• Classify objects by attributes using at least two categories at a time ( e.g., color, shape, size) MST3.E.MR1A.01.01;  MST3.E.MR1A.02.01
• Draw pictures to represent problems MST3.E.MR1A.01.02;  MST3.E.MR1A.02.02
• Use manipulatives to represent problems MST3.E.MR1A.01.03;  MST3.E.MR1A.02.03

     Analyze Mathematical Situations Using Patterns and Relationships

• Recognize patterns for sums & differences using concrete materials, tables, calculators, and number lines MST3.E.MR1B.01.01; MST3.E.MR1B.02.01
• Recognize patterns of numbers that add up to a specific sum (e.g., all combinations of numbers that add up to 6) MST3.E.MR1B.01.02; MST3.E.MR1B.02.02
• Use patterns & relationships to understand commutative and associative properties & identity elements MST3.E.MR1B.01.03;  MST3.E.MR1B.02.03

     Justify Answers and Solution Processes

• Explain to others how he/she went about solving a numerical problem MST3.E.MR1C.01.02
• Use concrete materials to justify solutions MST3.E.MR1C.01.03
• Use patterns and relationships to justify solutions MST3.E.MR1C.01.04
• Use a variety of topics in problem solving MST3.E.MR1C.01.05

     Reach Simple Conclusions Using Logical Reasoning

• Represent and solve problems in a variety of ways (e.g., concrete objects, pictorial representations, tables, and number lines) MST3.E.MR1D.01.01
• Know that different strategies are appropriate for solving different problems  MST3.E.MR1D.01.02

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• Understand cardinal numbers (e.g., arrangement of objects in a set is irrelevant) MST3.E.NN2A.01.01
• Know the names for numbers through 100 MST3.E.NN2A.01.02
• Understand ordinal numbers first to thirty-first and beyond
• Use tallies to count MST3.E.NN2A.01.04
• Count forward and backward MST3.E.NN2D.01.02
• Count forward by 1's, 2's, 3's, 4's, 5's 10's and backward by 1's, 2's, 5's, and 10's in various ways (e.g., calculator) MST3.E.NN2B.01.01
• Use words that describe order (e.g., first, last, before, after, between, middle) MST3.E.NN2D.01.03
• Order small sets of numbers MST3.E.NN2D.01.04
• Understand the relationship of many to one in preparation for the concept of ratio MST3.E.NN2E.01.01
• Represent 2 and 3 digit numbers up to 99 using concrete models (e.g., bundles of ten sticks) MST3.E.NN2B.01.02
• Understand the concept of even and odd numbers MST3.E.NN2B.01.03

     Fractions

• Understand that halves (thirds, etc.) of a whole are equal to each other MST3.E.NN2B.01.04
• Understand the relationship of fractional parts (1/2, 1/3, 1/4, 1/5, 1/8, 1/10) to a whole and a set MST3.E.NN2B.01.05
• Understand that a set of objects can be divided into equal parts MST3.E.NN2B.01.06
• Understand the need to use numbers between whole numbers MST3.E.NN2D.01.01

     Place Value

• Use metric measures and money problems to reinforce place value MST3.E.NN2C.01.01
• Understand money notation to ten dollars MST3.E.NN2C.01.02
• Understand regrouping of ones and tens
• Understand the meaning of zero in the place value system MST3.E.NN2C.01.03
• Understand the place value of 2 and 3 digit numbers MST3.E.NN2C.01.04
• Understand expanded notation for 2 and 3 digit numbers (e.g., 27-2 tens +7 ones =20+7 MST3.E.NN2C.01.05

     Ratio and Percent

• Understand the relationship of many to one in preparation for the concept of ratio MST3.E.NN2E.01.01

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• Understand the inverse relationship between addition and subtraction (using manipulatives) MST3.E.OP3A.01.01
• Add 2 and 3 digit numbers with no regrouping MST3.E.OP3A.01.02
• Subtract 2 and 3 digit numbers with no regrouping MST3.E.OP3A.01.03
• Add up to 2 digit numbers with regrouping
• Subtract up to 2 digit numbers with regrouping
• Combine sets to produce a new set MST3.E.OP3A.01.04
• Use addition strategies ( doubles doubles-plus-one, number families) MST3.E.OP3A.01.05

     Number Facts

• Know basic addition facts (master 0-18) MST3.E.OP3C.01.05
• Know basic subtraction facts (master 0-9)  MST3.E.OP3C.01.05
• Understand the basic concept of division as a process of sharing MST3.E.OP3C.01.02
• Understand the concept of multiplication using a variety of strategies (e.g., rectangular arrays, repeated addition, skip counting)
• Use manipulatives to relate division to repeated subtraction MST3.E.OP3C.01.03
• Understand the properties of zero MST3.E.OP3C.01.04

     Problem Solving

• Solve real-world problems involving addition and subtraction of whole numbers  MST3.E.OP3B.01.01
• Use division for finding the number of equivalent subsets in a given set MST3.E.OP3B.01.02
• Use multiplication to determine how many are needed of something for each student to have a given amount MST3.E.OP3B.01.03
• Use manipulatives to explore division (through 25)
• Use manipulatives to explore multiplication (through 25) 

     Properties

• Understand the identity property of zero in addition MST3.E.OP3B.01.04
• Understand the commutative property of addition 2+3 = 3+2 MST3.E.OP3D.01.01
• Understand the associative property  of addition (2+3) + 4 = 2+ (3+4) MST3.E.OP3D.01.02

