Content Standards
 Performance Indicators
 Instructional Practice
 Assessment Tools
 Reporting Tools

A. NUMBER: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems. (Correlates with EDM Strand 1: Number and Numeration, 1 NN) (Taught in EDM in units 1, 2, 5, & 9) (Practiced in units 4, 6, 8, 10, & 11) 
WHOLE NUMBER 




A.1. Students understand and use number notation and place value to 10,000 in numerals.
 a. Read and write numbers up to 10,000 in numerals and words.
(Correlates with EDM Strand 1 NN, Goal, Read and write whole numbers up to 1,000,000)
 Practice reading, writing and sequencing whole numbers through millions. Design and complete grid puzzles. Use base ten blocks to represent 2 and 3digit numbers and numbers that are 10 or 100 more or less than those numbers. Write or use equivalent names for numbers in NameCollection Boxes and playingName That Number. Compare numbers playing Number TopItthrough millions. Read, write, and compare large numbers using U.S. Census data. Estimate then count total value of class set of base10 blocks. Use a placevalue flip book to display a given number.   classroom tests
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 b. Recognize the place values of digits in numbers up to 10,000.
(Correlates with EDM Strand 1 NN, Goal 1, Identify places in such numbers and the values of the digits in those places)
 Practice reading, writing and sequencing whole numbers through millions. Identify place values of any given number from the hundredths place through the millionths place. Use base ten blocks to represent 2 and 3digit numbers and numbers that are 10 or 100 more or less than those numbers. Write or use equivalent names for numbers in NameCollection Boxes and playingName That Number. Compare numbers playing Number TopItthrough millions. Use a placevalue flip book to display a given number.   classroom tests
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 c. Compare and order numbers up to four digits.
(Correlates with EDM Strand 1 NN, Goal 6, Compare and order whole numbers up to 1,000,000; use manipulatives to order decimals through hundredths; use area models and benchmark fractions to compare and order fractions. )
 Use base ten blocks to represent 2 and 3digit numbers and numbers that are 10 or 100 more or less than those numbers. Write or use equivalent names for numbers in NameCollection Boxes and playingName That Number. Compare numbers read and/or written through millions. Compare numbers playing Number TopItthrough millions. Read, write, and compare large numbers using U.S. Census data. Estimate then count total value of class set of base10 blocks. Use a placevalue flip book to compare numbers through millions.   classroom tests
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A.2. Students understand and use procedures to add and subtract whole numbers with up to four digits.
(Correlates with EDM Strand 2: Operations and Computation, 2 OC)
(Taught in EDM in units 1, 2, 5, 9, 10, 11)
(Practiced in EDM in units 1 through 11)
 a. Display an understanding of the base ten place value system.
(Correlates with EDM Strand 1 NN, Goal 1(see A.1.a.); Goal 3: Find multiples of 2, 5, & 10; Goal 4: Use numerical expressions involving one or more of the basic four arithmetic operations to give equivalent names for whole numbers;, & 6(see A.1.c), as well as EDM Strand 2 OC, Goal 1: Demonstrate automaticity with all addition facts and subtraction facts through 10 + 10; use basic facts to compute fact extensions such as 80 + 70) )
 Practice addition facts through games: Less Than You , Addition TopIt , Beat the Calculator, TicTacToe Addition. Find differences between pairs of 2digit numbers using a number grid. Complete fact families and number families; understand the use of fact extensions. Solve problems involving multiples of 10 and fact extensions. Use calculators to find differences between number & multiple of ten. Solve number stories using tradefirst algorithm with 2 and 3 digit numbers. Practice adding three or four numbers in a convenient order using the commutative property. Practice multidigit addition and subtraction Practice basic facts through games "Name That Number", Addition TopIt, Subtraction TopIt, Beat the Calculator, Roll to 100. Take facts quiz (addition, subtraction). Estimate solutions for addition and subtraction problems.   classroom tests
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 b. Use an operation appropriate to a given situation.
(Correlates with EDM Strand 2 OC, Goal 2: Use manipulatives, mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the addition and subtraction of whole numbers and decimals in a money context; describe the strategies used and explain how they work; also Strand 2 OC, Goal 5: Make reasonable estimates for whole number addition and subtraction problems; explain how the estimates were obtained; as well as Goal 6: Recognize and describe change, comparison, and partandtotal situations)  Estimate solutions for addition and subtraction problems. Use diagrams (part/total, difference, and change) to help solve number stories Make and solve number stories using a variety of strategies. Solve open response problems showing strategies and explaining thinking. Solve frames and arrows puzzles by determining the correct operation needed for solution.
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A.3. Students understand and apply meanings of multiplication and division.
(Correlates with EDM Strand 2 OC)
 a. Multiply singledigit numbers and divide using singledigit divisors and up to twodigit dividends (division facts only, but remainders may be present).
(Correlates with EDM Strand 2 OC, Goal 3: Demonstrate automaticity with x0, x1, x2, x5, & x10 multiplication facts; use strategies to compute remaining facts up to 10 x 10; as well as Goal 4, Use arrays, mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the multiplication of 2and 3digit whole numbers by 1digit whole numbers; describe the strategies used.)  Practice multiplication & division facts through fact triangles and a variety of games. Review fact families and number families using fact tables and fact triangles. Review the inverse relationship between a number and a multiple of ten. Solve problems involving multiples of 10 and fact extensions. Review multiplication fact shortcuts. Find products and quotients involving multiples of 10, 100, and 1,000. Develop mental math strategies for multiplying 1digit numbers by multidigit numbers. Take facts quiz (multiplication and division facts)
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 b. Use an operation appropriate to a given situation.
(Correlates with EDM Strand 2 OC, Goal 6: Recognize and describe change, comparison, and partsandtotals situations; use repeated addition, arrays, and skip counting to model multiplication; use equal sharing and equal grouping to model division; also see Goal 4, A.3.a.)  Estimate solutions for multiplication and division problems. Make and solve number stories with 2 and 3 digit numbers using diagrams (part/whole, difference, and/or change); multiplication algorithms (partial products or lattice), or any other successful strategy. Solve open response problems showing strategies and explaining thinking. Solve frames and arrows puzzles by determining the correct operation needed for solution.   classroom tests
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 c. Recognize and use models for multiplication and division situations.
(Correlates with EDM Strand 2 OC, See Goal 6, A. 3. b.; also see Goal 4, A.3.a.)
 Review fact families and number families using fact tables and fact triangles. Understand how to use the concept of fact families to derive extended facts from known facts. Understand arrays as a physical model for division and multiplication, and the relationship between these two operations through this model Solve number stories using multiplication algorithms (partial products or lattice) with 2 and 3 digit numbers or any successful strategy. Develop mental math strategies for multiplying 1digit numbers by multidigit numbers.   classroom tests
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 d. Use multiple strategies for multiplication and division.
(Correlates with EDM Strand 2 OC, See Goal 6, A. 3. b.; also see Goal 4, A.3.a.)
 Review fact families and number families using fact tables and fact triangles. Complete fact families and number families. Solve problems involving multiples of 10 and fact extensions. Use arrays as a physical model for division and multiplication, and the relationship between these two operations through this model. Use fair share or forming equal groupings to model division. Understand that skip counting and repeated addition are basic strategies for multiplication. Understand that repeated subtraction is a basic model for division. Solve number stories using multiplication algorithms (partial products or lattice) with 2 and 3 digit numbers or any successful strategy. Use calculators to find products and quotients. Review multiplication fact shortcuts. Practice and extend multiplication and division facts. Find products and quotients involving multiples of 10, 100, and 1,000. Develop mental math strategies for multiplying 1digit numbers by multidigit numbers.   classroom tests
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RATIONAL NUMBER





