MCAS Math Pacing Guide Grade: 5

July 9, 2009

Core Standard 1: Number Sense and Computation
1A Multiplication and Division of Whole Numbers
Multiply and divide whole numbers. Understand and use standard algorithms for multiplication and division.
1B Comparing Fractions, Decimals, and Percents
Compare fractions, decimals and common percents.
1C Addition and Subtraction of Fractions and Decimals
Understand and perform addition and subtraction with fractions, including fractions with different denominators and mixed numbers. Add and subtract decimals, including money in decimal notation.
Core Standard 2: Geometry and Measurement
2A Polygons
Measure and describe the angles in degrees, and identify, classify, and draw polygons and triangles.
2B Shapes and Solids
Find and use the perimeter and area of triangles, parallelograms, and trapezoids. Find the surface area and volume of rectangular prisms.
Core Standard 3: Algebra and Functions
3A Variables
Use two-dimensional grids to represent points in the first quadrant that fit linear equations. Draw the line determined by the points.
3B Coordinate Grids Use two-dimensional coordinate grids to represent points in the first quadrant that fit linear equations. Draw the line determined by the points.

Math Pacing Guide

Grade 5

To successfully complete Fifth Grade the learner will

1A Multiplication and Division of Whole Numbers

  • Multiply and divide whole numbers. Understand and use standard algorithms for multiplication and division.

Essential Question:

  • How does my knowledge about multiplication and division facts help me solve problems?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.2.1 Solve problems involving multiplication and division of any whole numbers.
Not a Core Indicator:
5.1.6 Describe and identify prime and composite numbers.
5.6.2 Find the mean, median, mode, and range of a set of data and describe what each does, and does not tell, about the data set.
Learning Targets
Concepts: Need to Know
  • Algorithms for multiplication and division.
  • Key terms to identify operation
  • Prime and composite numbers
Skills: Be Able to Do
  • Multiply and divide whole numbers.
  • Use standard algorithms for multiplication and division.
  • Solve word problems using multiplication and division.
  • Describe and identify prime and composite numbers.

Key Vocabulary
Whole numbersFactorProductSolve
DividendQuotientPlace value
Prime CompositeDivisor

1B Comparing Fractions, Decimals, and Percents

  • Compare fractions, decimals and common percents.

Essential Questions:

  • How can I use fractions in everyday life?
  • How would you compare and order fractions, decimals, and whole numbers through the thousandths place?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.1.3 Arrange in numerical order and compare whole numbers or decimals to two decimal places by using symbols for less than (<), equals (=), and greater than (>).
5.1.4 Interpret percents as part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value.
5.1.7 Identify on a number line the relative position of simple positive fractions, positive mixed numbers and positive decimals.
Learning Targets
Concepts: Need to Know
  • Relationships among decimals, fractions, mixed numbers and percents
  • Column values
  • Rounding rules
  • <, > and =
  • Numerical relationships on a number line
Skills: Be Able to Do
  • Compute with whole numbers, decimals and fractions.
  • Convert between numbers in words and numbers up to one million and decimals to the thousandths place.
  • Round whole numbers.
  • Order and compare whole numbers and decimals to two decimal places using symbols.
  • Interpret percents. Find decimal and percent equivalents for common fractions.
  • Explain equivalency between fractions, decimals and whole numbers.
  • Identify on a number line simple positive fractions, mixed numbers and decimals. decimals to any place value.

Key Vocabulary
Whole numbersFractionsDecimalsPercent
EquivalentMixed numbersHundredthsThousandths
NumeratorDenominatorTenths

1C Addition and Subtraction of Fractions and Decimals

  • Understand and perform addition and subtraction with fractions, including fractions with different

denominators and mixed numbers. Add and subtract decimals, including money in decimal notation.

