6th Grade Homeschool Curriculum - Sixth Grade Math - Best Homeschool Curriculum - Cheap Homeschool...

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STUDENT MANUAL MATH LESSON 177-3

Directions: Order each set of integers from least to greatest.

16. -2, 5, 1, -15 __________________

17. 1, 8, -9, 13 __________________

18. -15, -14, -12, 0, -11 __________________

Directions: Add, subtract, multiply, or divide each pair as indicated.

19. -8 + 16 = _______

20. -10 + -24 = _______

21. 12 – 25 = _______

22. 1 – 4 = _______

23. 2 –16 = _______

24. 3 – (-10) = _______

25. (-12)(10) = _______

26. -9 x 8 = _______

27. -14 / -7 _______

28. -108 / -12 _______

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Lesson 178Solving Word Problems


As you near the end of your study of Math 6, you will learn how to solve any type of word problem using a 4-step problem solving model. This problem solving model can help you solve word problems using multiplication, fractions, percents and ratios, geometry, probability and algebra. It can be used for any story problem that you encounter.

The 4-step problem solving model can be seen below:

Step 1: Understand the problem

The key to completing this step is to truly and completely understand what the problem is asking. You need to know what you are solving for, and get rid of any pieces of information from the problem that you do not need.

Step 2: Plan

In this step, you need to plan out how you will solve the problem by examining what pieces of information you have been given that you need, and develop a plan and procedure for placing those pieces where they should be in the problem or equation you will need to set up to solve.

Step 3: Implement the plan

In this step, you will actually solve the problem you have set up or the equation you have de-veloped. Remember to check to make sure you have solved for the information the problem or question is asking you to find.

Step 4: Check your answer

It is a good idea to always go back and put your answer back into the problem to see if it makes sense to the problem. If it does not, you need to redo steps 1-3.

An example of the 4-step process being utilized in a word problem can be seen below.

At school, ice cream cones sell for $1.25. Amy buys one for herself and one for each of her three friends. How much change will she get back from a $20.00 bill?

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Step 1: Understand the problem. You need to know what you are solving for. In this problem, you will need to know how much money Amy spent total on all 4 ice cream cones, and then find the difference between that sum and $20.00

Step 2: Plan. You already planned a little in step 1, but ultimately, the plan will be to multiply $1.25 by 4 to get the total Amy spent, and then to subtract this total from $20.00

Step 3: Implement. This is where you actually solve the problem. $1.25 x 4 = $5.00. Therefore, Amy spent $5.00. Now, subtracting $20.00 - $5.00 gives a remainder of $15.00 that Amy will have in change.

Step 4: Check the answer. Does $15.00 make sense as an answer? Yes

Lesson Wrap-Up: You could really apply these four steps to any problem you encounter in life, whether it is a Math problem or involves something else. This process is a very logical way to approach any problem.

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Worksheet 178


Directions: Solve each word problem below by going through the 4-step problem solving model in each problem, illustrating each component of the process.

1. Anna has 5 red shirts, 3 pink shirts, and 3 yellow shirts. If she closes her eyes and chooses one shirt at random to wear on Compliments Day, what is the probability that she will not choose a yellow shirt?

_________________________________________________________________________________________

_____________________________________________________________________________________

2. Mrs. Jones is planning a barbecue for Mardi Gras Day. She will serve tea or coffee, barbecued chicken or ribs, and coleslaw or potato salad. How many combinations of choices of a beverage, a meat, and a salad does she have for her party?

_________________________________________________________________________________________

_____________________________________________________________________________________

3. Is there any pair of numbers whose product is the same as its sum?

______________________

4. In a creek bed, 1/6 of the gravel is less than 5 mm in diameter and 1/2 of it is between 5 and 10 mm in diameter. What fraction of the gravel is greater than one centimeter in diameter?

________

5. Devin found the sum of the first three even numbers and obtained a result of 48. Oops. What mistake must he have made and what is the correct answer?

_________________________________________________________________________________________

_____________________________________________________________________________________

6. In a weird new card game, Sierra scored 38,102 points during the first round. She scored two times that many points during the second round. How many points did she score in total during both rounds together?

