5th Grade Homeschool Curriculum - Fifth Grade Math - Best Homeschool Curriculum - Cheap Homeschool Curriculum (Affordable)!

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Acknowledgments

Complete Curriculum’s K-12 curriculum has 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 FIFTH GRADE MATH

Lesson 1 Introduction to Place Value Objective: The student will be able to understand the place value of a whole number. Lesson 2 Understanding Millions and Billions Objective: The student will be able to understand the place value of digits in the millions and billions. Lesson 3 Important Whole Numbers Objective: The student will be able to estimate values using specific important numbers, called benchmark numbers. Lesson 4 Comparing and Ordering Whole Numbers Whole Numbers Assessment Objective: The student will be able to put whole numbers in numerical order from least to greatest by comparing the value of each whole number. Lesson 5 Introduction to Decimal Place Value Objective: The student will be able to understand and use the place value of decimals. Lesson 6 Finding Decimal Equivalents Objective: The student will be able to understand and write equivalent decimals. Lesson 7 Ordering and Comparing Decimals Decimals Assessment Objective: The student will be able to order and compare decimals.

Lesson 8 Rounding Whole Numbers Objective: The student will be able to round whole numbers to a particular place value using his understanding of place value. Lesson 9 Rounding Decimals Objective: The student will be able to round decimals to a specific place value. Lesson 10 Estimating Objective: The student will be able to estimate the sum or difference in a problem using whole numbers or decimals. Lesson 11 Addition and Subtraction of Whole Numbers Objective: The student will be able to add and subtract whole numbers.

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Lesson 12 Addition and Subtraction with Decimals Addition and Subtraction with Decimals Assessment Objective: The student will be able to add and subtract with decimals

Lesson 13 Introduction to Expressions and Variables Objective: The student will be able to write and solve algebraic expressions using variables. Lesson 14 Learning How to Write Equations Objective: The student will be able to write basic algebraic equations. Lesson 15 Learning How to Solve Equations Objective: The student will be able to solve basic algebraic equations using mental math. Lesson 16 Understanding Inequalities Objective: The student will be able to understand and use basic inequalities. Lesson 17 The Algebraic Properties Introduction to Algebra Assessment Objective: The student will understand the algebraic properties, and be able to distinguish what property is being used in an expression. Lesson 18 Finding Patterns Objective: The student will be able to find patterns using multiples of 10. Lesson 19 Multiplication of 1-Digit Numbers Objective: The student will be able to multiply numbers by a 1-digit number.

Lesson 20 Multiplication by a 2-Digit Number Multiplication Assessment Objective: The student will be able to complete multiplication problems in which all factors have two or more digits.

Lesson 21 Patterns with Decimal Multiplication Objective: The student will be able to use various patterns to multiply decimals. Lesson 22 Multiplying with Decimals Objective: The student will be able to multiply decimals.

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Lesson 23 More Multiplication with Decimals Objective: The student will be able to solve word problems involving multiplication with decimals.

Lesson 24 Understanding Zeros Multiplying with Decimals Assessment Objective: The student will be able to multiply decimals that have zeros in the final answer.

Lesson 25 Estimating Quotients Objective: The student will be able to use compatible numbers to determine an estimate for a division problem. Lesson 26 Dividing by 1-Digit Divisors Objective: The student will be able to find a quotient of a division problem with a 1-digit divisor. Lesson 27 Using Zeros in Division Objective: The student will be able to use zeros in division problems correctly.

Lesson 28 Dividing by 2-Digit Divisors Objective: The student will be able to complete a division problem involving a 2-digit divisor.

Lesson 29 More Practice with Division Division Assessment Objective: The student will be able to practice division by a 1 and 2 digit divisor.

Lesson 30 Using Patterns When Dividing Decimals Objective: The student will be able to understand how to use place value and basic math to find patterns in division problems.

Lesson 31 Dividing Decimals by Whole Numbers Objective: The student will be able to divide a decimal by a whole number.

