GRADE 5 MATHEMATICS CURRICULUM GUIDE

Transcription

1 GRADE 5 MATHEMATICS CURRICULUM GUIDE Loudoun County Public Schools Complete scope, sequence, pacing and resources are available on the LCPS Intranet.

2 INTRODUCTION TO LOUDOUN COUNTY S MATHEMATICS CURRICULUM GUIDE This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun s teachers concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is the lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program that remains relatively unchanged over several student generations. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can combine them with the GUIDE for ease in lesson planning. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 3. Teachers should assure that the use of websites correlate with the objectives of lesson and provide students with the appropriate challenge. 4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.

3 Grade 5 Mathematics Nine Weeks Overview 1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter Geometry Expressions and Equations Order of Operations 5.7 Rational Numbers a, c 5.19 Rational Numbers (continued) Probability 5.14 Circles 5.9 Measurement 5.8 a, c, d, e Probability and Statistics a, b, c, d 5.17 Problem Solving 5.4 Problem Solving, (continued) b, d 5.19 Area and Volume 5.8 a, b Elapsed Time 5.10

4 Grade 5 Quarter 1 School Year Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) REQUIRED Critical Thinking Lessons INV: Investigations in Number, Data, and Space Standard(s) of Learning Essential Knowledge and Skills Additional Instructional Resources ESS: VDOE Enhanced Scope and Sequence 5 days Geometry 5.11 Essential Questions 5.11 Essential Understanding Understand how to measure acute, right, obtuse, and straight angles. SOL 5.11 The student will measure right, acute, obtuse, and straight angles Essential Knowledge and Skills Identify the appropriate tools (e.g., protractor and straightedge or angle ruler as well as available software) used to measure and draw angles and triangles. Measure right, acute, straight, and obtuse angles, using appropriate tools, and identify their measures in degrees. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angle measures on a diagram in practical and mathematical problems, (e.g., by using an equation with a symbol for the unknown angle measure). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.12 Essential Questions 5.12 Essential Understandings Understand that angles can be classified as right, acute, obtuse, or straight according to their measures. Understand that a triangle can be classified as either right, acute, or obtuse according to the measure of its largest angle. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.12 The student will classify a) angles as right, acute, obtuse, or straight; and b) triangles as right, acute, obtuse, equilateral, scalene, or isosceles Essential Knowledge and Skills Classify angles as right, acute, straight, or obtuse. Classify triangles as right, acute, or obtuse. Classify triangles as equilateral, scalene, or isosceles.

5 Grade 5 Quarter 1 School Year Understand that a triangle can be classified as equilateral, scalene, or isosceles according to the number of sides with equal length. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.13 Essential Questions 5.13 Essential Understandings Understand that simple plane figures can be combined to make more complicated figures and that complicated figures can be subdivided into simple plane figures. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will a) develop definitions of these plane figures; and b) investigate and describe the results of combining and subdividing plane figures Essential Knowledge and Skills Understand that simple plane figures can be combined to make more complicated figures and that complicated figures can be subdivided into simple plane figures. 10 days Expressions and Equations 5.18 a, c Essential Questions What is a variable? What is an expression? What is an equation? Compare and contrast expressions and equations. How can real life problem situations be modeled using expressions and/or equations? 5.18 Essential Understandings Understand that a variable is a symbol that can stand for an unknown number or object. Understand that a variable expression is a variable or combination of variables, numbers, SOL 5.18 The student will a) investigate and describe the concept of variable; c ) model one-step linear equations in one variable, using addition and subtraction; and 5.18 Essential Knowledge and Skills Recognize that an equation contains an equals sign (=) whereas an expression does not. Understand that an equation has a variable and an equal sign (=). Describe the concept of a variable (presented as boxes, letters, or other symbols) as a representation of an unknown quantity. Write an equation with addition, subtraction, multiplication, or division, using a variable Grade 5 ESS Lessons: (found in lessons/activities tab) Writing Algebraic Expressions Variables in Open Sentences Geometric Situations Hands-on Equations: Book 1 Illuminations: The Variable Machine Cracking the Code ws NLVM: Algebra Balance Scales:

