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Harrisburg School District
Math Pacing Guide
2010-2011
Grade 6
Connected Math 2
August and
September
Data About Us: Investigation 1, 2, & 3 and
Prime Time: Investigation 1
October
Prime Time: Investigation 2, 3, & 4 and
Bits and Pieces I: Investigation 1
November
Bits and Pieces I: Investigation 2, 3, & 4
December
Algebra and Numbers and Operations (supplemental materials)
How Likely Is It?: Investigation 1 & 2
January
Bits and Pieces II: Investigation 1, 2, 3, & 4
February
Shapes and Designs: Investigation 1, 2, 3, & 4 and
Bits and Pieces III: Investigation 1
March
Bits and Pieces III: Investigation 2, 3, 4.1, & 5.3 and
Covering and Surrounding: Investigation 1, 4, & 5.2
Elapsed Time (supplemental materials)
April
Review and PSSA Testing
Covering and Surrounding: Investigation 2, 3, & 5
May
How Likely Is It?: Investigation 3 & 4
Bits and Pieces III: Investigation 4 & 5
May and
June
Preview Pre-Algebra
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Harrisburg School District
Math Pacing Guide
2010-2011
Grade 6
Connected Math 2
Suggested Time Frame
August 30-September 3
Resources
DATA ABOUT US
Investigation 1: Looking at Data
Introduce Unit and Unit Project
1.1 Organizing and Interpreting Data
1.2 Useful Statistics
September 7-13
September 14-20
1.3 Experimenting With Median
1.4 Using Different Data Types (Intro to 1.5)
1.5 Vertical and Horizontal Bar Graphs
Math Reflections and Assessment
Investigation 2: Using Graphs to Explore
Data
2.1 Traveling to School
2.3 Relating Height to Arm Span
2.4 Relating Travel Time to Distance
Math Reflections and Assessment
Investigation 3: What Do We Mean by
Mean
3.1 Finding the Mean
3.2 Data With the Same Mean
3.3 Using the Mean
Math Reflections and Assessment
Unit Project
Anchors
M6.E.1.1.1
M6.E.1.1.2
M6.E.1.1.1
M6.E.1.1.2
M6.E.2.1.1
M6.E.1.1.3
Topics and Concepts
line plots and bar graphs
mode, median, tables, line plots
median
categorical or numerical data
bar graphs, numerical and categorical bar
graphs
M6.E.1.1.1
M6.C.3.1.1
M6.C.3.1.1
stem-and-leaf plot
paired values on coordinate graphs
scatter plot
M6.E.2.1.1
Mean
M6.E.2.1.1
Mean
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Suggested Time Frame
September 21-28
September 29-October 1
October 4-8
Resources
PRIME TIME
Investigation 1: Factors and Products
Introduce Unit and Unit Project
1.1 Playing the Factor Game
1.2 Playing to Win
1.3 Playing the Product Game
Math Reflections and Assessment
Investigation 2: Whole-Number Patterns
and Relationships
2.1 Finding Patterns
2.2 Reasoning with Even and Odd Numbers
(optional)
2.3 Classifying Numbers
Math Reflections and Assessment
Investigation 3: Common Multiples and
Common Factors
3.1 Riding Ferris Wheels
3.2 Looking at Cicada Cycles
3.3 Bagging Snacks
3.4 Planning a Picnic
October 12-15
Math Reflections and Assessment
Investigation 4: Searching for Factor
Strings
4.1 The Product Puzzle
4.2 The Longest Factor String
(Supplement Exponents)
Anchors
Topics and Concepts
M6.A.1.3
M6.A.1.3.3
M6.A.1.3.3
M6.D.2.2
M6.A.1.3
Factors
M6.A.1.3
M6.A.2.1.1
prime, composite and square , factor pairs
Conjectures
M6.D.1.1
common factors and common multiples
M6.A.1.3.2
M6.A.2.1
M6.A.1.3.2
M6.A.2.1
M6.A.1.3.1
M6.A.2.1
M6.D.2.1
M6.D.2.2
M6.A.1.3.1
M6.A.2.1
M6.D.2.1
M6.D.2.2
common multiples
M6.A.1.3
M6.A.1.1.3
prime factorization
exponents
Factors
Multiples
LCM
common factors
factors
GCF
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Suggested Time Frame
October 18-22
Resources
(Prime Time continued)
4.3 Using Prime Factorization
Math Reflections and Assessment
Investigation 5: Putting It All Together
5.1 The Locker Problem (optional)
Unit Project
October 25-October 29
BITS AND PIECES I
Investigation 1: Fundraising Fractions
Introduce Unit
1.1 Reporting Progress
1.2 Folding Fraction Strips (2 days)
