math curriculum modules skills standards

8/3/2019 Math Curriculum Modules Skills Standards

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Module Unit Section Standard Skills

Module 1Prime Time

Introduction Introduction 6.2.2.1: TG p. 5

Investigation 1Factors and Products

1.1 Playing theFactor Game

6.1.1.5: SE pp. 6-11TG pp. 16-24

Become familiar with the factors of the numbersfrom 2 to 30

Review multiplication and division of smallwhole numbers.

Begin to recognize

the difference between prime numbers andcomposite numbers.

Relate dividing and finding factors of a number.

1.2 Playing to Winthe Factor Game

6.1.1.5: SE pp. 6-11TG pp. 16-24

Classify numbers as prime or composite

Recognize that some numbers are rich infactors, while others have few factors

Review multiplication facts

1.3 Playing theProduct Game

6.1.1.5: SE pp. 6-11

Develop understanding of factors and multiplesand relationships between them.

Understand that some products are the result ofmore than one factor pair

Review multiplication facts

Homework6.1.1.5: TG pp. 31-346.3.3.1: SE pp. 17-18

TG pp. 32

Reflections

Investigation 2Whole-NumberPatterns andRelationships

2.1 Finding Patterns 6.2.2.1: SE pp. 23

Recognize that factors come in pairs and thatonce one factor is found, another can also befound

Visualize and represent a factor pair as thedimensions of a rectangle

Determine whether a number isprime/composite, square/non-square, andeven/odd based on its factor pairs

Develop an informal sense of what factors mustbe checked to be sure all the factors of a numberare found

2.2 Reasoning withEven and OddNumbers

Make conjectures about the result of operations

on odd numbers, on even numbers, and oncombinations of odd and even numbers, andcreate arguments to show which conjectures arevalid and which are not.

Determine whether a product is even or oddbased on its factors

Determine whether a sum is even or odd basedon its addends.

2.3 ClassifyingNumbers

6.2.2.1: SE pp. 266.1.1.6: SE pp. 26-29

Classify numbers by their characteristics usingVenn diagrams as a tool for sorting andclassifying.

Develop understanding of factors and multiples,common factors and common multiples, and therelationships among them

Homework6.2.2.1: SE pp. 31, 356.1.1.6: SE pp. 31-32, 34

Reflections

Investigation 3

Common Multiplesand Common Factors

3.1 Riding FerrisWheels 6.1.1.6: TG pp. 53-73

Recognize situations in which finding commonmultiples of whole numbers is important.

Develop strategies for finding common

multiplesObserve patterns in common multiples ofnumbers and use the patterns to reason aboutand predict future occurrences and solveproblems.


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3.2 Looking atCicada Cycles

6.1.1.6: TG pp. 53-73

Recognize situations in which finding commonmultiples of whole numbers is important

Develop strategies for finding the least commonmultiple

Observe patterns in common multiples ofnumbers and use the patterns to reason aboutand predict future occurrences and solveproblems

3.3 Bagging Snacks 6.1.1.6: TG pp. 53-73

Recognize situations in which finding commonfactors of whole numbers is important

Begin to develop strategies for finding commonfactors

Observe patterns in common factors of numbersand use the patterns to reason about and predictfuture occurrences and solve problems

3.4 Planning aPicnic

6.1.1.6: TG pp. 53-73

Recognize situations in which finding common

factors of whole numbers is important.Develop strategies for finding common factorsand, in particular, the greatest common factor.

Recognize when common factors and greatestcommon factors are helpful in solvingproblems.

Homework

Reflections

Investigation 4Factorizations:

SEarchingFor Factor Strings

4.1 The ProductPuzzle

Find factorizations of numbers and then breakthem down into prime factorizations

Understand that prime numbers are the essentialmultiplicative building blocks for wholenumbers

4.2 Finding theLongest String

Develop a systematic strategy for finding primefactorizations

Recognize that a number may have severaldifferent factorizations but, except for order,each whole number greater than 1 has exactlyone factorization into a product of primenumbers

4.3 Using PrimeFactorizations

Understand that prime numbers are the essentialmultiplicative building blocks for wholenumbers

Find common factors, greatest common factors,common multiples, and least common multiplesusing prime factorizations.

Homework

Reflections

Investigation 5Putting It All Together

5.1 Unraveling theLocker Problem

Use the multiplicative structure of numbers,such as primes, composites, factors, multiples,and square numbers, to reason mathematicallyand to solve interesting problems

Simulate a problem, gather data, makeconjectures, and create arguments to justifythose conjectures

Communicate ones mathematical ideas clearly

Homework

Reflections

Unit Project Unit Project

Module 2Bits and Pieces I

Introduction IntroductionInvestigation 1Fundraising Fractions

1.1 ReportingProgress

6.1.2.2: SE pp. 5-18TG pp. 15-43

Assess fraction knowledge students bring frompast experiences.


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1.2 Folding FractionStrips

6.1.2.2: SE pp. 5-18TG pp. 15-43

Develop strategies to partition fraction strips forhalves, thirds, fourths, fifths, sixths, eighths,ninths, tenths, and twelfths

Explore the role of the numerator and thedenominator and the part-to-whole nature offractions

Investigate equivalent fractions that result fromdifferent partitioning strategies

1.3 MeasuringProgress

6.1.2.2: SE pp. 5-18TG pp. 15-43

Understand the role of the numerator and thedenominator in a fraction and the part-to-wholenature of fractions

Use fractions to represent part-to-wholerelationships

Begin to use fractions to find fraction parts ofwhole number quantities

1.4 ComparingClasses

6.1.2.2: SE pp. 5-18TG pp. 15-43

Understand the need to consider the size of the

whole when comparing fraction amountsBegin to reason with fractions greater than one

