominators? How do we use fraction conversions in our daily life (cooking, slices, etc.)?

Unlike Denominators (changing to common denominators)

Add Fractions

Subtract Fractions


Unlike Denominators With Mixed Numbers

Add Mixed Numbers

Subtract Mixed Numbers

5.NF.2 How can we demonstrate fractions through story problems?

Story Problems (Addition/ Subtraction Common Denominators)




Story Problems



(Addition/ Subtraction Unlike Denominators)


Vocabulary: Sum, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, and Factors.


Benchmark Fraction: Benchmark fractions are common fractions that you can judge other numbers against. Normally, 1/4, 1/2, 3/4, and often 1/10 (because of its relationship with decimals) are referred to as benchmark fractions. Read more: http://wiki.answers.com/Q/What_is_benchmark_fraction#ixzz174UgbnsV

Vocabulary: Compare, Decimal, Decimal Point, Equivalent Decimals, Expanded Form, Hundredth, Round, Tenth, and Thousandth.

http://wiki.answers.com/Q/What_is_benchmark_fraction#ixzz174UgbnsV


Unit 6: Multiply and Divide Fractions and Mixed Numbers Approximate Duration of Study: 1 -2 weeks



5.NF.4a How do we multiply fractions? What are rules to multiplying fractions?

Multiplying Fractions/ Fractions

Multiply fractions with fractions

e.g. (a/b x c/d =ac/bd)


Multiplying Whole Numbers to Fractions

Multiply fractions with whole numbers

e.g. (a/b x q = aq/b)

5.NF.5b How do we anticipate the product of fractions?

Multiplying Fractions

Explain why multiplying a fraction greater than one by a given number will result in a larger product

Explain why multiplying a fraction less than one by a given number will result in a smaller product

5.NF.6 How does multiplication relate to real world scenarios?

Real World Problems of Multiplication

Solve real world problems using fractions and mixed numbers

Use fraction models and equations to represent the problem

6.NS.1 What is the strategy to compute quotients of fractions?

Dividing fractions by fractions

Compute quotient of fractions

Solve word problems involving division of fractions by fractions

Vocabulary: Product, Difference, Equivalent, Compare, Numerator, Denominator, Common Denominator, Mixed Number, and Factors, Reciprocal


Unit 7: Statistics, Probability, and Graphing Approximate Duration of Study: 4 weeks

CCS Essential

Questions

Concepts Skills Assessments Helpful Strategies

& Resources

6.SP.1 What is the process

of taking a survey and

displaying the

results?

Statistical questions Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers


6.SP.2 How do mean, median and mode describe a set of data?

Set of data Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape

6.SP.3 What method would you use to describe a given set of data using mean, median, mode and range?

Measure of data Recognize that a measure of center for a numerical data set summarizes all of its values with a single number

Recognize that a measure of variation describes how its values vary with a single number


6.SP.4 What questions should you ask to determine which numerical set of data would be the most appropriate to use for the data given?

Displaying numerical

data

Display numerical data in plots on a number line, including dot plots, histograms, and box plots

6.SP.5 How can you show the distribution of data using a box-and-whisker plot?

Summarize

numerical data sets

Report the number of observations

Describe the nature of the attribute under investigation including how it was measured and its units of measurement

Give quantitative measures of median and/or mean and interquartile range and/or mean, as well as describing any overall pattern and deviations with reference to the context in which the data was gathered

Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered


6.EE.9 How do we use variables to represent two quantities?

How do we write an equation to express the dependent variable to the independent variable?

How do we analyze the relationship between the dependent and independent variable using graphs and tables?

Dependent and

independent

variables

Use variables to represent two quantities in a real-world problem that change in relationship to one another

Write an equation to express the dependent variable in terms of the independent variable

Analyze the relationship between the dependent variable and the independent variable using graphs and tables, and relate these to the equation

Buckle Down ISAT: pg.

76-80

Buckle Down ISAT: pg

101-105

Vocabulary: Probability, chance, ratio, mean, median, mode, range, frequency, survey, variables, histogram, stem-and-leaf plot, box-and-whisker plot,

data, circle graph, line graph, bar graph, pictograph, frequency table, cumulative frequency, variables, comparing, census, averages, outlier,

interquartile, predictions, random, events, dependent, independent, permutation, outcomes, estimation, scatter plots


Unit 8: Integers Approximate Duration of Study: 2 weeks



6.NS.5 How can we understand that positive and negative numbers are used to describe quantities having opposite directions?