Lesson 32 Fraction Conversions Objective: The student will be able to convert a fraction to a decimal.

Lesson 33 Decimal Conversions Objective: The student will be able to convert a decimal to a fraction.

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Lesson 34 Dividing Decimals by Decimals Decimal Division Assessment Objective: The student will obtain a general understanding of how to divide Decimals.

Lesson 35 Working with Expressions Objective: The student will learn to work with algebraic expressions.

Lesson 36 Working with Equations Objective: The student will gain additional experience working with equations. Lesson 37 Order of Operations Objective: The student will be able to solve problems utilizing the order of operations. Lesson 38 Finding Patterns Objective: The student will be able to find the missing numbers in various patterns.

Lesson 39 Working with Functions Objective: The student will understand the definition of a function and be able to complete a function table by using an equation. Lesson 40 The Commutative and Associative Properties Objective: The student will be able to understand and use the commutative and associative properties of multiplication. Lesson 41 The Identity Property Objective: The student will be able to understand and use the identity property of multiplication. Lesson 42 The Distributive Property Division in Algebra Assessment Objective: The student will be able to understand and use the distributive property in multiplication. Lesson 43 Divisibility Objective: The student will be able to use Divisibility rules. Lesson 44 Prime and Composite Numbers Objective: The student will be able to identify whether a number is prime or composite.

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Lesson 45 Finding the Greatest Common Factor Objective: The student will be able to find the Greatest Common Factor of a pair of numbers. Lesson 46 Finding the Least Common Multiple Factors and Multiple Assessment Objective: The student will be able to find the Least Common Multiple of a pair of numbers. Lesson 47 Introduction to Exponents Objective: The student will be able to use exponential notation correctly. Lesson 48 Understanding the Expanded Form of a Number Objective: The student will be able to use place value to write the expanded form of a number. Lesson 49 Prime Factors and Exponents Introduction to Exponents Assessment Objective: The student will be able to use exponents to compose the prime factorization of a number. Lesson 50 Finding Equivalent Fractions Objective: The student will be able to create equivalent fractions

Lesson 51 Reducing Fractions Objective: The student will be able to reduce fractions using the Greatest Common Factor. Lesson 52 Mixed Numbers Objective: The student will be able to convert an improper fraction to a mixed number,and a mixed number to an improper fraction. Lesson 53 Comparing and Ordering Fractions Objective: The student will be able to compare fractions with unlike denominators, and put fractions in order from least to greatest.

Lesson 54 Fractions and Decimals Objective: The student will be able to convert fractions to decimals

Lesson 55 Fractions and Decimals Assessment Objective: The student will learn to convert decimals to fractions.

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Lesson 56 Addition and Subtraction of Fractions with Like Denominators Objective: The student will be able to add and subtract fractions with like denominators

Lesson 57 Addition and Subtraction of Fractions with Unlike Denominators Objective: The student will be able to add fractions with unlike denominators

Lesson 58 Subtraction with Unlike Denominators Objective: The student will be able to subtract fractions with unlike denominators

Lesson 59 Sums and Differences Objective: The student will be able to use estimation to figure out the sum or difference of a fraction problem where the fractions have unlike denominator

Lesson 60 More Addition and Subtraction of Fractions Objective: The student will be able to add and subtract fractions by converting fractions to common denominators.

Lesson 61 Addition and Subtraction of Fractions Assessment Objective: The student will practice adding and subtracting with fractions. Lesson 62 Addition of Mixed Fractions Objective: The student will be able to add mixed fractions by changing each fraction to the lowest common denominator. Lesson 63 Subtraction of Mixed Fractions Objective: The student will be able to subtract mixed fractions using the lowest common denominator.

Lesson 64 More Subtraction of Mixed Fractions Objective: The student will be able to subtract mixed fractions requiring renaming.

