Fifth Grade Mathematics - Advanced

SDE Course Code: 0506

MNPS Course Code: MTH4005Y

Course Description

The advanced fifth grade mathematics curriculum deals with problem solving and skill building that involves basic operations with rational numbers. Students will estimate, round, order and manipulate rational numbers from billions to millionths. Students will be provided opportunities to work with plane and solid figures, collect data, compute simple probabilities, use variable in simple expressions, and convert measurements from one form to another within the same system. Students will be asked to explain the mathematical processes used to solve problems and recognize relationships between multiple representations of information.

Course of Study

Numbers and Operations

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

° Recognize the place value of a given digit

° Read, write, and represent whole numbers and decimals in expanded notation

° Develop understanding of equivalent number representations (i.e., fractions, decimals, percents)

° Compare fractions, decimals, percents, and integers using the appropriate symbol (i.e., <, >, =)

° Connect whole numbers, fractions, decimals, percents, and integers on the number line

° Develop meaning for percents greater than 100 and less than one

° Develop meaning for ratios using real-world models and/or situations

° Use a variety of representations for ratios (e.g., 3 to 5; 3/5; 3:5)

° Develop and apply strategies to determine if two ratios form a proportion

° Develop the concept of prime and composite numbers ( include writing prime factorizations using exponents)

° Develop meaning for integers using real-world connections

° Use concrete, pictorial, and symbolic representations for integers

° Develop meaning for number theory concepts (i.e., divisibility, factors, multiples)

Understand operations and how they relate to one another.

° Understand the meaning and effects of arithmetic operations on fractions and decimals.

° Apply the associative, commutative, and identity properties of addition and multiplication and the property of zero to simplify computations with integers, fractions, and decimals

° use the distributive property to simplify computations with integers, fractions, and decimals

° Apply order of operations when computing with whole numbers and decimals

° understand and use the inverse relationships of addition and subtraction and multiplication and division to simplify computations and solve problems

Solve problems, compute fluently and make reasonable estimates

º Select and use appropriate methods and tools for computing with whole numbers, fractions, decimals, and percents in problem-solving situations (e.g., mental computation, estimation, calculators, computers, paper and pencil)

º Analyze procedures for computing with fractions, decimals, and integers

º solve one-step real-world problems involving whole numbers, fractions, and decimals

º use strategies to estimate the results of computations involving whole numbers, fractions, and decimals in real-world situations

º judge the reasonableness of the results of rational number estimates and computations

º Recognize when an estimate is more appropriate than an exact answer in a variety of problem situations.

Algebra

Understand patterns, relations, and functions

° Represent, analyze, and extend geometric and numerical patterns

° Use tables and graphs to generalize patterns in data

Represent and analyze mathematical situations and structures using algebraic symbols

° Develop an initial conceptual understanding of different uses of variables

° Represent mathematical statements and real-world situations using symbols

° Evaluate algebraic expressions for a given value of the variable

° Find missing addends or factors represented as variables in simple equations

° Model algebraic expressions using manipulatives, technology, and pencil and paper

Use mathematical models to represent and understand quantitative relationships

º Model simple real-world problems using graphs

Analyze change in various contexts

º Describe how changes in one quantity or variable result in changes in another

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric figures

º Describe, classify, and understand relationships among types of two-dimensional figures

º Compare and classify angles as acute, obtuse, right, and straight

º Use appropriate mathematical language to describe characteristics of lines (e.g., parallel, perpendicular, intersecting)

º Compare and classify quadrilaterals using their defining properties

º Describe similarity and congruence

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

º Plot a given set of points in all Quadrants of a coordinate system

Apply transformations and use symmetry to analyze mathematical situations

º Investigate, predict, and describe the results of transformations of two-dimensional figures (e.g., slides, flips, turns)

º Describe line and rotational symmetry in two-dimensional figures

º Describe a motion or a series of motions that will show that two shapes are congruent

