Math - Grade Five Unit 1 - Number Theory

Transcription

1 1 Time Frame: About 15 days (this includes a review days and testing days) Math - Grade Five Unit 1 - Number Theory Description: - To introduce students to the Student Reference, prime, composite, and square numbers - To review rectangular arrays, multiplication number models, and factoring - To develop exponents and square roots concepts Enduring Understandings: *Numeric fluency includes both the understanding of and the ability to appropriately use numbers. *The symbolic language of algebra is the used to communicate and generalize the patterns in mathematics. Essential Questions: *How do mathematical ideas interconnect and build on one to produce a coherent whole? *How can we compare contrast numbers? *How can counting, measuring, or labeling help to make sense of the world around us? *How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? Standards Topics Activities Resources Assessments 5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols - Factor Strings - Prime Factorization EDM 1.9 OA Gallery Walk ** OA Gallery Walk, Standards Solution, LLC

2 2 5.OA.2. Write simple expressions that record calculations with numbers, 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 ( ) is three times as large as , without having to calculate the indicated sum or product. 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 SRB - Factors (Factor Captor) - Square Numbers - Unsquare Numbers - SRB - Rectangular Arrays - Divisibility - Prime and Composite Numbers EDM 1.1 EDM 1.3 EDM 1.4 EDM 1.7 EDM 1.8 EDM 1.1, EDM 1.2 EDM 1.5 EDM 1.6 EDM 1.8 EDM Unsquaring Numbers 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. - Factor Strings and Prime Factorization - Factors (Factor Captor) EDM 1.4 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

3 3 Math - Grade Five Unit 2: Estimation and Computation Time Frame: About Days (this includes a review days and testing days) Description: - To develop addition, subtraction, and multiplication algorithms - To devise an estimation strategy to solve a problem - To make magnitude estimates for products of multidigit numbers - To understand the relative sizes of 1 million, 1 billion, and 1 trillion Enduring Understandings: *Numeric fluency includes both the understanding of and the ability to appropriately use numbers. *Computational fluency includes understanding the appropriate use of numerical operations and place value. *Experimental results tend to approach theoretical probabilities after a large number of trials. Essential Questions: *How do mathematical ideas interconnect and build on one another to produce a coherent whole? *How can we compare and contrast numbers? *How can counting, measuring, or labeling help to make sense of the world around us? *How can the collection, organization, interpretation, and display of data be used to answer questions? *How can experimental and theoretical probabilities be used to make predictions or draw conclusions?

4 4 Standards Topics Activities Resources Assessments 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. - Addition and Subtraction of Whole Numbers - Addition and Subtraction Number Stories Journal EDM 2.2 EDM 2.3 EDM 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 Multiplying and Dividing by Powers of 10 Journal MMR EDM NBT.3b. Read, write, and compare decimals to thousandths. b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. - Addition and Subtraction of Decimals - Reaction Time (Rounding to the hundredths place) Journal EDM 2.2 EDM NBT.4. Use place value understanding to round decimals to any place. - Reaction Time (Rounding to the hundredths place) Journal EDM 2.5, EDM 2.7, EDM 2.8

5 5 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. - Multiplication of Whole Numbers and Decimals Journal EDM NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based 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. - Multiplication of Whole Numbers and Decimals Journal EDM 2.2 EDM 2.3 EDM 2.4 EDM 2.5 EDM 2.7 EDM OA.2. Write simple expressions that record calculations with numbers, 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 ( ) is three times as large as , without having to calculate the indicated sum or product. 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - Addition and Subtraction Number Stories - Comparing Millions, Billions, and Trillions (Using Place Value to Compare Powers of 10) Journal Journal EDM 2.4 EDM 2.8 EDM 2.1 EDM 2.10 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

6 6 Math - Grade Five Unit 3 - Geometry Explorations and the American Tour Time Frame: About Days (this includes a review days and testing days)

7 7 Description: - To explore data collection, organization, and interpretation - To explore the geometric properties of polygons - To review types of angles, geometric figures, and the use of geometry Enduring Understandings: *Some attributes of objects are measureable, e.g. length, mass, capacity and can be quantified. *Two- dimensional objects can be described, classified, and analyzed by their attributes. Essential Questions: *How can we decide when to use an exact answer and when to use an estimate? *How do we describe, sort, and classify shapes? *How can objects be represented and compared using geometric attribute? *How can measurements be used to solve problems? *How can I tell whether my answer is reasonable? Standards Topics Activities Resources Assessments 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 Multiplying and Dividing by powers of 10 with and without decimals (Mental Math Reflexes) EDM OA.2. Write simple expressions that record calculations with numbers, 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 ( ) is three times as large as , without having to calculate the indicated sum or product. - Adding and Subtracting Number Stories (Journal Page 64) EDM 3.2

