Whole Numbers and Exponents:
1-1 Comparing and Ordering Whole Numbers
1-2 Estimating with Whole Numbers
1-3 Exponents
Using Whole Numbers
1-4 Order of Operations
1-5 Mental Math
1-6 Choose a Method of Computation
1-7 Find a Pattern
Understanding Variables and Expressions2-1 Variables and Expressions
2-2 Translates Between Words and Math
2-3 Equations and Their Solutions
2-4 Solving Addition Equations
2-5 Solving Subtractions Equations
2-6 Solving Multiplication Equations
2-7 Solving Division Equations
Understanding Decimals
3-1 Representing, Comparing, and Ordering Decimal
3-2 Estimating Decimals
3-3 Adding and Subtracting Decimals
3-4 Decimals and Metric Measurements
Multiplying and Dividing Decimals
3-5 Scientific Notation
3-6 Multiplying Decimals
3-7 Dividing Decimals by Whole Numbers
3-8 Dividing by Decimals
3-9 Interpret the Quotient
3-10 Solving Decimal Equations
M.O.5.1.1.
M.O.5.1.2
M.O.5.1.3
M.O.5.1.7
M.O.5.1.9
M.O.5.1.10
M.O.5.2.1
M.O.5.5.1
M.O.5.5.2
M.O.5.5.3
M.O.6.2.2
M.O.6.2.4
Use input/output models and spreadsheets to evaluate functions
Expressions and Formulas (MA.6.2.4)
Use variables to represent and solve real world problems appropriate for the sixth grade using multiple strategies (MA.6.2.9)
Expressions and Formulas
Simplify numerical expressions using order of operations Expressions and Formulas (MA.6.2.2)
Identify missing elements in arithmetic and geometric patterns (MA.6.2.2)
When working in Expressions and Formulas, explore arithmetic and geometric patterns.
Have students make a rule to define the pattern and continue the pattern using a table or graph.
Also, Algebra Tools: p._ 7-11; p. 31-32, 77-79
Find the percent of a number
Models You Can Count ON! Fraction Times, and More of Less
Model addition, subtraction, multiplication, and division of integers
(Fractions, decimals, and % (MA.6.2.7):
Models You Can Count On!, Fraction Times, and More or Less)
Negative integers can be found in book.
Expressions and Formulas
* Apply the order of operations E
* Organize calculations E
* Use inverse operations C,D
* Represent formulas using arrow strings A,B
* Extend tables and charts C,E
* Use a graph to represent word formulas or equations C,E
* Understand equivalent formulas (informal) C, D, E
* Mental Math
Models You Can Count On!
* Order and compare fractions, decimals, and percents on a number line B,C
* Order and compare fractions and decimals on a number line B,C
* Informal strategies for multiplication and division of fractions
* Conceptual understanding of ratio A
* Fractions as part/whole relationships C
* Introduced to models for solving problems involving ratio, proportion, percent and
fractions A,B,C
* Multiply whole number by decimals A
* Compare ratios and fractions B
* Use models for solving problems involving ratio, proportion, percent and fractions
Best Practices by Harrison County Teachers
techSteps Sixth Grade Project -
Reading - "Poetry in Motion"
M.O.6.2.2
SchoolKit E318
Odyssey 56183
M.O.6.2.4
SchoolKit E314
Odyssey 67201
Using NLVM
http://nlvm.usu.edu/en/nav/vlibrary.html
and whiteboard, use “Function Machine” applet to observe a “machine” to determine the function rule or pattern.
Multiplying and Dividing Decimals
3-5 Scientific Notation
3-6 Multiplying Decimals
3-7 Dividing Decimals by Whole Numbers
3-8 Dividing by Decimals
3-9 Interpret the Quotient
3-10 Solving Decimal Equations
Number Theory
4-1 Divisibilty
4-2 Factors and Prime Factorization
4-3 Greatest Common Factor
Understanding Fractions
4-4 Decimals and Fractions
4-5 Equivalent Fractions
4-6 Comparing and Ordering Fractions
4-7 Mixed Numbers and Improper Fractions
Introduction to Fraction Operations
4-8 Adding and Subtracting with Like Denominators
4-9 Multiplying Fractions by Whole Numbers
Multiplying and Dividing Fractions
5-1 Multiplying Fractions
5-2 Multiplying Mixed Numbers
5-3 Dividing Fractions and Mixed Numbers
5-4 Solving fractions Equations: Multiplication and Division
Adding and Subtracting Fractions
5-5 Least Common Multiple
M.O.6.1.1
M.O.6.1.2
M.O.6.1.3
M.O.6.2.2
M.O.6.2.3
Operations
* Convert among fractions, mixed numbers, decimals and %.
