6th Grade Mathematics Curriculum - Auburn School …district.auburn.cnyric.org/departments/math/Math Curriculum/6th_for...AECSD Grade_6_Math_Curr Rev 7-08.doc 1 6th Grade Mathematics

AECSD Grade_6_Math_Curr Rev 7-08.doc 1

6th Grade Mathematics Curriculum

Units 1, 2, 3, 4, 5, 7, 8, 10

Course Description:The 6th Grade Mathematics course serves as a culminating year for a lot of work with fractions,decimals and percents. Students convert among fractions, decimals and percents as well asperform operations with fractions. Students’ knowledge in the area of algebra continues toexpand to include solving more complicated equations and evaluating more complicatedexpressions. Circles, triangles, and quadrilaterals are all addressed in geometry units while themeasurement focus is on volume and capacity. Finally, students continue their work with thecollection, display and analysis of data and build upon the probability knowledge they developedin 5th grade. Problem solving and communication are emphasized across all these areas.

Course Essential Questions and Big Ideas:

Any number can be represented in multiple ways (fractions, decimals, percents, powers). Youcan make the math easier by choosing the best representation.

Ratios, fractions, percents, and division are just different ways of representing the same process.

6th Grade State Assessment Information:

Approximate Percentage of Questions Assessing Each Strand

Strand: Percent: Time allotted: Units:Number Sense and Operations: 37% (10 weeks) (Unit 1, 3, 4, 5, 8)Algebra: 19% (3 weeks) (Unit 2)Geometry: 17% (4 weeks) (Unit 6)Measurement: 11% (2 weeks) (Unit 7)Probability and Statistics: 16% (2 weeks) (Unit 9)


Table of Contents

Section Page #

6th Grade Mathematical Language ...............................................................................................3Post-March 5th Grade Performance Indicators .............................................................................76th Grade Local Math Standards ..................................................................................................8Math 6 Unit Sequence and Timeline: ........................................................................................10Unit 1 Whole Numbers, Place Value and Properties..........................................................12Unit 2 Algebra ..................................................................................................................14Unit 3 Adding and Subtracting Fractions ..........................................................................17Unit 4 Multiplying and Dividing Fractions........................................................................20Unit 5 Ratio, Proportion and Percents (N.1, N.5, N.12, G.3) .............................................23Unit 6 Geometry (G.1, G.5) ..............................................................................................26Unit 7 Measurement (M.5)................................................................................................30Unit 8 Rational Numbers (N.3, N.7)..................................................................................32Unit 9 Data and Statistics (D.2).........................................................................................34Review Unit for State Assessment (Test dates: March 15 and 16, 2006)....................................35Unit 10 Algebra ..................................................................................................................36Unit 11 Coordinate Geometry (G.7)....................................................................................38Unit 12 Collection and Display of Data (D.1) .....................................................................39Unit 13 Probability (D.3) ....................................................................................................40


6th Grade Mathematical Language

The language below is language that all students should be familiar with and should be usedthroughout instruction. Definitions for most words and expressions can be found in the PK-8Glossary.

Problem Solvinganalyzeapplycollaborationcounterexampledifferentiatediscussdraw a graphdraw a pictureexplainformulateidentityinterpret

invalid approachirrelevant informationlanguage of logic (and, or,

not)logiclogical reasoningmodel using manipulativesmonitorobserve patternsorganized chartorganized listprocess of elimination

reasonableness of asolution

reflectrelevant informationsolutionsolve a simpler problemstrategiestrial and errorvalid approachverify resultswork backwardswrite an equation

Reasoning and Proofalgebraicallyappropriate mathematical

termsargumentconjecture (noun)counterexampledevelop formulas

explaingraphicallyinterpretinvestigatejustifymanipulative(s)mathematical relationships

methods of proofmodelsnumericallyspecial case(s)verballyverify claims of others

Communicationaccurately label workanalyzeclarifying questionscomprehendconsolidate

decodedistinguishexplainextendmathematical relationships

organize workrationalesolutionverbal symbolswritten symbols

Connectionsapplycoherentconjecture (verb)connections

draw conclusionsexploreinvestigateirrelevant information

mathematical relationshipsmodel (noun)model problemsrelevant information


Representationapplydescribeexplainexploreextend

interpretinvestigatemathematical phenomenamodel(s)

nonstandardrepresentations

physical phenomenasocial phenomenastandard representations

Number Sense and Operationsabsolute valueadditive inverseassociative property of

additionassociative property of

multiplicationbase (of percent)base ten number systemcommutative property of

additioncommutative property of

multiplicationcounting (natural) numbersdistributive propertyequivalent fractionsequivalent numerical

expressionsequivalent ratiosestimateexponentexponential formextremes (of a proportion)fraction

identity elementidentity property of

additionidentity property of

multiplicationinequalityintegerinverse elementinverse operationlike (common)

denominatorslowest termsmathematical statementmeans (of a proportion)mixed numbermultiplicative inverse

(reciprocal)multiply (multiplication)negativenumber linenumber systemnumerical problem

numeric (arithmetic)expression

operationorder (verb)order of operationspercentpositivepowerproperties of real numbersproportionraterate of interestratiorational numberrepeating decimalround (verb)terminating decimalunlike denominatorsverbal expressionwhole numberzero property of

multiplication

Algebraalgebraalgebraic expressionalgebraic solutionequationevaluateexponents

formulainput valuesinterestinverse operationsproportionsolve

substitutetranslatevariableverbal expression


Geometryarcareacentral anglechordcirclecircumferencecoordinate geometrycoordinate planecorresponding sidesdevelop formulasdiametergeometric shape

geometryheightirregular polygonlengthperimeterpi (!)plotpointproportional reasoningquadrantquadrilateralradius

rectanglerectangular prismregular polygonrhombussectorsimilar trianglessquaretrapezoidtrianglevertexvolumewidth

Measurementcalculate volumecupcustomary units of

capacitydistanceequivalent customary units

of capacity

estimate area circumference volumegallonlitermeasure capacity

metric systemmetric units of capacitymilliliterpersonal references for

capacitypintquart

Statistics and Probabilitycircle graphcompound eventsdatadependent eventsfavorable outcomesfrequencyfrequency tablefundamental counting

principle

histogramimpossible outcomesinterpret graphsjustifyline graphmeanmedianmodepopulation

possible outcomespredictprobabilityrangerecord datasamplingstatisticsVenn diagram


Post-March 5th Grade Performance IndicatorsThe 5th Grade state performance indicators below are denoted by the state as post-test.Therefore, students will be responsible for this knowledge of the 6th Grade assessment.Attention should be given to them during the normal course of instruction or during review.