6 Grade 5 Quarter 1 School Year and symbols that represents a mathematical relationship. Understand that verbal expressions can be translated to variable expressions. Understand that an open sentence has a variable and an equal sign (=). Understand that problem situations can be expressed as open sentences. to represent n unknown quantity.. Model one-step linear equations. Create and write a word problem to match a given equation. 5 days Properties and the order of operations 5.7 Essential Questions How could the distributive property be used in computation strategies for whole numbers? Prove that the use of the distributive property does not change the value of the product. Why is there a specific order of operations? What is a variable? Why should real life situations be modeled using expressions and/or equations? Describe which operation is completed first when given an expression involving more than one operation. INV: Building on Numbers You Know Investigation 2: Multiplication and Division Situations, Sessions 1 6 SOL 5.7 The student will evaluate whole number numerical expressions, using the order of operations, 5.7 Essential Knowledge and Skills Simplify expressions by using the order of operations in a demonstrated step-by-step approach. Find the value of numerical expressions, using the order of operations. Given an expression involving more than one operation, describe which operation is completed first, which is second, etc. Illuminations.nctm.org Primary Krypto(order of operations game) 5.7 Essential Understanding Understand that the order of operations describes the order to use to simplify

7 Grade 5 Quarter 1 School Year expressions containing more than one operation. ~~~~~~~ 5 days Rational Numbers: Rounding 5.1 Essential Questions Demonstrate, explain, and justify various strategies for rounding rational numbers. Why would you use rounding with decimals? Why would you use estimation with rational numbers? 5.1 Essential Understandings Understand that decimals are rounded in a way that is similar to the way whole numbers are rounded. Understand that decimal numbers can be rounded to estimate when exact numbers are not needed for the situation at hand. SOL 5.1 The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth. 5.1 Essential Knowledge and Skills Round decimal numbers to the nearest whole number, tenth, or hundredth. Grade 6 ESS Lessons: (found in lessons/activities tab) Sieve of Erastosthenes (prime and composite numbers) Partners and Leftovers (odd and even numbers) Prime and Composite Illuminations: Factor Game ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.3 Essential Questions Demonstrate, explain, and justify at least two ways to show a number is even or odd. What is a prime number? What is a composite number? Compare and contrast prime and composite numbers. 5.3 Essential Understandings ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.3 The student will a) identify and describe the characteristics of prime and composite numbers; and b) identify and describe the characteristics of even and odd numbers. 5.3 Essential Knowledge and Skills Identify prime numbers less than or equal to 100. Identify composite numbers less than or

8 Grade 5 Quarter 1 School Year Understand and use the unique characteristics of certain sets of numbers, including prime, composite, even, and odd numbers. equal to 100. Explain orally and in writing why a number is prime or composite. Identify which numbers are even or odd. Explain and demonstrate with manipulatives, pictorial representations, oral language, or written language why a number is even or odd. ~~~~~~~ 10 days ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.4 Essential Questions 5.4 Essential Understandings Understand the meaning of mathematical operations and how these operations relate to one another when creating and solving single-step and multistep word problems. SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers. SOL 5.4 Essential Knowledge and Skills Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calculators according to the context and nature of the computation in order to compute with whole numbers. Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations. Estimate the sum, difference, product, and quotient of whole number computations. Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which sums, differences, and products will not exceed five digits; multipliers will not exceed two digits; divisors will not exceed two digits; or dividends will not exceed four digits. Use two or more operational steps to solve