Essential Questions:

  • How are models used to help us understand the addition and subtraction of decimals?
  • How are models used to help us understand the addition and subtraction of fractions?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.2.2 Add and subtract fractions (including mixed numbers) with different denominators.
5.2.5 Add and subtract decimals and verify the reasonableness of the results.
5.2.7 Use mental arithmetic to add or subtract simple decimals.
5.5.7 Add and subtract with money in decimal notation.
Learning Targets
Concepts: Need to Know
  • Common denominators
  • All components of mixed numbers
  • Improper fractions
  • Decimal notation
  • Place value rules for decimals
  • lining up decimals
  • add zeros to hold place value
Skills: Be Able to Do
  • Add and subtract fractions with different denominators
  • Add and subtract mixed numbers with different denominators
  • Add and subtract decimals
  • Verify results using estimation
  • Use mental arithmetic to add and subtract decimals
  • Add and subtract with money in decimal notation

Key Vocabulary
NumeratorDenominatorPlace valueMixed number
Lowest termsSimplifyTenthsHundredths
ThousandthsDecimalModel

Core Standard 2: Geometry and Measurement

2A Polygons

  • Measure and describe the angles in degrees, and identify, classify, and draw polygons and triangles.

Essential Questions:

  • How are angles measured and classified?
  • How are points, lines, line segments, rays and angles related?
  • What tools and units are used to measure the attributes of an object?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.4.1 Measure, identify and draw angles, perpendicular and parallel lines, rectangles, triangles and circles by using appropriate tools (e.g. ruler, compass, protractor, appropriate technology and media tools.)
5.4.2 Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right, acute, obtuse, and equiangular.
5.4. Identify congruent triangles and justify your decisions by referring to sides and angles.
5.4.4 Identify, describe, draw, and classify polygons, such as pentagons and hexagons.
Learning Targets
Concepts: Need to Know
  • Tool usage - protractor, compass, ruler
  • Congruence and lines of symmetry
  • Properties of polygons
  • Key vocabulary
Skills: Be Able to Do
Measure, identify and draw using the appropriate tools:
  • Angles
  • Parallel and perpendicular lines
  • Rectangles, circles and triangles.
Identify, describe, draw and classify triangles as:
  • equilateral
  • isosceles
  • scalene
  • right, acute, obtuse equiangular
Identify congruent triangles and justify your decisions by referring to sides and angles.
Key Vocabulary
Congruent Equilateral Equiangular Acute angles
Scalene Right triangle Right angle Intersecting
Obtuse angle Perpendicular Parallel Vertex
Bisecting Protractor Compass Diameter
Line segment Ray Radius
Pi CircumferenceIsosceles

Core Standard 2: Geometry and Measurement

2B Shapes and Solids

  • Find and use the perimeter and area of triangles, parallelograms, and trapezoids. Find the surface area and

volume of rectangular prisms.

Essential Questions:

  • How can objects be represented and compared using geometric attributes?
  • How do you find perimeter, area, and volume of geometric figures?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.5.1 Understand and apply the formulas for the area of a triangle, parallelogram, and trapezoid.
5.5.2 Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.5.3 Use formulas for area of rectangles and triangles to find the area of complex shapes by dividing them into basic shapes.
5.5.4 Find the surface area and volume of rectangular solids using appropriate units.
Learning Targets
Concepts: Need to Know
  • Formulas for area and perimeter of polygons.
  • Appropriate units of measure for each shape and application.
  • Characteristics of basic polygons.
  • Formula for volume of polygons.
Skills: Be Able to Do
Understand and apply formulas for the area of:
  • triangles
  • parallelograms
  • trapezoids
Solve problems using appropriate units involving perimeters and areas of:
  • triangles
  • rectangles
  • parallelograms
  • trapezoids
Use formulas to find the area of complex shapes by dividing them into basic shapes.
Find the surface area and volume of rectangular solids using appropriate units.
Key Vocabulary
AreaPerimeterVolume
DiameterRadiusLength
HeightLabels3-Dimensional width

Core Standard 3: Algebra and Functions

3A Variables

  • Use two-dimensional grids to represent points in the first quadrant that fit linear equations. Draw the line

determined by the points.