5.A.2 Translate simple verbal expressions into algebraic expressions5.A.3 Substitute assigned values into variable expressions and evaluate using order of

operations5.A.4 Solve simple one-step equations using basic whole-number facts 5.A.5 Solve and explain simple one-step equations using inverse operations involving whole

numbers5.G.12 Identify and plot points in the first quadrant5.G.13 Plot points to form basic geometric shapes (identify and classify)5.G.14 Calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles

and shapes composed of rectangles having sides with integer lengths and parallel to theaxes)

5.S.5 List the possible outcomes for a single-event experiment 5.S.6 Record experiment results using fractions/ratios 5.S.7 Create a sample space and determine the probability of a single event, given a simple

experiment (e.g., rolling a number cube)


6th Grade Local Math StandardsNumbering Key: Local.Grade level.Mathematics strand.standard #e.g. L.6.N.5 (L = local; 6 = 6th Grade; N = Number Sense and Operations; 5 = 5th standard)

Number and Operations:

L.6.N.1 Representationand Notation

Read and write whole numbers to trillions; convert among fractions, decimals(repeating and non-repeating), and percents (0 to 100).

L.6.N.3 Number Order Order rational numbers (positive and negative) including locating them on anumber line

L.6.N.5 Estimation Estimate a percent (0 to 100%) of a quantity; justify the reasonableness ofanswers using estimation including rounding

L.6.N.7 Properties andLaws

Identify, use, and explain: the commutative and associative properties of additionand multiplication, the distributive property of multiplication over addition, theidentity and inverse properties of addition and multiplication, and the zeroproperty of multiplication; define absolute value and determine the absolute valueof rational numbers

L.6.N.8 Computation andFacts

Evaluate numerical expressions using order of operations (may include exponentsof two and three)

L.6.N.10 Fractions Add, subtract, multiply, and divide fractions and mixed numbers with unlikedenominators

L.6.N.12 Percent, Ratio,Proportion

Understand the concepts of rate and ratio and distinguish between them; expressequivalent ratios as proportions, solve proportions (see L.6.A.2), and verifyproportionality (e.g. verify two triangles are similar, see L.6.G.3)); read, write,and identify percents of a whole (0% to 100%); solve percent applicationproblems

L.6.N.13 Power and Roots Convert between repeated multiplication and power notation

Algebra:

L.6.A.1 Patterns andRepresentations

Translate between two-step verbal and algebraic expressions and equations.

L.6.A.2 Solving Equationsand Inequalities

Solve and explain simple (whole number) two-step equations using inverseoperations; solve proportions (see L.6.N.12)

L.6.A.3 Expressions Substitute values (for 1 or 2 variables) into an expression (including exponents upto 3) and evaluate it (e.g. circumference, area, volume, distance, temperature,interest, etc.) (See L.6.N.8).

Geometry:

L.6.G.1 Shapes andFigures

Identify the radius and diameter (and the relationship between them), chords, andcentral angles of a circle; understand the relationship between the circumferenceand the diameter of a circle.

L.6.G.3 Similarity andCongruence

Calculate the length of corresponding sides of similar triangles using proportionalreasoning (see L.6.N.12 and L.6.A.2).

L.6.G.5 Perimeter, Area,and Volume

Estimate and determine the area of triangles and quadrilaterals (square, rectangle,rhombus, trapezoid) and develop area formulas; estimate and find the area ofregular and irregular polygons; estimate the volume of rectangular prisms bycounting cubes and calculate the volume after developing a formula; determinethe circumference and area of a circle using a formula, and calculate the area of asector of a circle, given the central angle and radius

L.6.G.7 CoordinateGeometry

Identify and plot points in all four quadrants of the coordinate plane; calculate thearea of shapes with sides parallel to the axes (see L.6.G.5).

Measurement:

L.6.M.5 Volume(Capacity)

Measure volume (capacity) using the appropriate tool and technique; identify andconvert between units of volume (capacity) within a given system (metric orcustomary); determine personal references for customary and metric units ofvolume (capacity); justify the reasonableness of an estimate of the volume of anobject.


customary); determine personal references for customary and metric units ofvolume (capacity); justify the reasonableness of an estimate of the volume of anobject.

Statistics and Probability:

L.6.S.1 Collect andDisplay Data

Explore data collection through sampling; record (e.g. with a frequency table) andchoose an appropriate display (e.g. Venn diagram, pictograph, bar graph, linegraph, histogram, or circle graph) for real-world data; construct Venn diagrams.

L.6.S.2 Analyze Data Calculate and use the mean, mode, median, and range of a set of data; read,interpret, and predict from (with justification) graphs

L.6.S.3 Probability For a compound-event: determine the sample space using the fundamentalcounting principle, list all possible outcomes, and determine the probability of asingle outcome; determine the probability of dependent events.

Problem Solving:

L.6.PS.1 Organization Analyze situations (identify the problem, identify needed and relevantinformation, find relationships, observe patterns, and generate possible strategies)and organize work to solve problems (e.g. use Auburn Problem Solving Process).

L.6.PS.2 Strategies Solve problems using a variety of strategies and representations (e.g. modelingwith manipulatives, acting out, drawing pictures or diagrams, guess and check(trial and error), making a list or chart, and process of elimination).

L.6.PS.3 Reflection Estimate possible solutions; examine solution to ensure it is reasonable in contextof problem; compare solution to original estimate; verify results.

Reasoning and Proof:

L.6.RP.1 Make, investigate, and evaluate conjectures; support (or refute) mathematicalstatements or conjectures with valid arguments including the use of models, facts,relationships, and (counter)examples to help explain their reasoning; expressarguments verbally, numerically, algebraically, pictorally, and in writing.

Communication:

L.6.CM.1 Decode and comprehend mathematics expressed verbally and in writing; clearlyand coherently communicate mathematical thinking verbally, pictorally,numerically, algebraically and in writing using appropriate mathematicalvocabulary and symbols; organize and accurately label work.

Connections:

L.6.CN.1 Recognize and use connections among branches of mathematics and real life (e.g.determine the perimeter of a bulletin board, construct tables to organize datashowing book sales, find the missing value: (3 + 4) + 5 = 3 + (4 + ___ ))

Representations:

L.6.Rep.1 Represent mathematical ideas in a variety of ways (verbally, in writing, pictorally,numerically, algebraically, or with physical objects); switch among differentrepresentations; investigate how different representations can express the samerelationship but may differ in efficiency.


