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$: Grade 5 - PC\|MACimages.pcmac.org/Uploads/NewberryCountySchools/New… · Web viewOverview. This overview provides only the highlights of the new learning that should take place$
Grade 5Overview

This overview provides only the highlights of the new learning that should take place at the fifth-grade level. The specific skills and subject matter that fifth graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators:

An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding.

An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency.

An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-five students are: applying an algorithm to divide whole numbers fluently; understanding the concept of prime and composite numbers; generating strategies to add and subtract fractions; applying an algorithm to add and subtract decimals through thousandths; classifying shapes as congruent; translating between two-dimensional representations and three-dimensional objects; predicting results of combined multiple transformations; analyzing shapes for line and/or rotational symmetry; using a protractor to measure angles; using equivalencies to convert units of measure within the metric system; applying formulas to determine perimeter and area; applying strategies and formulas to determine volume; applying procedures to determine elapsed time within a 24-hour period; applying procedures to calculate the measures of central tendency; concluding why the sum of the probabilities of the outcomes of an experiment must equal 1.

Grade 5Mathematical Processes

5-1

Big Ideas: Solve Problems, Reason, Communicate, Make Connections

Standard 5-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators:5-1.1 Analyze information to solve increasingly more sophisticated problems. 5-1.2 Construct arguments that lead to conclusions about general mathematical properties and

relationships.5-1.3 Explain and justify answers based on mathematical properties, structures, and

relationships.5-1.4 Generate descriptions and mathematical statements about relationships between and

among classes of objects. 5-1.5 Use correct, clear, and complete oral and written mathematical language to pose

questions, communicate ideas, and extend problem situations. 5-1.6 Generalize connections between new mathematical ideas and related concepts and

subjects that have been previously considered.5-1.7 Use flexibility in mathematical representations. 5-1.8 Recognize the limitations of various forms of mathematical representations.

Grade 5Number and Operations

5-2

Big Ideas: Place Value, Operations of Whole Numbers, Decimals, & Fractions

Standard 5-2: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions.

Indicators:5-2.1 Analyze the magnitude of a digit on the basis of its place value, using whole numbers and

decimal numbers through thousandths. 5-2.2 Apply an algorithm to divide whole numbers fluently. 5-2.3 Understand the relationship among the divisor, dividend, and quotient. 5-2.4 Compare whole numbers, decimals, and fractions by using the symbols <, >, and =.5-2.5 Apply an algorithm to add and subtract decimals through thousandths. 5-2.6 Classify numbers as prime, composite, or neither.5-2.7 Generate strategies to find the greatest common factor and the least common multiple of

two whole numbers. 5-2.8 Generate strategies to add and subtract fractions with like and unlike denominators. 5-2.9 Apply divisibility rules for 3, 6, and 9.

Essential Questions: How do place-value patterns help you understand large numbers? (5-2.1) How does place-value change the value of a digit? (5-2.1) How does place value help you compare numbers? (5-2.1) What are the advantages of various division algorithms?( long division, partial sums)

(5-2.2) How does the divisor relate to the quotient? (5-2.3) What are some tools we can use to help us compare numbers using place value? (5-2.4) What are some strategies you can use to add or subtract decimals accurately? (5-2.5) What digit is used as a place holder when adding or subtracting decimals? (5-2.5) What is the difference between a prime number and a composite number? (5-2.6) Can a number be neither prime nor composite? (5-2.6) What is the difference between a factor and a multiple? (5-2.7) What are real-life situations in which we need to add or subtract fractions? (5-2.8) Can you add or subtract fractions without finding a common denominator? (5-2.8) How do divisibility rules help you analyze numbers without paper and pencil? (5-2.9)

Help Page for Standard 5-2

Notes:Assessments

5-3

Assessment examples can be accessed at http://www.s2martsc.org/

Module 1-1 (5-2.1, 5-2.4)Module 1-2 (5-2.2, 5-2.3, 5-2.9) Module 1-3 (5-2.7, 5-2.6)Module 1-4 (5-2.5, 5-2.8)

Formative Assessment is embedded within the lesson through questioning and observation; however, other formative assessment strategies should be employed.

Assessment Examples:Chapter Review and Test PrepChapter Tests MAP Testing OdysseyQuestioning StrategiesExit ticketsJournaling/Written AssessmentProjectsPair Shares

Textbook Correlations

5-2.1 Lessons 1.1, 1.2, 1.3, 4.1, 4.2, 4.3, 4.4, 5-2.2 Lessons 2.3, 2.4, 2.5, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 5-2.3 Lessons 2.1, 2.2, 2.4, 2.5, 3.4, 3.5, 5-2.4 Lessons 1.3, 4.2, 4.3, 4.45-2.5 Lessons 5.1, 5.2, 5.3, 5.4, 5.5, 7.6, 5-2.6 Lessons 6.3, 6.4, 6.5, 6.7, 5-2.7 Lessons 6.1, 6.2, 6.4, 6.6, 6.7, 7.3, 8.4, 8.55-2.8 Lessons 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.75-2.9 Lesson 2.7

Key Concepts (Vocabulary)

periodplace value tenths hundredthsthousandthsdecimaldivisordividend

factorsmultiples greatest common factorleast common multipleprime numbercomposite numberalgorithmsum

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http://www.s2martsc.org/

quotientdivisibilitydivisible

addenddifference

Literature

A Place for Zero: A Math Adventure by Angeline LoPresti

Math Potatoes: Mind-stretching Brain Food by Greg Tang

The Tarantula in My Purse: And 172 Other Wild Pets by Jean Craighead George,

Remainder of One by Elinor J. Pinczes (Division) Marvelous Multiplication: Games and Activities That

Make Math Easy and Fun by Lynette LongThe Doorbell Rang by Pat Hutchins (Division)

Dazzling Division: Games and Activities That Make Math Easy and Fun by Lynette Long

Divide and Ride by Stuart J. Murphy Fabulous Fractions: Games, Puzzles, and Activities

that Make Math Fun and Easy by Lynette Long Funny and Fabulous Fraction Stories by Dan

Greenberg Polar Bear Math: Learning About Fractions from

Klondike and Snow by Ann Whitehead Nagda The World’s Tallest Buildings Online: Math Concept

Readers www.harcourtschool.com/hspmath Multiplying Menace: The Revenge of Rumpelstiltskin

by Pam Calvert Riddle-iculous Math by Jan Holub Math Challenges: Puzzles, Tricks & Games by Glen

Vecchione Fundraising Fair Online: Math Concept Readers www.harcourtschool.com/hspmathh

Technology

Supporting Content Web Sites S.C. Standards http//:www.ed.sc.gov/apps/cso/standards NCTM's Online Illuminations http://illuminations.nctm.org District Web Site: Math Links

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_TOC_Page.html

Multimedia Math Glossary Kit

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http://illuminations.nctm.org/

http://www.harcourtschool.com/hspmathh

http://www.harcourtschool.com/hspmath

www.harcourtschool.com/hspmath Mega Math - Fraction Action, The Number Games, Ice Station Exploration

District Web Site: Math Videoshttp://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

