5.PS.1 Know the difference between relevant and irrelevant information when solving problems

5.PS.2 Understand that some ways of representing a problem are more efficient than others 5.PS.3 Interpret information correctly, identify the problem, and generate possible strategies and solutions

5.PS.4 Act out or model with manipulatives activities involving mathematical content from literature

5.PS.5 Formulate problems and solutions from everyday situations 5.PS.6 Translate from a picture/diagram to a numeric expression 5.PS.7 Represent problem situations verbally, numerically, algebraically, and/or graphically

5.PS.8 Select an appropriate representation of a problem 5.PS.9 Understand the basic language of logic in mathematical situations (and, or, not)

5.PS.10 Work in collaboration with others to solve problems 5.PS.11 Translate from a picture/diagram to a number or symbolic expression. 5.PS.12 Use trial and error and the process of elimination to solve problems

5.PS.13 Model problems with pictures/diagrams or physical objects 5.PS.14 Analyze problems by observing patterns 5.PS.15 Make organized lists or charts to solve numerical problems

5.PS.16 Discuss with peers to understand a problem situation 5.PS.17 Determine what information is needed to solve problems 5.PS.18 Determine the efficiency of different representations of a problem

5.PS.19 Differentiate between valid and invalid approaches 5.PS.20 Understand valid counterexamples 5.PS.21 Explain the methods and reasoning behind the problem solving strategies used 5.PS.22 Discuss whether a solution is reasonable in the context of the original problem 5.PS.23 Verify results of a problem

5.RP.1 Recognize that mathematical ideas can be supported using a variety of strategies

5.RP.2 Understand that mathematical statements can be supported, using models, facts, and relationships to explain their thinking

5.RP.3 Investigate conjectures, using arguments and appropriate mathematical terms

5.RP.4 Make and evaluate conjectures, using a variety of strategies

5.RP.5 Justify general claims or conjectures, using manipulatives, models, expressions, and mathematical relationships

5.RP.6 Develop and explain an argument verbally, numerically, and/or graphically 5.RP.7 Verify claims other students make, using examples and counterexamples when appropriate

5.RP.8 Support an argument through examples/counterexamples and special cases

5.CM.1 Provide an organized thought process that is correct, complete, coherent, and clear

5.CM.2 Explain a rationale for strategy selection 5.CM.3 Organize and accurately label work

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

5.CM.5 Answer clarifying questions from others

5.CM.6 Understand mathematical solutions shared by other students

5.CM.7 Raise questions that elicit, extend, or challenge others’ thinking 5.CM.8 Consider strategies used and solutions found by others in relation to their own work

5.CM.9 Increase their use of mathematical vocabulary and language when communicating with others

5.CM.10 Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale 5.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning

5.CN.1 Understand and make connections and conjectures in their everyday experiences to mathematical ideas

5.CN.2 Explore and explain the relationship between mathematical ideas 5.CN.3 Connect and apply mathematical information to solve problems

5.CN.4 Understand multiple representations and how they are related

5.CN.5 Model situations with objects and representations and be able to draw conclusions

5.CN.6 Recognize and provide examples of the presence of mathematics in their daily lives

5.CN.7 Apply mathematics to problem situations that develop outside of mathematics

5.CN.8 Investigate the presence of mathematics in careers and areas of interest 5.CN.9 Recognize and apply mathematics to other disciplines and areas of interest

5.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations

5.R.2 Explain, describe, and defend mathematical ideas using representations

5.R.3 Read, interpret, and extend external models 5.R.4 Use standard and nonstandard representations with accuracy and detail

5.R.5 Use representations to explore problem situations

5.R.6 Investigate relationships between different representations and their impact on a given problem

5.R.7 Use mathematics to show and understand physical phenomena (e.g., determine the perimeter of a bulletin board)

5.R.8 Use mathematics to show and understand social phenomena (e.g., construct tables to organize data showing book sales)

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 + ___ )

*Number Systems*

5.N.1 Read and write whole numbers to millions

5.N.2 Compare and order numbers to millions

5.N.3 Understand the place value structure of the base ten number system

10 ones = 1 ten

10 tens = 1 hundred

10 hundreds = 1 thousand

10 thousands = 1 ten thousand

10 ten thousands = 1 hundred thousand

10 hundred thousands = 1 million

5.N.4 Create equivalent fractions, given a fraction 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. 5.N.6 Understand the concept of ratio 5.N.7 Express ratios in different forms

5.N.8 Read, write, and order decimals to thousandths 5.N.9 Compare fractions using <, >, or = 5.N.10 Compare decimals using <, >, or = 5.N.11 Understand that percent means part of 100, and write percents as fractions and decimals

*Number Theory*

5.N.12 Recognize that some numbers are only divisible by one and themselves (prime) and others have multiple divisors (composite)

5.N.13 Calculate multiples of a whole number and the least common multiple of two numbers

5.N.14 Identify the factors of a given number 5.N.15 Find the common factors and the greatest common factor of two numbers

*Operations*

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.