8 8 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. - Properties of Polygons - Using a Protractor to Measure Angles EDM 3.4 EDM 3.7 EDM 3.8 (Math Masters 87A) 5.G.4. Classify two-dimensional figures in a hierarchy based on properties. - Classify Triangles and Quadrilaterals Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

9 9 Time Frame: About 15 Days (this includes a review days and testing days) Math - Grade Five Unit 4 - Division Description: - To review multiplication and division facts and apply basic facts to division with 1- digit divisors - To review and practice the partial- quotients division algorithm, with whole numbers and division of decimals by whole numbers - To practice solving division number stories and interpreting the remainder. Enduring Understandings: *A variety of problem solving strategies can be utilized to solve mathematical problems. *Numeric fluency includes both the understanding of and the ability to appropriately use numbers. *Reasoning is used to support mathematical conclusions/solutions. Essential Questions: *When is it appropriate to use estimation and/ or approximation? *What problem solving strategies do I use to solve a variety of problems? *How do mathematical operations relate to each other? *How can I use reasoning to support mathematical conclusions? Standards Topics Activities Resources Assessments 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. - Division Facts and Extensions - Partial-Quotients Division - Interpret the Remainder EDM 4.1 EDM 4.2 EDM 4.4 EDM 4.6

10 10 5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based 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. 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. - Division of Decimals - Interpreting the Remainder - Making Magnitude Estimates with Multiplication and Division (First to 100) - Quadrangle Relationships EDM 4.5 EDM 4.6 EDM 4.1 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

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12 12 Time Frame: About 25 Days (this includes a review days and testing days) Math - Grade 5 Unit 5 - Fractions, Decimals, and Percents Description: - To explore mixed numbers, comparing and ordering fractions, and finding equivalent fractions - To practice turning fractions into decimals and percents - To review the properties and construction of bar and circle graphs Enduring Understandings: *A fraction is another representation for division. *Computational fluency includes understanding the appropriate use of numerical operations and place value. *The results of a statistical investigation can be used to support or refute an argument. *Experimental results tend to approach theoretical probabilities after a large number of trials. *The idea of common denominators shows that each fraction has an equivalent name. Essential Questions: *How do we use fractions in everyday life? *How are fractions related and how do we use patterns to understand them? *How can we compare and contrast numbers? *How can the collection, organization, interpretation, and display of data be used to answer questions? Standards Topics Activities Resources Assessments 5.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 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) - Comparing and Ordering Fractions EDM 5.3

13 13 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 represent 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. - Comparing and Ordering Fractions Fractions Lesson Plans: ** Betty Bloom s Party Fabric Shop Get Off the Bus How Does Your Garden Grow EDM 5.3 Fractions Lesson Plans, Standards Solution, LLC 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 or mixed numbers, 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 - Fraction Word Problems - Converting Improper Fractions to Mixed Numbers EDM 5.1 EDM 5.6 that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally 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.4a. 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 - Fraction Of Problems EDM 5.12 (Study Link)

14 14 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.) 5.NBT.3a. Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) Converting Fractions to Decimals with/ without a calculator - Using a Calculator to Convert Fractions to Percents EDM 5.5 EDM 5.6 EDM 5.7 EDM 5.8 EDM 5.9 (1/1000). - Bar and Circle Graphs 5.NBT.4. Use place value understanding to round decimals to any place. - Rounding Decimals - Using a Calculator to Convert Fractions to Percents EDM 5.5 EDM 5.6 EDM NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based 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. - The Percent Circle: Making Circle Graphs EDM 5.11 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

15 15 Math - Grade 5 Unit 6 - Using Data, Addition and Subtraction of Fractions Time Frame: About 21 Days (this includes a review days and testing days) Description: - To use data from surveys, investigate the effect of the sample size, and use stem- and leaf plots and other displays - To revisit addition and subtraction Enduring Understandings: *A fraction is another representation for division. *The denominator determines how many parts make the whole; that is why quantities must have the same denominator to be combined. *Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected, as well as how best to collect, represent, and summarize it. *Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another. *Computational fluency includes understanding the appropriate use of numerical operations and place value. Essential Questions: *How can the collection, organization, interpretation, and display of data be used to answer questions? *How can the representation of data influence conclusions? *How can sampling techniques affect data reliability? *How do operations affect numbers? Standards Topics Activities Resources Assessments