_________________________________________________________________________________________

_____________________________________________________________________________________

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All rights reserved; No part of this publication may be reproduced or transmitted in any form or by any means without prior permission from the Publisher or Authorized Agent.

Published in electronic format in the U.S.A.

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Acknowledgments

Complete Curriculum’s K-12 curriculum been team-developed by a consortium of teachers, administrators, educational and subject matter specialists, graphic artists and editors.

In a collaborative environment, each professional participant contributed to ensuring the quality, integrity and effectiveness of each Compete Curriculum resource was commensurate with the required educational benchmarks and contemporary standards Complete Curriculum had set forth at the onset of this publishing program. �

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TABLE OF CONTENTS AND OBJECTIVES SIXTH GRADE MATH

Lesson 1Understanding Place ValueObjective: The student will learn how to express, compare, and order Whole Numbersthrough the use of Place Value.

Lesson 2Estimating with Whole NumbersObjective: The student will be able to find Sums, Differences, Products, and Quotientsusing different estimation techniques.

Lesson 3Addition and SubtractionObjective: The student will apply Addition and Subtraction to real-life problems.

Lesson 4Multiplication and DivisionObjective: The student will be able to solve real-life applicable word problems usingMultiplication and Division.

Lesson 5Algebraic ExpressionsObjective: ��

Lesson 6Algebraic EquationsObjective: The student will be able to use mental math and substitution to solveAlgebraic Equations.

Lesson 7Algebraic PropertiesObjective: The student will be able to identify and apply the Commutative, Associative,Distributive, and Identity properties of addition and multiplication.

Lesson 8ExponentsObjective: The student will be able to represent numbers using Exponents.

Lesson 9Order of OperationsObjective: The student will be able to understand and use the Order of Operations.

Lesson 10Representing, Comparing, and Ordering DecimalsObjective: The student will be able to represent, order, and compare decimals usingPlace Value

Lesson 11Estimation with DecimalsObjective: The student will be able to estimate sums, differences, products, and quotientswith decimals.

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Lesson 12Decimals and PercentsObjective: The student will be able to express a decimal as a percent and a percent as a decimal.

Lesson 13Adding and Subtracting DecimalsObjective: The student will be able to add and subtract decimals

Lesson 14Multiplying DecimalsObjective: The student will be able to multiply decimals.

Lesson 15Dividing Decimals by a Whole NumberObjective: The student will be able to divide a decimal by a whole number.

Lesson 16Dividing Decimals by DecimalsObjective: The student will be able to divide decimals by decimals.

Lesson 17Evaluating Decimal Expressions and EquationsObjective: The student will be able to use various strategies such as mental math andsubstitution to solve expressions and equations with decimals.

Lesson 18DivisibilityObjective: The student will be able to use divisibility rules correctly.

Lesson 19Prime and Composite NumbersObjective: The student will be able to identify whether a number is Prime or Composite.

Lesson 20Prime FactorizationObjective: The student will be able to write a composite number as a product of primenumbers.

Lesson 21Least Common Multiple and GreatestCommon FactorObjective: The student will be able to find the Least Common Multiple and GreatestCommon Factor of a number and use these to solve problems.

Lesson 22Equivalent Fractions and Simplest FormObjective: The student will be able to write Equivalent Fractions and fractions in theSimplest Form.

Lesson 23Mixed NumbersObjective: The student will be able to write Mixed Numbers as fractions, and writefractions as Mixed Numbers.


Lesson 24Comparing and Ordering FractionsObjective: The student will be able to compare and order fractions.

Lesson 25Fractions and DecimalsObjective: The student will be able to convert fractions to decimals.

Lesson 26Fractions, Decimals and PercentsObjective: The student will be able to convert fractions to decimals, decimals to fractions,and fractions to percents.

Lesson 27Estimating Sums and DifferencesObjective: The student will be able to estimate sums and differences of fractions andmixed numbers

Lesson 28Adding and Subtracting FractionsObjective: The student will be able to add and subtract fractions.

Lesson 29Adding and Subtracting Mixed NumbersObjective: The student will be able to add and subtract mixed numbers.