Ask Dr. Math http://mathforum.org/dr.math/

Base-Ten Blocks http://nlvm.usu.edu/en/nav/category_g_2_l.html

Comparison Estimator and Estimator www.shodor.org/interactivate/activities/estm2/index.html www.shodor.org/interactivate/activities/estm/index.html

Hundreds Board and Calculator http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm

Lots of Dots and A Million Dots on One Page www.vendian.org/envelope/

The Mega Penny Project www.kokogiak.com/megapenny/default.asp

Rectangle Multiplication http://nlvm.usu.edu/en/nav/frames_asid_192_g_l_tl.html

Beat Calc & Estimator Four http://mathforum.org/k12/mathtips/beatcalc.html Fraction Track

http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm

Fraction Pointer www.shodor.org/interactive/activities/fracfinder1/index.html

Who Wants Pizza? A Fun Way to Learn Fractions http://math.rice.edu/%7Elanius/fractions/index.html

Visualizing Fractions http://nlvm.usu.edu/en/nav/frames_asid_103_g_l_t.html

Additional practice: http://www.aplusmath.com/ http://www.aaamath.com/g72b-grt-com-fac.htmlhttp://www.onlinemathlearning.com/fractions-math-games.htmlhttp://www.aaamath.com/fra63a-primecomp.htmlhttp://illuminations.nctm.org/mathlets/factor/index.html http://www.funbrain.com/football/http://www.math-play.com/Decimal-Game.html http://www.coolmath4kids.com/http://www.figurethis.org/index.html

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http://www.figurethis.org/index.html

http://www.math-play.com/Decimal-Game.html

http://www.funbrain.com/football/

http://illuminations.nctm.org/mathlets/factor/index.html

http://www.aaamath.com/fra63a-primecomp.html

http://www.onlinemathlearning.com/fractions-math-games.html

http://www.onlinemathlearning.com/fractions-math-games.html

http://www.aaamath.com/g72b-grt-com-fac.html

http://nlvm.usu.edu/en/nav/frames_asid_103_g_l_t.html

http://www.shodor.org/interactive/activities/fracfinder1/index.html

http://www.shodor.org/interactive/activities/fracfinder1/index.html



http://mathforum.org/k12/mathtips/beatcalc.html

http://nlvm.usu.edu/en/nav/frames_asid_192_g_l_tl.html

http://www.kokogiak.com/megapenny/default.asp

http://www.vendian.org/envelope/



http://www.shodor.org/interactivate/activities/estm/index.html

http://www.shodor.org/interactivate/activities/estm2/index.html

http://www.shodor.org/interactivate/activities/estm2/index.html

http://nlvm.usu.edu/en/nav/category_g_2_l.html

http://mathforum.org/dr.math/


http://www.funbrain.com/ http://www.harcourtschool.com/menus/auto/13/5.html# 1

Suggested Streamline Video Prime and Composite Numbers (7:12) Factors and Multiples (7:54) Equivalent Fractions, Decimals, and Percents (7:41) Odd and Even Numbers (6:33) Place Value (6:22) Relationships Among Numbers (7:54) Number Models (10:43) Math Mastery: Decimals and Percents (30:00) Math Mastery: Fractions (30:00) Lesson 4: More About Fractions (7:44) Fraction Basics (6:49) Adding and Subtracting Fractions (13:15) Fractions and Percentages (20:07) Lesson 1: Reading and Writing a Decimal Number

(5:14) Lesson 7: Finding the Least Common Denominator

(3:08) Example 3: Adding Fractions with Different

Denominators (1:58)

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Cross Curricular Opportunities

Social StudiesCompare the distances of migration maps using maps of North America. Compare the distances and order them from least to greatest.

Calculate the value of paper money. At the birth of the US, the government issued bonds worth a portion of a dollar. The paper bills were worth ½, 1/3, ¼, and 1/10 of a dollar. Have students work in pairs to calculate the value of each bill.

Science Calculate density of an object by dividing its mass by its volume. Have students calculate the density of an object that has a mass of 15 grams and a volume of 5 cubic centimeters. (3 g/cm3)

Students calculate the final mass of zinc, copper, and tin mixture found in the alloy, brass. See Teacher’s edition 106C.

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Fifth Grade---Support Document

Number and Operations

Standard 5-2: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions.

The indicators for this standard are grouped by the following major concepts: Number Structure and Relationships – Whole Numbers Number Structure and Relationships – Whole Numbers, Fractions, and Decimals Operations – Addition and Subtraction Operations – Division

The indicators that support each of those major concepts and an explanation of the essential learning for each major concept follows.

Number Structure and Relationships - Whole Numbers

Indicators5-2.7 Generate strategies to find the greatest common factor and the least common multiple of

two whole numbers.

5-2.6 Classify numbers as prime, composite, or neither.

As the verb “Generate” implies in Indicator 5-2.7, students should be given opportunities to generate and share strategies as they develop a conceptual understanding of the greatest common factor and the least common multiple of two whole numbers. Students should be familiar with the terms factor and multiple since the concept of multiplication was introduced in third grade. In addition, fourth grade students were expected to explain the effect on the product when one of the factors were changed. As a result, fifth grade students should build on that knowledge when generating strategies to find the greatest common factor and the least common multiple of two whole numbers.

Experiences involving least common multiples and greatest common factors provide opportunities for students to work with rational numbers in a variety of problem solving situations. This will later help fifth grade students to begin generating strategies to add and subtract fractions with like and unlike denominators (indicator 5-2.8) as well as simplifying fractions. The emphasis is on student understanding, not memorizing a process. Continuing to

5-9

use models and pictorial representations in fifth grade will help students connect to the symbolic representation of the concept of applying algorithms for simplifying fractions and adding and subtracting fractions with unlike denominators in later grades.

Fifth grade is the first year students classify whole numbers as prime, composite, or neither. In order to do so, many opportunities must be provided for students to conceptually understand these classifications. Experiences such as constructing arrays for whole numbers and categorizing the arrays into 2 groups of arrays with “Factors of 1 and Itself” (The number 11 only has 2 factors, 1 and 11) and arrays with “More than 1 Factor and Itself ” (The number 10 has 4 factors of 1, 2, 5, 10) will enhance students’ conceptual understanding. The number 1 is neither prime nor composite because it has only one factor - itself.

Initially using concrete or pictorial representations of multiplication arrays will enable students to concretely see and begin to classify numbers as prime, composite, or neither as the chart below indicates.

EXAMPLE: Composite Prime

More than 1

Factor and Itself1 Factor and Itself

Numbers Factors Factors

2 1,23 1,34 1,2,4 5 1,56 1,2,3,6 7 1,78 1,2,4,8 9 1,3,9

10 1,2,5,10

Teacher Note: Students typically confuse the concepts of greatest common factor and multiples. Therefore, when engaging in classroom discussion, require students to use those terms in their explanations. Teacher should pose questions in such a way that students are able to make the connection between “factor” and the “parts of a multiplication problem”. Students’ experiences should help them see that multiples are derived from multiplying or using repeated addition.

5-10

Number Structure and Relationships - Whole Numbers, Fractions, and Decimals

Indicators5-2.1 Analyze the magnitude of a digit on the basis of its place value, using whole numbers and

decimal numbers through thousandths. 5-2.4 Compare whole numbers, decimals, and fractions by using the symbols <, >, and =.