Math 6 Unit Sequence and Timeline:

Unit 1 Whole Numbers, Place Value and Properties (N.1, N.7)Length: ~ 2 weeksTimeframe: Early September to Mid-September

Unit 2 Algebra (N.5, N.8, N.13, A.1, A.3)Length: ~ 3 weeksTimeframe: Mid-September to early October

Unit 3 Adding and Subtracting Fractions (N.1, N.10)Length: ~2 weeksTimeframe: Mid-October to Late October

Unit 4 Multiplying and Dividing Fractions (N.1, N.10)Length: ~2 weeksTimeframe: Early November

Unit 5 Ratio, Proportion and Percents (N.1, N.5, N.12, G.3)Length: ~ 3 weeksTimeframe: Mid-November to Mid-December

Unit 6 Geometry (G.1, G.5)Length: ~4 weeksTimeframe: Mid-December to Mid-January

Unit 7 Measurement (M.5, G.5)Length: ~2 weeksTimeframe: Late January

Unit 8 Rational Numbers (N.3, N.7)Length: ~1 weekTimeframe: First week of February

Unit 9 Data and Statistics (D.2)Length: ~ 2 weeksTimeframe: February

State Assessment Review and AdministrationLength: ~ 2 weeksTimeframe: Early to mid-March (State Assessment: 3/15 and 3/16)

Unit 10 Algebra (A.2)Length: ~ 1 weekTimeframe: End of March (after assessment)


Unit 11 Coordinate Geometry (G.7)Length: ~ 2 weeksTimeframe: Early April

Unit 12 Collection and Display of Data (D.1)Length: ~ 3 weeksTimeframe: Late April to Early May

Unit 13 Probability (D.3)Length: ~ 2 weeksTimeframe: Mid-May


Unit 1 Whole Numbers, Place Value and PropertiesLength: ~ 2 weeksTimeframe: Early September to Mid-September

State Standards (Shaded statements are identified as Post-March Indicators):6.N.1 Read and write whole numbers to trillions6.N.2 Define and identify the commutative and associative properties of addition and

multiplication6.N.3 Define and identify the distributive property of multiplication over addition6.N.4 Define and identify the identity and inverse properties of addition and multiplication6.N.5 Define and identify the zero property of multiplication6.N.19 Identify the multiplicative inverse (reciprocal) of a number

Local Standards (Stricken text is covered in a different unit):L.6.N.1 Read and write whole numbers to trillions; convert among fractions, decimals

(repeating and non-repeating), and percents (0 to 100).L.6.N.7 Identify, use, and explain: the commutative and associative properties of addition and

multiplication, the distributive property of multiplication over addition, the identityand inverse properties of addition and multiplication, and the zero property ofmultiplication; define absolute value and determine the absolute value of rationalnumbers

Big Ideas:Whole numbers are an infinite set.Using the properties of addition and multiplication will simplify the mental math process.Properties are the ground rules for the game of math.

Essential Questions:How is each place value related to the one on the right?How can the associative property help add a large group of numbers in a series?

Prior knowledge:to know basic addition and multiplication math factsto know place value of digits in a numberto read and write whole numbers to millionsto use parenthesis to show the grouping of numbers (Holt 1-4)to represent, compare and order decimals (Holt 3-1)to add and subtract decimals (Holt 3-3)

Unit Objectives:to read whole numbers to trillionsto write whole numbers to trillionsto identify the commutative, associative, distributive, identity, and zero properties of

addition and multiplicationto use the commutative, associative, distributive, identity, and zero properties ofaddition and multiplication


to explain the commutative, associative, distributive, identity, and zero properties ofaddition and multiplication

Resources:Holt: 1-1 (read and write large numbers)

1-5 (distributive, commutative, associative)Holt Text: Skills Bank page 757 (identity, and zero properties)Holt WB: Are You Ready- Skill 48 (identity, and zero properties)

Review Template (No Calculators):All operations with whole numbers

1. Find the sum of 1665 and 18,0242. Find the difference of 4,835 and 1,2873. The product of 3,655 and 61 is:4. What is the quotient of 4,810 and 10?

Rounding whole numbers and place value to millions1. Round 81,294,537 to the given place:

a. thousands b. millions2. Give the place value of the digit 4 in 2,549,013.

Use of parenthesis1. Simplify:

a. 7 ( 8 + 3)b. ( 11-5 ) ∏ 3

Problem Solving:1. At every hour of the day, a clock beeps the same number of times as the hour. Itbeeps once at 1:00, twice at 2:00, three times at 3:00, and so on. How many times does itbeep in one day? (Answer: 156 times)

2. Oops! The 5 key on your calculator just broke. Using this calculator, how could youfind the answer to 597 x 84. [One answer: Using the distributiveproperty: (600-3) x 84 = (600 x 84) – (3 x 84) = 50,148]

3. From: SFAW: DT 2-7:On her birthday, Jennifer spent half of her savings at the mall and then donated $5 tocharity. She received $25 as a birthday gift. Now she has $128. How much money didJennifer have before she went to the mall? (Answer: $216)


Unit 2 AlgebraLength: ~ 3 weeksTimeframe: Mid-September to Mid-October

State Standards (Shaded statements are identified as Post-March Indicators):6.N.22 Evaluate numerical expressions using order of operations (may include exponents of

two and three)6.N.23 Represent repeated multiplication in exponential form6.N.24 Represent exponential form as repeated multiplication6.N.25 Evaluate expressions having exponents where the power is an exponent of one, two,

or three6.N.26 Estimate a percent of quantity (0% to 100%)6.N.27 Justify the reasonableness of answers using estimation (including rounding)6.A.1 Translate two-step verbal expressions into algebraic expressions6.A.2 Use substitution to evaluate algebraic expressions (may include exponents of one, two

and three)6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance,

temperature, interest, etc.)

Local Standards (Stricken text is covered in a different unit):L.6.N.8 Evaluate numerical expressions using order of operations (may include exponents of

two and three)L.6.N.13 Convert between repeated multiplication and power notationL.6.N.5 Estimate a percent (0 to 100%) of a quantity; justify the reasonableness of answers

using estimation including roundingL.6.A.1 Translate between two-step verbal and algebraic expressions and equations.L.6.A.3 Substitute values(for 1 or 2 variables) into an expression (including exponents up to

3) and evaluate it (e.g. circumference, area, volume, distance, temperature, interest,etc.) (See L.6.N.8).

Big Ideas:There are alternate solutions to math problems.The set of rules known as the order of operations, guarantees that everyone gets the same

solution for a problem.Phrases and situations can be translated into mathematical expressions.

Essential Questions:What is the difference between a constant and a variable?What is the advantage of using exponents to write numbers?Is n7 the same the same as n * 7?What happens when you raise a base number to the zero power? First power?