Homework6.1.2.2: SE pp. 5-18

TG pp. 15-43

Reflections 6.1.2.2: SE pp. 5-18

Investigation 2Sharing andComparing WithFractions

2.1 EquivalentFractions andEqual Shares

6.1.1.4: SE pp. 19-23, 26-29, 31-346.1.1.7: SE pp. 19-23, 26-29, 31-34

Recognize the role of the numerator anddenominator when partitioningthat the size of

the partition is different but we may need moreor fewer partitions to create an equal

amount

Use fractions as operators to find the actualmeasure of a fraction length of a whole

Understand the need to consider the size of thewhole when comparing fractions

2.2 FindingEquivalentFractions

6.1.1.1: SE pp. 22, 25, 30, 32-336.1.1.4: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-766.1.1.7: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-76

Understand that a place on a number line canhave more than one fraction name

Recognize that fractions can represent alocation on a number line and the length fromone point to another on a number line

Develop strategies for finding equivalent

fractions

2.3 ComparingFractions toBenchmarks

6.1.3.4: SE pp. 23, 336.1.3.5: SE pp. 23

TG pp. 57, 616.1.1.4: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-766.1.1.7: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-766.1.1.2: SE pp. 23-25, 29-30, 33, 34

TG pp. 57-62

Use benchmarks to estimate the size of fractionsand compare fractions

Develop strategies for comparing and orderingfractions

2.4 FractionsBetweenFractions

6.1.1.1: SE pp. 22, 25, 30, 32-336.1.1.2: SE pp. 23-25, 29-30, 33, 34

Develop a strategy for finding a fractionbetween any two given fractions

Begin to recognize that by using smallerpartitions one can always find a fractionbetween two given fractions.

2.5 NamingFractionsGreater Than

One

6.1.2.1: SE pp. 27TG pp. 72

6.1.1.4: SE pp. 19-23, 26-29, 31-34TG pp. 51-59, 61-62, 67-69, 71-72, 73-76

6.1.1.7: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-766.1.1.2: SE pp. 23-25, 29-30, 33, 346.1.1.1: TG pp. 68, 74-76

Understand the underlying structure of fractionsgreater than one

Develop meaningful strategies for representingfraction amounts larger than one as both mixed

numbers and improper fractions

Build understanding of fractions as numbersthat measure lengths between whole numbers


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Homework

6.1.1.1: SE pp. 22, 25, 30, 32-33TG pp. 68, 74-76

6.1.1.2: SE pp. 23-25, 29-30, 33, 346.1.1.4: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-766.1.1.7: SE pp. 19-23, 26-29, 31-34

TG pp. 51-59, 61-62, 67-69, 71-72, 73-766.1.3.4: SE pp. 23, 33

TG pp. 756.2.2.1: SE pp. 336.2.3.2: SE pp. 33

TG pp. 75

Reflections

6.1.1.4: SE pp. 19-23, 26-29, 31-34TG pp. 51-59, 61-62, 67-69, 71-72, 73-76

6.1.1.7: SE pp. 19-23, 26-29, 31-34TG pp. 51-59, 61-62, 67-69, 71-72, 73-76

6.1.1.2: SE pp. 23-25, 29-30, 33, 34

Investigation 3Moving BetweenFractions andDecimals

3.1 Making SmallerParts

Understand relationship between tenths andhundredths including how tenths are partitionedto create hundredths

Represent decimals as fractions withdenominators of ten and one hundred

Move between fraction strip models, gridmodels, and numerical forms for both fractionand decimal numbers

3.2 Moving EvenSmaller Parts

Read and write fractions and decimal numbers

Extend understanding of fractions and decimalsto include place values greater than hundredths

Develop ways to find a decimal between anytwo given decimals

3.3 DecimalBenchmarks

Represent fractions and decimals with

hundredths grids

Use these representations to find approximate orexact decimal equivalents for fractionbenchmarks

3.4 Moving From

Fractions toDecimals

6.3.3.1: SE pp. 44TG pp. 97, 99

Recognize fractions as indicated division

problemsUnderstand why division is an appropriateinterpretation of a fraction

3.5 OrderingDecimals

6.1.2.3: SE pp. 46TG p. 101

Use the decimal place-value system to interpret,

compare, and order decimals

Connect understanding of decimals as fractionsto the interpretation of decimals as an extensionof the place-value system

Develop strategies for comparing and orderingdecimals

Homework

Reflections

Investigation 4Working WithPercents

4.1 Whos the Best

6.1.1.3: SE pp. 54-68TG pp. 112-135

6.1.3.3: SE pp. 54-68TG pp. 112-135

Introduce percents as a part-whole relationshipwhere the whole is not out of 100 but scaled to

be out of 100

Use fraction partitioning and fractionbenchmarks to make sense of percents

4.2 Choosing the

Best

6.1.1.3: SE pp. 54-68TG pp. 112-135

6.1.3.3: SE pp. 54-68TG pp. 112-135

Develop strategies, including percents, to use in

comparisons where the whole is less than 100

Understand that comparing situations with

different numbers of trials is difficult unless weuse percents or some other form of equivalent

representation

4.3 Finding aGeneral Strategy

6.1.1.3: SE pp. 54-68TG pp. 112-135

6.1.3.3: SE pp. 54-68TG pp. 112-135

Work with situations where the whole issometimes greater than 100 and sometimes lessthan 100

Develop connections between fractions,decimals, and percents

Develop strategies for expressing data inpercent form


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3.3 Back to theBees!

Decide which regular polygons will tile bythemselves or in combinations usinginformation about interior angles

3.4 Exterior Anglesof Polygons

Explore the sum of the exterior angles of apolygon

Homework

6.1.3.4: SE pp. 67TG pp. 80

6.2.1.2: SE pp. 55, 57, 67-68TG pp. 64-66, 68, 70, 80-81

6.2.3.1: SE pp. 55, 68-69

Reflections6.2.1.1: SE pp. 55, 68-696.2.3.1: SE pp. 55, 68-69

Investigation 4Building Polygons

4.1 Building

Triangles

Build triangles given three side lengths

Decide whether any three lengths will make atriangle

Find that the sum of two side lengths of atriangle must be greater than the third sidelength

4.2 BuildingQuadrilaterals

Build quadrilaterals given four side lengths

Decide whether any four side lengths will makea quadrilateral

Find that the sum of three side lengths of aquadrilateral must be greater than the fourthside length

4.3 TheQuadrilateralGame

Use the properties of quadrilaterals to buildspecific quadrilaterals.