9 Grade 5 Quarter 1 School Year a multistep problem. Operations can be the same or different. ~~~~~~~ 12 days Working with Rational Numbers: Decimals 5.4 Essential Questions Justify estimation strategies for the sum, difference, product, or quotient of two numbers. What is the meaning of mathematical operations and how these operations relate to one another when creating and solving single-step and multistep word problems? Compare and contrast multiplication and division of whole numbers and decimals. How can the distributive property help with computation involving decimals? Prove that using the distributive property does not change the value of an expression. 5.4 Essential Understanding Use similar procedures as those developed for whole number computation and apply them to decimal place values, giving careful attention to the placement of the decimal point in the solution. Select appropriate methods and tools from among paper and pencil, estimation, mental computation, INV: Name That Portion Investigation 2: Models for Fractions, Sessions 1 9 Investigation 3: Exploring Decimals, Sessions The student will a) find the sum, difference, product and quotient of two numbers expressed as decimals; and b) create and solve practical problems involving decimals. 5.5 Essential Knowledge and Skills Determine an appropriate method of calculation to find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths, selecting from among paper and pencil, estimation, mental computation, and calculators. Estimate to find the number that is closest to the sum, difference, and product of two numbers expressed as decimals through thousandths. Find the sum, difference, and product of two numbers expressed as decimals through thousandths, using paper and pencil, estimation, mental computation, and calculators. Determine the quotient, given a dividend expressed as a decimal through thousandths and a single-digit divisor. For example, 5.4 divided by 2 and 2.4 divided by 5. Use estimation to check the reasonableness of a sum, difference, product, and quotient. Create and solve single-step and multistep problems. A multistep problem needs to incorporate

10 Grade 5 Quarter 1 School Year and calculators according to the context and nature of the computation in order to compute with decimal numbers. Understand the various meanings of division and its effect on whole numbers. Understand various representations of division, i.e., two or more operational steps (operations can be the same or different). dividend divisor = quotient quotient divisor dividend dividend = quotient. divisor Understand the meaning of mathematical operations and how these operations relate to one another when creating and solving single-step and multistep word problems 1 day Enrichment, Assessment, and Remediation Summary: Fifth graders will begin the school year with developing skills needed in building computational strategies and algebraic concepts. Focus will be on establishing an understanding of variables and their use in algebraic expressions and equations in real life problem situations. Students will develop a greater number sense of place value using decimals. Key vocabulary: Students will be introduced to correct mathematical vocabulary as their understanding of mathematical concepts is being developed. Throughout the first quarter, students will be expected to correctly use the following identified vocabulary: variable, expression, equation, even, odd, prime, composite, decimal, tenths, hundredths, and thousandths.

11 Grade 5 Quarter 2 School Year Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) REQUIRED Critical Thinking Lessons INV: Investigations in Number, Data, and Space Standard(s) of Learning Essential Knowledge and Skills Additional Instructional Resources / Comments ESS: VDOE Enhanced Scope and Sequence 4 days Working with Rational Numbers: Decimals (cont) 5.5 Essential Questions Justify estimation strategies for the sum, difference, product, or quotient of two numbers. What is the meaning of mathematical operations and how these operations relate to one another when creating and solving single-step and multistep word problems? Compare and contrast multiplication and division of whole numbers and decimals. How can the distributive property help with computation involving decimals? Prove that using the distributive property does not change the value of an expression. 5.5 Essential Understandings Use similar procedures as those developed for whole number computation and apply them to decimal place values, giving careful attention to the placement of the decimal point in the solution. Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and SOL 5.5 The student will a. find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and b) create and solve practical problems involving decimals. 5.5 Essential Knowledge and Skills Determine an appropriate method of calculation to find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths, selecting from among paper and pencil, estimation, mental computation, and calculators. Estimate to find the number that is closest to the sum, difference, and product of two numbers expressed as decimals through thousandths. Find the sum, difference, and product of two numbers expressed as decimals through thousandths, using paper and pencil, estimation, mental computation, and calculators. Determine the quotient, given a dividend expressed as a decimal through thousandths and a single-digit divisor. For example, 5.4 divided by 2 and 2.4 divided by 5. Use estimation to check the reasonableness of a sum, difference, product, and quotient. Create and solve single-step and multistep problems.