Lesson 65 Addition and Subtraction of Mixed Fractions Assessment Objective: The student will practice adding and subtracting mixed fractions.

Lesson 66 Multiplication of Fractions by Fractions Objective: The student will be able to multiply a fraction by a fraction.

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Lesson 67 Multiplication of Fractions by Whole Numbers Objective: The student will be able to multiply a fraction by a whole number.

Lesson 68 Multiplication of Fractions by Mixed Numbers Objective: The student will be able to multiply a fraction by a mixed number.

Lesson 69 Multiplication of Mixed Numbers Objective: The student will be able to multiply two mixed fractions together.

Lesson 70 Multiplication Review - Multiplication of Fractions Assessment Objective: The student will be able to review the multiplication of fractions.

Lesson 71 Reciprocals Objective: The student will be able to find the reciprocal of a number.

Lesson 72 Dividing a Fraction by a Fraction Objective: The student will be able to divide a fraction by a fraction.

Lesson 73 Dividing a Fraction by a Whole Number Objective: The student will be able to divide a fraction by a whole number

Lesson 74 Dividing a Fraction by a Mixed Number Objective: The student will be able to divide a fraction by a mixed number.

Lesson 75 Dividing Mixed Fractions Objective: The student will be able to divide two mixed fractions.

Lesson 76 Division Review - Division of Fractions Assessment Objective: The student will be able to review the various types of fraction division he has already learned.

Lesson 77 Geometry Terminology Objective: The student will be able to understand and apply basic geometric Vocabulary related to lines and angles. Lesson 78 Angles Objective: The student will be able to use measuring tools to measure angles.

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Lesson 79 Polygons Objective: The student will be able to classify an angle and polygon by type. Lesson 80 Circles Objective: The student will be able to understand and identify the properties of circles,and use a compass to draw circles correctly given specific information Lesson 81 Congruent and Similar Figures Objective: The student will be able to identify two figures as congruent or similar. Lesson 82 Symmetry Geometry Assessment Objective: The student will be able to draw lines of symmetry into a figure, and determine whether a figure has rotational symmetry. Lesson 83 Introduction to Plane and Solid Figures Objective: The student will be able to use an artistic collage to classify plane and solid figures.

Lesson 84 Triangles Objective: The student will be able to classify triangles. Lesson 85 Quadrilaterals Objective: The student will be able to classify quadrilaterals. Lesson 86 Transformations Objective: The student will be able to understand and use the various types of transformations. Lesson 87 Plane and Solid Figures Assessment Objective: The student will be able to identify solid figures. Lesson 88 Graphing Introduction Objective: The student will be able to use an X-Y table to graph on the coordinate plane. Lesson 89 Graphing on a Coordinate Plane Objective: The student will

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Lesson 90 Integers Introduction Objective: The student will be able to understand the number line and find the absolute value of a number. Lesson 91 Comparing Integers Objective: The student will be able to compare integers using the greater than, less than, or equal to symbols. The student will also be able to place integers in order from least to greatest. Lesson 92 Operations with Integers – Part 1 Objective: The student will be able to add integers.

Lesson 93 Operations with Integers – Part 2 Objective: The student will be able to subtract two integers.

Lesson 94 Coordinate Plane and Integers Review Objective: The student will be able to review the skills he has learned in preparation for the Assessment given on the coordinate plane and integers.

Lesson 95 Coordinate Plane and Integers Assessment Objective: The student will be able to display her understanding of Coordinate Planes and Integers by taking the Coordinate Plane and Integers Assessment.

Lesson 96 Length Objective: The student will be able to understand length in terms of the metric system. Lesson 97 Length Activity Objective: The student will be able to understand the metric system as it relates to measuring length.

Lesson 98 Metric Conversions Objective: The student will be able to make conversions using metric units of length.

Lesson 99 Customary Conversions Objective: The student will be able to make conversions using customary units of Length. Lesson 100 Capacity and Weight Objective: The student will be able to make conversions using customary units of capacity and weight. Lesson 101 Capacity and Mass Objective: The student will be able to make conversions using metric units of capacity and mass.