Lesson 30Subtracting Mixed Numbers with RenamingObjective: The student will be able to subtract mixed numbers that require renaming.

Lesson 31Multiplication of FractionsObjective: The student will be able to multiply two fractions.

Lesson 32More Multiplication of FractionsObjective: The student will be able to multiply a fraction by a whole number.

Lesson 33Multiplication with Mixed FractionsObjective: The student will be able to multiply a proper fraction by a mixed fraction ortwo mixed fractions

Lesson 34Dividing FractionsObjective: The student will be able to divide two fractions.

Lesson 35More Division of FractionsObjective: The student will be able to divide a fraction by a whole number.

Lesson 36Dividing Fractions and Mixed NumbersObjective: The student will be able to divide a fraction by a mixed number.


Lesson 37Dividing Two Mixed FractionsObjective: The student will be able to divide two mixed fractions.

Lesson 38Multiplication and Division of Fractions ReviewObjective: The student will review the skills learned in the previous Lessons teachingmultiplication and division of fractions.

Lesson 39Multiplication and Division of Fractions AssessmentObjective: The student will be able to display knowledge and understanding ofmultiplication and division of fractions.

Lesson 40Working with Algebraic ExpressionsObjective: The student will be able to write Algebraic Expressions

Lesson 41Evaluating Algebraic ExpressionsObjective: The student will be able to write Algebraic Expressions��

Lesson 42Working with Square RootsObjective: The student will be able to evaluate expressions with square roots.

Lesson 43Writing EquationsObjective: The student will be able to write an Algebraic Equation from a verbal orwritten statement.

Lesson 44Solving One-step Addition EquationsObjective: The student will learn how to solve addition equations.

Lesson 45Solving Subtraction EquationsObjective: The student will be able to solve subtraction equations.

Lesson 46Expressions and Equations ReviewObjective: The student will review all the skills learned in Lessons 40 through 45.

Lesson 47Expressions and Equations AssessmentObjective: The student will be able to display a knowledge and understanding ofexpressions and equations on an Assessment.

Lesson 48Solving Multiplication EquationsObjective: The student will be able to solve multiplication equations.


Lesson 49Solving Division EquationsObjective: The student will be able to solve a division equation.

Lesson 50Inequality BasicsObjective: The student will be able to identify what an nequality is, and what symbolsare used in mathematical sentences representing nequalities.

Lesson 51Solving Inequalities Part 1Objective: The student will be able to solve addition and subtraction inequalities andgraph the solution on a number line.

Lesson 52Solving Inequalities Part 2Objective: The student will be able to solve multiplication and division nequalities andrepresent the solution using a number line.

Lesson 53Solving Inequalities Part 3Objective: The student will be able to solve two-step inequalities and graph the solutionon a number line.

Lesson 54Equations and Inequalities ReviewObjective: The student will be able to review the skills learned throughout the Lessonsteaching how to solve equations and solve and graph inequalities.

Lesson 55Equations and Inequalities AssessmentObjective: The student will be able to display knowledge and understanding of solvingequations and inequalities

Lesson 56Geometry TerminologyObjective: The student will be able to understand and apply basic geometric vocabularyrelated to lines and angles.

Lesson 57AnglesObjective: The student will be able to use measuring tools to measure angles.

Lesson 58PolygonsObjective: The student will be able to classify an angle and polygon by type.

Lesson 59CirclesObjective: The student will be able to understand and identify the properties of Circles,and use a compass to draw Circles that illustrate given specific information.

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Lesson 60Congruent and Similar FiguresObjective: The student will be able to identify two figures as congruent or similar.

Lesson 61SymmetryObjective: The student will be able to draw Lines of Symmetry into a figure, anddetermine whether a figure has Rotational Symmetry.

Lesson 62Geometry Review and Assessment 1Objective: The student will be able to review the skills learned in the first GeometryLessons taught, and successfully complete the ssessment

Lesson 63Introduction to Plane and Solids FiguresObjective: The student will be able to make an artistic collage to classify lane and olidfigures.

Lesson 64TrianglesObjective: The student will be able to classify the types of riangles.

Lesson 65QuadrilateralsObjective: The student will be able to classify the types of uadrilaterals.