(Fractions, decimals , and %: Models You Can Count On!, Fraction Times, and More of Less)
* Read, write, order, and compare numbers, using scientific notations. Facts and Factors (MA.6.1.1)
* Identify prime and composite numbers up to 100. Facts and Factors
(MA.6.1.2)
* Use prime factorization to determine the greatest common factor and the least common multiple. Facts and Factors
(MA.6.1.3)
* Explore a variety of patterns, including perfect squares, square roots, exponents Facts and Factors
(MA.6.2.3)
* Identify missing elements in arithmetic and geometric patterns (MA.6.2.2)
Can be explored and practiced during this unit.
SEE: Items for Models You Can Count On!
and More or Less for specific items that apply to this book
The three number books in the 6th grade build on each other to meet the number criteria items for West Virginia.
Models You Can Count On!
* Fractions as part/whole relationships C
* Introduced to models for solving problems involving ratio, proportion, percent and fractions A,B,C
* Multiply whole number by decimals A
* Compare ratios and fractions B
Use models for solving problems involving ratio, proportion, percent and fractions
Fraction Times
* Fractions as part/whole relationsips A
* Relationships between percent, fractions, decimals, and ratios A,B,D
* Change fractions to decimals to percents D
* Common denominator B
* Simplify fractions D
* Informal addition, subtraction
* Fractions as part/whole relationsips A
* Relationships between percent, fractions, decimals, and ratios A,B,D
* Change fractions to decimals to percents D
* Common denominator B
* Simplify fractions D
* Informal addition, subtraction and multiplication of fractions
techSteps Sixth Grade Project -
English - "Investigate Paper Copters"
M.O.6.1.1
Odyssey 5302
M.O.6.1.2
SchoolKit E321
Odyssey 56283
M.O.6.1.3
SchoolKit E330
Odyssey 5329
M.O.6.2.2
SchoolKit E318
Odyssey 6637
M.O.6.2.3
SchoolKit E324
Odyssey 67201
Using the National Library of Virtual Manipulatives and a whiteboard (http://nlvm.usu.edu/en/nav/vlibrary.html).
Use “Factor Tree” applet to introduce prime factorization using factor trees.
http://illuminations.nctm.org
Building Bridges (6-8 Math Lessons – Algebra)
Students will solve expressions using an Algebra Balance from NLVM (National Library of Virtual Manipulatives)
http://nlvm.usu.edu/en/nav/vlibrary.html
Adding and Subtracting Fractions
5-6 Estimating Fraction Sums and Differences
5-7 Adding and Subtracting with Unlike Denominators
5-8 Adding and Subtracting Mixed Numbers
5-9 Renaming to Subtract Mixed Numbers
5-10 Solving Fraction Equations: Addition and Subtraction
Orangize Data
6-1 Make a Table
6-2 Range, Mean, Median, and Mode
6-3 Additional Data and Outliers
Display and Interpreting Data
6-4 Bar Graphs
6-5 Frequency Tables and Histograms
6-6 Ordered Pairs
6-7 Line Graphs
6-8 Misleading Graphs
6-9 Stem-and-Leaf Plots
Lines and Angles
7-1 Points, Lines, and Planes
7-2 Angles
7-3 Angle Relationships
7-4 Classifying Lines
Polygons
7-5 Triangles
7-6 Quadrilaterals
7-7 Polygons
7-8 Geometric Patterns
M.O.6.1.1
M.O.6.1.2
M.O.6.1.3
M.O.6.2.2
M.O.6.2.3
M.O.6.2.4
M.O.6.2.5
M.O.6.2.6
M.O.6.3.1
M.O.6.3.2
M.O.6.5.1
M.O.6.5.2
* Solve a proportion using cross multiplication (MA.6.2.5)
* Model addition, subtraction, multiplication, and division of integers (MA.6.2.7)
Negative integers are covered in Operations
* Collect, organize, display, and read data using appropriate graphs and tables. (MA 6.5.1)
* Interpret data using mean, median, mode, and range (MA6.5.2)
* Locate and plot points within the four quadrants. (MA.6.2.8) Found in Operations
When creating graphs, use date that will require the students to locate and plot points within the four quadrants, (i.e.Celsius temperature) Picturing Numbers
* Classify lines as parallel, intersecting, perpendicular, or skey
(MA.6.3.1)
* Locate and plot points within the four quadrants
(MA .6.2.8)
When working on the grid maps, locate and plot points within the 4 quadrants
Figuring All the Angles
* Determine the sum of measures of angles in polygons
(MA.6.3.2)
Fraction Times
* Multiply whole number by decimals C
* Compare rations and fractions B,C,E
* Use models for solving problems A,B involving ratio, proportion, percent and fractions ( a ratio table, percent bar, a double line, a calculator.)