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Lesson 102 Time Objective: The student will be able to determine elapsed time and make conversions using units of time. Lesson 103 Temperature Objective: The student will be able to convert between Fahrenheit and Celsius. Lesson 104 The Metric System Review Objective: The student will be able to review the Metric System.

Lesson 105 The Metric System Assessment Objective: The student will be able to display knowledge about the Metric System.

Lesson 106 Measuring Perimeter Objective: The student will be able to use a ruler to measure the perimeter of various objects in the real world. Lesson 107 Finding Perimeter Objective: The student will be able to find the perimeter of an object when she is not given all of the lengths of the object. Lesson 108 Finding Circumference Objective: The student will be able to find the circumference of a circle. Lesson 109 Circumference and Diameter Objective: The student will be able to understand the relationship between circumference and diameter. Lesson 110 Perimeter Review Objective: The student will review finding perimeter and circumference in preparation for an Assessment. Lesson 111 Perimeter Assessment Objective: The student will be able to display his knowledge of finding perimeter and circumference by completing the Perimeter Assessment. Lesson 112 What is Area? Objective: The student will be able to use grid paper to estimate area.

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Lesson 113 Finding Area – Part 1 Objective: The student will be able to find the area of a rectangle or square.

Lesson 114 Area and Perimeter Objective: The student will be able to practice finding area and perimeter of squares and rectangles. Lesson 115 Finding Area – Part 2 Objective: The student will be able to find the area of a triangle. Lesson 116 Finding Area – Part 3 Objective: The student will be able to find the area of a parallelogram. Lesson 117 Area Review Objective: The student will practice finding the area of rectangles, squares, triangles, and parallelograms. Lesson 118 Area Assessment Objective: The student will complete the Area Assessment

Lesson 119 Million Dollar Home Project – Part 1 Objective: The student will be able to use knowledge of area and perimeter to design a million-dollar home. Lesson 120 Million Dollar Home Project – Part 2 Objective: The student will be able to use knowledge of area and perimeter to design a home if he was given one million dollars. Lesson 121 Million Dollar Home Project – Part 3 Objective: The student will determine the scale for her dream-home drawing, and will calculate total area and perimeter of the lot and floor plan. Lesson 122 Million Dollar Home Project – Part 4 Objective: The student will pick out furnishings and begin budgeting his million-dollar home.

Lesson 123 Million Dollar Home Project – Part 5 Objective: The student will calculate the average square footage and cost-to-furnish of her million dollar home. She will also answer questions she will need for the presentation she will give in Lesson 124.

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LLesson 124 Million Dollar Home Project Presentation Objective: The student will orally present his Million Dollar Home Project

Lesson 125 Surface Area Objective: The student will be able to find the surface area of a rectangular prism. Lesson 126 Finding Volume – Part 1 Objective: The student will be able to find the volume of a rectangular prism.

Lesson 127 Finding Volume – Part 2 Objective: The student will be able to find the volume of a rectangular prism when given only two of the three determining measurements. Lesson 128 Perimeter, Area, and Volume Objective: The student will be able to find the surface area of a rectangular prism.

Lesson 129 Volume Review Objective: The student will be able to find the volume of various figures using the appropriate measurement tool. Lesson 130 Perimeter, Area, and Volume Assessment Objective: The student will be able to find the surface area and volume of a solid figure. Lesson 131 What is a Ratio? Objective: The student will be able to understand what a ratio is. Lesson 132 Writing Ratios Objective: The student will be able to write ratios.

Lesson 133 Proportions Objective: The student will be able to determine if two ratios are equivalent. Lesson 134 More Proportions Objective: The student will be able to determine if two ratios are equivalent in order to solve proportions. Lesson 135 Solving Proportions Objective: The student will be able to determine the missing value in a proportion.