16 16 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - Natural Measures of Length EDM 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 identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - Organizing Data Using a Line Plot EDM 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 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) - Clock Fractions and Common Denominators - Quick Common Denominators EDM 6.8 EDM 6.9 EDM 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 represent 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. - Clock Fractions and Common Denominators - Quick Common Denominators - Fraction Word Problems EDM 6.8 EDM 6.9 EDM 6.10 EDM 12.7 (Math Masters 365)

17 17 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 or mixed numbers, 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 - Fractions as Division EDM 6.8 that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally 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.5b. Interpret multiplication as scaling (resizing), by: 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 fraction 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 - Clock Fractions and Common Denominators EDM 6.9 effect of multiplying a/b by 1. 5.NBT.3a. Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). - Stem and Leaf Plots EDM 6.3

18 18 5.NBT.4. Use place value understanding to round decimals to any place. - Mystery Pots EDM 6.1 EDM NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based 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 Stories EDM 6.5 EDM 6.7 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Math - Grade 5 Unit 8 - Fractions and Ratios (Complete Unit 7 once you have completed Unit 8) Time Frame: About 20 Days (this includes a review days and testing days) Description: - To rename fractions as equivalent fractions and mixed numbers - To use equivalent names for fractions and mixed numbers to perform operations - To introduce algorithms for the multiplication of fractions and mixed numbers and division of fractions with visual models - To practice estimating and calculating a percent of a number Enduring Understandings: *Computational fluency includes understanding the appropriate use of numerical operations and place value. *The denominator determines how many parts make the whole; that is why quantities must have the same denominator to be combined. Essential Questions: *How do mathematical operations relate to each other?

19 19 *Why is it necessary to rename fractions and mixed numbers to solve addition and subtraction problems? *How can I model multiplication of a whole number by a fraction? *How do we compute mixed numbers? Standards Topics Activities Resources Assessments 5.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 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) - Comparing Fractions - Adding and Subtracting Mixed Numbers EDM 8.1 EDM 8.2 EDM 8.3 EDM 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 represent 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 - Comparing Fractions - Adding Mixed Numbers EDM 8.1 EDM 8.2 EDM 8.3 EDM 8.4 observing that 3/7 < 1/2.

20 20 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 or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result - Number Stories: Division with Fractions EDM 8.12 EDM 12.5 (Journal Page 414) of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally 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.4a. 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 - Fractions of Fractions - Multiplication of Fractions and Whole Numbers EDM 8.5 EDM 8.6 EDM 8.7 EDM 8.8 for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.)

21 21 5.NF.4b. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 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. - Multiplication of Fractions and Whole Numbers - An Area Model for Fraction Multiplication EDM 8.6, 8-7 EDM NF.5ab. 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. 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 fraction 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. - Comparing Fractions - Multiplication of Mixed Numbers EDM 8.7 EDM 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. - Multiplication of Mixed Numbers - Area Model for Fraction Multiplication EDM 8.6 EDM 8.8

22 22 5.NF.7a,b,c. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) a. Interpret division of a unit fraction by a nonzero 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. 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. 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 - Fraction Division EDM 8.12 EDM 12.5 (Journal Page 414) of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

23 23 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Time Frame: About 8 Days (this includes a review days and testing days) Description: - To understand the conventions associated with exponents - To organize and analyze data using line graphs and line plots Math - Grade 5 Unit 7 - Exponents and Negative Numbers Enduring Understandings: *Operations must be done in order. *The symbolic language of algebra is used to communicate and generalize the patterns in mathematics. *Algebraic representations can be used to generalize patterns and relationships. Essential Questions: *How can change be best represented mathematically? *How would you describe the Order of Operations? *How can the collection, organization, interpretation, and display of data to be used to answer questions? Standards Topics Activities Resources Assessments 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 Exponential Notation - Exponential Notation for Powers of 10 - Parentheses in Number Sentences Journal EDM 7.1 EDM 7.2 EDM OA.1. Use parentheses, brackets, or braces in - Order of Operations

24 24 numerical expressions, and evaluate expressions with these symbols - Parentheses in Number Sentences Journal 5.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. - Line Graphs Journal EDM 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 identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - Line Plots Journal EDM 7.10 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

