PROCESS STRANDS |
- Problem solving
- Reasoning and Proof
- Communication
- Connections
- Representation
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Problem solving |
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 solving 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 |
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Reasoning and Proof |
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 |
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Communication |
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, drawings, 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 Listen for understanding of 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 |
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Connections |
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 |
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Representation |
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) |
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CONTENT STRANDS |
Number Sense and Operations Strand |
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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4.N.1 - Skip count by 1,000’s
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4.N.2 - Read and write whole numbers to 10,000
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4.N.3 - Compare and order numbers to 10,000
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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
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4.N.6 - Understand, use, and explain the associative property of multiplication
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4.N.7 - Develop an understanding of fractions as locations on number lines and as divisions of whole numbers
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4.N.8 - Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and tenths) using manipulatives, visual models, and illustrations
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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)
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4.N.10 - Develop an understanding of decimals as part of a whole
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4.N.11 - Read and write decimals to hundredths, using money as a context
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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
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Number Theory
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4.N.13 - Develop an understanding of the properties of odd/even numbers as a result of multiplication
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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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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
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4.N.16 - Understand various meanings of multiplication and division
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4.N.17 - Use multiplication and division as inverse operations to solve problems
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4.N.18 - Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with and without regrouping)
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4.N.19 - Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with and without regrouping)
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4.N.20 - Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000
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4.N.21 - Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and without remainders)
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4.N.22 - Interpret the meaning of remainders
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4.N.23 - Add and subtract proper fractions with common denominators
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4.N.24 - Express decimals as an equivalent form of fractions to tenths and hundredths
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4.N.25 - Add and subtract decimals to tenths and hundredths using a hundreds chart
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Students will compute accurately and make reasonable estimates.
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Estimation
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4.N.26 - Round numbers less than 1,000 to the nearest tens and hundreds
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4.N.27 - Check reasonableness of an answer by using estimation
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Algebra Strand |
Students will represent and analyze algebraically a wide variety of problem solving situations.
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Variables and Expressions
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4.A.1 - Evaluate and express relationships using open sentences with one operation
Number Sentences
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Students will perform algebraic procedures accurately.
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Equations and Inequalities
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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)
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4.A.3 - Find the value or values that will make an open sentence true, if it contains < or >
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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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4.A.4 - Describe, extend, and make generalizations about numeric (+, -, x, ÷) 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
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Geometry Strand |
Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Shapes
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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)
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4.G.2 - Identify points and line segments when drawing a plane figure
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4.G.3 - Find perimeter of polygons by adding sides
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4.G.4 - Find the area of a rectangle by counting the number of squares needed to cover the rectangle
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4.G.5 - Define and identify vertices, faces, and edges of three-dimensional shapes
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Students will identify and justify geometric relationships, formally and informally.
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Geometric Relationships
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4.G.6 - Draw and identify intersecting, perpendicular, and parallel lines
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4.G.7 - Identify points and rays when drawing angles
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4.G.8 - Classify angles as acute, obtuse, right, and straight
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Measurement Strand |
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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4.M.1 - Select tools and units (customary and metric) appropriate for the length measured
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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)
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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)
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4.M.5 - Measure mass, using grams
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4.M.6 - Select tools and units appropriate to the capacity being measured (milliliters and liters)
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4.M.7 - Measure capacity, using milliliters and liters
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Students will use units to give meaning to measurements.
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Units
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4.M.8 - Make change, using combined coins and dollar amounts
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4.M.9 - Calculate elapsed time in hours and half hours, not crossing A.M./P.M.
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4.M.10 - Calculate elapsed time in days and weeks, using a calendar
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Statistics and Probability Strand |
Students will collect, organize, display, and analyze data.
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Collection of Data
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4.S.1 - Design investigations to address a question from given data
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4.S.2 - Collect data using observations, surveys, and experiments and record appropriately
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Organization and Display of Data
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4.S.3 - Represent data using tables, bar graphs, and pictographs
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Analysis of Data
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4.S.4 - Read and interpret line graphs
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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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4.S.5 - Develop and make predictions that are based on data
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4.S.6 - Formulate conclusions and make predictions from graphs
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