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Lesson 136 Ratios Review Objective: The student will be able to work with ratios and proportions.

Lesson 137 Ratios Assessment Objective: The student will be able to display her knowledge of ratios and proportions on the Assessment for this chapter. Lesson 138 Scale Drawing – U.S. Map Objective: The student will be able to use proportions to determine distances in scale drawings. Lesson 139 Scale Drawing – Workspace Objective: The student will be able to create a scale drawing.

Lesson 140 Scale Drawing Project – Living Room Objective: The student will be able to use proportions to construct a scale drawing of his living room. Lesson 141 Scale Drawing Project – Kitchen Objective: The student will be able to use proportions to construct a scale drawing.

Lesson 142 Scale Drawing Project – Back Yard Objective: The student will be able to use proportions to construct a scale drawing.

Lesson 143 Scale Drawing Project – Shrinking it Down Objective: The student will be able to use proportions to construct a scale drawing.

Lesson 144 Understanding Percentages Objective: The student will be able to understand how to write a percentage. Lesson 145 Changing Decimals to Percentages Objective: The student will be able to convert a decimal to a percentage.

Lesson 146 Changing Percentages to Decimals Objective: The student will be able to convert a percentage to a decimal.

Lesson 147 Changing Fractions to Percentages Objective: The student will be able to understand how to convert a fraction to a percentage. Lesson 148 Changing Percentages to Fractions Objective: The student will be able to convert a percentage to a fraction.

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Lesson 149 Fractions, Decimals, and Percentages Objective: The student will be able to make conversions between fractions, decimals, and percentages. Lesson 150 Comparing Fractions, Decimals, and Percentages Objective: The student will be able to make comparisons between fractions, decimals,and percentages. Lesson 151 Finding a Percentage of a Number Objective: The student will be able to find a requested percentage of a number.

Lesson 152 Percentage Review Objective: The student will review percentage computations.

Lesson 153 Percentages Assessment Objective: The student will complete an Assessment covering percentages.

Lesson 154 Permutations Objective: The student will see how to determine the number of permutations possible in a given set. Lesson 155 Combinations Objective: The student will be able to arrange numbers and objects into combinations. Lesson 156 The Fundamental Counting Principle Objective: The student will become familiar with the fundamental counting principle

Lesson 157 Combinations, Permutations, and Counting Review Objective: The student will gain additional practice building combinations and permutations and in using the fundamental counting principle before moving on to a study of probability and statistics. Lesson 158 Introduction to Probability Objective: The student will be able to understand what probability is and how it is used. Lesson 159 Probability Objective: The student will be able to understand and apply the basic concepts of Probability Lesson 160 Probability Activity Objective: The student will be able to use probability activities to determine if a game is fair.

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Lesson 161 Understanding Probability and Odds Objective: The student will use a combination of pattern making, counting, and real world experimentation to better understand probability and odds.

Lesson 162 Writing Probability Objective: The student will be able to use fractions to write probabilities.

Lesson 163 Probability and Counting Review Objective: The student will complete a review of probability and combinations.

Lesson 164 Probability and Counting Assessment Objective: The student will be able to display all knowledge learned by completing the Probability Assessment.

Lesson 165 Mean Objective: The student will be able to determine the mean of a set of data.

Lesson 166 Median Objective: The student will be able to find the median of a set of data.

Lesson 167 Mode Objective: The student will be able to find the mode of a set of data.

Lesson 168 Frequency Table Objective: The student will be able to make a frequency table in order to analyze data.

Lesson 169 Line Plot Objective: The student will be able to represent data by creating a line plot.

Lesson 170 Stem and Leaf Plot Objective: The student will be able to create a stem and leaf plot to represent data.

Lesson 171 Pie Chart Objective: The student will be able to create a pie chart to display data.

Lesson 172 Bar Graph Objective: The student will be able to represent data by creating a bar graph.