Prior knowledge:to know the difference between a constant and a variableto know sum, difference, product, and quotientto know the words that suggest each operation


to know multiplication is repeated additionto know the difference between an expression and an equationto solve 1-step equations using inverse operation

Unit Objectives:to translate 1 or 2 step verbal and algebraic expressionsto evaluate numerical and algebraic expressions using substitution and order of

operationsto determine if an equation is true or falseto find the value of a variable to make an equation trueto identify the base number and exponent in a powerto use exponents to express repeated multiplicationto write numbers in standard form, exponential notation, and as a product of factors

6A: Enriched Objectives and Resources to solve two step equations (POST MARCH)

(Holt pages 90-91)(Are You Ready Workbook: Skill 60)

to use grouping symbols /brackets and braces(supplement materials)

to use powers of ten to represent place value(supplement materials)

Resources:Holt: 1-3 (exponents)

1-4 (order of operations)2-1 (variables and expressions)2-2 (translate expressions)Holt pages 90-91 (translate 2 step verbal and algebraic expressions)2-4 (equations and their solutions)2-5 through 2-8 (solving 1-step equations)

Supplement: evaluating 2 variables in an expression using substitution

Hands-On Equations

Review Template (No Calculators):Constant and variables

Identify each as a variable or a constant.1. the price of a pair of sneakers2. the number of days in October3. the number of people in Auburn

Expressions, equations1. Write each phrase as an expression.

a. a number, n, decreased by 7b. half of k


c. r cubedd. 18 more than x

3. Which one is not an equation?a. 6 x 9 b. 12 - 4 + n = 9 c. 24 ∏ 3 = 8

Problem Solving:Rufus has $3.45 in quarters and dimes. He has four more quarters than dimes. How

many of each coin does he have? (Answer: 11 quarters, 6 dimes)


Unit 3 Adding and Subtracting FractionsLength: ~2 weeksTimeframe: Mid-October to Late October

State Standards (Shaded statements are identified as Post-March Indicators):6.N.16 Add and subtract fractions with unlike denominators6.N.18 Add, subtract, multiply and divide mixed numbers with unlike denominators6.N.20 Represent fractions as terminating or repeating decimals6.N.21 Find multiple representations of rational numbers (fractions, decimals, and percents 0

to 100)


(repeating and non-repeating), and percents (0 to 100).L.6.N.10 Add, subtract, multiply, and divide fractions and mixed numbers with unlike

denominators

Big Ideas:Fractions are used in real-life situations.Fractions represent parts of a whole, a group, or a set.Divisibility rules make working with fractions easier.

Essential Questions:Why do you need like denominators to add or subtract fractions?Why is it easier to add fractions using the least common denominator instead of any

common denominator?Could you add mixed numbers by first changing them to decimals? Explain.In a subtraction problem, when might you need to convert a whole number into a mixed

number?

Prior knowledge:to know the rules of divisibility (Holt 4-1)to identify the numerator and denominator of a fractionto know the difference between a proper and improper fraction (Holt 4-6)to compare and order fractions (Holt 4-7)to know prime and composite numbers (Holt 4-1)to find the LCM of two or more numbers (Holt 5-1)to find the GCF of two or more numbers (Holt 4-3)to find equivalent fractions (Holt 4-5)to reduce fractions to lowest terms (Holt 4-5)to convert between mixed numbers and improper fractions (Holt 4-6)to add and subtract like fractions and mixed numbers (Holt 4-8)

Unit Objectives:to find equivalent fractions


to find a lowest term fractionto find the LCDto add and subtract fractions with unlike denominatorsto add and subtract mixed numbers with unlike denominators

6A: Enriched Objectives and Resources to find the LCM of two or more numbers using prime factorization

(Holt: 5-1) (see Holt: Know It Notebook) to find the GCF of two or more numbers using prime factorization

(Holt: 4-3) (see Holt: Know It Notebook) to solve addition and subtraction fraction equations

(Holt: 5-5)(see Holt: Chapter 5 Resource Book)

Resources:Holt: 4-5 (Understanding equivalent fractions)

4-5 (Fractions in lowest terms)5-2 (Adding and subtracting fractions with unlike denominators)5-3 (Adding and subtracting mixed numbers)5-4 (Regrouping to subtract mixed numbers)

Review Template (No Calculators):Divisibility rules, LCM, GCF

1. Test each number for divisibility by 2, 3, 5,6,9 and 10.a. 104 b. 660 c. 450 d. 1,233

2. Find the LCM for each number paira. 14 and 24b. 21 and 35

3. Find the GCF of the given pair of numbers.a. 15 and 20b. 18 and 45c. 17 and 21

Lowest terms, compare and order fractions1. Write in lowest terms.

a. 8/10 b. 21/28 c. 36/54 d. 12/152. Compare these fractions:

a. 2/3 � 8/12 b. 3/6 � 6/9 c. 7/11 � 2/3

3. Order from least to greatest using repeated inequalitiesa. 2/3 , 7/8 , 3/4 b. 2/5 , 1/4, 1/2 c. 3/4 , 3/5 , 5/6

Add and subtract like fractions/mixed numbers1. 1 1/4 + 3/42. 5 3/8 + 4 1/8


3. 2 712 – 4 11/124. 8 3/7 + 1 1/7

Prime and composite numbers1. Given the number and its factors, tell whether it is prime or composite.

a. 29: 1,29b. 57: 1,3,19,57c. 92: 1,2,4,23,46,92d. 83: 1,83

2. Which number is a prime number?a. 63 b. 78 c. 115 d. 29

Problem Solving:

A string is cut in half, and on e of the halves is used ot bundle newspapers. Then, one fifth of theremaining string is cut off. The piece left is 8 feet long. How long was the stringoriginally?

Answer: 20 feet


Unit 4 Multiplying and Dividing FractionsLength: ~2 weeksTimeframe: Early November

State Standards (Shaded statements are identified as Post-March Indicators):6.N.17 Multiply and divide fractions with unlike denominators6.N.18 Add, subtract, multiply and divide mixed numbers with unlike denominators6.N.20 Represent fractions as terminating or repeating decimals6.N.21 Find multiple representations of rational numbers (fractions, decimals, and percents 0

to 100)


(repeating and non-repeating), and percents (0 to 100).L.6.N.10 Add, subtract, multiply, and divide fractions and mixed numbers with unlike

denominators

Big Ideas:The same value can be expressed as both a fraction and a decimal.Multiplying by a number less than 1, results in a smaller product.Dividing by a whole number is the same as multiplying by its reciprocal. (e.g. dividing by

3 is the same as multiplying by 1/3)

Essential Questions:Can every fraction be changed into a decimal? Why or why not?How is multiplying two fractions different from adding two fractions?What is really happening when you divide a whole number by a proper fraction? What

does it mean? Will the quotient be larger or smaller than the whole number?Why?