Students have analyzed the magnitude of a digit based on its place value since kindergarten. Therefore, this concept is not new. The only change and where emphasis should be placed is on the decimal portion. Decimals were introduced for the first time in fourth grade and students analyzed digits through hundredths. Fourth grade students also generated strategies to add and subtract decimals through hundredths. Now in fifth grade students should have an understanding through thousandths. Fifth grade students should also examine the relationship between the place value structure of whole numbers and the place value structure of decimals through thousandths.

Students in fifth grade should build on prior concrete experiences and learn to move fluently and confidently among and between the representations of whole numbers, fractions and decimals using symbols for comparison. Students should be able to decompose whole numbers and extend this notion to decimal numbers. (Principles and Standards for School Mathematics, p. 150) Again, however, student work with decimals should be limited to thousandths and there is no limit on the magnitude of fractions. Sound educational practice dictates that fractions should be of reasonable size that emphasis is on understanding the relative magnitude NOT on applying some memorized pneumonic device when making comparisons.

In fourth grade students had opportunities to analyze decimal numbers as a part of a whole using concrete and pictorial models. The focus was on conceptual understanding of decimals through hundredths. Fifth grade builds on that knowledge and extends decimal place value through thousandths.

Operations - Addition and Subtraction

Indicators5-2.5 Apply an algorithm to add and subtract decimals through thousandths.5-2.8 Generate strategies to add and subtract fractions with like and unlike denominators.

Fourth grade students were introduced to the concept of decimals for the first time. Besides creating concrete and pictorial models to gain an understanding of decimals through hundredths, they generated strategies to add and subtract decimals through hundredths. As discussed in the major concept above, fifth grade students extend that knowledge to thousandths. Also, fifth grade students should be able to fluently add and subtract decimals through thousandths. While fourth grade work was limited to concrete and pictorial models in an effort to develop an in-depth conceptual understanding, fifth grade should place an emphasis on symbolic manipulation (numbers only when adding and subtracting through thousandths). Of course, addition and subtraction experiences should be in context.

5-11

Fifth grade is the first year students begin to develop computational strategies for adding and subtracting fractions with like and unlike denominators. In fourth grade students generated equivalent fractions which laid the foundation for their work this year. As the verb “Generate” implies in indicator 5-2.5, students should generate and share their own strategies for adding and subtracting fractions. That means that all addition and subtraction work with fractions during fifth grade should be with concrete and pictorial models. Also, problems should be posed in context – not adding and subtracting for the sake of doing so – but having a reason, a problem to solve that requires addition or subtraction of fractions. Ample time should be provided for students to share their strategies and learn from each other. Such sharing and discussing leads students to discover an efficient algorithm that they understand – not just memorize a strategy that they soon forget.

Connections To:

Other Fifth Grade Indicators:5.2.7 Generate strategies to find the greatest common factor and the least common multiple of two whole numbers.5-3.4 Identify applications of commutative, associative, and distributive properties with whole numbers.

Since these connections are self-explanatory, please see the essential learning explanation for 5.27 under “Number Structure and Relationships – Whole Numbers” above and for 5-3.4 under the Algebra standard.

Operations - Division

5-2.2 Apply an algorithm to divide whole numbers fluently. 5-2.3 Understand the relationship among the divisor, dividend, and quotient. 5-2.9 Apply divisibility rules for 3, 6, and 9.

Fourth grade students generated strategies to divide whole numbers by a single digit divisor with no remainders. That means their learning experiences involved strictly concrete and pictorial models for division – an emphasis on understanding division. In fifth grade student work should link those previous concrete and pictorial experiences to the symbolic. While fifth grade students should become fluent with division, sound educational practice dictates that the magnitude of the divisor and dividend should be reasonable. Division should not be a laborious task to be dreaded by students. In the contrary, students should see and understand division as a means to problem solving. Fifth grade learning experiences should involve quotients both with and without remainders. If students have a conceptual understanding of division, they have an understanding of the relationship among the divisor, dividend, and quotient.

By applying an algorithm to divide whole numbers fluently, students should be able to explain what each number in a division algorithm means and understand the relationship among the divisor, dividend and quotient. For example, how the quotient becomes larger when the divisor is changed to a smaller digit or how the quotient becomes smaller when the divisor is

5-12

changed to a larger digit. Students should also understand that if they are unable to efficiently find the answer to a problem such as 39 ÷ 3, they can decompose the dividend 39 to 30 + 9 then divide each easily by 3 so that 30 ÷ 3 = 10 and 9 ÷ 3 = 3 so that the quotients of 10 and 3 can be added to get 13. Again, the emphasis is on understanding and dividing fluently – not on pages of symbolic manipulation.

In fourth grade, students were introduced to the concept of divisibility rules for 2, 5, and 10. After fifth grade students are comfortable with applying an algorithm to divide whole numbers, the divisibility rules for 3, 6, and 9 should be introduced as a way of quickly determining by what numbers a whole number may be evenly divided.

Teacher Note: Multiplication is not mentioned in the fifth grade standards, however, students should maintain multiplication fluency as part of the division algorithm.

Connections to:

Other Fifth Grade Indicators5-3.4 Identify applications of commutative, associative, and distributive properties with whole numbers.

Since the connection is self-explanatory, please see the essential learning explanation 5-3.4 under the Algebra standard.

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Grade 5Algebra

Big Ideas: Patterns, Functions, Algebraic Expressions & Equations, Properties of Whole Numbers

Standard 5-3: The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts.

Indicators:5-3.1 Represent numeric, algebraic, and geometric patterns in words, symbols, algebraic

expressions, and algebraic equations. 5-3.2 Analyze patterns and functions with words, tables, and graphs. 5-3.3 Match tables, graphs, expressions, equations, and verbal descriptions of the same

problem situation. 5-3.4 Identify applications of commutative, associative, and distributive properties with whole

numbers. 5-3.5 Analyze situations that show change over time.

Essential Questions: How can you find patterns among numbers? (5-3.1) What steps can you take to extend number patterns? (5-3.1) How express patterns using words or algebraic symbols? (5-3.2) What is the difference between an expression and an equation? (5-3.3) How can tables, charts, or graphs be used to analyze patterns in data? (5-3.3, 5-3.2) How can we use algebraic expressions or equations to represent the patterns found in a

specific table, chart, or graph? (5-3.1, 5-3.2) What are the differences in commutative, associative, and distributive properties? (5-3.4) What are advantages of applying each of the algebraic properties? (5-3.4) How can each property be used to develop mental math skills? (5-3.4) Which graph is best used to show change over time? (5-3.5)


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Notes:Assessments

Assessment examples can be accessed at http://www.s2martsc.org/

Module 2-1 (5-3.2)Module 2-2 (5-3.1, 5-3.3, & 5-3.4) Module 2-3 (5-3.5)

Textbook: South Carolina Math, Houghton Mifflin Harcourt

Chapter 10 (5-1.7, 5-3.5, 5-6.1, 5-6.2, 5-6.3, 5-6.4) Chapter 12 ( 5-3.1, 5-3.4)Chapter 13 (5-3.1, 5-3.2, 5-3.3)Chapter 15 (5-3.1, 5-4.5, 5-4.6)Chapter 19 (5-3.1, 5-4.4, 5-5.5)