12 Grade 5 Quarter 2 School Year calculators according to the context and nature of the computation in order to compute with decimal numbers. Understand the various meanings of division and its effect on whole numbers. Understand various representations of division, i.e., A multistep problem needs to incorporate two or more operational steps (operations can be the same or different). dividend divisor = quotient quotient divisor dividend dividend divisor = quotient. 25 days Working with Rational Numbers: Fractions 5.2 Essential Questions How can the same quantity be represented as both a fraction and a decimal? Create and solve a practical problem using estimation of decimals and/or fractions. Why are common denominators necessary to add or subtract fractions with unknown sums or differences? Justify that a fraction is in simplest form. Demonstrate, explain, and justify strategies for adding fractions with unlike denominators. 5.2 Essential Understandings Understand the relationship between INV: Name That Portion Investigation 2: Models for Fractions, Sessions 1 9 Investigation 3: Exploring Decimals, Sessions 1-8 SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form and vice versa; and b) compare and order fractions and decimals in a given set from least to greatest and greatest to least. 5.2 Essential Knowledge and Skills Represent fractions (halves, fourths, fifths, eighths, tenths, and twelfths) in their equivalent decimal form and vice versa. Recognize and name equivalent relationships between decimals and fractions with denominators up to 12. Compare and order from least to greatest and greatest to least a given set of no more than five numbers written as decimals, fractions, and mixed numbers with denominators of 12 or less. ESS ing/sol/standards_docs/mathema tics/index.shtml Serving Up Fractions Eggs cellent Fractions

13 Grade 5 Quarter 2 School Year fractions and their decimal form and vice versa. Understand that fractions and decimals can be compared and ordered from least to greatest and greatest to least. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.6 Essential Questions 5.6 Essential Understandings Develop and use strategies to estimate and compute addition and subtraction of fractions. Understand the concept of least common multiple and least common denominator as they are important when adding and subtracting fractions. Understand that a fraction is in simplest form when its numerator and denominator have no common factors other than 1. The numerator can be greater than the denominator. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form. 5.6 Essential Knowledge and Skills Solve single-step and multistep practical problems involving addition and subtraction with fractions having like and unlike denominators. Denominators in the problems should be limited to 12 or less (e.g., ) and answers should be expressed in simplest form. Solve single-step and multistep practical problems involving addition and subtraction with mixed numbers having like and unlike denominators, with and without regrouping. Denominators in the problems should be limited to 12 or less, and answers should be expressed in simplest form. Use estimation to check the reasonableness of a sum or difference.

14 Grade 5 Quarter 2 School Year Probability 5 days 5.14 Essential Questions What strategies are used to determine the sample space for an experiment? How can experimental or theoretical probability help predict an outcome in an event? 5.14 Essential Understandings Understand that the basic concepts of probability can be applied to make predictions of outcomes of simple experiments. Understand that a sample space represents all possible outcomes of an experiment. SOL 5.14 The student will make predictions and determine the probability of an outcome by constructing a sample space Essential Knowledge and Skills Construct a sample space, using a tree diagram to identify all possible outcomes of a single event. Construct a sample space, using a list or chart to represent all possible outcomes of a single event. Predict and determine the probability of an outcome by constructing a sample space. The sample space will have a total of 24 or less possible outcomes 5 days Circles 5.9 Essential Questions Compare and contrast chord, diameter, and radius in a circle. What is the relationship between the radius of a circle and its diameter? What is the relationship between the radius of a circle and its circumference? 5.9 Essential Understandings Understand that a chord is a line segment that extends between any two unique points of a circle. Understand that a diameter is also a special chord that goes through the center of a circle. Understand the relationship between the measures of diameter and radius and the relationship between the SOL 5.9 The student will identify and describe the diameter, radius, chord, and circumference of a circle. 5.9 Essential Knowledge and Skills Identify and describe the diameter, radius, chord, and circumference of a circle. Describe the relationship between diameter and radius; diameter and chord; radius and circumference; and diameter and circumference. The length of the diameter of a circle is twice the length of the radius. ESS ing/sol/standards_docs/mathema tics/index.shtml Human Circles AIMS: The Amazing Circle book Illuminations: Circle Tool

15 Grade 5 Quarter 2 School Year measures of radius and circumference. Understand that a radius is a line segment that extends between the center and the circumference of the circle. Understand that the circumference is the distance around the circle. Perimeter is the measure of the circumference. 2 days Enrichment, Assessment, and Remediation