Lesson 66TransformationsObjective: The student will be able to understand and use the various types of��

Lesson 67Understanding Solid FiguresObjective: The student will be able to identify olid igures.

Lesson 68Geometry Review and Assessment 2Objective: Students will be able to review the skills learned in this unit regardingriangles, uadrilaterals, olygons, and ransformations.

Lesson 69Measuring Length with the Metric SystemObjective: The student will be able to understand length in terms of the Metric System.

Lesson 70Length ActivityObjective: The student will be able to understand the Metric System as it relates tomeasuring length.


Lesson 71Metric ConversionsObjective: The student will be able to make onversions using metric units of length.

Lesson 72Customary ConversionsObjective: The student will be able to make conversions using customary units of length.

Lesson 73Capacity and WeightObjective: The student will be able to make conversions using customary units of apacityand eight.

Lesson 74Capacity and MassObjective: The student will be able to make conversions using metric units of capacity andmass.

Lesson 75TimeObjective: The student will be able to determine elapsed time and make conversionsusing units of time.

Lesson 76TemperatureObjective: The student will be able to make conversions with temperatures.

Lesson 77The Metric System ReviewObjective: The student will review the skills taught and learned in the previous Lessons the metric system and conversion of units of measure.

Lesson 78Measurement AssessmentObjective: The student will be able to display knowledge attained throughout theLessons taught the metric system and conversions.

Lesson 79Measuring PerimeterObjective: The student will be able to use a ruler to measure the erimeters of variousobjects in the real world.

Lesson 80Finding PerimeterObjective: The student will be able to find the erimeter of an object even when notgiven all of the lengths of the sides of object

Lesson 81Finding CircumferenceObjective: The student will be able to find the ircumference of a circle.


Lesson 82Circumference and DiameterObjective: The student will be able to understand the relationship betweenircumference and iameter.

Lesson 83Perimeter ReviewObjective: The student will review finding erimeter and ircumference in preparationfor the erimeter ssessment.

Lesson 84Perimeter AssessmentObjective: The student will be able to display knowledge of finding erimeter andircumference by completing the erimeter ssessment.

Lesson 85What is Area?Objective: The student will be able to use grid paper to estimate rea.

Lesson 86Finding Area Part 1Objective: The student will be able to find the rea of a rectangle or square.

Lesson 87Area and PerimeterObjective: The student will be able to practice finding rea and erimeter of squares andrectangles.

Lesson 88Finding Area Part 2Objective: The student will be able to find the rea of a triangle.

Lesson 89Finding Area Part 3Objective: The student will be able to find the rea of a parallelogram.

Lesson 90Finding Area ReviewObjective: The student will be able to practice finding the rea of rectangles, squares,triangles, and parallelograms.

Lesson 91Area AssessmentObjective: The student will be able to display knowledge and understanding of findingthe rea of squares, rectangles, triangles, and parallelograms.

Lesson 92Surface Area of a PrismObjective: The student will be able to understand how to find the ateral rea of a prismand use the ateral rea to find the urface rea.��


Lesson 93Surface Area of a PyramidObjective: The student will be able to find the lateral area and surface area of a pyramid.

Lesson 94Surface Area of a CylinderObjective: The student will be able to find the lateral area and surface area of acylinder.

Lesson 95Surface Area of a ConeObjective: The student will be able to find the lateral area and surface area of a cone.

Lesson 96�� of a PrismObjective: The student will be able to find the volume of a prism.��

�Lesson 97Volume of a PyramidObjective: The student will be able to find the volume of a pyramid.

Lesson 98Volume of a CylinderObjective: The student will be able to find the volume of a cylinder.

Lesson 99Volume of a ConeObjective: The student will be able to find the volume of a cone.

Lesson 100Surface Area and Volume ReviewObjective: The student will review how to find the surface area and volume of a prism,pyramid, cone, and cylinder in preparation for the assessment in lesson 101.

Lesson 101Surface Area and Volume AssessmentObjective: The student will be able to display knowledge of how to find the lateral andsurface area and Volume of a prism, pyramid, cylinder, and cone.