5-3.1 Lessons 12.3, 13.2, 13.3, 13.4, 13.5, 15.2, 15.3, 15.4, 15.5, 18.1, 18.3, 18.4, 18.5, 19.2, 19.3, 19.45-3.2 Lessons 13.1, 13.2, 13.3, 13.4, 13.55-3.3 Lessons 10.5, 10.6, 13.1, 13.2, 13.3, 13.4, 13.5, 5-3.4 Lessons 12.1, 12.2,12.35-3.5 Lessons 10.5, 10.6


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patternfunctionruleinputoutputnumeric patternexpressionalgebraic patternequationgeometric patternsymbolvariable

propertycommutative property associative propertydistributive propertychangeincreasingvaryingtrendsdecreasing

Literature

A Place for Zero: A Math Adventure by Angeline Spargana LoPresti

Pluckrose by Henry Arthur Anno’s Magic Seeds by Mitsumasa Anno Anno’s Mysterious Seeds by Mitsumasa Anno Math Curse by Jon Scieszka A Gebra Named Al by Wendy Isdell Forecast: Sunny Skies! Online: Math Concept

Readers Park Visitors www.harcourtschool.com/hspmath Measuring Penny by Loreen Leeedy Tiger Math: Learning to Graph from a Baby Tiger by

Ann Whitehead Nagda and Cindy Bickel

Technology

Supporting Content Web Sites S.C. Standards

http//:www.ed.sc.gov/apps/cso/standards NCTM's Online Illuminations

http://illuminations.nctm.org Multimedia Math Glossary Kit

www.harcourtschool.com/hspmath http://www.newberry.k12.sc.us/InstructionalLinks/

math/Math_Videos.htm Function Machine

www.fi.uu.nl.toepassingen/02022/toepassing_wiseben.en.html

Graph Sketcher www.shodor.org/interactive/activities/sketcher/index.ht

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http://www.shodor.org/interactive/activities/sketcher/index.html

http://www.fi.uu.nl.toepassingen/02022/toepassing_wiseben.en.html

http://www.fi.uu.nl.toepassingen/02022/toepassing_wiseben.en.html

http://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm





ml Understanding Distance, Speed, and Time

html://standards.nctm.org/document/eexamples/chap5/5.2/index.htm

Suggested Streamline Video Discovering Math – Algebra Patterns and Rules (6:17) Variables (7:38) Effects of Arithmetic Operations (8:22) Properties and Relationships of Arithmetic Operations

(10:41) Solving Problems Using Operations (7:42) The Language of Operations (8:09) Math Mastery: Equations (30:00) Lesson 6: Solving Equations in Two Steps (5:21) Lesson 5: Solving Word Problems with Equations

(4:46)


Social Studies: Marshall and his friends are making a map of their neighborhood. They are drawing the map on one-inch grid paper. Amy includes a scale of 1 inch = 2miles. The school is 6 miles from the park. Write and solve an equation to find the distance that Amy should place between the school and the park on the map.

Science: As an object falls, gravity increases the object’s speed until it hits a maximum terminal speed of between 53 to 56 meters per second. How does an object’s speed change over time? Write a rule that describes this change. Explain how you found a rule to describe the way the speed of a falling object changes.


Algebra

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http://www.shodor.org/interactive/activities/sketcher/index.html

Standard 5-3: The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts.

The indicators for this standard are grouped by the following major concepts: Patterns, Relationships, and Functions Representations, Properties, and Proportional Reasoning Change in Various Contexts


Patterns, Relationships, and Functions

Indicators5-3.2 Analyze patterns and functions with words, tables, and graphs.

Fourth grade students focused on analyzing numeric, nonnumeric, and repeating patterns involving all operations and decimal patterns through hundredths. Fifth grade students are analyzing patterns and functions with words, tables, and graphs. Students should recognize the connections between these three representations which will lay the foundation for the understanding of functions in middle school. When students analyze functions in fifth grade they should look for patterns within the function. For example: Teachers could use an input/output table, function machine, etc. This is the first time that students are required to use function rules to make generalizations.

Teacher Note: This is the first time students are exposed to the word “function”.

Representations, Properties, and Proportional Reasoning

Indicators5-3.1 Represent numeric, algebraic, and geometric patterns in words, symbols, algebraic

expressions, and algebraic equations. 5-3.3 Match tables, graphs, expressions, equations, and verbal descriptions of the same

problem situation. 5-3.4 Identify applications of commutative, associative, and distributive properties with whole

numbers.

Fourth grade students used variables to represent an unknown quantity and to write a mathematical expression and equations in symbolic form. They had experience analyzing numeric, nonnumeric, and repeating patterns. Fifth grade students for the first time will represent numeric, algebraic, and geometric patterns using words, symbols, algebraic expressions and algebraic equations. The focus for new learning is on algebraic and geometric patterns.

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Geometric patterns could include triangular numbers and square numbers. Algebraic patterns include patterns with variables as well as numbers.

Fifth grade students should be able to make associations of tables, graphs, expression, equations, and verbal descriptions of the same problem situation. For example: Teachers could represent several problem situations using tables, graphs, expressions, and equations and cut them into “pieces”. Students could match the tables, graphs, expressions, and equations that represented the same problem situation. Students should be able to verbally explain the matched pieces.

Students as far back as first grade were exposed to the concept of commutativity when working with basic facts for addition and subtraction. In fifth grade, students will identify applications of commutative, associative, and distributive properties with whole numbers. For example: Given 3+4 = 7 and 4+3 = 7 which property does this represent?

Change in Various Contexts

Indicators5-3.5 Analyze situations that show change over time.

Fourth grade students illustrated situations that show change over time as increasing, decreasing, or varying. Students in fifth grade are expected to analyze situations that show change over time. In other words, they should examine situations that show increasing, decreasing, or varying change over time and describe the relationship between time and the change. Students should be provided with multiple opportunities to analyze real world situations and describe the change that occurs.

Teacher Note: Great connections can be made here with science.

Grade 5Geometry

Big Ideas: Properties of Quadrilaterals, Congruency, Transformations

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Standard 5-4: The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among the properties of quadrilaterals.

Indicators:5-4.1 Apply the relationships of quadrilaterals to make logical arguments about their properties. 5-4.2 Compare the angles, side lengths, and perimeters of congruent shapes. 5-4.3 Classify shapes as congruent. 5-4.4 Translate between two-dimensional representations and three-dimensional objects. 5-4.5 Predict the results of multiple transformations on a geometric shape when combinations

of translation, reflection, and rotation are used.5-4.6 Analyze shapes to determine line symmetry and/or rotational symmetry.

Essential Questions: What are the properties of a quadrilateral? (5-4.1) Which quadrilateral is not a parallelogram? (5-4.1) How does a trapezoid differ from other quadrilaterals? (5-4.1) Can shapes be classified by their angles and side lengths? How can you determine if

shapes are congruent? (5-4.2) If two shapes are congruent, will their perimeter be congruent? (5-4.3) Can two shapes be similar, yet not congruent? (5-4.3) What is the difference between a two-dimensional and a three-dimensional object?

