Highlights of the New Learning for Grade-Five Students Are

Grade 5

Overview

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 5

Mathematical Processes

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 5

Number and Operations

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
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 Prep
Chapter Tests
MAP Testing
Odyssey
Questioning Strategies
Exit tickets
Journaling/Written Assessment
Projects
Pair 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, 4.4
5-2.5 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, 8.5
5-2.8 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, 9.7
5-2.9 Lesson 2.7
Key Concepts (Vocabulary)
period
place value
tenths
hundredths
thousandths
decimal
divisor
dividend
quotient
divisibility
divisible / factors
multiples
greatest common factor
least common multiple
prime number
composite number
algorithm
sum
addend
difference
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 Long
The 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
www.harcourtschool.com/hspmath
Mega Math - Fraction Action, The Number Games,
Ice Station Exploration
· District Web Site: Math Videos
http://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.html
http://www.onlinemathlearning.com/fractions-math-games.html
http://www.aaamath.com/fra63a-primecomp.html
http://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
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)
Cross Curricular Opportunities
Social Studies
Compare 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.

Fifth Grade---Support Document

Number and Operations

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

Indicators

5-2.7 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 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 Itself / 1 Factor and Itself
Numbers
Factors / Factors
2 / 1,2
3 / 1,3
4 / 1,2,4
5 / 1,5
6 / 1,2,3,6
7 / 1,7
8 / 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.

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

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.

5-2.4 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.