A.4. Students recognize name, compare, illustrate and use simple fractions.
(Correlates with EDM Strand 1: EDM Numbers and Numeration)
 a. Recognize, name, and illustrate fractions with denominators from two to ten.
(Correlates with EDM Strand 1 NN, Goal 2, Read, write, and model fractions)
 Name fractional parts of regions and sets of objects. Rename pattern blocks as fractional parts of one another. Explore fractions in everyday life through a class Fractions Museum. Make a numberline poster ordering fractions Find and name equivalent fractions using Fraction Cards. Identify equivalent fractions on the Fraction NumberLine poster and through playingEquivalent Fraction Game. Name and compare fractions to 1/2, 0, and 1 using Fraction Cards. Name and compare fractions playingFraction TopIt.   classroom tests
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 b. Recognize, name, and illustrate parts of a whole.
(Correlates with EDM Strand 1 NN, Goal 2, Read, write, and model fractions)
 Understand the concept of a whole as "one" and compare to fractions of the whole. Name fractional parts of regions and sets of object. Rename pattern blocks as fractional parts of one another. Use measuring tools to describe relationships among different forms of measures in fractional terms. Make a numberline poster ordering fractions. Find equivalent fractions using Fraction Cards.   classroom tests
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 c. Compare and order fractions with like numerators or with like denominators.
(Correlates with EDM Strand 1 NN, Goal 5, Use manipulatives and drawings to find and represent equivalent names for fractions; use manipulatives to generate equivalent fractions)
 Rename pattern blocks as fractional parts of one another. Explore fractions in everyday life through a class Fractions Museum. Make a numberline poster ordering fractions. Sort Fraction Cards by fractions with common denominators, common numerators, and equivalent shaded areas. Find equivalent fractions using Fraction Cards Identify equivalent fractions on the Fraction NumberLine poster and through playingEquivalent Fraction Game. Comparing fractions to 1/2, 0, and 1 using Fraction Cards. Comparing fractions playing Fraction TopIt.   classroom tests
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REAL NUMBERS