(5-4.4) Could an object have only one dimension? (5-4.4) How do transformations affect shapes? (5-4.5) What is the difference between a reflection and a rotation? (5-4.5) What shapes have both line symmetry and rotational symmetry? (5-4.6)

Help Page for Standard 5-4:

Notes:Assessments

Assessment examples can be accessed at http://www.s2martsc.org/.

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Module 2-5 (5-4.1, 5-4.2, 5-4.3, & 5-4.4)Module 3-2 ( 5-4.5 & 5-4.6)




5-4.1 Lessons 14.2, 16.1, 16.25-4.2 Lesson 14.35-4.3 Lesson 14.45-4.4 Lessons 16.3, 16.45-4.5 Lessons 15.15-4.6 Lessons 14.2, 15.5


congruentangledegreemeasurerayvertex sidesright angleacute angleobtuse angleprotractorparallelperpendicular diagonalpolygontwo-dimensional

rectanglecubetrapezoidthree-dimensionalnetpyramidprismrectangular prismcylindermidpointtransformationtranslationreflectionsymmetryline symmetryhorizontal

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quadrilateralparallelogramtrapezoidsquarerhombus (rhombi)

verticalrotationrotational symmetryclockwisecounterclockwise

Literature

Grandfather Tang’s Story by Ann Tompert Mummy Math: An Adventure in Geometry by Cindy

Neuschwander What’s Your Angle, Pythagoras?: A Math Adventure

by Julie Ellis Cubes, Cones, Cylinders, and Spheres by Tana Hoban Captain Invincible and the Space Shapes (3-D Shapes)

by Stuart J. Murphy Eight Hands Round (Shapes) by Ann Whitford Paul Groovy Geometry by Lynette Long Shape Up! Fun with Triangles and Other Polygons

by David A. Adler Sir Cumference and the Great Knight of Angleland

(Angles) by Cindy Neuschwander The Adventures of Penrose by Theoni Pappas The Greedy Triangle (Shapes) by Marilyn Burns City of the Future Online: Math Concept Readers www.harcourtschool.com/hspmath

Technology

Supporting Content Web Sites S.C. Standards http//:www.ed.sc.gov/apps/cso/standards NCTM's Online Illuminations http://illuminations.nctm.org Multimedia Math Glossary Kit www.harcourtschool.com/hspmath Create congruent triangles from the National Library of

Virtual Manipulatives athttp://nlvm.usu.edu/en/nav/frames_asid_165_g_2_t_3.html?open=instructions&from=category_g_2_t_3.html

Isometric Dot Paper Virtually…http://nlvm.usu.edu/en/nav/frames_asid_129_g_2_t_3.html?open=activities&from=category_g_2_t_3.html

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http://nlvm.usu.edu/en/nav/frames_asid_129_g_2_t_3.html?open=activities&from=category_g_2_t_3.html



http://nlvm.usu.edu/en/nav/frames_asid_165_g_2_t_3.html?open=instructions&from=category_g_2_t_3.html






http://illuminations.nctm.org/ActivityDetail.aspx?ID=125 Contexts for Learning www.contextsforlearning.com http://www.newberry.k12.sc.us/InstructionalLinks/

math/Math_Videos.htm

Suggested Streamline Video Names for Geometric Shapes (6:25) Properties of Geometric Figures (7:47) Altering Shapes (6:54) Congruent and Similar Shapes (7:53) Motion Geometry (6:34) Areas and Perimeters (7:45) Lines and Angles (4:37) Maps and Drawing Scales (7:40) Math Mansions: Show 38: Rotations (9:20) Math Mansions: Show 39: On Reflection (9:11) Math Mansions: Show 34: Better Get Back in Shape and

Be a Square (9:19) Recognizing Cube Edges and Faces Recognizing and Making Cubes


Social StudiesHave students research to find similarities between geometric solids and Native American tools. See Teacher’s Edition 306C.

ScienceTable salt has a crystal structure in the shape of a cube. Students should sketch the top view of a cube of salt. See Teachers’ Edition 306C.

Grade 5---Support Document

Geometry

Standard 5-4: The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among the properties of quadrilaterals.

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http://www.contextsforlearning.com/

http://illuminations.nctm.org/ActivityDetail.aspx?ID=125

The indicators for this standard are grouped by the following major concepts: Dimensional Plane and Transformational


Dimensional

Indicators5-4.1 Apply the relationships of quadrilaterals to make logical arguments about their properties. 5-4.2 Compare the angles, side lengths, and perimeters of congruent shapes. 5-4.3 Classify shapes as congruent.

5-4.4 Translate between two-dimensional representations and three-dimensional objects.

In fifth grade, students apply the relationships of quadrilaterals to make logical arguments about their properties. This will include making and testing conjectures and explaining conclusions about quadrilateral properties and relationships. For example, are all squares rectangles? Are all rectangles squares? Why or why not?

In fourth grade students used transformations to prove congruency. In fifth grade, students will compare the angles, side lengths and perimeters of congruent shapes. Given congruent shapes, students will discover that the corresponding angles are the same, the corresponding side lengths are the same, and the perimeters are the same. Therefore, students will conclude that congruent shapes have the same shape and same size. In sixth grade, students will compare the angles, side lengths, and perimeters of similar shapes. It is essential that students understand congruent shapes in order to progress to the concept of similarity in shapes.

Students in fifth grade must also classify shapes as congruent. The definition of congruent is factual understanding. For students to classify shapes as congruent, they will need to have a conceptual understanding.

It is in fifth grade that students begin exploring methods for translating between two-dimensional representations and three-dimensional objects. In fifth grade, students should sketch the front, top, and side views of a three-dimensional object built with cubes. Students should be able to draw a net for a given three-dimensional shape and construct and/or state the three-dimensional shape when given its two-dimensional representation (net). Teachers should incorporate isometric dot paper in guiding the students to draw three-dimensional objects.

Plane and Transformational

Indicators5-4.5 Predict the results of multiple transformations on a geometric shape when combinations

of translation, reflection, and rotation are used.5-4.6 Analyze shapes to determine line symmetry and/or rotational symmetry.

5-24

In fourth grade, students have predicted the results of multiple transformations of the same type, but now they use multiple transformations of different types. "Students should consider three important kinds of transformations: reflections (flips), translations (slides), and rotations (turns). Younger students generally convince themselves that two shapes are congruent by physically fitting one on top of the other, but fifth grade students can develop greater precision as they describe the motions needed to show congruence (turn it 90 degrees or flip it vertically, then rotate it 180 degrees). They should be able to visualize what will happen when a shape is rotated or reflected and predict the result. Students should also explore shapes with more than one line of symmetry. Students often create figures with rotational symmetry, but often have difficulty describing the regularity they see. They should be using language about turns and angles to describe these figures." (Principles and Standards for School Mathematics, 167-168)For the first time, fifth grade students are introduced to the concept of rotational

symmetry. A shape that rotates onto itself before turning 360o has rotational symmetry. Students’ prior experiences have been limited to identification of lines of symmetry. Students will now analyze shapes to determine line symmetry and/or rotational symmetry. It is important to note that all regular polygons have rotational symmetry.