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• Know that pictures can be created using geometric shapes MST3.E.MM4A.01.01
• Understand the concept of congruency MST3.E.MM4A.01.02

     Display and Analyze Data

• Organize data with tallies, blocks, and pictographs MST3.E.MM4B.01.01
• Use appropriate terms (e.g., longer than, taller than, smaller than, shorter than, as long as, farther, nearer) to compare dimensions of various objects MST3.E.MM4C.01.01

     Use Multiple Representations (simulations, manipulative materials, pictures, and diagrams) as Tools to Explain the Operation of Everyday Procedures

• Understand the concepts of more, less, and same MST3.E.MM4C.01.02

      Predict and Measure Change Over Time

• Understand that change can be predicted and measured over time (e.g. in terms of height, weight, temperature) MST3.E.MM4D.01.01

     Use Physical Materials, Pictures and Diagrams to Explain Mathematical Ideas and Processes and to Demonstrate Geometric Concepts

• Understand that geometric shapes are useful for representing and describing real-world situations
• Compare objects by attributes (e.g., size, shape, weight, texture)
• Understand the concept of symmetry including bilateral symmetry (e.g., through drawing, folding paper, mirrors)

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• Understand that comparisons can be made in general terms (e.g., comparing weather, time, temperature) and that there is a need for standard units of measure
• Understand the need for standard units of measure

Select Appropriate Standard and Nonstandard Measure Tools in Measurement Activities

• Use non-standard measuring tools (e.g., blocks, books, children's feet, bowlfuls)
• Measure time with analog and digital clocks and convert between the two
• Use a ruler to measure to the nearer centimeter
• Use a balance scale to determine mass (weight of objects)

     Understand the Attributes of Area, Length, Capacity, Volume, Weight, Time, Temperature, and Money

• Use language (e.g., bigger than, more than, bigger than, greater than, less than, one more than, the same size, equal to, before, after, and between) to make comparisons in a variety of situations
• Use direct comparison to measure capacity and weight of objects
• Measure time to the day, month, and year, using a calendar
• Measure time in hour, half hour, quarter hour, and minute intervals
• Weigh objects using grams
• Use coins ( penny, nickel, dime, quarter, fifty cent piece) to count up to one dollar
• Make change for amounts of money up to $1.00, using pennies, nickels, dimes, quarter, and half-dollars
• Know that weight is measured in kilograms and volume is measured in liters
• Understand the measure of temperature and that you use a thermometer to measure it.

      Estimate Measures Such as Length, Perimeter, Area, and Volume, Using Both   Standard and Nonstandard Units

• Use appropriate language (e.g., about as long as, almost as long as, wider than…) to Estimate Size and Length
• Use metric units for measuring capacity (liter), length (meter, centimeter, and decimeter), and mass (kilogram, gram)
• Use customary units for measuring capacity (cups, pint, quart), length (foot, inch), and weight (pound and ounces)
• Find perimeter of squares, rectangles, and triangles
• Understand area in terms of square units

     Collect and Display  & Interpret Data

• Collect data using real-world information (e.g., size of feet, favorite game)
• Organize and display data in bar graphs
• Use appropriate language to compare data (e.g., number, equality, inequality, similarities, differences)
• Understand that observations about objects can be organized and displayed in simple graphs

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• Know that estimating is helpful in many real-world situations

     Estimation Strategies

• Use manipulative materials for estimating quantity

     Predict Experimental Probability

• Understand certainty or uncertainty of events (Likely or unlikely)
• Understand that some events are more likely to happen than others
• Understand fairness of a game and why a game is fair or unfair
• Predict outcomes of coin tosses
• Record data from experiments using spinners and colored tiles/cubes
• Use data to predict which two events is more likely to occur if the experiment is repeated

     Make Estimates and Compare to Actual Results

• Estimate quantities and make quantitative estimates of familiar lengths, widths, and time intervals and check them against measurements
• Estimate answers before solving problems and compare estimates with solutions

     Determine Reasonableness of Results and Make Predictions Using Unbiased Random Samples

• Predict outcomes by guessing or estimating and compare guess or estimate with outcome
• Understand that one can find out about a group of things by studying just a few of them

     Determine Probabilities of Simple Events

• Perform experiments with two or three likely outcomes
• Understand the concept of chance (use language such as one chance in three)
• Solve problem that can have more than one outcome
• Understand the concept of combination or arrangement

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• Recognize, describe, and extend number sequences and patterns in the range of 1-1000
• Recognize, describe, extend, and create patterns with geometric shapes

• Understand the concepts of greater than, less than and equal to and use symbols <, >, =
• Read and Write Numerals from 0 to 100

        Use of Manipulatives and Technology to Solve Patterns

• Understand the concepts of inside and outside
• Understand properties of 3-D shapes
• Skip Count with manipulatives
• Use manipulatives to explore and understand symmetry
• Use manipulative materials to explore and understand linear patterns such as #+*#+*

     Interpret Graphs

• Use language for mode, median, and mean

     2D and 3D Geometric Shapes

• Understand the basic properties of circles, squares, rectangles, and triangles

     Patterns in Nature, Art, Music, and Literature

• Recognize symmetry in nature, art, and music

     Variables and Open Sentences

• Understand the number relationships of equality and inequality
• Write open sentences and use counters to solve open sentences

      Use Manipulatives to Solve for an Unknown

• Use counters to understand the commutative and associative properties

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