Picturing Numbers
* Creating and interpreting bar graphs, pie graphs, pictographs, number line graphs, and line graphs. A,B,C,D
* Mean, median, and mode as measures of central tendency C
* Describe a distribution of data including minimum and maximum, and outliers. A,D
* Use date and graphs to build an argument. B,C,D
Figuring All the Angles
* Absolute and relative directions B,C,G
* Polar grids and rectangular grids B,D
* Use scale line as a representation on a map B,C,G
* Concept of an angle F
* Estimate angle measures B,C,G
* Define right, obtuse, acute, and straight angles
* Formal vocabulary and notations for angles and measures G
techSteps Sixth Grade Project -
Social Studies - "How Does Fair Food Fare?"
M.O.6.2.5
SchoolKit E314
Odyssey 6706
M.O.6.3.1
Odyssey 66948
M.O.6.3.2
Odyssey 5423
M.O.6.5.1
SchoolKit E64
Odyssey 56276
M.O.6.5.2
SchoolKit E312
Odyssey 5314
Tremendous Trees www.thesolutionsite.com/lesson/14151/treeslp.html
www.illuminations.nctm.org
BUNGEE BARBIE Lesson
http://standards.nctm.org/document/
eexamples/chap6/6.6/index.htm
www.thesolutionsite.com/lesson/17061/lesson1.html
7-10 Transformations
7-11 Symmetry
7-12 Tessellations
Ratios and Proportions
8-1 Ratio and Rates
8-2 Proportions
8-3 Proportions and Customary Measurement
8-4 Similar Figures
8-5 Indirect Measurement
8-6 Scale Drawings and
Maps
Percents
8-7 Percents
8-8 Percents, Decimals, and Fractions
8-9 Percent Problems
8-10 Using Percents
M.O.6.1.4
M.O.6.1.5
M.O.6.1.7
M.O.6.1.8
M.O.6.3.3
M.O.6.3.4
M.O.6.3.5
M.O.6.4.5
M.O.6.5.4
* Identify line symmetry and rotational symmetry in plane figures. (MA.6.3.5)
This can be addressed when looking at regulart polygons.
Figuring All the Angles
* Construct scale drawings (MA.6.4.6)
When using a scale line develop this concept. Then work on drawings using a scale.
Figuring All the Angles
* Bisect a line segment using a compass and straightedge (MA.6.3.3.)
* Draw and angle of a given measure (MA.6.3.4)
When drawing and measuring an angle, bisect a line segment and an angle.
Figuring All the Angles
* Identify and represent integers on a number line. (MA 6.1.4)
- fractions, decimals and %
* Find a % of a mumber (MA.6.1.8)
* Convert among fractions, mixed numbers, decimals, and % (MA.6.1.5)
* Use a variety of estimation strategies to solve problems with whole numbers, fractions, and decimals (MA.6.1.5)
* Solve problems in context involving all operations (addition, subtraction, multiplication, and division) of whole numbers, fractions, mixed numbers, and decimals (MA.6.2.7)
Figuring All the Angles
* Interior angles of polygons E
* Measure and draw angles G
See: Reallotment
More or Less
* Find sale price with discounts as a fraction or percent C,D
* Use multipllication to increase or decrease size by a percent D
* Use one and multiplication to find percent increase (e.g., 25% increase is x 1.25.) C
* Benchmark fractions are related to ratio, percents, and decimals B,C
Choose an appropriate model or tool to solve problems where fractions, decimals, percents, and ratios are involved. B,C,D
SEE: Models You Can Count On!