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Lesson 173 Data Analysis Review Objective: The student will study for an Assessment over data analysis techniques.

Lesson 174 Data Analysis Assessment Objective: The student will be able to display his knowledge and understanding of data analysis.

Lesson 175 Culminating Project – Part 1 Objective: The student will demonstrate her knowledge of 5th grade math by composing an Assessment.

Lesson 176 Culminating Project – Part 2 Objective: The student will continue to work on his culminating project.

Lesson 177 Culminating Project – Part 3 Objective: The student will continue to work on her culminating project.

Lesson 178 Culminating Project – Part 4 Objective: The student will review his questions so far, and add more in this final drafting Lesson. Lesson 179 Culminating Project – Part 5 Objective: The student will rewrite her Assessment to make sure it is neat, legible, and presentable. Lesson 180 Culminating Project Completion Objective: The student will administer and / or take the 5th grade Math final Assessment

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Fifth Grade Math Common Core Alignment Complete Curriculum Lesson

Operations and Algebraic Thinking

--Write and interpret numerical expressions.5.0A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

13, 37, 40, 42, 88

5 0A 2 Write simple expressions that record calculations with 37 40 425.0A.2 Write simple expressions that record calculations withnumbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

37, 40, 42

--Analyze patterns and relationships.5.OA.3 Generate two numerical patterns using two given rules. *395.OA.3 Generate two numerical patterns using two given rules.Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence Explain informally why this is so

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sequence. Explain informally why this is so.

Number and Operations in Base Ten

--Understand the place value system.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5, 6, 7, 21, 48

5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

48

5.NBT.3 Read, write, and compare decimals to thousandths.a. Read and write decimals to thousandths using base-ten 5, 55, 149gnumerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5, 55, 149

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons

7

results of comparisons.

5.NBT.4 Use place value understanding to round decimals to any place.

9

--Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.5 Fluently multiply multi-digit whole numbers using the 18, 19, 20y p y g gstandard algorithm.

8, 9, 0

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5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

25-30

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and strategies

12, 21-24, 30, 31, 34, 175hundredths, using concrete models or drawings and strategiesbased on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Number and Operations—Fractions

--Use equivalent fractions as a strategy to add and subtract fractions

5.NF.1 Add and subtract fractions with unlike denominators 57-655.NF.1 Add and subtract fractions with unlike denominators(including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

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5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators e g by using visual fraction models or equations to

56, 61

denominators, e.g., by using visual fraction models or equations torepresent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

--Apply and extend previous understandings of multiplication and division to multiply and divide fractions.p y

5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions, mixed numbers, or decimal fractions, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared

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multiplied by 4 equals 3, and that when 3 wholes are sharedequally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

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b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

*112

5.NF.5 Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

19, 20, 21

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a

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familiar case); explaining why multiplying a given number by afraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n b) to the effect of multiplying a/b by 1.

5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.a. Interpret division of a unit fraction by a non-zero whole number, 73, 74, 76a. Interpret division of a unit fraction by a non-zero whole number,and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

73, 74, 76

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

73, 76

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c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

73, 76

Measurement and Data

--Convert like measurement units within a given measurement system.

5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to

96-101, 103-105units within a given measurement system (e.g., convert 5 cm to0.05 m), and use these conversions in solving multi-step, real world problems.

--Represent and interpret data.5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in

f f

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identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

--Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

126-130understand concepts of volume measurement.a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

126, 128

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

126, 128

5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

126, 128

5.0 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

126

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the

126-130side lengths by packing it with unit cubes, and show that thevolume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

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

126, 127, 129, 130

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by

126, 128composed of two non-overlapping right rectangular prisms byadding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Geometry

--Graph points on the coordinate plane to solve real-world and mathematical problems.p

5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis with the convention that the names of the two axes

88, 94, 95

second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

88, 89, 94, 95

--Classify two-dimensional figures into categories based on their properties.