Grade 5Measurement

Big Ideas: Customary and Metric Measurement, Use of Measurement Tools and Formulas

Standard 5-5: The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

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Indicators:5-5.1 Use appropriate tools and units to measure objects to the precision of one-eighth inch. 5-5.2 Use a protractor to measure angles from 0 to 180 degrees. 5-5.3 Use equivalencies to convert units of measure within the metric system: converting

length in millimeters, centimeters, meters, and kilometers; converting liquid volume in milliliters, centiliters, liters, and kiloliters; and converting mass in milligrams, centigrams, grams, and kilograms.

5-5.4 Apply formulas to determine the perimeters and areas of triangles, rectangles, and parallelograms.

5-5.5 Apply strategies and formulas to determine the volume of rectangular prisms. 5-5.6 Apply procedures to determine the amount of elapsed time in hours, minutes, and

seconds within a 24-hour period. 5-5.7 Understand the relationship between the Celsius and Fahrenheit temperature scales. 5-5.8 Recall equivalencies associated with length, liquid volume, and mass:

10 millimeters = 1 centimeter, 100 centimeters = 1 meter, 1000 meters = 1 kilometer;10 milliliters = 1 centiliter, 100 centiliters = 1 liter, 1000 liters = 1 kiloliter; and10 milligrams = 1 centigram, 100 centigrams = 1 gram, 1000 grams = 1 kilogram.

Essential Questions: How does your understanding of fractions help when using measurement tools?(5-5.1) How is a ruler similar to a number line? (5-5.1) What are the important steps to remember when using a protractor? (5-5.2) How are metric prefixes helpful? What pattern do you see? (5-5.3) How are powers of ten used in the metric system? (5-5.3) Is there a connection between the perimeter of a shape and its area? (5-5.4) Can you use the area of a rectangle to find the area of its inscribed triangles? (5-5.4) How do the formulas for determining the perimeter of a shape compare to the formulas

for determining the area of a shape? (5-5.4) Compare the formulas for finding the areas of parallelograms and rectangles. What is the

connection between Base x Height and Length x Width? (5-5.4) What is the relationship between a two-dimensional shape and its area in square units?

(5-5.4) Can you calculate the volume of a two-dimensional shape? (5-5.5) What is the relationship between a three-dimensional shape and its volume in cubic

units? (5-5.5) What steps are used to determine lapse of time? (5-5.6) Describe your thinking process when adding or subtracting different units of time. (5-5.6) How would you convert a temperature measured in Celsius to Fahrenheit? (5-5.7)

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Notes:Assessments


Module 2-4 (5-5.2)Module 3-1 (5-5.4 & 5-5.5) Module 3-2 (5-2.7, & 5-2.6)Module 3-3 (5-5.1)Module 3-4 (5-5.3 & 5-5.3)Module 3-5 (5-5.6) Module 3-6 (5-5.7)

5-27


Chapter 14 (5-1.6, 5-4.2, 5-4.3, 5-5.2)Chapter 17 ( 5-5.1, 5-5.2, 5-5.3, 5-5.6, 5-5.8)Chapter 18 ( 5-5.4)Chapter 19 (5-3.1, 5-4.4, 5-5.5)




5-5.1 Lesson 17.15-5.2 Lessons 14.1, 14.45-5.3 Lessons 17.2, 17.3, 17.4, 17.55-5.4 Lessons 18.1, 18.2, 18.3, 18.4, 18.5, 19.3, 19.45-5.5 Lessons 19.1, 19.2, 19.3, 19.45-5.6 Lesson 17.65-5.7 Lessons 17.7, 17.8, 17.95-5.8 Lessons 17.2, 17.4


metric measurementcustomary measurementbenchmarksinchhalf-inch (1/2 inch)quarter-inch (1/4 inch)one-fourth–inch (1/4)eighth-inch (1/8 inch)three-quarter-inch (3/4 inch)three-fourths-inch (3/4 inch) rectangle

formulaequivalencyconversionmillicentikilometerlitergramweightmass

5-28

parallelogramtriangleperimeter areabaseheightunits2

prismvolumeunits3

liquid volumeelapsed timehourminutesecondtemperaturethermometerscaleCelsiusFahrenheit

5-29

Literature

How Tall, How Short, How Faraway? by David A. Adler,

Spaghetti and Meatballs for All: A Mathematical Story by Marilyn Burns

Summer Ice: Life Along the Antarctic Peninsula by Bruce

Designing a Skate Park Online: Math Concept Readers www.harcourtschool.com/hspmath How Big is a Foot? (Length) by Rolf Myller Cook-A-Doodle-Doo! (Capacity) by Susan Stevens

Crummel A House for Birdie (Volume or Capacity)by Stuart J.

Murphy Is a Blue Whale the Biggest Thing There Is? (Size)

by Robert E. Wells Length: Math Counts by Henry Pluckrose Jack and the Beanstalk (Length) by Steven Kellogg Me and the Measure of Things (Length, Weight,

Capacity) by Joan Sweeney Measurement Mania: Games and Activities by Lynette

Long Measuring Penny (Length, Weight, Capacity) by

Loreen Leedy Millions to Measure (Length, Weight, Volume) by

David M. Schwartz Racing Around (Length) by Stuart J. Murphy Super Sand Castle Saturday (Non-standard

Measurement) by Stuart J. Murphy Twelve Snails to One Lizard: A Tale of Mischief and

Measurement (Non-standard Measurement and Length)by Susan Hightower

Technology



http://illuminations.nctm.org Multimedia Math Glossary Kit

www.harcourtschool.com/hspmath Sites for Children’s Literature

http://sci.tamucc.edu/~eyoung/literature.html/

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Paper Tape Measures found atwww.scribd.com/doc/7090539/Tape-Measure

Access Marathon Results for 2009 at http://www.nycmarathon.org/Results.htm

A Weeks Worth of Weather Found at www.weather.com or www.wistv.com http://www.newberry.k12.sc.us/InstructionalLinks/

math/Math_Videos.htm

Suggested Streamline Video Basic Measures (8:35) Selecting Units (10:38) Tools for Measurement (5:03) Sizes of Standard Units (6:22) Converting Units in the Metric System: Length (2:34) Measure for Measure: Time and Temperature (56:00) Example 2: Volume and Capacity (2:11)


Social StudiesFind a recipe Western explorers used. Have students use measurement tools to revise the recipe. (For example: Double or triple it.)

ScienceRivers are important to many communities around the world for many resources. The Nile, the Amazon, and the Yangtze are some of the world’s longest. Find the shortest width of the Nile and find the area of a 30 m section of the water’s surface. See Teacher’s Edition 372C.


5-31



http://www.wistv.com/

http://www.weather.com/

http://www.nycmarathon.org/Results.htm

http://www.scribd.com/doc/7090539/Tape-Measure

Measurement

Standard 5-5: The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

The indicators for this standard are grouped by the following major concepts: Length Time Temperature Angles Perimeter, Area, and Volume Equivalencies Conversions


Length

Indicator5-5.1 Use appropriate tools and units to measure objects to the precision of one-eighth inch.