Prior knowledge:to know the rules of divisibilityto know the difference between a proper and improper fractionto find the GCF of two or more numbersto reduce fractions to lowest termsto convert between mixed numbers and improper fractions

note: to multiply and divide decimals (Holt 3-5, 3-6, 3-7)Unit Objectives:

to know that the fractional bar means to divide the numerator by the denominatorto convert between fractions and decimalsto identify a repeating and non-repeating (terminating) decimalsto multiply fractions with unlike denominators by a whole number, a fraction, and a

mixed numberto find the reciprocal of a whole number, mixed number, and fractionto simplify common factors before multiplying


to divide fractions with unlike denominators by a whole number, a fraction, and a mixednumber

6A: Enriched Objectives and Resources to solve multiplication and division fraction equations

(Holt: 5-10) (see Holt: Chapter 5 Resource Book) to interpret the quotient in word problems

(Holt: 3-8)(see Holt: Ready to Go On workbook page 57)

Resources:Holt: 4-4 (Converting fractions to decimals)

5-6 (Multiplying by a whole number)5-7 (Multiplying fractions)5-8 (Multiplying mixed numbers)5-9 (Dividing fractions and mixed numbers)

Review Template (No Calculators):GCF

1.Find the GCF of the given pair of numbers.a. 15 and 20b. 10 and 12c. 18 and 45d. 21 and 28

Proper and improper fractions1. Identify each fraction as proper or improper.

a. 9/12b. 12/3c. 3/2

2. Write as a improper fraction or mixed number.a. 3 1/3b. 99/10c. 14/5d. 2 9/12e. 1 1/4f. 5 4/5

Problem Solving:

A box of laundry detergent contains 35 cups. If you use 1 and 1/4 cups per load of laundry, howmany loads can you wash with 1 box?

Answer: 28 loads


Placido, Dexter, and Scott play guard, forward, and center on a team, but not necessarily in thatorder. Placido and the center dove Scott to practice on Saturday. Placido does not playguard. Who is the guard?

Answer: Scott


Unit 5 Ratio, Proportion and Percents (N.1, N.5, N.12, G.3)Length: ~ 3 weeksTimeframe: Mid-November to Mid-December

State Standards (Shaded statements are identified as Post-March Indicators):6.N.6 Understand the concept of rate6.N.7 Express equivalent ratios as a proportion6.N.8 Distinguish the difference between rate and ratio6.N.9 Solve proportions using equivalent fractions6.N.10 Verify the proportionality using the product of the means equals the product of the

extremes6.N.11 Read, write, and identify percents of a whole (0% to 100%)6.N.12 Solve percent problems involving percent, rate, and base6.N.20 Represent fractions as terminating or repeating decimals6.N.21 Find multiple representations of rational numbers (fractions, decimals, and percents 0

to 100)6.N.26 Estimate a percent of quantity (0% to 100%)6.N.27 Justify the reasonableness of answers using estimation (including rounding)6.A.5 Solve simple proportions within context6.G.1 Calculate the length of corresponding sides of similar triangles, using proportional

reasoning


(repeating and non-repeating), and percents (0 to 100).L.6.N.5 Estimate a percent (0 to 100%) of a quantity; justify the reasonableness of answers

using estimation including roundingL.6.N.12 Understand the concepts of rate and ratio and distinguish between them; express

equivalent ratios as proportions, solve proportions (see L.6.A.2), and verifyproportionality (e.g. verify two triangles are similar, see L.6.G.3)); read, write, andidentify percents of a whole (0% to 100%); solve percent application problems

L.6.A.2 Solve and explain simple (whole number) two-step equations using inverse operations;solve proportions (see L.6.N.12)

L.6.G.3 Calculate the length of corresponding sides of similar triangles using proportionalreasoning (see L.6.N.12 and L.6.A.2).

Big Ideas:Ratios and proportions are found in real-life situations.Proportions are the key to solving percent problems.Working with ratios is the same as working with fractions.

Essential Questions:What does it mean to say quantities are proportional?Can you solve a proportion without using cross products? Explain.Is it possible to have more than 100% of a quantity or less than 1% of a quantity?What do you know about the sides of similar triangles?


Why is it necessary to change a percent to its fraction or decimal equivalent?

Prior knowledge:to know the concept of ratioto know the concept of percentto identify similar triangles and their corresponding sides and angles to use multiplication to find cross productsto be able to estimate and roundto evaluate algebraic expressions

Unit Objectives:to write a ratio three waysto express two quantities as a ratioto find ratios equal to a given ratioto express two quantities with different units as a rateto know a proportion is two equal ratiosto decide if two ratios form a proportionto solve proportions using cross productsto use proportions to calculate the lengths of the corresponding sides of similar trianglesto read, write, and identify a quantity as a percent of a wholeto estimate percents of a quantityto express percents as fractions and decimalsto express fractions and decimals as percentsto use estimation (including rounding) of percents to justify the reasonableness of

answersto solve percent application problems using proportions (only % of a number)to find interest by substituting values into the formula and evaluating (I = PRT)

6A: Enriched Objectives and Resources to read and use maps and scale drawings

(Holt: 7-6) (see Holt: Chapter 7 Resource Book) to solve all percent application problems using proportions

(supplement: Holt Grade 7 Text: 6-5) to solve percent problems using discounts, tips and sales tax

(Holt 7-10)


Resources:Holt: 7-1, 7-2 (Ratios and Rates) 7-3 (Proportions; solving proportions using cross products)

7-4 (Similar figures)7-7 (Percent)7-8 (Percents, decimals and fractions)

7-9 (Percent problems)Holt Text: (Finding Interest) Extension pages 400-401Supplement: (Estimating a percent)

(see Holt Grade 7 Text: 6-3)

Review Template (No Calculators):Define ratio and percent, similar triangles and corresponding parts

1. Complete each statement with one of the following terms: ratio, percent, corresponding parts, similar figures

a. Figures that have the same shape, but not necessarily the same size arecalled ________________________.

b. A comparison of two quantities, often written as a fraction is a _____.c. If two figures are similar, their _________________ are proportional.d. A ratio that compares a part to a whole using the number 100 is a

_____________. Cross products

1. Compare ( > , < , = ) using cross products.a. 5/6 � 7/8 b. 8/11 � 5/7 c. 3/4 � 5/6

Evaluate algebraic expressions1. Evaluate:

a.

�

4b + 6 if b = 3 b.