5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

79, 84, 85, 176

5 G 4 Classify two-dimensional figures in a hierarchy based on 77 79 84 85 1765.G.4 Classify two-dimensional figures in a hierarchy based onproperties.

77, 79, 84, 85, 176

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Lesson 178 Culminating Project – Part 4

By now, you have written 36 questions, but you may remember that this project requires you to write 40.

You will spend this Lesson completing two activities:

First:

Write four more questions. They can be on any 5th grade math topic you like. You should take this opportunity to challenge yourself. While addition and subtraction were part of your studies this year, did they give you trouble? Try to write questions on something that was hard for you.

If you think probability is confusing, write a question that covers calculating odds. If you get frustrated when it’s time to divide fractions, ask questions about that. Change it up, and try to face anything that gave you problems head-on!

Second:

Go back through the questions you already wrote and double-check your answers. It is very important that your answer key be correct so that you can prove to your teacher that you know this material.

Lesson Wrap-Up: Some of the hardest questions this year were on the Assessments and in the reviews. Go look at them for ideas if you are having a hard time coming up with questions.

STUDENT MANUAL MATH—LESSON 178-1

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Lesson 179 Culminating Project – Part 5

\�� #�� to your teacher or to a fellow student. If you have any questions for your teacher, you should ask them in this Lesson.

You’ve worked hard on your 40 questions, and now you’re going to make sure that whoever takes your Assessment can understand them. You will spend the entire class period rewriting your Assessment so that it looks good and is easy to read.

Be sure to include clear instructions for anyone taking your test. Look at this example below:

Example of bad instructions


Do this:

1. 3.25

Convert the following decimal to a percentage:

1. 3.25 = __________%

Example of good instructions

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You also have to have an answer key. An answer key is a list of all the answers to all the problems on an Assessment. If you think back to Lesson 175, you were instructed to answer your problems as you made them. Now, you will have to write them all down in one place so that they are easy ��&��

A Bad Answer Key:

A bad answer key just puts all the answers on a sheet of paper, maybe separated by commas, or maybe just in a big jumble. It doesn’t look good, and it’s very hard to read.


Answers: 2, 4, 6, 8, yes

Answers: 1. 22. 43. 64. 85. Yes

A Satisfactory Answer Key:

A satisfactory answer key will give the number of the problem and its corresponding answer so that it’s easier to see which answer goes to which problem:

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A Great Answer Key:

A great answer key looks a lot like the Assessment that is being graded, but it has the answers written in. It lets the teacher know the answer right away, and it helps the teacher answer the student’s questions if there is any confusion.


1. 4-2 = Answer = 2

2. 3+1 = Answer = 4

3. 3x2 = Answer = 6

4. 5+3 = Answer = 8

5. Are all these numbers even? Answer = Yes

Do your best, and ask your teacher if you have any questions!

Lesson Wrap-Up: Show your Assessment to the teacher to make sure it is good looking, clear, and easy to read.

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Lesson 180 Culminating Project Completion

�� #��|�� =�� either with another student, or with your teacher.

@�� =�� =��Assessment to complete – if not, then your teacher will be completing the Assessment you wrote, and reviewing it with you.

X��#��>�� grade. In Math, concepts build on each other. Think of some of the study combinations you’ve had in the last year:

Subtraction led into division, which led into fractions, which led in to decimals, ratios, and percentages.

Percentages and ratios led up to Lessons on probability and statistics, which helped you prepare for data analysis and visual presentations of data.

Your study of lines and angles led into a study of polygons, which in turn allowed you to study area and perimeter, and then you expanded on these fundamentals to study volume and surface area.

As you can see, everything in Math is connected, and that means that what you’ve studied in 5th grade is just the beginning of what you will learn in 6th!

If you have traded papers with another student, complete the Assessment. If you are not trading, go through your Assessment with the teacher. When �� =� ��= ��¤�� keep your Assessment to study as a warm-up for 6th grade.

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