Lesson 102Geometry in Art Project PreparationObjective: The student will be given a review of basic geometry concepts and termsneeded in order to be prepared for geometry in rt roject in essons 103-114.

Lesson 103Geometry in Art, Project Part 1Objective: The student will be able to use the various concepts learned about geometryto apply them to art and architecture. The student will understand that a connection can be made between geometry and art, and be able to analyze the importance of thatconnection.

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Lesson 104Geometry in Art, Project Part 2Objective: The student will be able to use the various concepts learned about Geometryto apply them to Art and Architecture. The student will understand that a connection canbe made between Geometry and Art, and be able to analyze its importance.


Lesson 106Geometry in Art, Project Part 4Objective: The student will be able to use the various concepts learned about Geometryand apply them to Art and Architecture. The student will understand that a connection can be made between Geometry and Art, and be able to analyze its importance.


Lesson 108Geometry in Art, Project Part 6Objective: The student will be able to compare and contrast the Art of the Renaissanceperiod with Art of the 20th and 21st centuries using a Venn diagram.

Lesson 109Geometry in Art, Project Part 7Objective: The student will be able to compare and contrast the Art of the Renaissanceperiod with Art of the 20th and 21st centuries in the first draft of a well-written5-paragraph essay.

Lesson 110Geometry in Art, Project Part 8Objective: The student will be able to compare and contrast the Art of the Renaissanceperiod with Art of the 20th and 21st centuries in a well-written 5-paragraph essay.


Lesson 112Geometry in Art, Project Part 10Objective: The student will be able to compare and contrast the Art of the Renaissanceperiod with Art of the 20th and 21st centuries in a slide show using presentation software.


Lesson 113Geometry in Art, Project Part 11Objective: The student will be able to compare and contrast the Art of the Renaissanceperiod with Art of the 20th and 21st centuries in a slide show using presentation software.


Lesson 115RatiosObjective: The student will learn how to write atios.

Lesson 116Unit RatesObjective: The student will be able to find nit ates.

Lesson 117ProportionsObjective: The student will be able to write and solve a roportion.

Lesson 118ScaleObjective: The student will be able to use cale to find the true dimensions of a drawingor object.

Lesson 119Ratio and Proportion ReviewObjective: The student will review the skills learned in writing and calculating atios androportions, and using cale drawings.

Lesson 120Ratio, Proportion and Scale AssessmentObjective: The student will be able to display knowledge of atios, roportions andcale.

Lesson 121PercentObjective: The student will be able to write and compare ercents.

Lesson 122Percents and DecimalsObjective: The student will be able to write ercents as ecimals and ecimals asercents.

Lesson 123Writing Percents from FractionsObjective: The student will be able to write a ercent from a raction that does not havea denominator of 100. The student will also be able to write a raction from a ercent.

Lesson 124Finding a Percent of a NumberObjective: The student will be able to find a ercent of a number.


Lesson 125DiscountObjective: The student will be able to solve money problems involving a iscount.

Lesson 126Percent and Discount in the Real World Part 1Objective: The student will be able to understand how to find a percent of a number anddiscount in a real-world situation.

Lesson 127Percent and Discount in the Real World Part 2Objective: The student will be able to understand how percent is used in a real-worldsituation.

Lesson 128Percent ReviewObjective: The student will prepare for the ssessment on ercent.

Lesson 129Percent AssessmentObjective: The student will be able to display knowledge and understanding of ercenton the Assessment.

Lesson 130Shop ‘til You Drop with $500 – Part 1Objective: The student will be able to show relationships between fractions, decimals,and percents in a real world situation. The student will also be able to solve problemsinvolving percents.

Lesson 131Shop ‘til You Drop with $500 – Part 2Objective: The student will be able to show relationships between fractions, decimals,and percents in a real-world situation. The student will also be able to solve problemsinvolving percents.

Lesson 132Shop ‘til You Drop with $500 – Part 3Objective: The student will be able to show relationships between fractions, decimals,and percents in a real-world situation. The student will also be able to solve problemsinvolving percents.

Lesson 133Math Service Project – Part 1Objective: The student will creatively apply various 6th grade Math skills.