�

24t

if t = 8


Unit 6 Geometry (G.1, G.5)Length: ~4 weeksTimeframe: Mid-December to Mid-January

State Standards (Shaded statements are identified as Post-March Indicators):6.G.2 Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi, and

trapezoids) and develop formulas6.G.3 Use a variety of strategies to find the area of regular and irregular polygons6.G.4 Determine the volume of rectangular prisms by counting cubes and develop the

formula6.G.5 Identify radius, diameter, chords and central angles of a circle6.G.6 Understand the relationship between the diameter and radius of a circle6.G.7 Determine the area and circumference of a circle, using the appropriate formula6.G.8 Calculate the area of a sector of a circle, given the measure of a central angle and the

radius of the circle6.G.9 Understand the relationship between the circumference and the diameter of a circle6.M.1 Measure capacity and calculate volume of a rectangular prism6.M.7 Estimate volume, area, and circumference (see figures identified in geometry strand)

Local Standards (Stricken text is covered in a different unit):L.6.G.1 Identify the radius and diameter (and the relationship between them), chords, and

central angles of a circle; understand the relationship between the circumference andthe diameter of a circle.

L.6.G.5 Estimate and determine the area of triangles and quadrilaterals (square, rectangle,rhombus, trapezoid) and develop area formulas; estimate and find the area of regularand irregular polygons; estimate the volume of rectangular prisms by counting cubesand calculate the volume after developing a formula; determine the circumference andarea of a circle using a formula, and calculate the area of a sector of a circle, given thecentral angle and radius

Big Ideas:Geometric patterns and designs are evident everywhere, such as in art, history, and

science.Perimeter measures the length or distance around a shape or an object.Circumference is the distance around or the perimeter of a circle.Area measures square units inside the figure.Volume is the number of cubic units needed to fill a solid figure.

Essential Questions:How is finding the area of a triangle different than finding the area of a rectangle or

square?For a given rectangle, if you switch the numbers for the base and height, do you get a

different area? Explain.What is difference between perimeter, area and volume?Why do we use 3 as an estimate for pi?If two circles have the same circumference, must they have the same area?


Prior knowledge:to identify triangles and quadrilaterals (Holt Text: 8-5; 8-6)to evaluate algebraic expressionsto identify and plot points in the first quadrant (Holt Text 6-6)to plot points to form basic geometric shapes (identify and classify)to calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles

and shapes composed of rectangles having sides with whole number lengths andparallel to the axes) (supplement: Coach Workbook)

Unit Objectives:to know the difference between perimeter, area, and volume of polygonsto estimate the area of quadrilaterals and trianglesto identify the base and height of triangles and quadrilateralsto develop the area formulas for triangles and quadrilateralsto find the area of triangles and quadrilaterals using formulasto find the area of regular and irregular polygonsto estimate the volume of rectangular prisms by counting cubesto calculate the volume of rectangular prisms by developing a formulato identify the radius, diameter, chords, and central angles of a circleto know the relationship between radius and diameterto know the relationship between the circumference and the diameter of a circle (value of

pi is circumference divided by diameter)to know pi is approximately = to 3.1416 (Note: Do not use this approximation in

calculations) (to estimate circumference and area, use 3 as an approximationfor !)

to find the circumference of a circle using a formula (Note: students should leaveanswer in terms of !, the only approximation of ! that is acceptable is the !key on a calculator)

to find the area of a circle using a formula (Note: students should leave answer interms of !, the only approximation of ! that is acceptable is the ! key on acalculator)

to calculate the area of a sector of a circle given the central angle and radius

6A: Enriched Objectives and Resources to calculate the radius or diameter when given the circumference or area of a circle

(Holt: 7-6) to identify pairs of angle relationships

(Holt 8-3)(Holt Text: Hands on Lab: pages 432-433)

to find the area of composite figures when comprised of quadrilaterals, triangles, and/or circles

(Holt 10-3)(Supplement: Holt Grade 7 Text 9-6)


Resources:Holt: 9-7 (Perimeter) 10-1 (Estimating and finding area)

10-2 (Area of triangles-only)10-3 (Area of composite figures) 9-8 (Circles and circumference)10-4 (Comparing Perimeter and Area)10-5 (Area of a circle) note: answer must be in terms of ! when estimating use 3 instead of 3.14 to find the answerSupplement: chord

central anglearea of sector of a circle (Holt text page 764; Coach Workbook)

10-6 (Three-dimensional figures)10-7 (Volume of prisms)

Problem solving:A rectangular prism has a volume of 36 cubic inches. Its length is 2 inches, itsdepth 9 inches. How wide is it? Explain how you found your answer.

(Answer: 2 inches)

Review Template (No Calculators):Geometry vocabulary

1, Which quadrilaterals have 2 pair of parallel sides?2. Classify a triangle that has two sides that measure 4 cm. each, and one side

with a length of 5 cm.3. Explain why all squares are rectangles, but not all rectangles are squares?4. True or false?

a. A square is also a parallelogram.b. Every four-sided figure can be classified as more than one type of

quadrilateral.c. All triangles are quadrilaterals.d. A rectangle is a parallelogram.e. A square is a quadrilateral.f. Triangles have 4 sides.


Plot points in first quadrant

Plot points to form, identify, and classify basic geometric shapes

Calculate perimeter of basic geometric shapes on the coordinate plane


Unit 7 Measurement (M.5)Length: ~2 weeksTimeframe: Late January

State Standards (Shaded statements are identified as Post-March Indicators):6.M.1 Measure capacity and calculate volume of a rectangular prism6.M.2 Identify customary units of capacity (cups, pints, quarts, and gallons)6.M.3 Identify equivalent customary units of capacity (cups to pints, pints to quarts, and

quarts to gallons)6.M.4 Identify metric units of capacity (liter and milliliter)6.M.5 Identify equivalent metric units of capacity (milliliter to liter and liter to milliliter)6.M.6 Determine the tool and technique to measure with an appropriate level of precision:

capacity6.M.8 Justify the reasonableness of estimates6.M.9 Determine personal references for capacity

Local Standards (Stricken text is covered in a different unit):L.6.M.5 Measure volume (capacity) using the appropriate tool and technique; identify and

convert between units of volume (capacity) within a given system (metric orcustomary); determine personal references for customary and metric units of volume(capacity); justify the reasonableness of an estimate of the volume of an object.

Big Ideas:The metric system is used in almost every country in the world while customary units are

used in the United States.Conversions are simple in the metric system because every unit is based on the number

10.

Essential Questions:Is it easier to convert in the metric or the customary system? Why?