No performance indicator. Although no performance indicators are stated, students are expected to have instructional experiences in which they use only rational numbers. 




B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:
 understand that most measurements are approximations and that taking repeated measurements reveals this variability;
 understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
 understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.
(Correlates with EDM Strand 3: Data and Chance, DC, as well as EDM Strand 4: Measurement and Reference Frames, MRF ) 
MEASUREMENT AND APPROXIMATION





B.1. Students understand and use measurement of time and temperature.
(Correlates with EDM Strand 4 MRF, Goal 4, Tell and show time to the nearest minute on an analog clock; tell and write in digital notation, as well as Goal 3, Describe relationship between minutes in an hour, hours in a day, days in a week)
*(Note that reading temperature on both the Fahrenheit and Celsius scales is a EDM Strand 4 MRF, Goal 5 for second grade, and while not taught, it continues to be practiced in third grade.)  a. Select appropriate tools and units for these measures.
 Review telling time, and reading thermometers (in Fahrenheit and Celsius). Explore the need for standard units of measure and estimate measurements. Make and record body measurements. Select appropriate units to measure a variety of items. Understand the relationships between minutes in an hour, hours in a day, days in a week
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 b. Solve and justify problems with these measures.
 Calculate length of daylight (elapsed time) through the "Sunrise Sunset Project". Practice telling and calculating elapsed time. Determine temperature differences in the "High Low Temperature Project". Solve elapsed time number stories. Determine total age in minutes for last birthday, excluding and including leap years. Use the "National High Low Temperatures" project, collect and analyze actual high and low temperatures in the U.S. and display temperature differences with a line graph.   classroom tests
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DATA ANALYSIS





B.2. Students read, construct and interpret bar graphs.
(Correlates with EDM Strand 3 DC, Goal 1: Collect and organize data or use given data to create charts, tables, bar graphs, and line plots, as well as Goal 2: Use graphs to ask and answer simple questions and draw conclusions; find the maximum, minimum, range, mode, and median of a data set)
(Taught in units 1, 5, 10, & 11)
(Practiced in units 2, 3, 4, 6, 8 & 9)

 Use the "Letters in Name" project, make predictions, interview partners, collect data, organize data using tally marks, display data with bar graph, analyze data to find maximum, minimum, range, and mode. Use the "National High Low Temperatures" project, collect and analyze actual high and low temperatures in the U.S. and display temperature differences with a line graph. Use "SunriseSunset" project to collect, read, interpret, and solve problems based on a bar chart and a line graph. Make or read given bar graphs and frequency table, finding maximum, minimum, mean, median, mode, range, and compare mean and median. Organize and display data to make it easier to interpret. Students are encouraged throughout the program to communicate their thinking to others and express their understanding of various concepts and relationships both orally and through visual and written recordings, including simple tables & graphs. Organize and display data to make it easier to interpret. Discuss median using Animal Clutches Poster Find and show average "class shoe" length on graph. Analyze survey data and make predictions based on data and graph. Read, interpret, and solve problems based on bar graphs and line graphs.   classroom tests
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PROBABILITY