16 Grade 5 Quarter 3 School Year Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) Standard(s) of Learning Essential Knowledge and Skills REQUIRED Critical Thinking Lessons Additional Instructional Resources 12 days Measurement 5.8 Essential Questions How is perimeter used? How might the distributive property help to find perimeter? Why are equivalent measures within the metric system useful? Describe a situation when converting from one unit of measure to another is appropriate. What are three examples of objects measured by each unit of measure in the both the U.S. Customary and metric systems? 5.8 Essential Understandings Understand the concept of perimeter. Understand and use appropriate units of measure for perimeter. Understand how to select a measuring device and unit of measure to solve problems involving measurement. Perimeter is the distance around a polygon and iis a measure of length Estimate and determine the perimeter and area of polygons. The distributive property can be used in finding the perimeter of a rectangle. (e.g. (2 length) + (2 SOL 5.8 The student will a) find perimeter, in standard units of measure; c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S. Customary and metric units; and e) choose an appropriate unit of measure for a given situation involving measurement using U.S. Customary and metric units 5.8 Essential Knowledge and Skills Determine the perimeter of a polygon, with or without diagrams, when the lengths of all sides of a polygon that is not a rectangle or a square are given; the length and width of a rectangle are given; or the length of a side of a square is given. Estimate and determine the perimeter of a polygon, and area of a square, rectangle, and right triangle following the parameters listed above, using only whole number measurements given in metric or U.S. Customary units, and record the solution with the appropriate unit of measure (e.g., 24 square inches). Estimate and determine the area of a square, with or without diagrams, when the length of a side is given. INV: Measurement Benchmarks Investigation 1: Measures of Length and Distance, Sessions 1 6 Investigation 2: Measures of Weight and Liquid Volume, Sessions 1 6 SFAW

17 Grade 5 Quarter 3 School Year width ) = 2 (length + width). Identify equivalent measurements within the metric and U.S. Customary systems. Estimate and determine the area of a rectangle, with or without diagrams, when the length and width are given. Estimate and determine the area of a right triangle, with or without diagrams, when the base and the height are given. Differentiate among the concepts of area, perimeter, and volume. Develop a procedure for finding volume using manipulatives (e.g., cubes). Determine volume in standard units. Describe practical situations where area, perimeter, and volume are appropriate measures to use, and justify their choices orally or in writing. Identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation. Identify equivalent measurements within the metric system for the following: length: millimeters, centimeters, meters, and kilometers; mass: grams and kilograms; liquid volume: milliliters, and liters.

18 Grade 5 Quarter 3 School Year Outcomes, Data, and Patterns 5.14 Essential Questions What strategies are used to determine the sample space for an experiment? How can experimental or theoretical probability help predict an outcome in an event? SOL 5.14 The student will make predictions and determine the probability of an outcome by constructing a sample space Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Construct a sample space, using a tree diagram to identify all possible outcomes of a single event. INV: Patterns of Change Investigation 1: Number Patterns in Changing Shapes, Sessions 1 4 Investigation 2: Number Motion Stories, Graphs, and Tables, Sessions 1 5 INV: Data, Cats, and Kids Investigation 2: Examining Cats, Sessions 1 2 Investigation 5: Researching Play Injuries, Sessions days ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.15 Essential Questions How does the data collected help determine the type of representation used? Construct a sample space, using a list or chart to represent all possible outcomes of a single event. Predict and determine the probability of an outcome by constructing a sample space. The sample space will have a total of 24 or less possible outcomes. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.15 The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots and line graphs Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Formulate the question that will guide

19 Grade 5 Quarter 3 School Year the data collection. Collect data, using observations (e.g., weather), measurement (e.g., shoe sizes), surveys (e.g., hours watching television), or experiments (e.g., plant growth). Organize the data into a chart, table, stem-and-leaf plots, and line graphs. Display data in line graphs and stemand-leaf plots. Construct line graphs, labeling the vertical axis with equal whole number, decimal, or fractional increments and the horizontal axis with continuous data commonly related to time (e.g., hours, days, months, years, and age). Line graphs will have no more than six identified points along a continuum for continuous data (e.g., the decades: 1950s, 1960s, 1970s, 1980s, 1990s, and 2000s). Construct a stem-and-leaf plot to organize and display data, where the stem is listed in ascending order and the leaves are in ascending order, with or without commas between leaves. Title the given graph or identify the title. Interpret the data in a variety of forms (e.g., orally or in written form). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.16 Essential Questions How do the measures of center measure center in data? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.16 The student will a) describe mean, median, and mode as measures of center;