Prior knowledge:to determine personal references and approximate comparisons for metric unitsto determine personal references and approximate comparisons for customary unitsto identify the basic metric units and prefixes for measuring length, mass, capacityto convert equivalent metric units of length and massto identify the customary equivalent units of length and massto convert equivalent customary units of length and mass

Unit Objectives:to identify metric units of capacity (liter and milliliter)to convert equivalent metric units of capacity(liter to milliliter and milliliter to liter)to identify customary units of capacity(cups, pints, quarts, and gallons)to convert equivalent customary units of capacity(cups to pints, pints to quarts, quarts to

gallons)to determine the tool and technique to measure an appropriate level of precision: capacit


Resources:Holt: 9-1 (Understanding Customary Units of Measure)

9-2 (Understanding Metric Units of Measure)9-3 (Converting Customary Units)9-4 (Converting Metric Units)Supplement: tools and techniques for measuring capacity

Review Template (No Calculators):Calculate elapsed time in hours and minutes

1. Reuben is going out, but has promised he would be home by 5:30 PM. Ittakes him 20 minutes to skate over to his friend’s house. He will stay therefor two hours. On the way home, he always stops for a snack, so the returntrip takes 30 minutes. If Reuben is to keep his promise, by what time must heleave home?

2. Bryan got to school at 8:05 AM. It took him 1/4 hour to walk from home, 1/4 hour to look at some magazines along the way, and 1/2 hour to eat breakfast. What time did he sit down to eat?

Metric basic units and prefixes1. Choose the most appropriate unit of measure to estimate the length of each

object. Write centimeter or meter.a. book b. school bus c, postcard d. computer desk

Process for converting within metric systemComplete:1. 90 mm = ____________cm2. 17 cm = _____________mm3. 100 cm = ____________m4. 8000 mm = __________ m5. 5 m = ______________mm6. 3000 mL = ___________L7. 1.3 L = ______________mL8. 14 L = _____________mL9. 2.75 kg = ____________g10. 1900 g = ____________kg

Customary units for length and massComplete:1. 36 in. = _____________ft.2. 4 yd. = ____________ft.3. 2 ft. = _____________in.4. 10 yd. = ____________in.

Personal references/approximate comparisons for both metric and customary units


Unit 8 Rational Numbers (N.3, N.7)Length: ~1 weekTimeframe: First week of February

State Standards (Shaded statements are identified as Post-March Indicators):6.N.13 Define absolute value and determine the absolute value of rational numbers

(including positive and negative)6.N.14 Locate rational numbers on a number line (including positive and negative)6.N.15 Order rational numbers (including positive and negative)

Local Standards (Stricken text is covered in a different unit):L.6.N.3 Order rational numbers (positive and negative) including locating them on a number

lineL.6.N.7 Identify, use, and explain: the commutative and associative properties of addition and

multiplication, the distributive property of multiplication over addition, the identityand inverse properties of addition and multiplication, and the zero property ofmultiplication; define absolute value and determine the absolute value of rationalnumbers

Big Ideas:Numbers can be either positive or negative.Negative numbers are necessary in real-life situations, such as to express temperatures

below zero.On a number line, any number to the left of another number is smaller.Positive and negative numbers are used to express opposites.

Essential Questions:Is a negative number always less than a positive number? Explain.Is the absolute value of a – 3 the same as the absolute value of a + 3? Explain.

Prior knowledge:to order and compare whole numbersto order and compare decimals and fractions

Unit Objectives:to define rational numbersto locate rational numbers on a number line (including positive and negative)to compare and order rational numbers (including positive and negative) (Holt Text:4-4)to know absolute value of rational numbersto determine the absolute value of rational numbers( including positive and negative)


6A: Enriched Objectives and Resources to add integers (POST MARCH)

(Holt 11-4) (see Holt: Chapter 11 Resource Book) to subtract integers (POST MARCH)

(Holt: 11-5) (see Holt: Chapter 11 Resource Book)

Resources:Supplement: Holt Text Skills Bank page 762; Coach Workbook (Rational numbers;define and locate on number line)

Supplement: Holt Grade 7 Text 2-11; Coach Workbook (Comparing, ordering rationalnumbers)

Supplement: Holt Text Skills Bank page 762; Coach Workbook (Absolute Value)

Review Template (No Calculators):Compare and order whole number, decimals, and fractions

Compare using > , < , or =.1. 1/2 � 7/8

2. 5/8 � 2/3

3. 1 7/8 � 2 5/6

4. 1 4/7 � 1 4/9

5. 4.6 � 4.60

6. 98.23 � 98.3

7. 7.32 � 7.320

8. 21.7 � 21.07

9. 0.46 � 2/3

10. 9/10 � 0.9

11. 0.11 � 1/5

12. 7/8 � 0.78


Unit 9 Data and Statistics (D.2)Length: ~ 2 weeksTimeframe: February

State Standards (Shaded statements are identified as Post-March Indicators):6.S.5 Determine the mean, mode and median for a given set of data6.S.6 Determine the range for a given set of data6.S.7 Read and interpret graphs6.S.8 Justify predictions made from data

Local Standards (Stricken text is covered in a different unit):L.6.S.2 Calculate and use the mean, mode, median, and range of a set of data; read, interpret,

and predict from (with justification) graphs

Big Ideas:Graphs make it easier to compare data and find possible patterns.Mean, median and mode are all measures of central tendency but they tell us different

things.

Essential Questions:Why might a graph showing data be better than a list of data?Why might someone want to create a misleading graph?Must the mean, the median, or the mode of a data set a member of the set? Explain.How are the mean, median and the mode similar? Different? Why would you use one

before another?

Prior knowledge:to read and interpret line and bar graphsto calculate the mean of a set of data

Unit Objectives:to identify types of graphs (line, bar, circle, pictograph, histogram, Venn diagram)to identify common ways that a graph can suggest misleading relationshipsto read and interpret different types of graphsto make predictions based on data analysisto determine the mean, mode and median for a given set of datato determine the range for a given set of data

6A: Enriched Objectives and Resources to learn the effect of additional data and outliers

(Holt: 6-3) to make and analyze stem-and-leaf plots

(Holt: 6-9) to choose an appropriate way to display data (POST MARCH)

(Holt: 6-10)


Resources:Holt: 6-2 (Mean, median, mode, range)

6-4 (Bar graphs)6-5 (Histogram) Holt Text, page 7656-7 (Line graphs)6-8 (Misleading graphs)Supplement:

Holt Text: Extension pages 212-213 (Venn Diagrams)Holt Text: Hands on Lab pages 524-525 (Circle Graphs)Holt Text: page 251, 759 (pictograph)

Optional: “M” States Project

Review Template (No Calculators):Read and interpret line and bar graphs

***Find and scan in graphs

Mean for a set of dataCalculate the mean for each set of data.1. 8,10,7.6.5,7,132. 12, 18,10, 13, 15, 19, 22, 273. 1.6, 2.2, 3.1, 2.4, 1.7, 2.2. 2.2

Problem solving:1. Fifteen customers have dessert with lunch. Seven order ice cream and 10 order applepie. How many order both? (Answer: 2 - Use a Venn diagram)

Review Unit for State Assessment (Test dates: March)Length: 1 weekTimeframe: first week in March


Unit 10 AlgebraLength: ~1 weekTimeframe: End of March (after assessment)

State Standards (Shaded statements are identified as Post-March Indicators):6.A.3 Translate two-step verbal sentences into algebraic equations6.A.4 Solve and explain two-step equations involving whole numbers using inverse

operations6.A.5 Solve simple proportions within context

Local Standards (Stricken text is covered in a different unit):L.6.A.1 Translate between two-step verbal and algebraic expressions and equations.L.6.A.2 Solve and explain simple (whole number) two-step equations using inverse

operations; solve proportions (see L.6.N.12)

Big Ideas:Phrases and situations can be translated into mathematical equations.Only the variables are replaced by numbers when evaluating equations.Equations must be balanced on both sides of the equal sign.