25 25 Time Frame: About 9 Days (this includes a review days and testing days) Description: - To work with coordinate graphs - To extend area concepts - To develop a formula for volume and consider capacity relationships Math - Grade 5 Unit 9 - Coordinates, Area, Volume, and Capacity Enduring Understandings: *Coordinate geometry can be used to verify and represent geometric/algebraic relationships. *A point on a coordinate plane represents the two facets of information associated with an ordered pair. *Patterns exhibit relationships that can be extended, described, and generalized. *Two- and three-dimensional objects can be described, classified, and analyzed by their attributes, and their location can be described quantitatively. *Some attributes of objects are measureable, e.g. length, mass, capacity and can be quantified. *Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it. Essential Questions: *How does the coordinate system work? *How can we represent numerical patterns on a coordinate grid? *How can number patterns help us understand numerical relationships? *What is the relationship between categories and sub-categories of two-dimensional shapes? *How can using graphs help us to solve problems and describe data we collect?

26 26 Standards Topics Activities Resources Assessments 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 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. - Coordinate Grid Structure and Vocabulary - Coordinate Grid Structure and Vocabulary Journal Study Journal Study EDM 9.1 EDM 9.2 EDM 9.3 EDM 9.1 EDM 9.2 Using Graphs to Solve Problems Mini Unit ** Using Graphs to Solve Problems handout Happy Hamster Chow Straight Edge Graphing Practice Using Graphs to Solve Problems Mini Unit, Standards Solution, LLC 5.NF.4b. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 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 - Area, Tiling, and Using a Formula - Area of rectangles with fractional side Journal EDM 9.4 EDM 9.10

27 27 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. length Study 5.NF.7a,b,c. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) a. 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. 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. 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? 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - Area of Rectangles Journal Study EDM Capacity (Liter, Milliliter, Cubic Centimeter) Journal Study EDM 9.10

28 28 5.MD.3a, b. Recognize volume as an attribute of solid figures and understand 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. 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. - Volume of Rectangular Prisms Journal Study EDM MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - Volume of Rectangular Prisms Journal Study EDM 9.4 EDM 9.8 EDM MD.5a. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume 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. - Volume of Rectangular Prisms Journal Study EDM 9.8 EDM MD.5b. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. c. 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. - Area of Rectangles Journal Study EDM 9.4 EDM 9.8 EDM 9.9 EDM 9.10

29 29 5.MD.5c. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. d. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. - Volume of Right Prisms Journal Study EDM 9.9 Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Time Frame: About 8 Days (this includes a review days and testing days) Description: - To represent relationships as algebraic expressions - To generate input- output tables - To link data in tables to corresponding points on coordinate grids Enduring Understandings: *Algebraic representations can be used to generalize patterns and relationships. *Patterns exhibit relationships that can be extended, described, and generalized. Math - Grade 5 Unit 10 - Using Data; Algebra Concepts and Skills

30 30 Essential Questions: *How do you apply algebraic properties to evaluate expressions? *How do I express a pattern to show a relationship? *How do you interpret data on a line graph? Standards Topics Activities Resources Assessments 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 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 identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - Converting Units of Measure - Displaying Fractions on a Line Plot EDM 10.9 (Journal Page 366A- 366B) EDM 10.2 (Journal Page 339) 5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - Finding Volume EDM 10.1 (Journal Page 334A- 334B)

31 31 5.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. - Patterns and Relationships - Rules, Tables, and Graphs 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. - Patterns and Relationships - Rules, Tables, and Graphs Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Math - Grade 5 Unit 11 - Volume

32 32 Time Frame: About 7 Days (this includes a review days and testing days) Description: - To develop volume formulas - To find surface area of rectangular prisms Enduring Understandings: *Volume is the amount of space that a three-dimensional object can occupy. Essential Questions: *How can we apply volume to the real world? *How do we convert units of measurement? Standards Topics Activities Resources Assessments 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - Finding Equivalent Measures EDM 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 identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. - Line Plot Using Fractions EDM 11.7 (Journal 390A- 390B) 5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. - Volume of Rectangular Prisms EDM 11.1 (Journal Page 371A- 371B)

33 33 5.MD.5a, b. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume 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. 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. - Volume of Rectangular Prisms in Word Problems Yummy s Candy Company ** EDM 11.1 (Journal Page 371A- 371B) EDM 11.3 Yummy s Candy Company, Standards Solution, LLC 5.MD.5c. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. - Solving Real World Volume Problems EDM 11.5 (Journal 384A- 384B) Additional Resources/ Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

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