1.3 Measuring Progress
1.4 Comparing Classes
November 1-5
November 8-15
Math Reflections and Assessment
Investigation 2: Sharing and Comparing
With Fractions
2.1 Equivalent Fractions and Equal Shares
2.2 Finding Equivalent Fractions
2.3 Comparing Fractions to Benchmarks
2.4 Fractions Between Fractions (optional)
(Supplement Ordering and Comparing
Fractions)
2.5 Naming Fractions Greater Than 1
Math Reflections and Assessment
Investigation 3: Moving Between Fractions
and Decimals
3.1 Making Smaller Parts
3.2 Making Even Smaller Parts
Anchors
M6.A.1.3.1
M6.A.1.3.2
Topics and Concepts
GCG, LCM
M6.D.1.1
M6.A.1.2.1
using prior knowledge, fraction/percent
M6.A.1.2.1
numerator/denominator,
equivalent fractions
part-to-whole relationships
M6.A.3.2.1
M6.A.1.4.1
M6.A.1.2.1
M6.A.1.4.1
considering the size of whole when
comparing fractions
M6.A.1.2.1
M6.A.1.2.1
M6.A.1.1.4
M6.A.1.2.1
M6.A.1.2.1
partitions and equivalent fractions
equivalent fractions
ordering fractions from 0-1 ½
M6.A.1.1.4
M6.A.1.2.1
mixed numbers
M6.A.1.1.2
M6.A.1.1.2
converting fractions to decimals
decimal place value
ordering and comparing fractions
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Suggested Time Frame
November 16-19
November 22-24
Resources
(Bits and Pieces I continued)
3.3 Decimal Benchmarks
3.4 Moving From Fractions to Decimals
3.5 Ordering Decimals
Math Reflections and Assessment
Investigation 4: Working With Percents
4.1 Who’s The Best
(optional)
4.2 Choosing the Best
4.3 Finding a General Strategy
4.4 Changing Forms
Anchors
Topics and Concepts
M6.A.1.4.1
M6.A.1.1.2
M6.A.1.2.1
modeling decimals, estimating
relate fractions to division
ordering and comparing decimals
M6.A.1.1.1
percent of a scaled whole
M6.A.1.1.1
M6.A.1.1.1
M6.A.1.1.2
M6.A.1.1.1
M6.A.1.1.2
comparing situations using percent
connecting fractions, decimals and
percents
converting between fractions decimals
and percents
creating and extending patterns (tables)
determining the rule for a pattern
identifying inverse operations and solving
equations
matching equations or expressions to
math situations
identifying properties (associative,
commutative, distributive, identity)
solving problems using the order of
operations
Math Reflections and Assessment
November 30 - December 3
Algebra
Numbers and Operations
Supplemental Material
Supplemental Material
Supplemental Material
December 6-10
Supplemental Material
M6.D.1.1.1
M6.D.1.2.1
M6.D.2.1.1
M6.D.2.1.2
M6.D.2.2.1
Supplemental Material
M6.A.2.1.1
Supplemental Material
M6.A.2.1.1
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Suggested Time Frame
December 13-17
Resources
How Likely Is It
Investigation 1: A First Look at Chance
Introduce Unit
1.1 Choosing Cereal
1.2 Tossing Cups (optional)
1.3 One More Try (optional)
1.4 Analyzing Events
Investigation 2: Experimental and
Theoretical Probability
2.1 Predicting to Win
2.2 Exploring Probabilities
December20-22
2.3 Winning the Bonus Prize
2.4 Pondering Possible and Probable
Anchors
Topics and Concepts
M6.E.1.1.1
M6.E.3.1.1
M6.E.1.1.1
M6.E.3.1.1
M6.E.1.1.1
M6.E.3.1.1
M6.E.3.1.1
introducing probability
M6.E.3.1.1
M6.E.3.1.1
theoretical probability
properties of probability
(and/or)
tree diagrams
fair and unfair
likely and not likely
M6.E.3.1.2
M6.E.3.1.1
M6.E.3.1.2
experimental probability
fair and unfair
equally likely and not equally likely
Math Reflections and Assessment
January 3-7
Bits and Pieces II
Investigation 1: Estimating With Fractions
Introduce Unit
1.1 Getting Close
1.2 Estimating Sums
Math Reflections and Assessment
Investigation 2: Adding and Subtracting
Fractions
2.1 Land Sections
2.2 Visiting the Spice Shop
(May substitute spices with more common
ingredients)
M6.A.3.1.1
M6.A.3.2.1
M6.A.3.1
M6.A.3.2.1
estimating decimals and fractions
M6.A.1.3.2
M6.A.3.2.1
M6.A.3.2.1
developing strategies for adding and