Essential Questions:

  • Why do we use variables?
  • How would you describe the order of operations?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.3.1 Use a variable to represent an unknown number.
5.3.2 Write simple algebraic expressions in one or two variables and evaluate them by substitution.
Learning Targets
Concepts: Need to Know
  • Variables represent numbers
  • Order of operations
Skills: Be Able to Do
  • Evaluate a simple algebraic expression.
  • Use variables to represent numbers
  • Write algebraic expressions in one or two variables.
  • Evaluate expressions by substitution.

Key Vocabulary
Variable SolutionEvaluate Operations
Substitute ExpressionEquation

Core Standard 3: Algebra and Functions

3B Coordinate Grids

  • Use two-dimensional coordinate grids to represent points in the first quadrant that fit linear equations. Draw the line determined by the points.

Essential Questions:

  • What are the tools needed to solve linear equations and inequalities?
  • When are algebraic and numeric expressions used?
  • In problem solving, how do I decide which approach to use to organize my data, communicate my thinking, and

show the solution?

5.3.4 Identify and graph ordered pairs of positive numbers.
5.3.5 Find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they determine.
Learning Targets
Concepts: Need to Know
  • X-axis
  • Y-axis
  • Plotting points
Skills: Be Able to Do
  • Use two-dimensional coordinate grids to represent points in the first quadrant that fit linear equations.
  • Draw lines connecting coordinates.
  • Identify and graph ordered pairs of positive numbers.
  • Find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they determine.

Key Vocabulary
X-axisY-axisLinearOrdered pair
QuadrantCoordinatesInequalitiesLinear equation

Mathematics Curriculum Map Grade 5

To successfully complete fourth grade the learner will:

  • Demonstrate with 100% accuracy multiplication facts.
  • Master and continued to develop understanding of algorithms.
  • Read and write numbers to any place value (decimals included).
  • Convert between fractions, decimals, and percents.
  • Solve problems involving volume, area, and perimeter of all polygons given a formula.
  • Be able to solve problems with variables.
  • Explain how to solve a problem in writing and show their work.

Mathematics Teaching Models, and Suggested supplementary materials may include:

  • Everyday Math Program (MCAS adopted math program)
  • Math Exemplars ( )
  • Purdue Collaborative Problem Solving (Dr. David Feikus, Purdue North Central)
  • Math Their Way ( )
  • Indiana State Standards Mathematics Resources: Curriculum Frameworks
  • Compass Learning

Math Academic Milestones to be achieved by all fifth graders by the end of the current school year :

  • 80% accuracy on EDM unit tests.
  • Demonstrate grade appropriate problem solving strategies (including the scientific method).
  • Achieve targeted RIT score on Fall and Spring NWEA test.
  • Proficient in basic computation skills: Addition, Subtraction, Multiplication, and Division

Highlighted items: “Power/Critical Standards”