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.

5.N.18 Evaluate an arithmetic expression using order of operations including multiplication, division, addition, subtraction and parentheses 5.N.19 Simplify fractions to lowest terms 5.N.20 Convert improper fractions to mixed numbers, and mixed numbers to improper fractions 5.N.21 Use a variety of strategies to add and subtract fractions with like denominators 5.N.22 Add and subtract mixed numbers with like denominators 5.N.23 Use a variety of strategies to add, subtract, multiply, and divide decimals to thousandths

*Estimation*

5.N.24 Round numbers to the nearest hundredth and up to 10,000

5.N.25 Estimate sums and differences of fractions with like denominators .

5.N.26 Estimate sums, differences, products, and quotients of decimals 5.N.27 Justify the reasonableness of answers using estimation

*Variables and Expressions*

5.A.1 Define and use appropriate terminology when referring to constants, variables, and algebraic expressions

5.A.2 Translate simple verbal expressions into algebraic expressions

*Variables and Expressions*

5.A.3 Substitute assigned values into variable expressions and evaluate using order of operations

*Equations and Inequalities*

5.A.4 Solve simple one-step equations using basic whole-number facts

5.A.5 Solve and explain simple one-step equations using inverse operations involving whole numbers

5.A.6 Evaluate the perimeter formula for given input values

*Patterns, Functions, and Relations*

5.A.7 Create and explain patterns and algebraic relationships (e,g.,2,4,6,8...) algebraically: 2n (doubling)

5.A.8 Create algebraic or geometric patterns using concrete objects or visual drawings (e.g., rotate and shade geometric shapes)

*Shapes*

5.G.1 Calculate the perimeter of regular and irregular polygons

*Geometric Relationships*

5.G.2 Identify pairs of similar triangles

5.G.3 Identify the ratio of corresponding sides of similar triangles 5.G.4 Classify quadrilaterals by properties of their angles and sides 5.G.5 Know that the sum of the interior angles of a quadrilateral is 360 degrees 5.G.6 Classify triangles by properties of their angles and sides 5.G.7 Know that the sum of the interior angles of a triangle is 180 degrees 5.G.8 Find a missing angle when given two angles of a triangle 5.G.9 Identify pairs of congruent triangles 5.G.10 Identify corresponding parts of congruent triangles

*Transformational Geometry*

5.G.11 Identify and draw lines of symmetry of basic geometric shapes

*Coordinate Geometry*

5.G.12 Identify and plot points in the first quadrant

5.G.13 Plot points to form basic geometric shapes (identify and classify) 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)

*Units of Measurement*

5.M.1 Use a ruler to measure to the nearest inch, and inch

5.M.2 Identify customary equivalent units of length 5.M.3 Measure to the nearest centimeter 5.M.4 Identify equivalent metric units of length 5.M.5 Convert measurement within a given system

*Tools and Methods*

5.M.6 Determine the tool and technique to measure with an appropriate level of precision: lengths and angles

*Units*

5.M.7 Calculate elapsed time in hours and minutes

5.M.8 Measure and draw angles using a protractor

*Estimation*

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.)

5.M.10 Determine personal references for metric units of length

5.M.11 Justify the reasonableness of estimates

*Collection of Data*

5.S.1 Collect and record data from a variety of sources (e.g., newspapers, magazines, polls, charts, and surveys)

*Organization and Display of Data*

5.S.2 Display data in a line graph to show an increase or decrease over time

*Analysis of Data*

5.S.3 Calculate the mean for a given set of data and use to describe a set of data

*Predictions from Data*

5.S.4 Formulate conclusions and make predictions from graphs

*Probability*

5.S.5 List the possible outcomes for a single-event experiment

5.S.6 Record experiment results using fractions/ratios 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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Prekindergarten |
Kindergarten |
Grade 1 |
Grade 2 |
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Grade 3 |
Grade 4 |
Grade 6 |
Grade 7 | Grade 8 | ||

Integrated Algebra | Geometry | Algebra 2 and Trigonometry |

06/20/2006