MCAS Math Pacing Guide Grade: 5



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 numbers Factor Product Solve |

|Dividend Quotient Place value |

|Prime Composite Divisor |

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 (). |

|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 numbers Fractions Decimals Percent |

|Equivalent Mixed numbers Hundredths Thousandths |

|Numerator Denominator Tenths |

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 |

|Numerator Denominator Place value Mixed number |

|Lowest terms Simplify Tenths Hundredths |

|Thousandths Decimal Model |

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 Circumference Isosceles |

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 |

|Area Perimeter Volume |

|Diameter Radius Length |

|Height Labels 3-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 Solution Evaluate Operations |

|Substitute Expression Equation |

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-axis Y-axis Linear Ordered pair |

|Quadrant Coordinates Inequalities Linear 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 |Assessment Suggestions |

| |Addressed | |

|On-going: |5.7.1.....Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing |Math Facts in a Flash |

|Review each |patterns. |Unit EDM Tests |

|Quarter | |EDM Mid-year and Year-end tests |

| |5.7.2.....Decide when and how to break a problem into simpler parts. |EDM Math Boxes and Math Journals |

| | |Student Writing Across Curriculum |

| |5.7.3.....Apply strategies and results from simpler problems to more complex problems. |math Journals |

| | |Curriculum Frameworks |

| |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 |Compass Odyssey Learning Path…pre and|

| |symbolic work. |post tests |

| | |Timed Math Fact Tests |

| |5.7.7.....Make precise calculations and check the validity of the results in the context of the problem. |EDM Games |

| | |Daily Assignments |

| |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. | |

| | | |

|Time-frame|Content/Performance Standards |EDM Pacing Guide |Assessment Suggestions |

| |Addressed |Data Analysis/Evaluation of Assessments | |

|First |5.1.1 Convert between numbers in words and numbers in figures for numbers up to millions. |Unit 1 |Aug. 26 – Sept. 16 |Math Facts in a Flash |

|Quarter: :| | | | |

|August |5.1.2 Round whole numbers and decimals to any place. | | |Units 1-3 EDM Unit Tests |

|26-October| | | | |

|30, 2009 |5.1.6 Describe and identify prime and composite numbers. |Unit 2 |Sept. 17 – Oct. 8 |EDM Math Boxes and Math |

| | | | |Journals |

| |5.2.1 Solve problems involving multiplication and division of any whole numbers. | | | |

| | | | |Student Writing Across |

| |5.2.5 Add and subtract decimals and verify the reasonableness of the results. |Unit 3 |Oct. 8 – Oct. 23 | |

| | | | |Curriculum Math Journals |

| |5.2.6 Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication, and division problems. | | |Curriculum Frameworks |

| | |Unit 4 |Oct. 26- Nov. 12 | |

| |5.2.7 Use mental arithmetic to add or subtract simple decimals. | | |Compass Odyssey Learning Path…pre|

| | | | |and post tests |

| |5.3.1 Use a variable to represent an unknown number. | | | |

| | | |See additional Pacing |Timed Math Fact Tests |

| |5.4.1 Measure, identify, draw angles, perpendicular and parallel lines, rectangles, triangles and circles by using appropriate | |Guide Suggestions |EDM Games |

| |tools (e.g., ruler, compass, protractor, appropriate technology, media tools). | |Modified for ISTEP. |Daily Assignments |

| | | | | |

| |5.4.2 Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right acute, obtuse, and equiangular. | | |United Streaming Assignment |

| | | | |builder and quiz builder |

| |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. | | | |

|Time-frame |Content/Performance Standards |EDM Pacing Guide |Assessment Suggestions |

| |Addressed |Bank Day December 8, 2006: Data | |

| | |Analysis/Evaluation of Assessments | |

|Second Quarter: |5.1.4 Interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they |Unit 4 |Oct. 26- Nov. 12 |Math Facts in a Flash |

|November |represent the same value. | | | |

|2-January 20, | | | |Units 4-6 EDM Unit |

|2010 |5.1.2 Round whole numbers and decimals to any place value. | | |Tests |

| | |Unit 5 |Nov. 13- Dec. 7 | |

| |5.1.3 Arrange in numerical order and compare whole numbers or decimals to two decimal places by using the symbols for less than | | |EDM Math Boxes and Math|

| |(). | | |Journals |

| | | | | |

| |5.1.5 Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole|Unit 6 |Dec 8 – Jan. 20 | |

| |numbers. | | |Student Writing Across |

| | | | |Curriculum math |

| |5.1.7 Identify on a number line the relative position of simple positive fractions, positive mixed numbers, and positive | |Mid-year Test |Journals |