Homework

Reflections


Module 4Bits and Pieces II

Introduction Introduction6.2.2.1: TG p. 8-96.1.3.4: TG pp. 3-12

Investigation 1Estimating WithFractions

1.1 Getting Close 6.1.1.2: TG pp. 20, 23-24Use benchmarks and decimal-fractionrelationships to develop estimation strategies forfinding fraction and decimal sums

1.2 Estimating Sums

6.1.3.5: SE pp. 8-11, 15TG pp. 25-30, 31-33

6.3.3.2: SE pp. 8-11TG pp. 30

Use estimation skills in contextual situationswhere an exact answer is not needed to make aninformed decision

Make decisions about whether an overestimateor an underestimate will suffice

Homework

6.1.1.1: SE pp. 12, 14TG pp. 32-33

6.1.1.2: SE pp. 13-146.1.2.2: SE pp. 12

TG pp. 326.1.1.3: SE pp. 12

TG pp. 326.1.1.4: SE pp. 12-13

TG pp. 32-336.1.1.7: SE pp. 12-13

TG pp. 32-336.1.2.4: SE pp. 12

TG pp. 326.1.3.3: SE pp. 12

TG pp. 32

6.1.3.5: SE pp. 8-11, 15TG pp. 25-30, 31-33

6.3.3.2: SE pp. 8-11

Reflections6.1.3.5: SE pp. 8-11, 156.3.3.2: SE pp. 8-11


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Investigation 2Adding andSubtracting Fractions

2.1 Land Sections

6.1.2.1: SE pp. 18-19, 24-25, 28-29TG pp. 34-58

6.1.3.1: SE pp. 16-31TG pp. 34-58

6.1.3.4: SE pp. 16-316.3.3.1: SE pp. 17

TG pp. 35

Use number sentences to express sums anddifferences

Develop strategies for adding and subtractingfractions

Explore the use of fractions as operators (e.g.2/3 of 640 acres)

2.2 Visiting theSpice Shop

6.1.2.1: SE pp. 18-19, 24-25, 28-29TG pp. 34-58

6.1.3.1: SE pp. 16-31TG pp. 34-58

6.1.3.4: SE pp. 16-316.2.3.2: TG pp. 41-506.2.1.1: TG pp. 43, 46, 48-50, 566.2.3.1: TG pp. 43, 46-50, 56

Write number sentences to represent situationsfor adding and subtracting fractions and mixednumbers

Develop strategies for adding and subtractingfractions and mixed numbers

2.3 Just the Facts

6.1.3.1: SE pp. 16-31TG pp. 34-58

6.1.3.4: SE pp. 16-316.2.1.1: SE pp. 21-22, 26-27, 29

TG pp. 43, 46, 48-50, 566.2.2.1: SE pp. 21-22, 26-27, 296.2.3.1: SE pp. 21-22, 24, 26-27, 29

TG pp. 43, 46-50, 566.2.3.2: SE pp. 21-22, 26-27, 29

TG pp. 41-506.1.2.1: TG pp. 34-58

Explore the inverse relationship between theaddition and subtraction of fractions

Develop and use efficient strategies for addingand subtracting fractions and mixed numbers

2.4 DesigningAlgorithms forAddition andSubtraction

6.1.3.1: SE pp. 16-31TG pp. 34-58

6.1.3.4: SE pp. 16-316.2.1.1: SE pp. 21-22, 26-27, 296.2.2.1: SE pp. 21-22, 26-27, 296.2.3.1: SE pp. 21-22, 24, 26-27, 296.2.3.2: SE pp. 21-22, 26-27, 296.1.2.1: TG pp. 34-58

Develop an efficient algorithm for adding andsubtracting fractions

Homework

6.1.2.3: SE pp. 29TG pp. 57

6.1.3.1: SE pp. 16-31

TG pp. 34-586.1.3.4: SE pp. 16-316.2.2.1: SE pp. 21-22, 26-27, 296.2.3.1: SE pp. 21-22, 24, 26-27, 29

TG pp. 43, 46-50, 566.2.3.2: SE pp. 21-22, 26-27, 296.1.2.1: TG pp. 34-586.2.1.1: TG pp. 43, 46, 48-50, 56

Reflections

6.1.3.1: SE pp. 16-31TG pp. 34-58

6.1.3.4: SE pp. 16-316.2.1.1: SE pp. 21-22, 26-27, 296.1.2.1: TG pp. 34-58

Investigation 3

Multiplying WithFractions

3.1 How Much ofthe Pan HaveWe Sold?

6.1.3.2: SE pp. 32-47TG pp. 59-88

Estimate products of fractions

Use models to represent the product of twofractions

Understand that finding a fraction ofa numbermeans multiplication

3.2 Finding a Part of

a Part

6.1.3.2: SE pp. 32-47

TG pp. 59-88


Use models to represent the product of twofractions

Understand that finding a fraction ofa numbermeans multiplication

3.3 Modeling MoreMultiplicationSituations

6.1.3.2: SE pp. 32-47TG pp. 59-88


Develop and use strategies and models formultiplying combinations of fractions, wholenumbers, and mixed numbers to solve problems

Determine when multiplication is an appropriateoperation


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3.4 Changing Forms6.1.3.2: SE pp. 32-47

TG pp. 59-88

Explore the relationships between two numbersand their product

Develop and use algorithms for multiplyingcombinations of fractions, whole numbers, andmixed numbers

3.5 Writing aMultiplicationAlgorithm

6.1.3.2: SE pp. 32-47TG pp. 59-88

Develop and use an efficient algorithm to solveany fraction multiplication problem