subtracting fractions
creating equations using fractions
estimating sums
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Suggested Time Frame
January 10-14
January 18-24
January 25-28
January 31 -February 7
Resources
(Bits and Pieces II continued)
2.3 Just the Facts
2.4 Designing Algorithms for Addition and
Subtraction
Math Reflections and Assessment
Investigation 3: Multiplying With
Fractions
3.1 How Much of the Pan Have We Sold
3.2 Finding a Part of a Part
3.3 Modeling More Multiplication Situations
Anchors
Topics and Concepts
M6.A.3.2.1
M6.A.1.3.2
M6.A.3.2.1
fractional fact families
developing strategies for adding and
subtracting fractions and mixed numbers
M6.A.3.1
M6.A.3.2.1
M6.A.3.2.1
3.4 Changing Forms
M6.A.3.2.1
3.5 Writing a Multiplication Algorithm
Math Reflections and Assessment
Investigation 4: Dividing With Fractions
4.1 Preparing Food
4.2 Fund Raising Continues
4.3 Summer Work
4.4 Writing a division algorithm
Math Reflections and Assessment
M6.A.3.2.1
using models to estimate fraction products
finding a fraction of a fraction
using models to estimate multiplying
fractions and mixed numbers
developing strategies for multiplying
fractions and whole numbers
solving fraction multiplication problems
M6.A.3.2.1
M6.A.3.2.1
M6.A.3.2.1
M6.A.3.2.1
whole number divided by a fraction
fraction divided by a whole number
fraction divided by a fraction
solving fraction division problems
M6.C.1.1.1
M6.C.1.1.2
classifying polygons
Shapes and Designs
Investigation 1: Bees and Polygons
Introduce Unit and Unit Project
1.1 Sorting Shapes
(Identify triangles by sides and angles)
1.2 Symmetries of Shapes
(not assessed)
1.3 Tiling a Beehive
(not assessed)
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Suggested Time Frame
February 8-14
February 15-18
Resources
(Shapes and Designs continued)
Investigation 2: Polygons and Angles
2.1 Understanding Angles
2.2 Developing Angle Benchmarks
(Relate angles to triangles)
2.3 Using an Angle Ruler
(Introduce Protractor)
2.4 Analyzing Measurement Errors
(optional)
2.5 Angles and Parallel Lines
Math Reflections and Assessment
Investigation 3: Polygon Properties and
Tiling
3.1 Angle Sums of Regular Polygons
3.2 Angle Sums of Any Polygon
3.3 Back to the Bees (not assessed)
3.4 Exterior Angles of Polygons
(not assessed)
Math Reflections and Assessment
Investigation 4: Building Polygons
4.1 Building Triangles (optional)
4.2 Building Quadrilaterals (optional)
4.3 The Quadrilateral Game (optional)
Unit Project
Anchors
Topics and Concepts
M6.C.1.2.2
M6.B.2.3.1
estimating angle sizes
comparing angles
M6.B.2.1.3
measuring angles
M6.C.1.2.1
M6.C.1.2.2
intersecting and parallel lines
M6.C.1.1.4
M6.C.1.1.4
relationship between sides and angles
angle sums
constructing triangles
constructing quadrilaterals
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Suggested Time Frame
February 22-25
February 28 - March 4
March 7-11
Resources
Bits and Pieces III
Investigation 1: Decimals-More or Less
Introduce Unit
1.1 About How Much
1.2 Adding and Subtracting Decimals
1.3 Using Fractions to Add and Subtract
Decimals (optional or combine with 1.2 or
1.4)
1.4 Decimal Sum and Difference Algorithms
Math Reflections and Assessment
Investigation 2: Decimal Times
2.1 Relating Fraction and Decimal
Multiplication
2.2 Missing Factors (optional)
2.3 Finding Decimal Products
2.4 Factor-Product Relationships
Math Reflections and Assessment
Investigation 3: The Decimal Divide
3.1 Deciphering Decimal Situations
3.2 The Great Equalizer
(Getting Ready)
3.3 Exploring Dividing Decimals
3.4 Representing Fractions as Decimals
Math Reflections and Assessment
Investigation 4: Using Percents
4.1 Determining Tax
Investigation 5: More About Percents
5.3 Making Circle Graphs
Math Reflection and Assessment
Concepts not assessed in 6th grade will be
taught following PSSA testing.
