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5.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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5.PS.1
Know the difference between relevant and irrelevant information when solving problems
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5.PS.2
Understand that some ways of representing a problem are more efficient than others
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5.PS.3
Interpret information correctly, identify the problem, and generate possible strategies and solutions
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Students will solve problems that arise in mathematics and in other contexts.
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5.PS.4
Act out or model with manipulatives activities involving mathematical content from literature
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5.PS.5
Formulate problems and solutions from everyday situations
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5.PS.6
Translate from a picture/diagram to a numeric expression
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5.PS.7
Represent problem situations verbally, numerically, algebraically, and/or graphically
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5.PS.8
Select an appropriate representation of a problem
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5.PS.9
Understand the basic language of logic in mathematical situations (and, or, not)
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Students will apply and adapt a variety of appropriate strategies to solve problems.
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5.PS.10
Work in collaboration with others to solve problems
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5.PS.11
Translate from a picture/diagram to a number or symbolic expression
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5.PS.12
Use trial and error and the process of elimination to solve problems
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5.PS.13
Model problems with pictures/diagrams or physical objects
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5.PS.14
Analyze problems by observing patterns
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5.PS.15
Make organized lists or charts to solve numerical problems
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Students will monitor and reflect on the process of mathematical problem solving.
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5.PS.16
Discuss with peers to understand a problem situation
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5.PS.17
Determine what information is needed to solve problem
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5.PS.18
Determine the efficiency of different representations of a problem
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5.PS.19
Differentiate between valid and invalid approaches
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5.PS.20
Understand valid counterexamples
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5.PS.21
Explain the methods and reasoning behind the problem solving strategies used
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5.PS.22
Discuss whether a solution is reasonable in the context of the original problem
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5.PS.23
Verify results of a problem
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5.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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5.RP.1
Recognize that mathematical ideas can be supported using a variety of strategies
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5.RP.2
Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking
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Students will make and investigate mathematical conjectures.
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5.RP.3
Investigate conjectures, using arguments and appropriate mathematical terms
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5.RP.4
Make and evaluate conjectures, using a variety of strategies
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Students will develop and evaluate mathematical arguments and proofs.
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5.RP.5
Justify general claims or conjectures, using manipulatives, models, expressions, and mathematical relationships
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5.RP.6
Develop and explain an argument verbally, numerically, and/or graphically
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5.RP.7
Verify claims other students make, using examples and counterexamples when appropriate
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Students will select and use various types of reasoning and methods of proof.
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5.RP.8
Support an argument through examples/counterexamples and special cases
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5.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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5.CM.1
Provide an organized thought process that is correct, complete, coherent, and clear
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5.CM.2
Explain a rationale for strategy selection
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5.CM.3
Organize and accurately label work
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Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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5.CM.4
Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form
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5.CM.5
Answer clarifying questions from others
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Students will analyze and evaluate the mathematical thinking and strategies of others.
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5.CM.6
Understand mathematical solutions shared by other students
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5.CM.7
Raise questions that elicit, extend, or challenge others' thinking
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5.CM.8
Consider strategies used and solutions found by others in relation to their own work
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Students will use the language of mathematics to express mathematical ideas precisely.
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5.CM.9
Increase their use of mathematical vocabulary and language when communicating with others
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5.CM.10
Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale
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5.CM.11
Decode and comprehend mathematical visuals and symbols to construct meaning
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5.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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5.CN.1
Understand and make connections and conjectures in their everyday experiences to mathematical ideas
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5.CN.2
Explore and explain the relationship between mathematical ideas
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5.CN.3
Connect and apply mathematical information to solve problems
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Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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5.CN.4
Understand multiple representations and how they are related
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5.CN.5
Model situations with objects and representations and be able to draw conclusions
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Students will recognize and apply mathematics in contexts outside of mathematics.