Positive and negative numbers

Understand that positive and negative numbers are used to describe quantities having opposite directions.

Be able to explain meaning of zero in relation to + and – numbers.


Vocabulary: absolute value, integer, positive number, negative number, additive inverse, ordering, patterns, opposites


Unit 9: Rational Numbers Approximate Duration of Study: 2 weeks



6.NS.6a How can we recognize opposite signs of numbers on a number line?

Rational numbers and the number line

Rational numbers and the coordinate plane

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line;

Recognize that the opposite of the opposite of a number is itself.


6.NS.6b How can we understand signs of numbers in ordered pairs as locations on a coordinate plane?


Understand signs of numbers in ordered pairs as locations in quadrants of the coordinate plane;

Recognize that when two ordered pairs differ only by signs, the locations will be reflections across one or both axes.

6.NS.6c How can we find and position integers and other rational numbers on a horizontal and


Find and position integers and other rational numbers on a horizontal or vertical number line diagram;

Find and position pairs of


vertical number line?

integers and other rational numbers on a coordinate plane.

6.NS.7a How can we interpret statements of inequality as statements about the relative position of two numbers on a number line?

Ordering and absolute value of rational numbers

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

6.NS.7b How can we write, interpret, and explain order for rational numbers in real-world contexts?

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

6.NS.7c How can we understand the absolute value of a rational number as its distance from zero on a number line?

Understand the absolute value of a rational number as its distance from zero on the number line;

Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

6.NS.7d How can we distinguish comparisons of absolute value from statements about order?

Distinguish comparisons of absolute value from statements about order.


6.NS.8 How can we solve real-world and math problems by graphing points on a coordinate and use coordinates to find distances between points on a coordinate plane?

Coordinate Plane Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane;

Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Vocabulary: comparing, rational numbers, irrational numbers, coordinates, ordered pairs, coordinate plane, quadrant, absolute value, inequality


Unit 10: Expressions and Equations Approximate Duration of Study: 2 -3 weeks



6.EE.1

How do we solve a numerical expression using exponents?

Numerical expressions

Write and evaluate numerical expressions involving whole-number exponents


www.mathgoodies.com/lessons/vol7/equations.html

6.EE.2

How do we solve the value of an unknown? How do we solve an expression using the order of operations?

Letters in expressions

Write expressions that record operations with numbers in which letters stand for numbers

Identify parts of an expression using mathematical terms

View one or more parts of an expression as a single entity

Evaluate expressions at specific values of their variables

Include expressions that arise from formulas used in real-world problems

Perform arithmetic operations in the conventional order when there are no parenthesis

http://msteacher.org/epubs/math/math14/expressions.aspx

S:\Evans\Algebra_Tiles powerpoint good.ppt

Sequence: Versatile: pg 4 & 9

Sequence- Versatile: pg 22-23

Buckle Down ISAT pg 88-89

http://www.mathgoodies.com/lessons/vol7/equations.html

http://msteacher.org/epubs/math/math14/expressions.aspx


6.EE.3 How do we apply the properties of operations to generate equivalent expressions?

Properties of operations

Apply the properties of operations to generate equivalent expressions

Interactive:

www.mathgoodies.com/Lessons/vol7/order_operations.ht

ml

6.EE.4 How do we identify when two expressions are equivalent?

Equivalent expressions

Identify when two expressions are equivalent

Numbers- Versatile: pg 28

Vocabulary: algebraic, evaluating, numerical, order of operations, equivalent, variables

http://www.mathgoodies.com/Lessons/vol7/order_operations.html

http://www.mathgoodies.com/Lessons/vol7/order_operations.html


Unit 11: Equations, Inequalities and Variables Approximate Duration of Study: 2 – 3 weeks



6.EE.5 How do we solve an equation and/or inequality? How do we use substitution to determine whether a given number in a set makes an equation?

Solving an equation or inequality

Understand solving an equation or inequality as a process of answering a question

Which values from a specified set, if any, make the equation or inequality true?

Use substitution to determine whether a given number in a specified set makes an equation or inequality true


Ratio – Versatile: pg 15-16

www.purplemath.com/modules/ineq

solv.htm

6.EE.6 How do we use variables to represent numbers?

How do we write expressions when solving real word problems?

Variables Use variables to represent numbers and write expressions when solving real-world or mathematical problems

Understand that a variable can represent an unknown number or any number in a specified set

Buckle Down ISAT: pg 86-87


6.EE.7 How do we solve real world problems by writing equations?