Anchors
Topics and Concepts
M6.A.1.2.1
M6.A.3.1.1
M6.A.3.2.1
M6.A.3.2.1
estimating decimal sums
M6.A.3.2.1
solving decimal addition and subtraction
problems
M6.A.3.1.1
M6.A.3.2.1
M6.A.3.1.1
M6.A.3.1.1
estimating and solving decimal
multiplication
solving decimal equations
estimating decimal products
placing the decimal point
M6.A.3.2.1
M6.A.3.2.1
choosing an operation
terminology
M6.A.112
dividing decimals
terminating and repeating decimals
M6.A.1.1.1
converting decimals to percents
M6.A.1.4.1
creating a circle graph
adding and subtracting decimals
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March 14-18
Review and PSSA Testing
March 21-25
Review and PSSA Testing
Suggested Time Frame
April 4-8
April 11-15
Resources
Covering and Surrounding
Investigation 1: Designing Bumper Cars
1.1 Designing Bumper Car Rides
1.2 Pricing Bumper Car Rides
1.3 Decoding Designs
Math Reflections and Assessment
Investigation 4: Measuring Parallelograms
4.1 Finding Measures of Parallelograms
Topics and Concepts
M6.B.2.2.1
M6.B.2.2.1
M6.B.2.2.1
experimenting with area and perimeter
experimenting with area and perimeter
area and perimeter formulas
M6.B.2.2.1
M6.B.2.2
M6.B.2.2.1
M6.B.2.2
M6.B.2.2.1
M6.B.2.2
M6.B.2.2.1
M6.B.2.2
area and perimeter
M6.B.2.1.1
M6.C.1.1.3
circumference of a circle
(Supplemental) Determine time to the minute
M6.B.1.1.1
elapsed time
Covering and Surrounding (revisited)
Investigation 2: Changing Area, Changing
Perimeter
2.1.Building Storm Shelters
M6.B.2.2
fixed area
4.2 Parallelograms From Triangles
4.3 Designing Parallelograms Under
Constraints
4.4 Parks, Hotels, and Quilts
Investigation 5: Measuring Irregular
Shapes and Circles
5.2 Surrounding a Circle
(Focus on terms, finding radius and finding
diameter, and using a ruler.)
Reflections and Assessment
(4 & 5.2)
Concepts not assessed in 6th grade will be
taught following PSSA testing.
March 28- April 1
Anchors
relationship of triangles, rectangles, and
parallelograms
solving area and perimeter problems
solving area and perimeter problems
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Suggested Time Frame
April 18-27
April 28- May 3
May 4-11
May 12-17
2.2 Stretching the Perimeter
Resources
(Covering and Surrounding continued)
2.3 Fencing in Spaces
2.4 Adding Tiles to Pentaminos
Reflections and Assessment
Investigation 3: Measuring Triangles
3.1 Triangles on Grids
3.2 More Triangle
3.3 What’s the Area?
3.4 Designing Triangles Under Constraints
Reflections and Assessment
Investigation 5: Measuring Irregular
Shapes and Circles
5.1 Measuring Lakes
(optional)
5.3 Pricing Pizzas
5.4 “Squaring” a Circle
Math Reflections and Assessment
How Likely Is It (revisited)
Investigation 3: Making Decisions With
Probability
3.1 Designing A Spinner
3.2 Making Decisions
3.3 Scratching Spots
Math Reflections and Assessment
Investigation 4: Probability, Genetics, and
Games
4.1 Genetic Traits
4.2 Tracing Traits
4.3 Roller Derby
Math Reflections and Assessment
M6.B.2.2
Anchors
fixed area
M6.B.2.2.1
fixed perimeter
area and perimeter of non-rectangular
figures
M6.B.2.2
M6.B.2.2
M6.B.2.2
area of a triangle
area of a triangle
triangle families using triangle families
M6.B.2.2
area and perimeter of irregular figures
M6.B.2.2
M6.B.2.2
estimating area of a circle
formula for area of a circle
M6.E.3.1.1
M6.E.3.1.1
M6.E.3.1.1
probability
analyze probability
experimental and theoretical probability
M6.E.3.1.1
M6.E.3.1.1
M6.E.3.1.1
experimental probability
theoretical probability
experimental and theoretical probability
Topics and Concepts
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Suggested Time Frame
May 18-20
May 23-June 9
Resources
Bits and Pieces III (revisited)
Investigation 4: Using Percents
4.2 Computing Tips
4.3 Finding Bargains
Investigation 5: More About Percents
5.1 Clipping Coupons
5.2 How Much Can We Spend
Math Reflections and Assessment
Anchors
Topics and Concepts
M8.A.2.2
M8.A.2.2
using percents
using percents
M8.A.2.2
M8.A.2.2
using percents
using percents
Supplemental Materials
Supplemental Materials
M6.D.2.1.2
M6.A.2.1
M8.A.3.3.1
M8.A.3.3.1
Supplemental Materials
M8.A.3.3.1
Supplemental Materials
Supplemental Materials
M6.D.1.1.1
M6.D.1.2.1
M8.A.3.3.1
reviewing expressions, equations, and
order of Operations
introducing negative numbers
ordering negative numbers on a number
line
adding and subtracting positive and
negative integers
reviewing patterns and rules
Supplemental Materials
M6.C.3.1
Preview Pre-Algebra
Supplemental Materials
multiplying and dividing positive and
negative numbers
plotting numbers on the coordinate plane
in 4 quadrants using ordered pairs
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Notes