Homework

6.1.3.2: SE pp. 32-47TG pp. 59-88

6.3.1.2: SE pp. 42TG pp. 86

Reflections6.1.3.2: SE pp. 32-47

TG pp. 59-88

Investigation 4Dividing WithFractions

4.1 Preparing Food

Use models to represent a whole numberdivided by a fraction

Develop and use strategies for dividing a wholenumber by a fraction

Understand when division is an appropriateoperation

4.2 FundraisingContinues

Use models to represent a fraction divided by awhole number

Develop and use strategies for dividing afraction by a whole number


4.3 Summer Work

Use models to represent a fraction divided by afraction

Develop and use strategies for dividing afraction by a fraction


4.4 Writing aDivisionAlgorithm

Develop an efficient algorithm to solve anyfraction division problem

Explore the inverse operations of multiplicationand division

HomeworkReflections


Module 5Covering andSurrounding

Introduction Introduction

Investigation 1Designing BumperCars

1.1 DesigningBumper CarRides

6.3.1.2: SE pp. 5-18TG pp. 17-36

Learn that the area of a figure is the number ofsquare units needed to cover it

Learn that the perimeter of an object is thenumber of units of length needed to surround it

1.2 Pricing BumperCar Rides

6.3.1.2: SE pp. 5-18TG pp. 17-36

Learn that the area of a figure is the number ofsquare units needed to cover it

Learn that the perimeter of an object is thenumber of units of length needed to surround it

Understand that two figures with the same areamay have different perimeters

1.3 DecodingDesigns

6.3.1.2: SE pp. 5-18TG pp. 17-36

Use the relationship between length and widthto develop formulas for the area and perimeterof a rectangle

Homework

6.3.1.2: SE pp. 5-18TG pp. 17-36

6.1.3.4: SE pp. 13-17TG pp. 34-366.2.2.1: SE pp. 15

TG pp. 356.3.3.1: SE pp. 15-17

TG pp. 35-36

Reflections

6.3.1.2: SE pp. 5-18TG pp. 17-36

6.1.3.4: TG pp. 34-366.3.3.1: TG pp. 35-36


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Investigation 2Changing Area,Changing Perimeter

2.1 Building StormShelters

6.1.1.1: SE pp. 21, 24, 27, 29

Explore questions of maximum and minimumin the context of finding the largest and smallestperimeter for rectangles of fixed area

Understand that the perimeters of rectangleswith a fixed area can vary considerably

Continue to develop facility using formulas forfinding perimeter and area of rectangles

Continue to develop a conceptual understandingof area and perimeter

2.2 Stretching thePerimeter

6.3.1.3: SE pp. 22-23, 28TG pp. 43-46, 57

Understand that the perimeters of rectangleswith a fixed area can vary considerably

Explore questions of maximum and minimumin the context of finding the largest and smallestperimeter for rectangles of fixed area



2.3 Fencing in Space 6.1.1.1: SE pp. 21, 24, 27, 29

Find the minimum and maximum area of arectangle with a fixed perimeter

Understand that the areas of rectangles with afixed perimeter can vary considerably

Construct diagrams, tables, and graphs toorganize and represent data


2.4 Adding Tiles toPentominoes

Distinguish the case of fixed area from fixedperimeter

Apply understanding of the relationshipbetween area and perimeter to nonrectangularfigures


Homework

6.1.1.1: SE pp. 21, 24, 27, 296.1.2.1: SE pp. 33

TG pp. 586.3.1.3: SE pp. 22-23, 28

TG pp. 43-46, 57

Reflections

Investigation 3Measuring Triangles

3.1 Finding Areaand Perimeter ofTriangles

Develop and employ reasonable strategies forfinding the area of a triangle

Find relationships between rectangles andtriangles

Use these relationships to develop techniquesfor finding the area of a triangle

3.2 More Triangles

Distinguish among base, height, and sidelengths of triangles

Understand that depending upon how youposition a given triangle, it has more than onebase and height, but only one area

3.3 Whats the AreaExplore how triangles with the same base andheight can look different but have the same area

3.4 DesigningTriangles UnderConstraints

Apply techniques for finding the areas andperimeters of rectangles and triangles to avariety of problem situations

Homework 6.3.1.1: TG pp. 85-86

Reflections 6.3.1.1: SE pp. 50-51TG pp. 85-86

Investigation 4MeasuringParallelograms

4.1 FindingMeasures ofParallelograms

Develop and employ reasonable strategies forfinding the areas and perimeters ofparallelograms


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4.2 Parallelogramsfrom Triangles

6.2.1.1: SE pp. 56TG pp. 96

6.2.3.1: SE pp. 56TG pp. 96

Find area relationships between rectangles,triangles, and parallelograms

Use relationships between parallelograms andtriangles to develop techniques for finding theareas of parallelograms

Distinguish among the base, height, and sidelengths of a parallelogram

Understand that a parallelogram may bepositioned in more than one way, and thus mayhave more than one base-height pair, but only

one area

4.3 DesigningParallelogramsUnder

Constraints

Distinguish among the base, height, and sidelengths of a parallelogram

Understand that a parallelogram may bepositioned in more than one way, and thus mayhave more than one base-height pair, but only

one area

Apply techniques for finding the areas andperimeters of parallelograms to a variety ofproblem situations

4.4 Parks, Hotels,and Quilts

Apply techniques for finding the areas andperimeters of parallelograms to a variety ofproblem situations

Homework 6.3.2.1: SE pp. 65

Reflections 6.3.2.1: TG p. 107

Investigation 5Measuring IrregularShapes and Circles

5.1 MeasuringLakes

6.3.3.2: SE pp. 69-71, 75, 77-81, 83, 86, 88TG pp. 109-132

Develop counting techniques for estimatingareas and perimeters of irregular figures

Use ideas about area and perimeter to solvepractical problems


5.2 Surrounding aCircle

6.3.3.2: SE pp. 69-71, 75, 77-81, 83, 86, 88TG pp. 109-132

6.1.2.4: SE pp. 72-77, 80-87, 88TG pp. 115-125, 127-128, 129-133

Discover that it takes slightly more than threediameters to equal the circumference of a circle