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5.CN.6
Recognize and provide examples of the presence of mathematics in their daily lives
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5.CN.7
Apply mathematics to problem situations that develop outside of mathematics
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5.CN.8
Investigate the presence of mathematics in careers and areas of interest
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5.CN.9
Recognize and apply mathematics to other disciplines and areas of interest
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5.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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5.R.1
Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
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5.R.2
Explain, describe, and defend mathematical ideas using representations
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5.R.3
Read, interpret, and extend external models
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5.R.4
Use standard and nonstandard representations with accuracy and detail
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Students will select, apply, and translate among mathematical representations to solve problems.
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5.R.5
Use representations to explore problem situations
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5.R.6
Investigate relationships between different representations and their impact on a given problem
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Students will use representations to model and interpret physical, social, and mathematical phenomena.
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5.R.7
Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)
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5.R.8
Use mathematics to show and understand social phenomena (e.g., construct tables to organize data showing book sales)
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5.R.9
Use mathematics to show and understand mathematical phenomena (e.g., find the missing value that makes the equation true: (3 + 4) + 5 = 3 + (4 + ___)
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5.N
Number Sense and Operations
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Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
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Number Systems
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5.N.1
Read and write whole numbers to millions
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5.N.2
Compare and order numbers to millions
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5.N.3
Understand the place value structure of the base ten number system
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5.N.3.a
10 ones = 1 ten
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5.N.3.b
10 tens = 1 hundred
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5.N.3.c
10 hundreds = 1 thousand
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5.N.3.d
10 thousands = 1 ten thousand
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5.N.3.e
10 ten thousands = 1 hundred thousand
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5.N.3.f
10 hundred thousands = 1 million
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5.N.4
Create equivalent fractions, given a fraction
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5.N.5
Compare and order fractions including unlike denominators (with and without the use of a number line) Note: Commonly used fractions such as those that might be indicated on ruler, measuring cup, etc.
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5.N.6
Understand the concept of ratio
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5.N.7
Express ratios in different forms
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Ratios, proportions, and percents: Ratios: word problems (Fifth grade - U.3)
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Ratios, proportions, and percents: Equivalent ratios (Fifth grade - U.4)
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Ratios, proportions, and percents: Proportions (Fifth grade - U.5)
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Ratios, proportions, and percents: Unit rates and equivalent rates (Fifth grade - U.6)
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Ratios, proportions, and percents: Scale drawings (Fifth grade - U.7)
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5.N.8
Read, write, and order decimals to thousandths
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5.N.9
Compare fractions using <, >, or =
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5.N.10
Compare decimals using <, >, or =
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5.N.11
Understand that percent means part of 100, and write percents as fractions and decimals
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Number Theory
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5.N.12
Recognize that some numbers are only divisible by one and themselves (prime) and others have multiple divisors (composite)
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5.N.13
Calculate multiples of a whole number and the least common multiple of two numbers
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5.N.14
Identify the factors of a given number
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5.N.15
Find the common factors and the greatest common factor of two numbers
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Students will understand meanings of operations and procedures, and how they relate to one another.
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Operations
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5.N.16
Use a variety of strategies to multiply three-digit by three-digit numbers Note: Multiplication by anything greater than a three-digit multiplier/ multiplicand should be done using technology.
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5.N.17
Use a variety of strategies to divide three-digit numbers by one- and two-digit numbers Note: Division by anything greater than a two-digit divisor should be done using technology.
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5.N.18
Evaluate an arithmetic expression using order of operations including multiplication, division, addition, subtraction and parentheses
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5.N.19
Simplify fractions to lowest terms
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5.N.20
Convert improper fractions to mixed numbers, and mixed numbers to improper fractions
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5.N.21
Use a variety of strategies to add and subtract fractions with like denominators
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5.N.22
Add and subtract mixed numbers with like denominators
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5.N.23
Use a variety of strategies to add, subtract, multiply, and divide decimals to thousandths
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Students will compute accurately and make reasonable estimates.
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Estimation
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5.N.24
Round numbers to the nearest hundredth and up to 10,000
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5.N.25
Estimate sums and differences of fractions with like denominators
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5.N.26
Estimate sums, differences, products, and quotients of decimals
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5.N.27
Justify the reasonableness of answers using estimation
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5.A
Algebra
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Students will represent and analyze algebraically a wide variety of problem solving situations.