In previous years, students have used appropriate tools and units to measure objects to the quarter inch. By fifth grade students have worked with simple rulers and tapes. They should extend their knowledge by making rulers with subunits or fractional units. Fifth grade students have had a variety of experiences with measurement. Therefore, the emphasis should now be on

precision and appropriate units. For example, if the length of an object falls between say and

then the student must understand that if the length is more than half way between and the

length would be describe as . In essence, students are measuring to the nearest of an inch

because that is the half way point between and . Simply giving students measuring tools and

requiring that they measure in sixteenths is not sufficient to meet the expectation of this Indicator. It is knowing that if one needs to measure to the precision of one-eighth inch, using a measuring tool marked in sixteenths would be a better choice and why that is so.

A lesson that might be used as an introduction to the concept of precision might require that some students use rulers marked in fourths while other students use rulers marked in eighths. After measuring a variety of objects to the nearest eighth of an inch and recording the responses, the class might engage in a discussion as to which group had the more precise measurements and why. (The class should come to the conclusion that the smaller the measurement, the more precise.)

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Connections To:

Other Fifth Grade Indicators 5-2.4 Compare whole numbers, decimals, and fractions using the symbols <, >, and =.

Since the connection to this indicator is self explanatory, no further explanation will be provided. For details regarding the essential learning for 5-2.4 see the Number and Operations standard.

Time

Indicator5-5.6 Apply procedures to determine the amount of elapsed time in hours,

minutes, and seconds within a 24-hour period.

Fourth grade was the first time students were introduced to the concept of elapsed time. In fourth grade students applied strategies and procedures to determine the amount of elapsed time in hours and minutes within a 12-hour period, either a.m. or p.m. Fourth grade students did not “cross” between a.m. or p.m. but rather worked within those 12-hour intervals to determine elapsed time. In fifth grade students should not only move between a.m. and p.m. (24-hour interval) but also must consider elapsed time down to seconds.

A teaching strategy that could be used is to convert the circular measurement to a more linear measurement (similar to a ruler) since the students have experience measuring with rulers. To do so, take two strips of paper and mark them from 12:00 to 12:00. Each strip will be a different color, one representing a.m. and one representing p.m. Between each hour mark, make three smaller marks - each representing 15 minutes. Then demonstrate the use of the analog clock (hands need to be geared together so that the movement of the minute hand also show the movement of the hour hand) to show how much time has passed. Then connect the clock to the number-time line. This lesson can be extended to address smaller units of time.

Teacher Notes: Even though students have had experience in previous grades with both the upper and lower case of A.M. and P.M. it is sound practice to continue to expose students to both forms.

Temperature

Indicator5.5.7 Understand the relationship between the Celsius and Fahrenheit temperature scales.

In previous grades students have read thermometers using Celsius and Fahrenheit temperature scales. By the end of fifth grade students should know how to read both Celsius and Fahrenheit liquid and digital thermometers. Students need to know that the boiling point of water is 212˚ F and 100˚C and the freezing point is 32˚F and 0˚C. These two facts allow students to estimate and interpolate common temperatures such as hot days (above 95˚F or 35˚C), cold days (below 32˚F or below 0˚C), and comfortable days (80˚F or 25˚C). They should also become

5-33

aware that the temperature considered hot, cold, or comfortable varies from place to place and depends on other weather conditions such as wind and moisture and on personal preference. The goal for this Indicator is not for students to memorize or convert between scales, but to understand how the Celsius and Fahrenheit temperature scales relate to each other.

AnglesIndicator5.5.2 Use a protractor to measure angles from 0 to 180 degrees.

In third grade geometry, students classified angles as either right, acute, or obtuse. In fourth grade,students compared angle measures with referent angles of 45 degrees, 90 degrees, and 180 degrees to estimate measures. Fifth grade is the first time students are introduced to the measurement tool protractor. A connection should be made between the fourth grade referent angles knowledge and the actual measurement. This will enable students to avoid the common mistake of reading a protractor from the wrong direction when measuring angles.

Perimeter, Area, and Volume

Indicators5-5.4 Apply formulas to determine the perimeters and areas of triangles,

rectangles, and parallelograms.5-5.5 Apply strategies and formulas to determine the volume of

rectangular prisms.

In fourth grade students analyzed perimeters of polygons and generated strategies to determine the area of rectangles and triangles. In other words, students have had a variety of concrete experiences with perimeter and area of triangles, rectangles, and parallelograms. As a result, fifth grade students are ready to apply formulas to determine area and perimeters of triangles, rectangles, and parallelograms.

Fifth grade is the first time students are introduced to the concept of volume. However, the expectation is that students will progress from concrete to abstract problem solving situations that involve volume of rectangular prisms. Another important mathematical issue to consider is using the appropriate unit to describe volume versus perimeter or area. For example, when measuring area the unit should be expressed in square units and when measuring volume, cubic units should be used. It is extremely important that students understand when to use the appropriate unit and why that is so.

Equivalencies

Indicator5-5.3 Recall equivalencies associated with length, liquid volume, and mass:

5-34

10 millimeters = 1 centimeter, 100 centimeters = 1 meter, 1,000 meters = 1 kilometer; 10 milliliters = 1 centiliter, 100 centiliters = 1 liter, 1,000 liters = 1 kiloliter; and 10 milligrams = 1 centigram, 100 centigrams = 1 gram, 1,000 grams = 1 kilogram.

In previous grades, students recalled U.S. Customary equivalencies associated with time, length, liquid volume, and weight. Fifth graders should recall metric equivalencies related to length, liquid volume, and mass. These metric equivalencies will be used when fifth grade students make conversions within the metric system.

Conversions

Indicator5-5.3 Use equivalencies to convert units of measure within the metric system: converting

length in millimeters, centimeters, meters, and kilometers; converting liquid volume in milliliters, centiliters, liters, and kiloliters; and converting mass in milligrams, centigrams, grams, and kilograms.

In fourth grade students used equivalencies to convert units of measure within the U.S. Customary System. Fifth grade students will make conversions within the metric system. Fifth graders should have the understanding that when you change from one unit of measure to another, you need to know the relationship between the two units of measure.

Changing units in the metric system is like changing units in the customary system. But in the metric system, we use decimals instead of fractions and we don’t use mixed measures. Students should have experiences with the metric equivalencies cited in Indicator 5-5.3.

Grade 5Data Analysis and Probability

Big Ideas: Collect, Organize, Analyze, and Interpret Data

5-35

Standard 5-6: The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.

Indicators:5-6.1 Design a mathematical investigation to address a question.5-6.2 Analyze how data-collection methods affect the nature of the data set. 5-6.3 Apply procedures to calculate the measures of central tendency (mean, median, and

mode). 5-6.4 Interpret the meaning and application of the measures of central tendency.5-6.5 Represent the probability of a single-stage event in words and fractions. 5-6.6 Conclude why the sum of the probabilities of the outcomes of an experiment must equal 1.

Essential Questions: What is a mathematical investigation? (5-6.1) Would giving a survey to fifth graders be considered a mathematical investigation?