Use this discovery to develop a formula forcircumference of a circle

Develop strategies for organizing and

comparing data

5.3 Pricing Pizzas

6.1.2.4: SE pp. 72-77, 80-87, 88TG pp. 115-125, 127-128, 129-133

6.2.1.2: SE pp. 75, 81, 86TG pp. 119-122, 127-128, 130-131

6.3.3.2: SE pp. 69-71, 75, 77-81, 83, 86, 88

Develop techniques for estimating the area of acircle

Develop strategies for organizing andcomparing data

Use ideas about area and perimeter to solvepractical problems


5.4 Squaring aCircle

6.3.3.2: SE pp. 69-71, 75, 77-81, 83, 86, 88TG pp. 109-132

6.1.2.4: SE pp. 72-77, 80-87, 88TG pp. 115-125, 127-128, 129-133

6.2.1.2: TG pp. 119-122, 127-128, 130-131

Discover that it takes slightly more than threeradius squares to equal the area of the circle

Use this discovery to develop a formula for areaof a circle

Homework

6.1.2.4: SE pp. 72-77, 80-87, 88TG pp. 115-125, 127-128, 129-133

6.2.1.2: SE pp. 75, 81, 86TG pp. 119-122, 127-128, 130-131

6.3.3.2: SE pp. 69-71, 75, 77-81, 83, 86, 88TG pp. 109-132

Reflections6.3.3.2: SE pp. 69-71, 75, 77-81, 83, 86, 88TG pp. 109-1326.1.2.4: SE pp. 72-77, 80-87, 88

TG pp. 115-125, 127-128, 129-133


Module 6Bits and Pieces III

Introduction Introduction6.1.1.4: TG p. 4-86.1.1.7: TG p. 4-8


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Investigation 1Decimals-More orLess

1.1 About HowMuch?

6.1.1.1: SE pp. 56.1.1.2: SE pp. 5, 16

TG pp. 16-206.1.1.4: SE pp. 5, 10, 12, 15, 206.1.1.7: SE pp. 5, 10, 12, 15, 206.1.3.5: SE pp. 5-7, 11, 13-14, 20

TG pp. 16-17, 25-28, 33-35

Use benchmarks and decimal-fractionrelationships to develop estimation strategies forfinding decimal sums

Consider the relative size of a decimal prior todeveloping approaches to finding exact decimalsums or differences

1.2 Adding andSubtractingDecimals

6.1.3.1: SE pp. 7-20TG pp. 21-35

6.1.3.4: SE pp. 7-20TG pp. 21-35

6.1.3.5: SE pp. 5-7, 11, 13-14, 20

Develop place-value understanding of decimaladdition and subtraction

Develop strategies for adding and subtractingdecimal numbers

Solve problems that require decimal additionand subtraction

1.3 Using Fractionsto Add and

SubtractDecimals

6.1.1.4: SE pp. 5, 10, 12, 15, 206.1.1.7: SE pp. 5, 10, 12, 15, 206.1.3.1: SE pp. 7-20

TG pp. 21-35

6.1.3.4: SE pp. 7-20TG pp. 21-35

6.1.3.5: SE pp. 5-7, 11, 13-14, 20

Connect strategies for addition and subtractionof decimals to addition and subtraction offractions with powers of ten in the denominator

Relate renaming fractions to have commondenominators to the notion of adding valueswith the same place value

1.4 Decimal Sumand DifferenceAlgorithms

6.1.1.4: SE pp. 5, 10, 12, 15, 206.1.1.7: SE pp. 5, 10, 12, 15, 206.1.3.1: SE pp. 7-20

TG pp. 21-356.1.3.4: SE pp. 7-20

TG pp. 21-356.2.1.1: SE pp. 12, 15-18

TG pp. 32, 346.2.2.1: SE pp. 12, 15-18

TG pp. 29-32, 346.2.3.1: SE pp. 12, 15-18

TG pp. 32, 346.2.3.2: SE pp. 12, 15-18

TG pp. 32, 34-35

? Pages dont show up correctly from cd.

Homework

6.1.1.2: SE pp. 5, 166.1.1.7: SE pp. 5, 10, 12, 15, 206.1.3.1: SE pp. 7-20

TG pp. 21-356.1.3.4: SE pp. 7-206.1.3.5: SE pp. 5-7, 11, 13-14, 206.2.1.1: SE pp. 12, 15-18

TG pp. 32, 346.2.2.1: SE pp. 12, 15-18

TG pp. 29-32, 346.2.3.1: SE pp. 12, 15-18

TG pp. 32, 346.2.3.2: SE pp. 12, 15-18

TG pp. 32, 34-356.3.2.2: SE pp. 17

TG pp. 346.3.3.1: SE pp. 17-19

TG pp. 34-356.3.2.1: TG pp. 34

Reflections

6.1.1.7: SE pp. 5, 10, 12, 15, 206.1.3.1: SE pp. 7-20

TG pp. 21-356.1.3.4: SE pp. 7-20

TG pp. 21-35

6.1.3.5: SE pp. 5-7, 11, 13-14, 206.2.3.2: TG pp. 32, 34-356.3.3.1: TG pp. 34-35


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Investigation 2Decimal Times

2.1 RelatingFraction andDecimalMultiplication

6.1.3.2: SE pp. 21-24, 31, 336.1.2.3: TG pp. 42, 59

Estimate the relative size of a decimal productprior to finding an exact answer

Develop place-value understanding of decimalmultiplication

Solve problems that require decimalmultiplication

Consider how finding a decimal part ofand afraction part ofa quantity affects the relativesize of a product

2.2 Missing Factors6.1.2.3: SE pp. 23, 326.1.3.2: SE pp. 21-24, 31, 33

Use place value to reason about decimalmultiplication

Explore the relationship between factors andproducts in decimal multiplication

2.3 Finding DecimalProducts

6.1.3.2: SE pp. 21-24, 31, 33

Develop estimation strategies for findingdecimal products

Use estimation as a strategy for finding exactdecimal products

2.4 Factor-ProductRelationships

Generalize an approach to placing the decimalpoint into a product that involves counting andadding decimal places