Use visualization, spatial reasoning, and geometric modeling to solve problems

º Draw two-and three-dimensional geometric figures with specified properties, (e.g., side lengths, angle measure)

º Build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa

º Use visualization and spatial reasoning to solve real-world problems

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

º Understand both metric and customary systems of measurement

º Understand relationships among units and convert from one unit to another within the same system

º Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume

Apply appropriate techniques, tools, and formulas to determine measurements

º Use a variety of strategies to estimate length, perimeter, circumference, area, and volume

º Use a variety of manipulatives to develop formulas to determine the circumference of circles

º Use formulas to determine the area of triangles and parallelograms

º Use a variety of manipulatives to develop formulas to determine the area of trapezoids and circles

º Explore surface area and volume of selected prisms and cylinders using models and manipulatives

º Solve problems involving measurement using ratio and proportion

º Use scales to read maps

º Recognize the need for measurement precision

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions

º Formulate questions, design studies, and collect real-world data

º Understand how data-collection methods affect the nature of the data set

º Examine various representations of data to evaluate how accurately the data is depicted

º Construct, interpret, and use single-bar and single-line graphs to answer questions and solve real-world problems

Select and use appropriate statistical methods to analyze data

º Find, use, and interpret measures of center and spread (e.g., mean, median, mode, interquartile range)

º Discuss and understand the relationship between data sets and their graphical representations

Develop and evaluate inferences and predictions that are based on data

º Make conjectures and predictions based on data

º Explain the importance of sample size in investigations

º Conduct a survey using random sampling

º Determine whether or not a sample is biased

º Make conjectures to formulate new questions for future studies

Understand and apply basic concepts of probability

º Model situations by devising and carrying out experiments and simulations

º Make and test conjectures about the results of experiments and simulations

º Determine all possible outcomes of a simple event

Standards:

MNPS Standards

http://www.mnps.org/PageFactory.aspx?PageID=3403

State Standards

http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm

Textbook:

Greenes, et al, Houghton Mifflin Math, 1st Edition, 2005, Houghton-Mifflin (Grade 5)

Online Textbook:

http://www.eduplace.com/epe/mw/startup/main.html?s=TN&sn=Tennessee

Recommended and/or required resources:

· TI 83+ graphing calculator, scientific calculator, or four-function calculator

· TCAP Item Sampler - http://www.state.tn.us/education/tsachsamp.htm

· Manipulatives: graph paper, rulers, protractors, two-color counters, fraction bars, centimeter cubes or snap cubes, geoboards, miras, pattern blocks, algebra tiles, meter sticks, compasses, tape measure, tangrams, playing cards, number cubes(dice), popsicle sticks, Cuisenaire rods, base ten blocks, color tiles, unifix cubes, e.g. strategy games(rounding, checkers, monopoly, etc.)

· Workbook Resources: Greenes,Carole, George Immerzeel, Linda Schulman, and

Rika Spungin. Math By-Lines. Dale Seymour Publications, 1983.

Helton, Sonia M. Math Activities for Every Month of the

School Year. The Center for Applied Research in Education, 1991.

Lee, Martin and Marcia Miller. 40 Fabulous Math Mysteries Kids Can’t Resist. Scholastic Inc., 2001.

Lee, Martin and Marcia Miller. Menu Math. Scholastic

Inc., 2001.

Ritter, Darlene. Math Art. Creative Teaching Press, Inc.,

1995.

Wallaker, Jillayne Prince. Mixed Skills In Math. Instructional Fair, 1999.

· Literature Connections:
Briggs, Raymond. Jim and the Beanstalk. The Putman and Grosset Group, 1970.

Burns, Marilyn. The Greedy Triangle. Scholastic Inc., 1994.

Myller, Rolf. How Big Is A Foot?. Dell Publishing, 1962.

Neuschwander, Cindy. Sir Cumference and the First Round

Table. Charlesbridge Publishing, 1997.

· Website: http://pbskids.org/zoom/activities/sci