Lesson 134Math Service Project - Part 2Objective: The student will creatively apply various 6th grade Math skills.


Lesson 135Math Service Project - Part 3 Objective: The student will creatively apply various 6th grade Math skills.



Lesson 138Theoretical ProbabilityObjective: The student will be able to find the theoretical probability of an event.

Lesson 139Experimental ProbabilityObjective: The student will be able to find the experimental probability of an event.

Lesson 140Compound Events and Tree DiagramsObjective: The student will be able to find all possible outcomes for compound events.

Lesson 141Compound Events and the FundamentalCounting PrincipleObjective: The student will be able to find all possible outcomes for compound events.

Lesson 142Compound Events in Real LifeObjective: The student will be able to see how compound events are used in real life.

Lesson 143Independent EventsObjective: The student will be able to find the probability of independent events.

Lesson 144Dependent EventsObjective: The student will be able to find the probability of a dependent event.

Lesson 145Probability ReviewObjective: The student will review the objectives learned regarding probability.

Lesson 146Probability AssessmentObjective: The student will display knowledge and understanding of probability on theassessment.

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Lesson 147MeanObjective: The student will be able to find the mean of a set of data.

Lesson 148MedianObjective: The student will be able to find the median of a set of data.

Lesson 149ModeObjective: The student will be able to find the mode of a set of data.

Lesson 150Creating a Frequency TableObjective: The student will be able to create a Frequency Table to illustrate and displaydata.

Lesson 151Creating a Line PlotObjective: The student will be able to create a Line Plot as a statistical representation ofdata.

Lesson 152Stem and Leaf PlotObjective: The student will be able to create a Stem and Leaf Plot to represent data.

Lesson 153Fun with Stem and Leaf and Line PlotsObjective: The student will conduct an experiment and display the data in a Stem andLeaf Plot.

Lesson 154Creating a Pie ChartObjective: The student will be able to create a Pie Chart as a data representation.

Lesson 155Creating a Bar GraphObjective: The student will be able to create a Bar Graph to represent data.

Lesson 156Creating a Box and Whisker PlotObjective: The student will be able to create a Box and Whisker Plot to represent data.

Lesson 157Statistics ReviewObjective: The student will review the skills learned in the Lessons on statistics.

Lesson 158Statistics AssessmentObjective: The student will be able to display knowledge and understanding of how tofind the measures of central tendency and create the various statistical representations.


Lesson 159Scoring with the Stats - Part 1Objective: In this project, the student will be able to analyze real-world data and displayknowledge and understanding of the various concepts regarding statistics using this data.


Lesson 161Scoring with the Stats - Part 3Objective: In this project, the student will be able to analyze real-world data and displayknowledge and understanding of the various statistical concepts using this data.







Lesson 168Graphing 101Objective: The student will be able to graph a point on a coordinate plane.�� !��

Lesson 169More GraphingObjective: The student will be continue practicing how to graph on a coordinate plane.��


Lesson 170IntegersObjective: �� "�� #� ��

Lesson 171Comparing IntegersObjective: The student will be able to compare Integers with <, >, or =.

Lesson 172Operations with Integers – AdditionObjective: The student will be able to add integers.

Lesson 173Operations with Integers – SubtractionObjective: The student will be able to subtract two integers.

Lesson 174Operations with Integers – MultiplicationObjective: The student will be able to multiply integers.

Lesson 175Operations with Integers – DivisionObjective: The student will be able to divide integers.

Lesson 176Integer ReviewObjective: The student will review the skills he learned throughout the chapter on integers inpreparation for the Assessment given on the coordinate plane and integers.

Lesson 177Integer AssessmentObjective: The student will be able to display an understanding of integers by taking theInteger Assessment.

Lesson 178Solving Word ProblemsObjective: The student will be able to solve word problems using the 4-step problem solving method.

Lesson 179More Word ProblemsObjective: The student will be able to use the 4-step problem solving model to solve wordproblems.

Lesson 180Math 6 Wrap-Up and AssessmentObjective: The student will be able to review all the mathematics concepts introduced,practiced and assessed throughout this 6th Grade Math course.

