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Mathematics Toolkit
Curriculum Guidance Materials & Resources
Template for Analysis of Mathematics Programs/Series
March 2005
| Grade 5 -
Performance Indicators Process Strands |
Does the program/series support the development of the process/content in the performance indicator? | Are additional resources needed? | At what grade level is the indicator addressed? | Is the concept newly introduced this year? |
| 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 problem | ||||
| 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 + ___) |
| Grade 5 - Performance Indicators Content Strands |
Does the program/series support the development of the process/content in the performance indicator? | Are additional resources needed? |
At what grade level is the indicator addressed? | Is the concept newly introduced this year? |
| 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 |
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| 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 | ||||
| 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 | ||||
| 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 | ||||
| 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 | ||||
| 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 | ||||
| 5.A.3 Substitute assigned values into variable expressions and evaluate using order of operations | ||||
| 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 | ||||
| 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) | ||||
| 5.G.1 Calculate the perimeter of regular and irregular polygons | ||||
| 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 | ||||
| 5.G.11 Identify and draw lines of symmetry of basic geometric shapes | ||||
| 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) | ||||
5.M.1 Use a ruler to measure to
the nearest inch,
 ,
and
 inch |
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| 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 | ||||
| 5.M.6 Determine the tool and technique to measure with an appropriate level of precision: lengths and angles | ||||
| 5.M.7 Calculate elapsed time in hours and minutes | ||||
| 5.M.8 Measure and draw angles using a protractor | ||||
| 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 | ||||
| 5.S.1 Collect and record data from a variety of sources (e.g., newspapers, magazines, polls, charts, and surveys) | ||||
| 5.S.2 Display data in a line graph to show an increase or decrease over time | ||||
| 5.S.3 Calculate the mean for a given set of data and use to describe a set of data | ||||
| 5.S.4 Formulate conclusions and make predictions from graphs | ||||
| 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) |