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Mathematics Toolkit
Curriculum Guidance Materials & Resources
Template for Analysis of Mathematics Programs/Series
March 2005
| Grade 4 - 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? |
| 4.PS.1 Explore, examine, and make observations about a social problem or mathematical situation | ||||
| 4.PS.2 Understand that some ways of representing a problem are more helpful than others | ||||
| 4.PS.3 Interpret information correctly, identify the problem, and generate possible solutions | ||||
| 4.PS.4 Act out or model with manipulatives activities involving mathematical content from literature | ||||
| 4.PS.5 Formulate problems and solutions from everyday situations | ||||
| 4.PS.6 Translate from a picture/diagram to a numeric expression | ||||
| 4.PS.7 Represent problem situations in oral, written, concrete, pictorial, and graphical forms | ||||
| 4.PS.8 Select an appropriate representation of a problem | ||||
| 4.PS.9 Use trial and error to solve problems | ||||
| 4.PS.10 Use process of elimination to solve problems | ||||
| 4.PS.11 Make pictures/diagrams of problems | ||||
| 4.PS.12 Use physical objects to model problems | ||||
| 4.PS.13 Work in collaboration with others to solve problems | ||||
| 4.PS.14 Make organized lists to solve numerical problems | ||||
| 4.PS.15 Make charts to solve numerical problems | ||||
| 4.PS.16 Analyze problems by identifying relationships | ||||
| 4.PS.17 Analyze problems by identifying relevant versus irrelevant information | ||||
| 4.PS.18 Analyze problems by observing patterns | ||||
| 4.PS.19 State a problem in their own words | ||||
| 4.PS.20 Determine what information is needed to solve a problem | ||||
| 4.PS.21 Discuss with peers to understand a problem situation | ||||
| 4.PS.22 Discuss the efficiency of different representations of a problem | ||||
| 4.PS.23 Verify results of a problem | ||||
| 4.PS.24 Recognize invalid approaches | ||||
| 4.PS.25 Determine whether a solution is reasonable in the context of the original problem | ||||
| 4.RP.1 Use representations to support mathematical ideas | ||||
| 4.RP.2 Determine whether a mathematical statement is true or false and explain why | ||||
| 4.RP.3 Investigate the use of knowledgeable guessing by generalizing mathematical ideas | ||||
| 4.RP.4 Make conjectures from a variety of representations | ||||
| 4.RP.5 Justify general claims or conjectures, using manipulatives, models, and expressions | ||||
| 4.RP.6 Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms | ||||
| 4.RP.7 Discuss, listen, and make comments that support or reject claims made by other students | ||||
| 4.RP.8 Support an argument by trying many cases | ||||
| 4.RP.9 Disprove an argument by finding counterexamples | ||||
| 4.CM.1 Understand and explain how to organize their thought process | ||||
| 4.CM.2 Verbally explain their rationale for strategy selection | ||||
| 4.CM.3 Provide reasoning both in written and verbal form | ||||
| 4.CM.4 Organize and accurately label work | ||||
| 4.CM.5 Share organized mathematical ideas through the manipulation of objects, drawing, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form | ||||
| 4.CM.6 Answer clarifying questions from others | ||||
| 4.CM.7 Restate mathematical solutions shared by other students | ||||
| 4.CM.8 Consider strategies used and solutions found in relation to their own work | ||||
| 4.CM.9 Increase their use of mathematical vocabulary and language when communicating with others | ||||
| 4.CM.10 Describe objects, relationships, solutions, and rationale using appropriate vocabulary | ||||
| 4.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning | ||||
| 4.CN.1 Recognize, understand, and make connections in their everyday experiences to mathematical ideas | ||||
| 4.CN.2 Compare and contrast mathematical ideas | ||||
| 4.CN.3 Connect and apply mathematical information to solve problems | ||||
| 4.CN.4 Understand multiple representations and how they are related | ||||
| 4.CN.5 Model situations with objects and representations and be able to make observations | ||||
| 4.CN.6 Recognize the presence of mathematics in their daily lives | ||||
| 4.CN.7 Apply mathematics to solve problems that develop outside of mathematics | ||||
| 4.CN.8 Recognize and apply mathematics to other disciplines | ||||
| 4.R.1 Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations | ||||
| 4.R.2 Share mental images of mathematical ideas and understandings | ||||
| 4.R.3 Recognize and use external mathematical representations | ||||
| 4.R.4 Use standard and nonstandard representations with accuracy and detail | ||||
| 4.R.5 Understand similarities and differences in representations | ||||
| 4.R.6 Connect mathematical representations with problem solving | ||||
| 4.R.7 Construct effective representations to solve problems | ||||
| 4.R.8 Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree) | ||||
| 4.R.9 Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip) | ||||
| 4.R.10 Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems) |
| Grade 4 - 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? |