Time-frame / Content/Performance Standards
Addressed / Assessment Suggestions
On-going: Review each Quarter / 5.7.1.....Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
5.7.2.....Decide when and how to break a problem into simpler parts.
5.7.3.....Apply strategies and results from simpler problems to more complex problems.
5.7.4.....Express the solution clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
5.7.7.....Make precise calculations and check the validity of the results in the context of the problem.
5.7.8.....Decide whether a solution is reasonable in the context of the original situation.
5.7.9.....Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems. / Math Facts in a Flash
Unit EDM Tests
EDM Mid-year and Year-end tests
EDM Math Boxes and Math Journals
Student Writing Across Curriculum math Journals
Curriculum Frameworks
Compass Odyssey Learning Path…pre and post tests
Timed Math Fact Tests
EDM Games
Daily Assignments
Time-frame / Content/Performance Standards
Addressed / EDM Pacing Guide
Data Analysis/Evaluation of Assessments / Assessment Suggestions
First Quarter: : August 26-October 30, 2009 / 5.1.1 Convert between numbers in words and numbers in figures for numbers up to millions.
5.1.2 Round whole numbers and decimals to any place.
5.1.6 Describe and identify prime and composite numbers.
5.2.1 Solve problems involving multiplication and division of any whole numbers.
5.2.5 Add and subtract decimals and verify the reasonableness of the results.
5.2.6 Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication, and division problems.
5.2.7 Use mental arithmetic to add or subtract simple decimals.
5.3.1 Use a variable to represent an unknown number.
5.4.1 Measure, identify, draw angles, perpendicular and parallel lines, rectangles, triangles and circles by using appropriate tools (e.g., ruler, compass, protractor, appropriate technology, media tools).
5.4.2 Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right acute, obtuse, and equiangular.
5.4.3 Identify congruent triangles and justify your decisions by referring to sides and angles.
5.4.4 Identify, describe, draw, and classify polygons, such as pentagons and hexagons.
5.5.7 Add and subtract with money in decimal notation.
5.6.2 Find the mean, median, mode, range of a set of data and describe what each does and does not tell about the data set. / Unit 1
Unit 2
Unit 3
Unit 4 / Aug. 26 – Sept. 16
Sept. 17 – Oct. 8
Oct. 8 – Oct. 23
Oct. 26- Nov. 12
See additional Pacing Guide Suggestions
Modified for ISTEP. / Math Facts in a Flash
Units 1-3 EDM Unit Tests
EDM Math Boxes and Math
Journals
Student Writing Across
Curriculum Math Journals
Curriculum Frameworks
Compass Odyssey Learning Path…pre and post tests
Timed Math Fact Tests
EDM Games
Daily Assignments
United Streaming Assignment builder and quiz builder
Time-frame / Content/Performance Standards
Addressed / EDM Pacing Guide
Bank Day December 8, 2006: Data Analysis/Evaluation of Assessments / Assessment Suggestions
Second Quarter: November 2-January 20, 2010 / 5.1.4 Interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value.
5.1.2 Round whole numbers and decimals to any place value.
5.1.3 Arrange in numerical order and compare whole numbers or decimals to two decimal places by using the symbols for less than (<), equals (=), and greater than (>).
5.1.5 Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.
5.1.7 Identify on a number line the relative position of simple positive fractions, positive mixed numbers, and positive decimals.
5.2.1 Solve problems involving multiplication of any whole numbers.
5.2.2 Add and subtract fractions (including mixed numbers) with different denominators.
5.2.6 Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.3.2 Write simple algebraic expressions in one or two variables and evaluate them by substitution.
5.6.1 Explain which types of display are appropriate for various sets of data.
5.6.2 Find the mean, median, mode and range of a set of data and describe what each does and does not tell about the data set.
5.6.4 Express outcomes of experimental probability situations verbally and numerically. (3 out of 4 or 3/4) / Unit 4
Unit 5
Unit 6
Unit 7
Unit 8 / Oct. 26- Nov. 12
Nov. 13- Dec. 7
Dec 8 – Jan. 20
Mid-year Test
Unit 7 Moved to May
Jan. 22- Feb. 12
See additional Pacing Guide Suggestions. / Math Facts in a Flash
Units 4-6 EDM Unit Tests
EDM Math Boxes and Math Journals
Student Writing Across Curriculum math Journals
Curriculum Frameworks