Sixth Grade Math Common Core Alignment

Complete Curriculum Lesson

Ratios and Proportional Relationships--Understand ratio concepts and use ratio reasoning to solve problems.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship

115, 119, 120use at o a guage to desc be a at o e at o s pbetween two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0 and use rate

116, 119, 120associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.a. Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane Use tables to

168, 169

values on the coordinate plane. Use tables to compare ratios.b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

117 120

Fi d t f tit t 100 12 26 121 122 123 124 126c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

12, 26, 121, 122, 123, 124, 126130

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

115, 119, 120

The Number System--Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

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6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

34, 35, 36, 37, 38, 39, 134, 136,178, 179

C t fl tl ith lti di it b d--Compute fluently with multi-digit numbers and find common factors and multiples.6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

4, 18 23, 26, 133, 134, 136, 175,176, 177

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

10 17, 25, 26, 121, 130

6 NS 4 Find the greatest common factor of two 21 22 1236.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

21, 22, 123

express 36 8 as 4 (9 2).

--Apply and extend previous understandings of numbers to the system of rational numbers.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level credits/debits

*168, 170, 177

above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

168, 170, 176, 177

–(–3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

168, 176, 177

c. Find and position integers and other rational numbers on a horizontal or vertical number line

168, 176, 177numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.6.NS.7 Understand ordering and absolute value of rational numbers.a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

51, 52, 53, 55b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

5, 51, 52, 53, 54, 55, 171, 176,177

c. Understand the absolute value of a rational 170, *171, 177c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

170, 171, 177

d. Distinguish comparisons of absolute value from statements about order For example recognize

170, 178statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between and absolute value to find distances between points with the same first coordinate or the same second coordinate. 168, 169, 170, 176, 177Expressions and Equations --Apply and extend previous understandings of arithmetic to algebraic expressions.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. 86 EE 2 Write read and evaluate expressions in6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. 5, 17, 40, 42, 46, 47

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

5, 40

c Evaluate expressions at specific values of theirc. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to p ,find the volume and surface area of a cube with sides of length s = 1/2.

5, 40, 46, 476.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression

5, 40, 41

3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is

b tit t d i t th ) F l th

5, 7, 41, 44, 46, 47

substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

--Reason about and solve one-variable equations and inequalities.6.EE.5 Understand solving an equation or g qinequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6, 17, 41, 43, 46, 47, 54, 556.EE.6 Use variables to represent numbers and write expressions when solving a real-world or

5, 6, 40, 43, 46, 47write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q

6 43 44 45 46 47 48 49 54and x are all nonnegative rational numbers. 6, 43, 44, 45, 46, 47, 48, 49, 54,55

6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

1, 50, 51, 52, 53,54, 55, 171

--Represent and analyze quantitative relationships between dependent and independent variablesbetween dependent and independent variables.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship

41

p y pbetween the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Geometry--Solve real-world and mathematical problems involving area, surface area, and volume.6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 85, 88, 89, 90, 916.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism Apply the formulas V = l w h

96, 100, 101, 170

lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the

fi t di t th d

66

same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of

92, 96, 97

figures. Apply these techniques in the context of solving real-world and mathematical problems.

SAMPLE

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Statistics and Probability--Develop understanding of statistical variability.

6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical

ti b t “H ld th t d t i

157, 158, 159

question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

*151

p6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 147, 148, 149, 151, 153, 157,

158, 167--Summarize and describe distributions.6.SP.4 Display numerical data in plots on a number line including dot plots histograms and

151, 152, 153, 155, 156, 157,8 9 60 62 63 6number line, including dot plots, histograms, and

box plots.158, 159, 160, 162, 163, 164,165, 166, 167

6.SP.5 Summarize numerical data sets in relation to their context, such as by:a. Reporting the number of observations. 150, 153, 157, 158, 159, 160b. Describing the nature of the attribute under investigation, including how it was measured and it it f t

159, 165, 166, 167

its units of measurement.c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

147, 148, 156, 158

d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

151, 165, 166, 167SAMPLE

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6th Grade Homeschool Curriculum - Sixth Grade Math - Best Homeschool Curriculum - Cheap Homeschool...

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