Consider when various strategies are useful forfinding decimal products

Understand what happens to place value and theposition of the decimal when you multiply bypowers of 10

Develop at least one efficient algorithm formultiplying decimals

Homework

6.1.2.3: SE pp. 23, 326.1.2.4: SE pp. 28, 32

TG pp. 57, 596.1.3.2: SE pp. 21-24, 31, 336.3.1.2: SE pp. 33

Reflections6.1.2.3: TG pp. 42, 596.1.2.4: TG pp. 57, 596.3.1.2: TG pp. 59

Investigation 3The Decimal Divide

3.1 DecipheringDecimalSituations

6.2.1.2: SE p. 456.1.2.2: SE pp. 476.3.3.2: SE pp. 47

Choose between division, multiplication,addition, or subtraction as an appropriateoperation to use to solve a problem

Use models and the context to find solutions todivision problems

Estimate to find approximate solutions

3.2 The GreatEqualizer:CommonDenominators

Use the relationship between decimals andfractions to develop and understand decimaldivision

Use the common denominator approach tofraction division as a strategy to help understandand develop an algorithm for dividing decimals

Relate the emerging division algorithm to placevalue understanding

3.3 ExploringDecimals

Use knowledge about computation withfractions to understand algorithms for divisionwith decimals

Use place value to develop an algorithm fordivision with decimals

Develop and use efficient algorithms fordividing decimals

Explore the inverse relationship betweenmultiplication and division in fact families

3.4 RepresentingFractions asDecimals

Understand and predict the decimalrepresentation of a fraction (terminating orrepeating)

Homework

6.1.1.1: TG pp. 79, 816.2.1.2: TG pp. 806.1.2.2: TG pp. 816.3.3.2: TG pp. 81

Reflections


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Investigation 4Using Percents

4.1 Determining Tax

6.1.1.3: SE pp. 50-61TG pp. 83-99

6.1.3.3: SE pp. 50-61TG pp. 83-99

Understand that a percent is a decimal fractionwith a denominator of 100

Represent $1.00 as 100 pennies, and relate thisto partitioning a number line into 100 parts

Represent percents as decimals and use decimalcomputation to compute percents

4.2 Computing Tips

6.1.1.3: SE pp. 50-61TG pp. 83-99

6.1.3.3: SE pp. 50-61TG pp. 83-99

Represent percents as decimals and use decimalcomputation to compute percents

Explore the relationship between 1% and 10%and use these to compute 5%, 15%, and 20%tips

Work backwards to find the amount of the bill ifyou know the tip and the percent of tip for t hebill

4.3 Finding

Bargains

6.1.1.3: SE pp. 50-61TG pp. 83-99

6.1.3.3: SE pp. 50-61TG pp. 83-99

Use percents in estimating or computing taxes,tips, and discounts

Find what percent one number is of anothernumber

Solve problems using percents

Homework

6.1.1.3: SE pp. 50-61TG pp. 83-99

6.1.3.3: SE pp. 50-61TG pp. 83-99

Reflections

6.1.1.3: SE pp. 50-61TG pp. 83-99

6.1.3.3: SE pp. 50-61TG pp. 83-99

Investigation 5More About Percents

5.1 ClippingCoupons

Develop a strategy for finding the percent ofdiscount an amount taken off a price represents

Use percents in estimating taxes, tips, anddiscounts

5.2 How Much CanWe Spend?

Use percents in estimating or computing taxes,tips, and discounts

Solve problems using percents

5.3 Making CircleGraphs

Make and interpret circle graphs to representdata

Solve problems involving percentsHomework

Reflections


Module 7How Likely Is It?


Investigation 1A First Look atChance

1.1 Choosing Cereal

6.4.1.2: SE pp. 5-20TG pp. 14-35

6.4.1.3: SE pp. 5-20TG pp. 14-35

6.4.1.4: SE pp. 5-20TG pp. 14-35

Develop an intuitive sense of probabilitythrough a coin-tossing experiment

1.2 Tossing PaperCups

6.4.1.2: SE pp. 5-20TG pp. 14-35

6.4.1.3: SE pp. 5-20TG pp. 14-35

6.4.1.4: SE pp. 5-20TG pp. 14-35

Continue to develop an intuitive sense ofprobability through a cup-tossing experiment

Understand that probabilities are useful forpredicting what will happen over the long run

Toss cups to find an experimental probabilitywhere the outcomes are not equally likely

1.3 One More Try

6.4.1.2: SE pp. 5-20TG pp. 14-35

6.4.1.3: SE pp. 5-20TG pp. 14-35

6.4.1.4: SE pp. 5-20TG pp. 14-35

6.1.2.1: SE p. 8-9TG pp. 25-28

Develop strategies for finding experimentalprobabilities for a situation that involves tossingtwo coins

Begin to explore the notion of fair and unfair


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1.4 AnalyzingEvents

6.4.1.2: SE pp. 5-20TG pp. 14-35

6.4.1.3: SE pp. 5-20TG pp. 14-35

6.4.1.4: SE pp. 5-20TG pp. 14-35

Understand the concepts of equally likely andnot equally likely

Homework

6.4.1.1: SE pp. 196.4.1.2: SE pp. 5-20

TG pp. 14-356.4.1.3: SE pp. 5-20

TG pp. 14-356.4.1.4: SE pp. 5-20

TG pp. 14-356.1.1.2: SE pp. 166.1.1.3: SE pp. 16

TG pp. 346.1.2.2: SE pp. 16

TG pp. 346.1.2.4: SE pp. 16

TG pp. 346.1.3.3: SE pp. 16

TG pp. 34

Reflections

6.4.1.1: TG pp. 356.4.1.2: SE pp. 5-20

TG pp. 14-356.4.1.3: SE pp. 5-20

TG pp. 14-356.4.1.4: SE pp. 5-20

TG pp. 14-35

Investigation 2Experimental andTheoretical Probability

2.1 Predicting toWin

Find the theoretical probability by analyzing thepossible equally likely outcomes involved in agame of guessing the color of a block