(5-6.2) What are the steps for designing a mathematical investigation? (5-6.2) How would you conduct a survey so that a population is represented fairly? (5-6.2) Would surveying one class of fifth graders rather than the entire fifth grade provide you

with a random sample? (5-6.2) What are the differences between mean, median, and mode? (5-6.3) Which of the three measures of central tendency would an outlier have a greater effect

on? (5-6.3) How do you determine what number to divide the sum of a set of data by when

calculating mean? (5-6.4) Does every set of data always have a mode? Can there be more than one mode? (5-6.4) How does the mean and median relate to each other? (5-6.4) Can probability be represented in fraction form? (5-6.5) How could you represent probability in word form? (5-6.5) What is the difference between theoretical probability and experimental probability?

(5-6.5) How does knowing the number of favorable outcomes help find the theoretical

probability of an event occurring?(5-6.6)

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Notes:Assessments


Module 4-1 (5-6.1 & 5-6.2)Module 4-2 (5-6.3 & 5-6.4) Module 4-3 (5-6.5 & 5-6.6)Module 1-4 (5-2.5 & 5-2.8)


Chapter 10 (5-1.7, 5-3.5, 5-6.1, 5-6.2, 5-6.3, 5-6.4) Chapter 11 (5-6.5, 5-6.6)




5-6.1 Lessons 10.1, 10.25-6.2 Lessons 10.1, 10.2, 10.65-6.3 Lessons 10.3, 10.4, 10.65-6.4 Lessons 10.3, 10.45-6.5 Lessons 11.1, 11.2, 11.3, 11.45-6.6 Lessons 11.2, 11.3


surveysample size

modeprobability

investigationdatadata set measures of central tendencymeanmedian

outcomefavorable outcomessingle stage eventsample spaceexperimental probabilitytheoretical probability

Literature

Discovering Graph Secrets: Experiments, Puzzles, and Games Exploring Graphs by Sandra Markle

Do You Wanna Bet? by Jean Cushman Jumanji by Chris Van Allsburg Probably Pistachio by Stuart J. Murphy Fair is Fair! by Jennifer Dussling Great Graphs and Sensational Statistics (Grades 3-6)

by Lynette Long The Great Graph Contest by Loreen Leedy

Technology



http://illuminations.nctm.org Multimedia Math Glossary Kit www.harcourtschool.com/hspmath Lesson on mean, median, and mode

http://illuminations.nctm.org/LessonDetail.aspx?id=L297

Virtual Manipulatives www.shodor.org/interactivate/activities/adjustablespinner / http://www.mathwire.com/data/dicetoss1.htmlhttp://www.newberry.k12.sc.us/InstructionalLinks/math/Math_Videos.htm

Collect Data from:The U.S. Census Bureau at www.census.gov. The World Fact Book at www.odci.gov/cia/publications/factbook/index.html The Internet Movie Database at www.imdb.com

Suggested Streamline Video

http://www.imdb.com/

http://www.odci.gov/cia/publications/factbook/index.html

http://www.census.gov/



http://www.mathwire.com/data/dicetoss1.html

http://www.shodor.org/interactivate/activities/adjustablespinner/

http://www.shodor.org/interactivate/activities/adjustablespinner/





Chance (6:13) Certainty and Likelihood (5:10) Uniformity (6:36) Group and Individual Predictions (5:36) Sample Spaces (10:16) Example 2: Calculating the Mean (1:09) Example 3: Mean, Median, Mode, Range, and Overall

Distribution (3:02) Graphing Data (8:16) Data as Information (7:01) Reading Graphs (9:10) Collecting and Handling Data (9:08) Math Mastery: Graphs and Statistics (30:00) Lesson 7: Finding Range, Median, and Mode (7:38) Sample Size (7:59) Mathematical Eye: Statistics (20:27) Finding Mean, Median, and Mode (5:23) Lesson 5: Understanding Line Graphs (5:55) Lesson 6: Solving Problems Using Data Tables (3:00)


Social StudiesGraph the numbers of immigrants moving to the US from other countries. See the table on Teacher’s Edition 212C.

ScienceStudents will use data to compare the heights of three volcanoes. Use the internet to research. Find measures of central tendency. See Teacher’s Edition 212C.


Data Analysis and Probability

Standard 5-6: The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.

The indicators for this standard are grouped by the following major concepts: Data Collection and Representation Data Analysis Probability


Collection and Representation

Indicators5-6.1 Design a mathematical investigation to address a question.5-6.2 Analyze how data-collection methods affect the nature of the data set.

In third grade students compared the benefits of using different forms of data representation. In fourth grade students compared how data collection methods impact survey results. Now in fifth grade students should design a mathematical investigation to address a question and analyze how data collection methods affect the nature of the data set.

Frequent investigations with brief surveys should be used to acquaint students with collecting, representing, summarizing, comparing, and interpreting data while more extensive projects can allow students to analyze data—formulate, questions, collect and represent data, and consider whether the data gave them the information they needed to answer their question.

When designing the investigation students should decide whether data will be collected through observation, survey, or experiment. Students should compare data sets collected in different ways and determine how the methods used affect the data sets. Aspects of data collection to consider are: (a) how to word questions, (b) whom to ask, (c) what and when to observe, (d) what and how to measure, and (e) how to record data.

Data Analysis

Indicators5-6.3 Apply procedures to calculate the measures of central tendency (mean, median,

and mode). 5-6.4 Interpret the meaning and application of the measures of central tendency.

In third grade students applied a procedure to find the range of a data set. Now in fifth grade students should apply procedures to calculate the measures of central tendency (mean, median, and mode). Not only should students be able to calculate the measure of center, but most importantly, they should be able to interpret the meaning and application of the measures of center. In other words, fifth grade students should have clear knowledge about the relationship of the measures of central tendency to the data set. They should begin to see a set of data as a whole, describe its shape, and describe the features of data sets including measures of central tendency. Mean, median and mode provide a numeric picture of the shape of the data. While each of these measures represents a specific average, mean is computed by adding all of the values in the data set and dividing the sum by the number of data pieces added. Mode describes the value that occurs most frequently in the set and median describes the value in the center of the data when arranged in numeric order. The emphasis in fifth grade is on interpreting the relationship between the data set and the measures of central tendency and on knowing what the measures say about the data set. Students in sixth grade will progress to analyzing when one measure is more appropriate for a given situation than another.

Probability

Indicators5-6.5 Represent the probability of a single-stage event in words and fractions. 5-6.6 Conclude why the sum of the probabilities of the outcomes of an experiment

must equal 1.

Fourth grades students analyzed the possible outcomes for a simple event. Fifth grade students build on that to represent the probability of a single-stage event in words and fractions. (Fractions were introduced in third grade.) In grade 5, students should explore probability through experiments that have only a few outcomes. They should use common fractions to represent the probability of single stage.

In third grade students gained an understanding as to when the probability of an event is either 0 or 1. Now in fifth grade students should engage in learning experiences that that will enable them to come to the conclusion that the sum of the probabilities of the outcomes of a a single-stage event must equal 1.

Given information from a problem situation, students should be able to create a problem statement involving probability based on that situation. In other words, students should be comfortable enough with probability to take a problem situation like “the chance of landing on red is more likely” and translate that to a probability situation. In that case, students might create a spinner where the largest portion is red and be able to

explain why the spinner matches the problem situation. Through experiences, students should realize that although they cannot determine an individual outcome, they can predict the frequency of different outcomes. Students should be able to write the probability of an event as a fraction and use vocabulary such as likely, unlikely impossible, certain and equally likely.

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