Upload
truongtram
View
237
Download
3
Embed Size (px)
Citation preview
* 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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
Assessment
Core Practice- Independent Worksheets
Activities- Showing understanding
Quizzes
Pre- Post Test
Common Assessment
Observations
MAP Assessment
ISAT Assessment
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
Unit 2: Decimal Operations Approximate Duration of Study: 3 - 4 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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.
Pretest Pretest* Posttest Posttest* Quiz Quiz *
Vocabulary: comparing, equivalent, algorithm
* The asterisk next to a document represents an adapted document.
Unit 3: Number Theory Approximate Duration of Study: 1 - 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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.
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
* The asterisk next to a document represents an adapted document.
Unit 4: Fraction Concepts Approximate Duration of Study: 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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)
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.
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
* The asterisk next to a document represents an adapted document.
Unit 5: Add/Subtract Fractions and Mixed Numbers Approximate Duration of Study: 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
Use fraction models to represent the problem.
Use equations to represent the problem.
(Addition/ Subtraction Unlike Denominators)
Estimate mentally using benchmark fractions and number sense to assess the reasonableness of an answer.
Vocabulary: Sum, Difference, Equivalent, Numerator, Denominator, Common Denominator, Mixed Number, and Factors.
* The asterisk next to a document represents an adapted document.
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.
* The asterisk next to a document represents an adapted document.
Unit 6: Multiply and Divide Fractions and Mixed Numbers Approximate Duration of Study: 1 -2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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)
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
* The asterisk next to a document represents an adapted document.
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
Unit 8: Integers Approximate Duration of Study: 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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.
Pretest Pretest* Posttest Posttest* Quiz Quiz *
Vocabulary: absolute value, integer, positive number, negative number, additive inverse, ordering, patterns, opposites
* The asterisk next to a document represents an adapted document.
Unit 9: Rational Numbers Approximate Duration of Study: 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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.
Pretest Pretest* Posttest Posttest* Quiz Quiz *
6.NS.6b How can we understand signs of numbers in ordered pairs as locations on a coordinate plane?
Rational numbers and the number line
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
Rational numbers and the number line
Find and position integers and other rational numbers on a horizontal or vertical number line diagram;
Find and position pairs of
* The asterisk next to a document represents an adapted document.
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.
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
Unit 10: Expressions and Equations Approximate Duration of Study: 2 -3 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
6.EE.1
How do we solve a numerical expression using exponents?
Numerical expressions
Write and evaluate numerical expressions involving whole-number exponents
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
* The asterisk next to a document represents an adapted document.
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
* The asterisk next to a document represents an adapted document.
Unit 11: Equations, Inequalities and Variables Approximate Duration of Study: 2 – 3 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
Buckle Down ISAT: pg 84-85
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
Buckle Down ISAT: pg 86-87
Buckle Down ISAT: pg 93-96
* The asterisk next to a document represents an adapted document.
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
Buckle Down ISAT: pg 91-92
www.math.com/school/subject2/less
ons/S2U3L4EX.html
Buckle Down ISAT: pg 99-100
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,
* The asterisk next to a document represents an adapted document.
Unit 12: Patterns Approximate Duration of Study: 1 week
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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.
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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.
* The asterisk next to a document represents an adapted document.
Unit 13: Geometric Figures Approximate Duration of Study: 1 week
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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.
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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.
* The asterisk next to a document represents an adapted document.
Unit 14: Plane Figures Approximate Duration of Study: 2-3 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
Vocabulary: acute triangle, equilateral triangle, isosceles triangle, obtuse, right, scalene, diagonal, polygon, heptagon, decagon, vertex, nonagon, regular polygon
* The asterisk next to a document represents an adapted document.
Unit 15: Congruence and Motion Geometry Approximate Duration of Study: 1 week
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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)
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
* The asterisk next to a document represents an adapted document.
Unit 16: Solid Figures Approximate Duration of Study: 1 week
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
Vocabulary: net, base, lateral face, polyhedron, surface area
* The asterisk next to a document represents an adapted document.
Unit 17: Units of Measure Approximate Duration of Study: 1- 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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
* The asterisk next to a document represents an adapted document.
Unit 18: Perimeter Approximate Duration of Study: 1 week
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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)
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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.
* The asterisk next to a document represents an adapted document.
Unit 19: Area Approximate Duration of Study: 2-3 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
Helping with Math - Geometry
Math Drills - Geometry
Vocabulary: area, length, width, base, height, decompose, composing
* The asterisk next to a document represents an adapted document.
Unit 20: Volume Approximate Duration of Study: 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
Vocabulary: volume, cylinder, prism
* The asterisk next to a document represents an adapted document.
Unit 21: Ratio and Proportion Approximate Duration of Study: 2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
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.internet4classrooms.com
/skill_builders/ratio_proportion_mat
h_sixth_6th_grade.htm
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
* The asterisk next to a document represents an adapted document.
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.internet4classrooms.com
/skill_builders/ratio_proportion_mat
h_sixth_6th_grade.htm
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.internet4classrooms.com
/skill_builders/ratio_proportion_mat
h_sixth_6th_grade.htm
http://www.aaastudy.com/g6-unit-
rate.htm
Vocabulary: ratio, proportion, equivalent ratios, rate, unit rate, scale, scale drawing, odds,
* The asterisk next to a document represents an adapted document.
Unit 22: Percent and Change Approximate Duration of Study: 1-2 weeks
CCS Essential Question
Concept Skills Assessments Helpful Strategies and Resources
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
Pretest Pretest* Posttest Posttest* Quiz Quiz *
http://www.internet4classrooms.com
/skill_builders/ratio_proportion_mat
h_sixth_6th_grade.htm
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
* The asterisk next to a document represents an adapted document.
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