Compare experimental and theoreticalprobabilities

2.2 ExploringProbabilities

Observe some properties of probability

2.3 Winning theBonus Prize

Use organized lists and tree diagrams to find

theoretical probabilitiesUnderstand that experimental probabilities arebetter estimates of theoretical probabilitieswhen they are based on larger numbers of trials

2.4 PonderingPossible andProbable

Deepen understanding of equally likely and notequally likely

Understand that a game of chance is fair only ifeach player has the same chance of winning, notjust apossible chance of winning

Homework6.1.3.2: SE pp. 346.1.3.4: SE pp. 28, 32, 34

TG pp. 53-56

Reflections

Investigation 3

Making DecisionsWith Probability

3.1 Designing aSpinner

Develop strategies for finding experimental andtheoretical probabilities in situations involvingspinners

3.2 MakingDecisions

Analyze probability situations.

Use probability to make decisions.

Decide whether probability situations are fair orunfair.

3.3 Scratching SpotsDevelop strategies for finding bothexperimental and theoretical probabilities insituations involving scratch-off prize cards

Homework

6.1.1.4: SE pp. 48TG pp. 73

6.1.1.7: SE pp. 48TG pp. 73

Reflections


15/18

Investigation 4Probability, Genetics,and Games

4.1 Genetic TraitsUse class and survey data to find theexperimental probabilities for certain genetictraits

4.2 Tracing Traits

Appreciate the power of probability for makingpredictions

Develop strategies (for example, using a chartor table) for finding theoretical probabilitiesinvolving genetics

4.3 Roller Derby

Appreciate the power of probability indetermining strategies for winning a game

Develop strategies (for example, using a chartor table) for finding both experimental andtheoretical probabilities of winning a game

Homework6.3.1.1: SE pp. 68

TG pp. 89

Reflections


Module 8Data About Us


Investigation 1Looking at Data

1.1 Organizing andInterpreting Data

Describe data distributions

Use line plots and bar graphs to display datadistributions

1.2 Useful Statistics

Use mode, median, how data vary from the leastto the greatest values, and range to describewhat is typical about a data distribution

Use tables and line plots to display datadistributions

1.3 Experimentingwith the Median

Recognize how the median, as a measure ofcenter, responds to changes in the number andmagnitude of data values

Use line plots to display data distributions

1.4 Using DifferentData Types

Identify whether data are categorical ornumerical

Use bar graphs to display data distributions

Understand how median, mode, and range relateto numerical and categorical data

1.5Vertical BarGraphs andHorizontal BarGraphs

Distinguish between vertical and horizontal bar

graphsDistinguish how numerical data and categoricaldata are shown on a horizontal bar graph

Answer questions using both kinds of bargraphs

Homework6.1.3.5: SE pp. 25, 28

TG pp. 43, 45

Reflections

Investigation 2Using Graphs toExplore Data

2.1 Traveling toSchool

Group numerical data in equal intervals anddisplay their distribution using a stem-and-leafplot

Find measures of center and variation, includingrange and how data vary from the least to thegreatest values, when a distribution is displayed

using a stem-and-leaf plot

2.2 Jumping Rope

Compare two distributions displayed usingback-to-back stem-and-leaf plots

Compare two distributions using statistics, suchas median, range, and how the data vary fromleast to greatest values

Identify outliers in a distribution

2.3 Relating Heightto Arm Span

6.1.1.1: SE pp. 37-42, 46-48TG pp. 57-62, 63-66

Display distributions of paired-data values oncoordinate graphs

Explore relationships between paired-datavalues whose distributions are displayed usingcoordinate graphs

Explore intervals for scaling the vertical axis (y-axis) and the horizontal axis (x-axis)


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2.4 Relating TravelTime to Distance

6.1.1.1: TG pp. 57-62, 63-66

Explore relationships between paired-datavalues whose distributions are displayed usingcoordinate graphs

Explore intervals for scaling the vertical axis (y-axis) and the horizontal axis (x-axis)

Homework6.1.1.1: SE pp. 37-42, 46-486.2.1.2: SE pp. 46-47

TG pp. 71

Reflections

Investigation 3What Do We Mean by

Mean?

3.1 Finding theMean

Understand the mean as a number that evensout or balances a distribution

3.2 Data With theSame Mean

6.1.3.4: SE pp. 53, 57-58TG pp. 81-86, 92

Create distributions with designated means

Recognize that data with the same mean mayhave different distributions

Reason with a model that clarifies thedevelopment of the algorithm for finding themean

3.3 Using the MeanExperiment with how the mean, as a measure ofcenter, responds to changes in the number andmagnitude of data values

Homework6.1.3.4: SE pp. 53, 57-58

TG pp. 81-86, 92

Reflections



17/18

MinnesotaAcademic StandardsMathematics K-12

2007 version

6. MN Math Standards 2007 - Grade 66.1. Number and Operation

6.1.1. Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.6.1.1.1. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.6.1.1.2. Compare positive rational numbers represented in various forms. Use the symbols < , = and >.

6.1.1.2.1. For example: 12

> 0.36.

6.1.1.3. Understand that percent represents parts out of 100 and ratios to 100.6.1.1.3.1. For example: 75% corresponds to the ratio 75 to 100, which is equivalent to the ratio 3 to 4.

6.1.1.4. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems.6.1.1.4.1. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional $2.50 an hour, because $2.50 is 1

10or 10% of $25.

6.1.1.5. Factor whole numbers; express a whole number as a product of prime factors with exponents.6.1.1.5.1. For example: 324 2 3

6.1.1.6. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent f ractions.6.1.1.6.1. For example: Factor the numerator and denominator of a fraction to determine an equivalent fraction.

6.1.1.7. Convert between equivalent representations of positive rational numbers.6.1.1.7.1. For example: Express 10

7as 7 3 7 3 31

7 7 7 7.