Equations Solve real-world and mathematical problems by writing and solving equations in the form of x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers




6.EE.8 How do we write an inequality?

How do we recognize that inequalities have infinite solutions? How do we represent solutions of inequalities on a number line?

Inequalities Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem

Recognize that inequalities of the form x > c or x < c have infinite solutions

Represent solutions of such inequalities on number line diagrams

Interactive:

www.themathpage.com/Alg/inequali

ties.htm#number%20line


www.math.com/school/subject2/less

ons/S2U3L4EX.html


6.EE.9 How do we use variables to represent two quantities?

How do we write an equation to express the dependent variable to the independent variable?

How do we analyze the relationship between the dependent and independent variable using graphs and tables?

Dependent and independent variables

Use variables to represent two quantities in a real-world problem that change in relationship to one another

Write an equation to express the dependent variable in terms of the independent variable

Analyze the relationship between the dependent variable and the independent variable using graphs and tables, and relate these to the equation

Vocabulary: equations, inequalities, variables, analyze, substitution,

http://www.themathpage.com/Alg/inequalities.htm#number%20line

http://www.themathpage.com/Alg/inequalities.htm#number%20line

http://www.math.com/school/subject2/lessons/S2U3L4EX.html

http://www.math.com/school/subject2/lessons/S2U3L4EX.html


Unit 12: Patterns Approximate Duration of Study: 1 week



5.OA.3 What are the relationships between corresponding terms? Why are the relationships relevant? How can we use ordered pair to develop relationships in numbers?

Ordered Pairs

Generate two number patterns using a given rule X-value add 3, Y-value add 6.


Find ordered pair relationships (rule)

Compare two sequences of numbers to develop pattern.

Add 3, starting at 0 and Add 6 starting at 0, then identify that the sequence is twice the corresponding term.

Vocabulary: Ordered Pairs, Relevancy, Corresponding Terms, Term, Patterns, X-Value, Y-Value, Sequence, and Rule.


Unit 13: Geometric Figures Approximate Duration of Study: 1 week



5.G.3 How can the characteristics of shapes helps us categorize multiple figures?

Categorize Understand that a two-dimensional shape can be classified using different categorization (side lengths, degrees of angles, number of sides)

e.g. All rectangles have right angles, a square is rectangle, so all squares have right angles.


5.G.4 How can we sequentially order shapes according the properties from simplest to most complex?

Classify Organize two-dimensional shapes as being classified as more than one figure in order from simplest to most complex.

e.g. shape, quadrilateral, parallelogram, rhombus, square

Vocabulary: Two- Dimensional Shapes, Lengths, Degrees, Angles, Sides, Quadrilateral, Square, Parallelogram, Rhombus, Trapezoid, Rectangle, Angles, Degrees, Classify, Simple, and Complex.


Unit 14: Plane Figures Approximate Duration of Study: 2-3 weeks



6.G.3 How can I draw polygons in the coordinate plane? How can I find the dimensions of a given polygon on the coordinate plane using the coordinates?

Draw polygons Draw polygons in the coordinate plane given coordinates for the vertices

Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate

Apply these techniques to solving real-world and mathematical problems


Vocabulary: acute triangle, equilateral triangle, isosceles triangle, obtuse, right, scalene, diagonal, polygon, heptagon, decagon, vertex, nonagon, regular polygon


Unit 15: Congruence and Motion Geometry Approximate Duration of Study: 1 week



5.G.3 How do we classify angles? How do we measure using a protractor?

Angles Name an angle (right, acute, or obtuse)

Draw an angle (right, acute, or obtuse)

Measure an angle (right, acute, or obtuse)


5.G.4 How do you classify a polygon?

Polygons Use the properties of lines, points, and angles to classify polygons.

Name a polygon based on the polygons properties.

Identify the total number of diagonals within a polygon.

Evaluate a polygon to determine lines of symmetry.

Vocabulary: similar figures, corresponding angles, corresponding sides, exterior, interior, right, acute, obtuse, adjacent, ray, line, segment, straight, supplementary, complementary, parallel, perpendicular, bisect, midpoint, compass, protractor


Unit 16: Solid Figures Approximate Duration of Study: 1 week



6.G.4 How can I use a net to represent a three-dimensional figure? How can I use a net to find the surface area of a three-dimensional figure?

Three-dimensional figures

Represent three-dimensional figures using nets made up of rectangles and triangles

Use the nets to find the surface area of these figures

Apply these techniques to solving real-world and mathematical problems


Vocabulary: net, base, lateral face, polyhedron, surface area


Unit 17: Units of Measure Approximate Duration of Study: 1- 2 weeks



6.RP.3d How can we use ratio and rate reasoning to solve real world and mathematical problems?