20 Grade 5 Quarter 3 School Year How does range measure variation in data? How does the mean represent fair share? Why are mean, median, and mode described as measures of center? How do measures of center and range expressed in the context of other characteristics of the data best describe the results? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.17 Essential Questions What are the connections between a pattern or function and the words, table, and symbols that b) describe mean as fair share; c) find the mean, median, mode, and range of a set of data; and d) describe the range of a set of data as a measure of variation Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Describe and find the mean of a group of numbers representing data from a given context as a measure of center. Describe and find the median of a group of numbers representing data from a given context as a measure of center. Describe and find the mode of a group of numbers representing data from a given context as a measure of center. Describe mean as fair share. Describe and find the range of a group of numbers representing data from a given context as a measure of variation. Describe the impact on measures of center when a single value of a data set is added, removed, or changed. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

21 Grade 5 Quarter 3 School Year days represent it? How can you use numerical or algebraic symbols to represent change in a pattern? (Based on a pattern, a prediction can be made of the n th term.) Solving Practical Problems Justify estimation strategies for the sum, difference, product, or quotient of two numbers. What is the meaning of mathematical operations and how these operations relate to one another when creating and solving single-step and multistep word problems? 5.17 Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Describe numerical and geometric patterns formed by using concrete materials and calculators. Describe the relationship found in patterns, using words, tables, and symbols to express the relationship. SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtractions, multiplication, and division with and without remainders of whole numbers. 5.4 Essential Knowledge and Skills The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calculators according to the context and nature of the computation in order to compute with whole numbers. Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations. Investigations: Building Number Sense

22 Grade 5 Quarter 3 School Year Days Assessment, Enrichment, and Remediation Estimate the sum, difference, product, and quotient of whole number computations. Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which sums, differences, and products will not exceed five digits; multipliers will not exceed two digits; divisors will not exceed two digits; or dividends will not exceed four digits. Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

23 Grade 5 Quarter 3 School Year Number of Days Topic and Essential Questions (refer to 2009 SOL only) Standard(s) of Learning Essential Knowledge and Skills Essential Understandings Indicators for 2009 SOLs *Deleted or moved to a different grade level Remains the same New content to this grade REQUIRED Critical Thinking Lessons Additional Instructional Resources 5 days Assessment, Enrichment, and Remediation

24 Quarter 4 Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) Problem Solving 5.4 Essential Questions 5.4 Essential Understanding Standard(s) of Learning Essential Knowledge and Skills SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers. REQUIRED Critical Thinking Lessons Additional Instructional Resources 20 days Understand the meaning of mathematical operations and how these operations relate to one another when creating and solving single-step and multistep word problems. 5.4 Essential Knowledge and Skills Select appropriate methods and tools from among paper and pencil, estimation, mental computation, and calculators according to the context and nature of the computation in order to compute with whole numbers. Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations. Estimate the sum, difference, product, and quotient of whole number computations. Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which sums, differences, and products will not exceed five digits; multipliers will not exceed two digits; divisors will not exceed two digits; or dividends will not exceed four digits. Use two or more operational steps to solve a multistep problem. Operations can be the same or different.