 
No performance indicator. Although no performance indicators are stated, students are expected to have experiences with probability in grade three, but it is not expected that the knowledge will be secure.
(Correlates with EDM Strand 3: Data and Chance, Goals 3: Describe events using "certain", "very likely", "likely", "unlikely", "very unlikely", "impossible", and other basic probability terms; explain the choice of language, as well as Goal 4: Predict the outcomes of simple experiments and test the predictions using manipulatives: express the probability of an event by using "__out of ____" language)





C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct twodimensional and threedimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results. (Correlates with EDM Strand 5: Geometry, G) 
GEOMETRIC FIGURES





C.1. Students identify, describe, and classify familiar twodimensional shapes.
(Correlates with EDM Strand 5: Geometry, G)
(Taught in units 3, 6, 10)
(Practiced in units 5, 7, 8, & 9)
 a. Describe and classify twodimensional shapes according to the number of vertices and by number, length and shape of sides.
(Correlates with EDM Strand G, Goal 2: Identify, describe, model, and compare plane and solid figures including circles, polygons, spheres, cylinders, rectangular prisms, pyramids, cones, and cubes using appropriate geometric terms including the terms "face", "edge", "vertex", and "base", as well as Goal 1: Identify and draw points, intersecting and parallel line segments and lines, rays, and right angles)
 Model polygons with straws and twist ties. Make all possible triangles out of three sizes of straws. Introduce center, circumference, and diameter of circles and circular objects. Draw figures with given perimeters. Review line segments and introduce rays and lines Model parallel and intersecting pairs of lines, rays, and segments. Review properties of triangles and other polygons, sort by their characteristic properties. Count and record the number of small equilateral triangles inside larger equilateral triangles   classroom tests
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 b. Know how to put shapes together and take them apart to form other shapes.
(Correlates with EDM Strand 5, G. See Goal 1 & 2, C. 1. a.)  Construct quadrangles and observe their properties. Identify the meaning and properties of symmetry and identify lines of symmetry. Construct all patternblock shapes with one trapezoid and two triangles. Explore similar polygons by trying to build them with pattern blocks Explore spatial relationships by reassembling two same size squares and converting into a single square.   classroom tests
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 c. Identify edges, vertices, and right angles in twodimensional shapes.
(Correlates with EDM Strand 5, G. See Goal 1 & 2, C. 1. a.)
 Play Angle Race to practice making angles of specified measure. Make all possible triangles out of three sizes of straws. Introduce center, circumference, and diameter of circles and circular objects. Draw figures with given perimeters. Review line segments and introduce rays and lines. Model parallel and intersecting pairs of lines, rays, and segments, review properties of twodimensional shapes. Count and record the number of small equilateral triangles inside larger equilateral triangles   classroom tests
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 d. Tell whether a given angle is greater or smaller than a right angle.
(Correlates with EDM Strand 5, G. See Goal 1 & 2, C. 1. a.)
 Make various sized angles with straws and connectors. Locate angles in the classroom that are greater than, less than, or equal to 90^{o}. Classify triangles by angle and side measures. Classify quadrangles by angle and side measures. Review line segments and introduce rays and lines as elements of angles. Model parallel and intersecting pairs of lines, rays, and segments. Review properties of triangles. Introduce congruence of angle.   classroom tests
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GEOMETRIC MEASUREMENT





C.2. Students understand how to find the distance around a figure.
(Correlates with EDM Strand 4: Measurement and Reference Frames, MRF )
(Taught in units 3, 6, & 9)
(Practiced in units 2, 4, 5, 10, & 11)  a. Calculate and measure the distance around a figure whose perimeter is comprised of straight edges.
(Correlates with EDM Strand MRF , Goal Describe and use strategies to measure the perimeter of polygons; count unit squares to find the areas of rectangles)
 Measure sides and find perimeters of straw polygons. Find perimeters of triangles. Determine the perimeter of various polygons. Compare the perimeters and areas of four different shaped polygons. Solve measurement stories where perimeter and area measures are calculated and applied to the solution.
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TRANSFORMATIONS





C.3. No performance indicator. Although no performance indicators are stated, students are expected to have experiences with symmetry, transformations, and congruency in grade three, but it is not expected that the knowledge will be secure. 




D. ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations. (Correlates with EDM Strand 6: Patterns, Functions, and Algebra, PFA) 
SYMBOLS AND EXPRESSIONS





D.1. Students use equivalent expressions to aid computation such as knowing that 43 + 56 is the same as 40 + 3 + 50 + 6.
(Correlates with EDM Strand 6: PFA, Goal 1: Extend, describe, and create numeric patterns; describe rules for patterns and use them to solve problems; use words and symbols to describe and write rules for functions involving addition, subtraction, and multiplication and use those rules to solve problems) 
 Use base ten blocks to represent 2 and 3digit numbers and numbers that are 10 or 100 more or less than those numbers. Write or use equivalent names for numbers in NameCollection Boxes and playingName That Number. Determine the steps to skip count up and back on the calculator. Write numbers using expanded notation. Determine the composition of numbers by place value when determining partial sums or partial products for those algorithms.   classroom tests
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EQUATIONS AND INEQUALITIES



 
D.2. Students find the unknown in simple equations (or open sentences) in the context of numbers and operations as described in Standard 2.1: Number* for this grade level such as:
3 + 5 = [ ] + 3
3 + 9 = [ ] + 10
[ ] + ( ) = 10
(Correlates with EDM Strand 6: PFA, Goal 2: Read, write, and explain number sentences using the symbols +, , x, /, =, >, & <: solve number sentences; writes expressions and number sentences to model number stories, and also, Goal 3: Recognize that numeric expressions can have different values depending on the order in which operations are carried out; understand that grouping symbols can be used to affect the order in which operation are carried out, as well as Goal 4: Describe and apply the Commutative and Associative Property Addition and the Commutative and Associative Property of Multiplication, and the Multiplication Identity) 
 Solve "What's My Rule?" and FramesandArrows problems using addition, subtraction, multiplication and division. Solve FramesandArrows problems involving fractions. Give the missing number in open sentences given for mental math problems. Determine the missing operation symbol in between two sets of equations that may be equal to, greaten than, or less than each other. Use parentheses to write balanced equations. Read and understand number sentences using parentheses to determine the order of operation.
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FUNCTIONS AND RELATIONS


 

D.3. Students understand arithmetic relationships among positive whole numbers.
(Correlates with EDM Strand 6: PFA, Goal 2, Goal 3, & Goal 4, see D.2.)
(Taught in units 2, 4, & 7)
( Practiced in units 1, 3, 5, 6, 7, 8, & 9)
 a. Use the inverse relationships between addition and subtraction and between multiplication and division and the commutative laws of multiplication and addition to solve problems.
 Use patterns to solve number grid puzzles Solve problems involving a variety of number patterns Complete "What's My Rule?" tables with missing information Solve "What's My Rule?" and FramesandArrows problems. Look for patterns on Multiplication/Division Facts table. Understand the relationships between addition and subtraction on fact triangles and the concepts of fact families and fact extensions. Understand the relationships between multiplication and division on fact triangles and the concepts of fact families and fact extensions. Look for patterns in square numbers using arrays.   classroom tests
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 b. Be able to show that for whole numbers subtraction and division are not commutative and show that multiplication and addition are commutative.
 Explore the results of reversing numbers in addition, subtraction, multiplication, and division with physical models to prove that addition and multiplication are commutative while subtraction and division are not.
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D.4. Students create, describe, explain and extend patterns with numbers and geometric objects.
(Correlates with EDM Strand 6: PFA, Goal 1, see D.1.)

 Use patterns to solve number grid puzzles. Solve problems involving a variety of number patterns. Complete "What's My Rule?" tables with missing information. Solve "What's My Rule?" and FramesandArrows problems. Look for patterns on Multiplication/Division Facts table. Fill in missing numbers on a number line. Look for patterns on a 100number grid. Look for patterns in square numbers using arrays. Use patterns in the attributes of geometric shapes to classify twodimensional and threedimensional shapes. Use LengthofDay data too investigate the relationship between hours of sunlight and seasons of the year.
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