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Variables and Expressions
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5.A.1
Define and use appropriate terminology when referring to constants, variables, and algebraic expressions
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5.A.2
Translate simple verbal expressions into algebraic expressions
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Students will perform algebraic procedures accurately.
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Variables and Expressions
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5.A.3
Substitute assigned values into variable expressions and evaluate using order of operations
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Equations and Inequalities
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5.A.4
Solve simple one-step equations using basic whole-number facts
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5.A.5
Solve and explain simple one-step equations using inverse operations involving whole numbers
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5.A.6
Evaluate the perimeter formula for given input values
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Students will recognize, use, and represent algebraically patterns, relations, and functions.
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Patterns, Relations, and Functions
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5.A.7
Create and explain patterns and algebraic relationships (e.g., 2, 4, 6, 8...) algebraically: 2n (doubling)
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5.A.8
Create algebraic or geometric patterns using concrete objects or visual drawings (e.g., rotate and shade geometric shapes)
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5.G
Geometry
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Shapes
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5.G.1
Calculate the perimeter of regular and irregular polygons
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Students will identify and justify geometric relationships, formally and informally.
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Geometric Relationships
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5.G.2
Identify pairs of similar triangles
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5.G.3
Identify the ratio of corresponding sides of similar triangles
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5.G.4
Classify quadrilaterals by properties of their angles and sides
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5.G.5
Know that the sum of the interior angles of a quadrilateral is 360 degrees
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5.G.6
Classify triangles by properties of their angles and sides
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5.G.7
Know that the sum of the interior angles of a triangle is 180 degrees
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5.G.8
Find a missing angle when given two angles of a triangle
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5.G.9
Identify pairs of congruent triangles
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5.G.10
Identify corresponding parts of congruent triangles
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Students will apply transformations and symmetry to analyze problem solving situations.
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Transformational Geometry
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5.G.11
Identify and draw lines of symmetry of basic geometric shapes
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Students will apply coordinate geometry to analyze problem solving situations.
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Coordinate Geometry
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5.G.12
Identify and plot points in the first quadrant
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5.G.13
Plot points to form basic geometric shapes (identify and classify)
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5.G.14
Calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths and parallel to the axes)
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5.M
Measurement
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Students will determine what can be measured and how, using appropriate methods and formulas.
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Units of Measurement
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5.M.1
Use a ruler to measure to the nearest inch, 1/2, 1/4, and 1/8 inch.
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5.M.2
Identify customary equivalent units of length
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5.M.3
Measure to the nearest centimeter
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5.M.4
Identify equivalent metric units of length
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5.M.5
Convert measurement within a given system
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Tools and Methods
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5.M.6
Determine the tool and technique to measure with an appropriate level of precision: lengths and angles
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Students will use units to give meaning to measurements.
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Units
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5.M.7
Calculate elapsed time in hours and minutes
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5.M.8
Measure and draw angles using a protractor
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Students will develop strategies for estimating measurements.
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Estimation
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5.M.9
Determine personal references for customary units of length (e.g., your pace is approximately 3 feet, your height is approximately 5 feet, etc.)
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5.M.10
Determine personal references for metric units of length
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5.M.11
Justify the reasonableness of estimates
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5.S
Statistics and Probability
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Students will collect, organize, display, and analyze data.
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Collection of Data
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5.S.1
Collect and record data from a variety of sources (e.g., newspapers, magazines, polls, charts, and surveys)
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Organization and Display of Data
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5.S.2
Display data in a line graph to show an increase or decrease over time
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Analysis of Data
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5.S.3
Calculate the mean for a given set of data and use to describe a set of data
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Students will make predictions that are based upon data analysis.
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Predictions from Data
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5.S.4
Formulate conclusions and make predictions from graphs
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Students will understand and apply concepts of probability.
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Probability
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5.S.5
List the possible outcomes for a single-event experiment
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5.S.6
Record experiment results using fractions/ratios
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5.S.7
Create a sample space and determine the probability of a single event, given a simple experiment (e.g., rolling a number cube)
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