25 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.6 Essential Questions 5.6 Essential Understandings Develop and use strategies to estimate and compute addition and subtraction of fractions. Understand the concept of least common multiple and least common denominator as they are important when adding and subtracting fractions. Understand that a fraction is in simplest form when its numerator and denominator have no common factors other than 1. The numerator can be greater than the denominator. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.18 b, d Essential Questions 5.18 b, d Essential Understandings Understand that a variable is a symbol that can stand for an unknown number or object. Understand that a variable expression is a variable or combination of variables, numbers, and symbols that represents a mathematical relationship. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form. 5.6 Essential Knowledge and Skills Solve single-step and multistep practical problems involving addition and subtraction with fractions having like and unlike denominators. Denominators in the problems should be limited to 12 or less (e.g., ) and answers should be expressed in simplest form. Solve single-step and multistep practical problems involving addition and subtraction with mixed numbers having like and unlike denominators, with and without regrouping. Denominators in the problems should be limited to 12 or less, and answers should be expressed in simplest form. Use estimation to check the reasonableness of a sum or difference. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.18 b, d The student will b) write an open sentence to represent a given mathematical relationship, using a variable; d) create a problem situation based on a given open sentence, using a single variable b, d Essential Knowledge and Skills Describe the concept of a variable (presented as boxes, letters, or other symbols) as a representation of an

26 Understand that an open sentence has a variable and an equal sign (=). Understand that problem situations can be expressed as open sentences. unknown quantity. Write an open sentence with addition, subtraction, multiplication, or division, using a variable to represent a missing number. Create and write a word problem to match a given open sentence with a single variable and one operation. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 5.19 Essential Questions 5.19 Essential Understandings Understand that the distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products. Understand that using the distributive property with whole numbers helps with understanding mathematical relationships. Understand when and why the distributive property is used. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition Essential Knowledge and Skills Investigate and recognize the distributive property of whole numbers, limited to multiplication over addition using diagrams and manipulatives. Investigate and recognize an equation that represents the distributive property, when given several whole number equations, limited to multiplication over addition. 10 days Area and Volume 5.8 a, b Essential Questions Why is area expressed in square units? Why is volume expressed in cubic units? Compare and contrast the difference between perimeter, area, and volume. Describe practical situations where area, perimeter, and volume are appropriate measures to use, and justify their choices orally or in writing. SOL 5.8 a, b The student will a) find area, and volume in standard units of measure; b) differentiate among area, and volume and identify whether the application of the concept of area, or volume is appropriate for a given situation;. 5.8 Essential Knowledge and Skills Estimate and determine the area of a square, rectangle, and right triangle. Estimate and determine the area of a square, with or without diagrams, when the INV: Containers and Cubes Investigation 1: The Packaging Factory, Sessions 1 4 INV: Containers and Cubes Investigation 2: Packing Problems, Sessions 1 5 Investigation 3: Measuring the Space in Our Classroom, Sessions 1 3 ESS: Measurement Mania

27 5.8 a, b Essential Understandings Understand the concepts of perimeter, area, and volume. Understand and use appropriate units of measure for perimeter, area, and volume. Understand the difference between using perimeter, area, and volume in a given situation. Understand how to select a measuring device and unit of measure to solve problems involving measurement. length of a side is given. Estimate and determine the area of a rectangle, with or without diagrams, when the length and width are given. Estimate and determine the area of a right triangle, with or without diagrams, when the base and the height are given. Differentiate among the concepts of area, and volume. Develop a procedure for finding volume using manipulatives (e.g., cubes). Determine volume in standard units. Describe practical situations where area, and volume are appropriate measures to use, and justify their choices orally or in writing. Identify whether the application of the concept of area, or volume is appropriate for a given situation. Identify equivalent measurements within the metric system for the following: length: millimeters, centimeters, meters, and kilometers; liquid volume: milliliters, and liters. Investigate to discover the formulas for the area of a square, rectangle, and right triangle. Investigate to discover the formula for volume of a rectangular solid. 4 days Elapsed Time 5.10 Essential Question What are two strategies for determining elapsed time? 5.10 Essential Understandings Understand that elapsed time can be SOL 5.10 The student will determine an amount of elapsed time in hours and minutes within a 24-hour period Essential Knowledge and Skill Determine elapsed time in hours and minutes

28 found by counting on from the beginning time to the finishing time. Elapsed time is the amount of time that has passed between two given times. Elapsed time can be found by counting on from the beginning time to the finishing time. Count the number of whole hours between the beginning time and the finishing time. Count the remaining minutes. Add the hours and minutes 8 days Assessment, Enrichment, Remediation within a 24-hour period. Elapsed time is the amount of time that has passed between two given times.