For Ratio Tables
techSteps Sixth Grade Project -
Social Studies - "Time Line"
M.O.6.1.4
Odyssey 6710
M.O.6.1.5
Odyssey 6656
M.O.6.1.8
SchoolKit E279
Odyssey 56287
M.O.6.3.3
Odyssey 56274
M.O.6.3.4
Odyssey 67249
M.O.6.3.5
Odyssey 56274
After predicting and exploring with actual manipulatives, use the NLVM (http://nlvm.usu.edu/en/nav/vlibrary.html ) to perform all 3 transformations (“Transformation” applets)
On the whiteboard, pull up www.mapquest.com and enter a random address. Use the map to introduce parallel, perpendicular, intersecting, and skew lines.
www.schools.ash.org.au/
“Symmetry at the Beach”
Introduction to the commutative, associative, and distributive properties with this site. http://home.europa.com/~paulg/
mathmodels/commutative.html
Practice: www.algebrahelp.com/worksheets/view/
simplifying/distributionquiz
Check work: (Expression Calculator) www.algebrahelp.com/calculators/expressionloops/
Integers
9-1 Understanding Integers
9-2 Comparing and Ordering Integers
9-3 The Coordinate Plane
Integer Operations
9-4 Adding Integers
9-5 Subtracting Integers
9-6 Multiplying Integers
9-7 Dividing Integers
9-8 Solving Integer Equations
Perimeter, Area, and Circumference
10-1 Finding Perimeter
10-2 Estimating and Finding Area
10-3 Break Into Simplier Parts
10-4 Comparing Perimeter and Area
10-5 Circles
Volume and Surface Area
10-6 Solid Figures
10-7 Surface Area
10-8 Finding Volume
10-9 Volume of Cylinders
M.O.6.4.5
* Model addition, subtractions, multiplication, and division of integers (MA. 6.2.7)
capacity/volume using metric customary systems (MA.6.4.5)
* Understand area and volume C,E
* Estimate and compute area of regular polygons and irregular shapes using transformations and area model. A,B,C,D
* Use nonstandart and standard units to measure and describe area C,D
* Measure length, area and volume in metric and US systems C,D
* Use a formulas to compute area of rectangles, parallelograms, triangles, and circles D
* Estimate and calculate perimeters of "shapes" C,D,E
* Relate area and volume E
* Compute volume by reshaping irregular figures E
* Relate volume and surface area. E
techSteps Sixth Grade Project -
Science - "Famous Person Plaque"
M.O.6.4.5
SchoolKit E314
Odyssey 56306
www.illuminations.nctm.org/lessondetail.aspx?1d=l259
Lesson – Blue Squares and Beyond
Understanding Probability
11-1 Introduction to Probability
11-2 Experimental Probability
11-3 Theoretical Probability
Using Probability
11-4 Make an Organized List
11-5 Compound Events
11-6 Making Predictions / Introduction to Functions
12-1 Tables and Functions
12-2 Graphing Functions
Coordinate Geometry
12-4 Graphing Translations
12-5 Graphing Reflections
12-6 Graphing Rotations
12-7 Stretching and Shrinking
M.O.6.1.7
M.O.6.2.2
M.O.6.2.3
M.O.6.5.2
M.O.6.5.4
* Determine the probability of given events and express that probability as a ratio (MA 6.5.2)
* Determine combinations, permutations and probabililty using sample spaces by: listing and tree diagrams. (MA 6.5.4)
* identify missing elements in arithmetic and geometric patterns. (MA.6.2.2)
* Identify, demonstrate, and apply the distributive, commmutative, associative, and identity properties (MA.6.1.7)
(Apply in Expressions and Formulas)
* Identify like terms and monomials
* Use input/output models and spreadsheets to evaluate functions (MA 6.2.3)
* Explore a variety of patterns
* Use variables to represent and solve real world problems appropriate for the 6th grade using multiple strategies (MA 6.2.9)
Take a Chance
* Understand the meaning of fair and how it relates to chance A,B
* Informal definition of chances and fair
* Estimate and order chances B
* Use repeated trials to estimate chance D
* Determine all possible outcomes and combinations using tree diagrams, and tables (make a list) B,D
* Express chance for simple and multiple events using percents, fractions, or ratios B,C
* Compare theoretical and experimental probabilities B
* Use visual models to estimate and calculate chance. B,D
See: Reallotment, and Figuring all the Angles, and Buildling Formulas
techSteps Sixth Grade Project -
Math - "Write a Research Report"
M.O.6.1.7
SchoolKit E348
Odyssey 56315
M.O.6.2.2
SchoolKit E318
Odyssey 56183
M.O.6.2.3
SchoolKit E324
Odyssey 67212
M.O.6.5.2
SchoolKit E494
Odyssey 67229
M.O.6.5.4
Odyssey 56266
http://standards.nctm.org/document/
eexamples/chap6/6.6/index.htm
Introduce vocabulary for combination and permutation using www.mathisfun.com and search combinations and permutations.
http://illuminations.nctm.org
Building Bridges