Measurement units

Use ratio reasoning to convert measurement units

Manipulate and transform units appropriately when multiplying or dividing quantities


http://www.internet4classrooms.com/skill_b

uilders/ratio_proportion_math_sixth_6th_gra

de.htm

http://www.learner.org/interactives/dailymat

h/cooking.html

http://www.edhelper.com/math/math_sixth_g

rade_TTST6_7.htm

Vocabulary: capacity, Celcius, Fahrenheit, metric, customary, elapsed time, ante meridiem, post meridiem, unit rate

http://www.internet4classrooms.com/skill_builders/ratio_proportion_math_sixth_6th_grade.htm



http://www.learner.org/interactives/dailymath/cooking.html

http://www.learner.org/interactives/dailymath/cooking.html

http://www.edhelper.com/math/math_sixth_grade_TTST6_7.htm

http://www.edhelper.com/math/math_sixth_grade_TTST6_7.htm


Unit 18: Perimeter Approximate Duration of Study: 1 week



Review 5.NF.4b 5.NF.5a 5.NF.6

How do you solve for the perimeter? How does the perimeter relate to architecture?

Perimeter of polygons

Understand the concept of the perimeter of polygons

Use addition to solve for the perimeter

Use the formulas: (l + l + w + w) or (2 x l) + (2 x w)


5.G.3 5.G.4

Circumference of Circles

Understand the concept of the perimeter of circles

Use formulas:

(π • d) or (2πr)

Vocabulary: Perimeter, Circumference, Diameter, Radius, Length, Width, and Sum.


Unit 19: Area Approximate Duration of Study: 2-3 weeks



6.G.1 How can I find the area of triangles by composing or decomposing them into other shapes?

Area Find the area of right triangles, or other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes

Apply these techniques in the context of solving real-world and mathematical problems


Helping with Math - Geometry

Math Drills - Geometry

Vocabulary: area, length, width, base, height, decompose, composing

http://www.helpingwithmath.com/by_subject/geometry/geo_worksheets.htm

http://www.math-drills.com/geometry.shtml


Unit 20: Volume Approximate Duration of Study: 2 weeks



6.G.2 How can I find the volume of a right rectangular prism using unit cubes? How can I find the volume of a right rectangular prism using the formulas for volume?

Volume Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes

Show that the volume is the same as would be found by multiplying the edge lengths of the prism

Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths


Vocabulary: volume, cylinder, prism


Unit 21: Ratio and Proportion Approximate Duration of Study: 2 weeks



6.RP.1 What is a ratio? What is ratio language to describe a ratio relationship?

Ratios

Ratio language

Use ratio language to describe relationship between two quantities


Interactive Test:

http://cat.umbotests.com/te

sts/ratio-and-proportion-

problems

www.edhelper.com/ratios.

htm

Game:

http://www.aaamath.com/B/g62b_fx

1.htm#section2

http://www.internet4classrooms.com

/skill_builders/ratio_proportion_mat

h_sixth_6th_grade.htm

interactive:

www.themathpage.com/arth/Ar_Pr/r

atio1_1.htm

interactive:

www.math.com/school/subject1/less

ons/S1U2L.html#sm3

6.RP.2 What is unit rate associated with a ratio? How do you use rate language in the context of a ratio relationship?

Unit rate

Ratio relationships

Understand the concept of unit rate a/b associated with a ratio a:b with b ≠ 0

Use rate language in the context of a ratio relationship

Quiz:

http://math.rice.edu/~lanius/proporti

ons/quiz1.html




http://www.brainpop.com/math/ratio

proportionandpercent/ratios/preview.

weml

www.algebralab.org/Word/Word.asp

x?file=Algebra_Proportions.xml

www.yale.edu/ynhti/curriculum/unit

s/2004/5/04.05.08.x.html

http://cat.umbotests.com/tests/ratio-and-proportion-problems



http://www.aaamath.com/B/g62b_fx1.htm#section2

http://www.aaamath.com/B/g62b_fx1.htm#section2




http://www.themathpage.com/arth/Ar_Pr/ratio1_1.htm

http://www.themathpage.com/arth/Ar_Pr/ratio1_1.htm

http://math.rice.edu/~lanius/proportions/quiz1.html

http://math.rice.edu/~lanius/proportions/quiz1.html




http://www.brainpop.com/math/ratioproportionandpercent/ratios/preview.weml



http://www.algebralab.org/Word/Word.aspx?file=Algebra_Proportions.xml

http://www.algebralab.org/Word/Word.aspx?file=Algebra_Proportions.xml


6.RP.3a How can we use ratio and rate reasoning to solve real world and mathematical problems?