| |decimals. | | | |

| | |Unit 7 |Unit 7 Moved to May |Curriculum Frameworks |

| |5.2.1 Solve problems involving multiplication of any whole numbers. | | |Compass Odyssey |

| | | | |Learning Path…pre and |

| |5.2.2 Add and subtract fractions (including mixed numbers) with different denominators. | |Jan. 22- Feb. 12 |post tests |

| | |Unit 8 | |Timed Math Fact Tests |

| |5.2.6 Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication and division problems. | | |EDM Games |

| | | | |Daily Assignments |

| |5.3.2 Write simple algebraic expressions in one or two variables and evaluate them by substitution. | |See additional Pacing | |

| | | |Guide Suggestions. |United Streaming |

| |5.6.1 Explain which types of display are appropriate for various sets of data. | | |Assignment builder and |

| | | | |quiz builder |

| |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) | | | |

|Time-frame|Content/Performance Standards |EDM Pacing Guide |Assessment |

| |Addressed |Bank Day March 9, 2007: Data | |

| | |Analysis/Evaluation of Assessments | |

|Third |5.1.3 Arrange in numerical order and compare whole numbers or decimals to two places by using the symbols for less than (). | | | |

|January |5.1.4 Interpret percents as part of a hundred. Find decimal and percent equivalents for common fractions and explain why | | |Units 7-9 EDM Unit Tests |

|21-March |they represent the same value. | | | |

|26, 2010 |5.2.3 Use models to show an understanding of multiplication and division of fractions. |Unit 9 |Feb. 16- Mar. 3 |EDM Math Boxes and Math |

| |5.2.4 Multiply and divide fractions to solve problems. | | |Journals |

| |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. | | |Student Writing Across |

| |5.3.4 Identify and graph ordered pairs of positive numbers. |Unit 10 |Mar. 4- Mar. 18 |Curriculum math Journals |

| |5.3.5 Find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they| | |Curriculum Frameworks |

| |determine. | | | |

| |5.3.6 Understand that the length of a horizontal line segment on a coordinate plane equals the difference between the |Unit 11 |Mar. 19-April 1 |Compass Odyssey Learning |

| |x-coordinates and that the length of a vertical line segment on a coordinate plane equals the difference between the | | |Path…pre and post tests |

| |y-coordinates. | |See additional Pacing | |

| |5.3.7 Use information taken from a graph or equation to answer questions about a problem/situation. | |Guide Suggestions. |Timed Math Fact Tests |

| |5.4.5 Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter.| | |EDM Games |

| |5.4.6 Identify shapes that have reflectional and rotational symmetry. | | |Daily Assignments |

| |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. | | |United Streaming Assignment |

| |5.5.2 Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using | | |builder and quiz builder |

| |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. | | | |

|Time-frame|Content/Performance Standards |EDM Pacing Guide |Assessment Suggestions |

| |Addressed |Bank Day May 24, 2007: Data | |

| | |Analysis/Evaluation of Assessments | |

|Fourth |5.1.3 Arrange in numerical order and compare whole numbers and decimals to two decimal places by using the symbols for less than (). | | |Units 10-12 EDM Unit Tests |

|March | | | |EDM Math Boxes and Math |

|26-June 8,|5.2.1 Solve problems involving multiplication and division of any whole numbers. | | |Journals |

|2010 | |Unit 12 |April 12-April 30 | |

| |5.2.3 Use models to show an understanding of multiplication and division of fractions. | | |Student Writing Across |

| | | | | |

| |5.2.4 Multiply and divide fractions to solve problems. |Unit 7 |May 3-May 18 |Curriculum math Journals |

| | | | |Curriculum Frameworks |

| |5.3.3 Use the distributive property in numerical equations and expressions. | | | |

| | | | |Compass Odyssey Learning |

| |5.4.5 Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter. |Prior to June 8|End of Year Test |Path…pre and post tests |

| | | | | |

| |5.4.8 Construct prisms and pyramids using appropriate materials. | | |Timed Math Fact Tests |

| | | | |EDM Games |

| |5.4.9 Given a picture of a three-dimensional object, build the object with blocks. | |See additional Pacing |Daily Assignments |

| | | |Guide Suggestions. | |

| |5.5.3 Use formulas for area of rectangles and triangles to find the area or complex shapes by dividing them into basic shapes. | | |United Streaming Assignment |

| | | | |builder and quiz builder |

| |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). | | | |

7/7/09

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