Compass Odyssey Learning Path…pre and post tests
Timed Math Fact Tests
EDM Games
Daily Assignments
United Streaming Assignment builder and quiz builder
Time-frame / Content/Performance Standards
Addressed / EDM Pacing Guide
Bank Day March 9, 2007: Data Analysis/Evaluation of Assessments / Assessment
Third quarter: January 21-March 26, 2010 / 5.1.3 Arrange in numerical order and compare whole numbers or decimals to two places by using the symbols for less than (<), equals (=), and greater than (>).
5.1.4 Interpret percents as part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value.
5.2.3 Use models to show an understanding of multiplication and division of fractions.
5.2.4 Multiply and divide fractions to solve problems.
5.3.1 Use a variable to represent an unknown number.
5.3.2 Write simple algebraic expressions in one or two variables and evaluate them by substitution.
5.3.4 Identify and graph ordered pairs of positive numbers.
5.3.5 Find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they determine.
5.3.6 Understand that the length of a horizontal line segment on a coordinate plane equals the difference between the x-coordinates and that the length of a vertical line segment on a coordinate plane equals the difference between the y-coordinates.
5.3.7 Use information taken from a graph or equation to answer questions about a problem/situation.
5.4.5 Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter.
5.4.6 Identify shapes that have reflectional and rotational symmetry.
5.4.7 Understand that 90 º, 180º , 270º, and 360º, are associated with 1/4, 1/2, 3/4, and full turns, respectively.
5.5.1 Understand and apply the formulas for the area of a triangle, parallelogram, and trapezoid.
5.5.2 Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.5.3 Use formulas for area of rectangles and triangles to find the area of complex shapes by dividing them into basic shapes.
5.5.4 Find the surface area and volume or rectangular solids using appropriate units.
5.5.5 Understand and use the smaller and larger units for measuring weight (ounce, gram ton) and their relationship to pounds and kilograms.
5.6.1 Explain which types of display are appropriate for various sets of data. / Unit 8
Unit 9
Unit 10
Unit 11 / Jan. 22- Feb. 12
Feb. 16- Mar. 3
Mar. 4- Mar. 18
Mar. 19-April 1
See additional Pacing Guide Suggestions. / Math Facts in a Flash
Units 7-9 EDM Unit Tests
EDM Math Boxes and Math Journals
Student Writing Across Curriculum math Journals
Curriculum Frameworks
Compass Odyssey Learning Path…pre and post tests
Timed Math Fact Tests
EDM Games
Daily Assignments
United Streaming Assignment builder and quiz builder
Time-frame / Content/Performance Standards
Addressed / EDM Pacing Guide
Bank Day May 24, 2007: Data Analysis/Evaluation of Assessments / Assessment Suggestions
Fourth Quarter: March 26-June 8, 2010 / 5.1.3 Arrange in numerical order and compare whole numbers and decimals to two decimal places by using the symbols for less than (<) equal to (=) or greater than (>).
5.2.1 Solve problems involving multiplication and division of any whole numbers.
5.2.3 Use models to show an understanding of multiplication and division of fractions.
5.2.4 Multiply and divide fractions to solve problems.
5.3.3 Use the distributive property in numerical equations and expressions.
5.4.5 Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter.
5.4.8 Construct prisms and pyramids using appropriate materials.
5.4.9 Given a picture of a three-dimensional object, build the object with blocks.
5.5.3 Use formulas for area of rectangles and triangles to find the area or complex shapes by dividing them into basic shapes.
5.5.4 Find the surface area and volume of rectangular solids using appropriate units.
5.6.3 Understand that probability can take any value between 0 and 1, events that are not going to occur have probability 0, events certain to occur have probability 1, and more likely events have a higher probability than less likely events.
5.6.4 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4, 3/4). / Unit 11
Unit 12
Unit 7
Prior to June 8 / Mar. 19-April 1
April 12-April 30
May 3-May 18
End of Year Test
See additional Pacing Guide Suggestions. / Math Facts in a Flash
Units 10-12 EDM Unit Tests
EDM Math Boxes and Math Journals
Student Writing Across
Curriculum math Journals
Curriculum Frameworks
Compass Odyssey Learning Path…pre and post tests
Timed Math Fact Tests
EDM Games
Daily Assignments
United Streaming Assignment builder and quiz builder

7/7/09