Essential Questions:Can n have any value in 2n + 5 = 19? Explain.

Prior knowledge:to know the difference between a constant and a variable (may need to be taught ’05-06)to know sum, difference, product, and quotientto know the words that suggest each operationto know multiplication is repeated additionto know the difference between an expression and an equation (may need to be taught in

’05-06)to solve 1-step equations using inverse operation (may need to be taught in ’05-06)to translate 1 or 2 step verbal and algebraic expressions

Unit Objectives:to translate two-step verbal sentences into algebraic equationsto solve and explain simple (whole number) two-step equations using inverse operations

6A: Enriched Objectives and Resources to solve equations that have variables on both sides

(Supplement: Holt Grade 7 Text 12-3)

Resources:Supplement Holt Grade 7 Text 1-8 (two-step verbal sentences into algebraic equations)Supplement Holt Grade 7 Text 12-1 (solve two-step equations using inverse operationsHand-on Equations


Review Template (No Calculators):Translating expressionsSolving one-step equations


Unit 11 Coordinate Geometry (G.7)Length: ~ 2 weeksTimeframe: Early April

State Standards (Shaded statements are identified as Post-March Indicators):6.G.10 Identify and plot points in all four quadrants6.G.11 Calculate the area of basic polygons drawn on a coordinate plane (rectangles and

shapes composed of rectangles having sides with integer lengths)

Local Standards (Stricken text is covered in a different unit):L.6.G.7 Identify and plot points in all four quadrants of the coordinate plane; calculate the

area of shapes with sides parallel to the axes (see L.6.G.5).

Big Ideas:The coordinate plane can be used to locate any point on a flat surface.Using the signs of the coordinates of a point can help predict which quadrant the point is

in.

Essential Questions:How can you use mathematics to describe the location of something like a buried

treasure?In what real world situations, is it important to describe a location exactly?Are the points (2,3) and (3,2) the same? Explain.

Prior knowledge:to know positive and negative numbers on a number lineto identify and plot points in the first quadrant (Holt 6-6)to plot points to form a basic geometric shape (identify and classify)to calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles

and shapes composed of rectangles having sides parallel to the axes with wholenumber lengths)

Unit Objectives:to identify points on coordinate plane in all four quadrantsto plot points on a coordinate plane in all four quadrantsto calculate the area of basic polygons( rectangles and shapes composed of rectangles

having sides with integer lengths) drawn on a coordinate planeResources:

Holt: 11-3 (The coordinate plane)Supplement: (Coach Workbook) Plotting points to form basic polygons and calculatingthe areas

Review Template (No Calculators):Locate points on a number line (positive and negative)Perimeter of polygonsIdentify and classify basic geometric shapes


Unit 12 Collection and Display of Data (D.1)Length: ~ 3 weeksTimeframe: Late April- Early May

State Standards (Shaded statements are identified as Post-March Indicators):6.S.1 Develop the concept of sampling when collecting data from a population and decide

the best method to collect data for a particular question6.S.2 Record data in a frequency table6.S.3 Construct Venn diagrams to sort data6.S.4 Determine and justify the most appropriate graph to display a given set of data

(pictograph, bar graph, line graph, histogram, or circle graph)

Local Standards (Stricken text is covered in a different unit):L.6.S.1 Explore data collection through sampling; record (e.g. with a frequency table) and

choose an appropriate display (e.g. Venn diagram, pictograph, bar graph, line graph,histogram, circle graph) real-world data ; construct Venn diagrams.

Big Ideas:Data can be displayed in a variety of ways.Statistics can be used to inform you and also to mislead you.

Essential Questions:Why display data in a graph or a table?How do you decide what type of graph to use to display data?

Prior knowledge:to collect and record data from a variety of sourcesto display data with tables and graphsto use a line graph to show change over time

Unit Objectives:to collect data through samplingto record data collection in a frequency tableto determine the appropriate graph (pictograph, bar, line, histogram, or circle) to display a

given set of datato construct Venn diagrams to sort data

Resources:Holt: 6-3 (Choosing an appropriate display) 6-5(Line plots, frequency tables)Supplement: Holt Text Extension pages 212-213 (know, interpret and construct Venndiagrams to display data)

Review Template (No Calculators):


Unit 13 Probability (D.3)Length: ~ 2 weeksTimeframe: Mid-May

State Standards (Shaded statements are identified as Post-March Indicators):6.S.9 List possible outcomes for compound events6.S.10 Determine the probability of dependent events6.S.11 Determine the number of possible outcomes for a compound event by using the

fundamental counting principle and use this to determine the probabilities of eventswhen the outcomes have equal probability

Local Standards (Stricken text is covered in a different unit):L.6.S.3 For a compound-event: determine the sample space using the fundamental counting

principle, list all possible outcomes, and determine the probability of a singleoutcome; determine the probability of dependent events.

Big Ideas:You can never have a probability greater than 1 or less than 0.Probability not only expresses the chance that something will happen, but also the chance

that something will not happen.

Essential Questions:What is the probability that you will be in school today?

Prior knowledge:to list possible outcomes for single-event experimentto record experiment results using fractions or ratios (Holt 12-1, 12-2)to create a sample space and determine the probability of a single-event, given a sample

experiment (i.e., rolling a number cube)

Unit Objectives:to list the possible outcomes for compound eventsto determine the probability of a dependent eventsto determine number of the possible outcomes for compound events by using the

fundamental counting principle, tree diagramto determine the probability of events when the outcomes have equal probability

Resources:Holt: 12-3 (Counting methods and sample spaces) 12-4 (Theoretical probability) 12-5 (Compound events)

12-6 (Making predictions) Supplement: Holt Text Extension pages 700-701 (dependent/independent events)

Review Template (No Calculators):


Documents

6th Grade Mathematics Curriculum - Auburn School …district.auburn.cnyric.org/departments/math/Math Curriculum/6th_for...AECSD Grade_6_Math_Curr Rev 7-08.doc 1 6th Grade Mathematics