| 4.N.1 Skip count by 1,000’s | ||||
| 4.N.2 Read and write whole numbers to 10,000 | ||||
| 4.N.3 Compare and order numbers to 10,000 | ||||
| 4.N.4 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 |
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| 4.N.5 Recognize equivalent representations for numbers up to four digits and generate them by decomposing and composing numbers | ||||
| 4.N.6 Understand, use, and explain the associative property of multiplication | ||||
| 4.N.7 Develop an understanding of fractions as locations on number lines and as divisions of whole numbers | ||||
| 4.N.8 Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and tenths) using manipulatives, visual models, and illustrations | ||||
| 4.N.9 Use concrete materials and visual models to compare and order unit fractions or fractions with the same denominator (with and without the use of a number line) | ||||
| 4.N.10 Develop an understanding of decimals as part of a whole | ||||
| 4.N.11 Read and write decimals to hundredths, using money as a context | ||||
| 4.N.12 Use concrete materials and visual models to compare and order decimals (less than 1) to the hundredths place in the context of money | ||||
| 4.N.13 Develop an understanding of the properties of odd/even numbers as a result of multiplication | ||||
| 4.N.14 Use a variety of
strategies to add and subtract numbers up to 10,000 |
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| 4.N.15 Select appropriate computational and operational methods to solve problems | ||||
| 4.N.16 Understand various meanings of multiplication and division | ||||
| 4.N.17 Use multiplication and division as inverse operations to solve problems | ||||
| 4.N.18 Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with and without regrouping) | ||||
| 4.N.19 Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with and without regrouping) | ||||
| 4.N.20 Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000 | ||||
| 4.N.21 Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and without remainders) | ||||
| 4.N.22 Interpret the meaning of remainders | ||||
| 4.N.23 Add and subtract proper fractions with common denominators | ||||
| 4.N.24 Express decimals as an equivalent form of fractions to tenths and hundredths | ||||
| 4.N.25 Add and subtract decimals to tenths and hundredths using a hundreds chart | ||||
| 4.N.26 Round numbers less than 1,000 to the nearest tens and hundreds | ||||
| 4.N.27 Check reasonableness of an answer by using estimation | ||||
| 4.A.1 Evaluate and express relationships using open sentences with one operation | ||||
| 4.A.2 Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare whole numbers and unit fractions and decimals (up to hundredths) | ||||
| 4.A.3 Find the value or values that will make an open sentence true, if it contains < or > | ||||
4.A.4 Describe, extend, and make
generalizations about numeric ( ) and geometric patterns |
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| 4.A.5 Analyze a pattern or a whole-number function and state the rule, given a table or an input/output box | ||||
| 4.G.1 Identify and name polygons, recognizing that their names are related to the number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon) | ||||
| 4.G.2 Identify points and line segments when drawing a plane figure | ||||
| 4.G.3 Find perimeter of polygons by adding sides | ||||
| 4.G.4 Find the area of a rectangle by counting the number of squares needed to cover the rectangle | ||||
| 4.G.5 Define and identify vertices, faces, and edges of three-dimensional shapes | ||||
| 4.G.6 Draw and identify intersecting, perpendicular, and parallel lines | ||||
| 4.G.7 Identify points and rays when drawing angles | ||||
| 4.G.8 Classify angles as acute, obtuse, right, and straight | ||||
| 4.M.1 Select tools and units (customary and metric) appropriate for the length being measured | ||||
| 4.M.2 Use a ruler to measure to the nearest standard unit (whole, ½ and ¼ inches, whole feet, whole yards, whole centimeters, and whole meters) | ||||
| 4.M.3 Know and understand
equivalent standard units of length: 12 inches = 1 foot 3 feet = 1 yard |
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| 4.M.4 Select tools and units appropriate to the mass of the object being measured (grams and kilograms) | ||||
| 4.M.5 Measure mass, using grams | ||||
| 4.M.6 Select tools and units appropriate to the capacity being measured (milliliters and liters) | ||||
| 4.M.7 Measure capacity, using milliliters and liters | ||||
| 4.M.8 Make change, using combined coins and dollar amounts | ||||
| 4.M.9 Calculate elapsed time in hours and half hours, not crossing A.M./P.M. | ||||
| 4.M.10 Calculate elapsed time in days and weeks, using a calendar | ||||
| 4.S.1 Design investigations to address a question from given data | ||||
| 4.S.2 Collect data using observations, surveys, and experiments and record appropriately | ||||
| 4.S.3 Represent data using tables, bar graphs, and pictographs | ||||
| 4.S.4 Read and interpret line graphs | ||||
| 4.S.5 Develop and make predictions that are based on data | ||||
| 4.S.6 Formulate conclusions and make predictions from graphs |