6.1.2. Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real- world and mathematical problems.6.1.2.1. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction.

6.1.2.1.1. For example: In a classroom with 15 boys and 10 girls, compare the numbers by subtracting (there are 5 more boys than girls) or by dividing (there a re 1.5 times as many boys as girls). The comparison using division may be expressed as a ratio of boys to girls (3 to 2 or 36.1.2.2. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations.

6.1.2.2.1. For example: If 5 cups of trail mix contains 2 cups of raisins, the ratio of raisins to trail mix is 2 to 5. This ratio corresponds to t he fact that the raisins are 25

of the total, or 40% of t he total. And if one trail mix consists of 2 parts peanuts to 3 parts raisins, and another consi

peanuts to 8 parts raisins, then the first mixture has a higher concentration of peanuts.6.1.2.3. Determine the rate for ratios of quantities with different units.

6.1.2.3.1. For example: 60 miles for every 3 hours is equivalent to 20 miles for every one hour (20 mph).6.1.2.4. Use reasoning about multiplication and division to solve ratio and rate problems.

6.1.2.4.1. For example: If 5 items cost $3.75, and all items are the same price, then 1 item costs 75 cents, so 12 items cost $9 .00.6.1.3.

Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.6.1.3.1. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.

6.1.3.2. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions.6.1.3.2.1. For example: Just as 12 3

4means 12 3 4 , 52 4

3 5 6means 5 4 2

6 5 3.

6.1.3.3. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts.6.1.3.3.1. For example: If John has $45 and spends $15, what percent of his money did he keep?

6.1.3.4. Solve real-world and mathematical problems requiring arit hmetic with decimals, fractions and mixed numbers.6.1.3.5. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem.

6.1.3.5.1. For example: The sum 13

0.25 can be estimated to be between 12

and 1, and this estimate can be used to check the result of a more detailed calculation.

6.2. Algebra6.2.1. Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

6.2.1.1. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts.6.2.1.1.1. For example: If a student earns $7 an hour in a job, the amount of money earned can be represented by a variable and is related to the number of hours worked, which also can be represented by a variable.

6.2.1.2. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these r epresentations.6.2.1.2.1. For example: Describe the terms in the sequence of perfect squares t= 1, 4, 9, 16, .. . by using the rule 2t n for n = 1, 2, 3, 4, ...

6.2.2. Use properties of arithmetic to generate equivalent numerical expressions and evaluate e xpressions involving positive rational numbers.6.2.2.1. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers.

6.2.2.1.1. For example: 32 5 2 16 532 5 16 5 16215 6 15 6 3 5 3 2 9 2 5 9

.

6.2.2.1.2. Another example: Use the distributive law to write: 9 15 9 15 3 5 5 31 1 1 1 1 1 2 12 3 2 8 2 3 2 3 8 2 2 8 8 8

.

6.2.3. Understand and interpret equations and inequalities involving variables and positive rational numbers. Use equations and inequalities to represent real-world and mathematical problems; use the idea of maintaining equality to solve equations. Interpret solutions in the original context.6.2.3.1. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers.

6.2.3.1.1. For example: The number of miles m in a kkilometer race is represented by the equation m = 0.62 k.6.2.3.2. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results.

6.2.3.2.1. For example: A cellular phone company charges $0.12 per minute. If the bill was $11.40 in April, how many minutes were used?6.3. Geometry & Measurement

6.3.1. Calculate perimeter, area, surface area and volume of two- and three-dimensional figures to solve real-world and mathematical problems.6.3.1.1. Calculate the surface area and volume of prisms and use appropriate units, such as cm2 and cm3. Justify the formulas used. Justification may involve decomposition, nets or other models.


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6.3.1.1.1. For example: The surface area of a triangular prism can be found by decomposing the surface into two t riangles and three rectangles.6.3.1.2. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.

6.3.1.2.1. For example: The area of a kite is one-half the product of the lengths of the diagonals, and this can be justified by decomposing the kite into two triangles.6.3.1.3. Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm2.

6.3.2. Understand and use relationships between angles in geometric figures.6.3.2.1. Solve problems using the relationships between the angles formed by intersecting lines.

6.3.2.1.1. For example: If two streets cross, forming four corners such that one of the corners forms an angle of 120, determine the measures of the remaining three angles.6.3.2.1.2. Another example: Recognize that pairs of interior and exterior angles in polygons have measures that sum to 180.

6.3.2.2. Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a t riangle is 180. Use models of triangles to illustrate this fact.6.3.2.2.1. For example: Cut a triangle out of paper, tear off the corners and rearrange these corners to form a straight line.6.3.2.2.2. Another example: Recognize that the measures of the two acute angles in a right triangle sum to 90.

6.3.2.3. Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles.6.3.3. Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

6.3.3.1. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.6.3.3.2. Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units.

6.3.3.2.1. For example: Estimate the height of a house by comparing to a 6-foot man standing nearby.6.4. Data Analysis & Probability

6.4.1. Use probabilities to solve real-world and mathematical problems; represent probabilities using fractions, decimals and percents.6.4.1.1. Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tr ee diagrams, tables or pictorial representations.

6.4.1.1.1. For example: A 6 6 table with entries such as (1,1), (1,2), (1,3), , (6,6) can be used to represent the sample space for the experiment of simultaneously rolling two number cubes.6.4.1.2. Determine the probability of an event using the ratio between the size of t he event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood.

6.4.1.2.1. For example: Each outcome for a balanced number cube has probability 16

, and the probability of rolling an even number is 12

.

6.4.1.3. Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences.6.4.1.3.1. For example: Heads and tails are equally likely when flipping a fair coin, but if several different students flipped fair coins 10 times, it is likely that they will find a variety of relative frequencies of heads and tails.

6.4.1.4. Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.6.4.1.4.1. For example: Repeatedly draw colored chips with replacement from a bag with an unknown mixture of chips, record relative frequencies, and use the results to make predictions about the contents of the bag.

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