Make and use tables of equivalent ratios

Make tables of equivalent ratios relating quantities with whole number measurements

Find missing values within the tables

Plot the pairs of values on the coordinate plane

Use tables to compare ratios

Lesson and Worksheet:

http://tulyn.com/6th-grade-

math/equal-ratios




http://www.cimt.plymouth.ac.uk/proj

ects/mepres/book8/bk8i7/bk8_7i1.ht

m

Video -

http://www.nextvista.org/finding-

equivalent-ratios/

http://tulyn.com/wordproblems/ratio.

htm

http://www.ixl.com/math/practice/gr

ade-6-coordinate-graphs-review

http://nrich.maths.org/public/viewer.

php?obj_id=4827

6.RP.3b How can we use ratio and rate reasoning to solve real world and mathematical problems?

Unit rate problems

Solve unit rate problems including those involving unit pricing and constant speed




http://www.aaastudy.com/g6-unit-

rate.htm

Vocabulary: ratio, proportion, equivalent ratios, rate, unit rate, scale, scale drawing, odds,

http://tulyn.com/6th-grade-math/equal-ratios

http://tulyn.com/6th-grade-math/equal-ratios




http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i7/bk8_7i1.htm



http://www.nextvista.org/finding-equivalent-ratios/

http://www.nextvista.org/finding-equivalent-ratios/

http://www.ixl.com/math/practice/grade-6-coordinate-graphs-review

http://www.ixl.com/math/practice/grade-6-coordinate-graphs-review

http://nrich.maths.org/public/viewer.php?obj_id=4827

http://nrich.maths.org/public/viewer.php?obj_id=4827




http://www.aaastudy.com/g6-unit-rate.htm

http://www.aaastudy.com/g6-unit-rate.htm


Unit 22: Percent and Change Approximate Duration of Study: 1-2 weeks



6.RP.3c How can we use ratio and rate reasoning to solve real world and mathematical problems?

Percents Find a percent of a quantity as a rate per 100

Solve problems finding the whole, given a part and a percent





http://www.helpingwithmath.com/by

_subject/percentages/per_calculating

.htm

http://www.analyzemath.com/middle

_school_math/grade_6/percent.html

Vocabulary: sales tax, discount, percent




http://www.helpingwithmath.com/by_subject/percentages/per_calculating.htm



http://www.analyzemath.com/middle_school_math/grade_6/percent.html

http://www.analyzemath.com/middle_school_math/grade_6/percent.html


Useful Websites for All Standards: http://www.helpingwithmath.com/by_grade/gr6_worksheets.htm

http://www.prepdog.com/6th_grade/6th_grade_practice_tests.htm

http://www.math4children.com/

http://www.mathsisfun.com/

www.aaamath.com www.brainquest.com

www.mathfun.com www.aplusmath.com

www.webmath.com www.multiplication.com

www.kidsbank.com www.allmath.com

www.exploremath.com www.coolmath4kids.com

www.interventioncentral.org www.busyteacherscafe.com

www.mathmastery.com www.eduplace.com

www.planemath.com www.funbrain.com

www.moneyopolis.com www.edhelper.com

www.brainpop.com www.mathslideshow.com

http://math.pppst.com/mathmix.html

http://www.helpingwithmath.com/by_grade/gr6_worksheets.htm

http://www.prepdog.com/6th_grade/6th_grade_practice_tests.htm

http://www.math4children.com/

http://www.mathsisfun.com/

http://www.aaamath.com/

http://www.brainquest.com/

http://www.mathfun.com/

http://www.aplusmath.com/

http://www.webmath.com/

http://www.multiplication.com/

http://www.kidsbank.com/

http://www.allmath.com/

http://www.exploremath.com/

http://www.coolmath4kids.com/

http://www.interventioncentral.org/

http://www.busyteacherscafe.com/

http://www.mathmastery.com/

http://www.eduplace.com/

http://www.planemath.com/

http://www.funbrain.com/

http://www.moneyopolis.com/

http://www.edhelper.com/

http://www.brainpop.com/

http://www.mathslideshow.com/

http://math.pppst.com/mathmix.html

Mathematics Curriculum Map

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Transcript of Mathematics Curriculum Map