Grade Level: Grade 3

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
Symbols represent mathematical relationships and operations.
Patterns help make predictions and solve problems.

Skills
Create and describe patterns using different objects and symbols.
   1.)       Use a variety of materials to construct, reproduce, describe and extend numerical and spatial patterns.
   2.)       Explore and describe patterns and sequences using tables, graphs and charts.
   3.)       Sort and classify the same set of objects in more than one way and explain the reason for each sort.   
Identify mathematical relationships as equations.
   1.)       Model situations that reflect mathematical relationships involving addition, subtraction, multiplication and division as open number sentences and match to story problems.   
Represent quantities that have the same value with an equal sign.
   1.)       Demonstrate understanding of the = sign as an equality symbol and explore inequalities and the (does not equal) sign.
   2.)       Demonstrate equivalence using the commutative and associative properties of whole numbers.
   3.)       Use < and > to relate two quantities that are not equivalent.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Fractional parts represent equal shares of a region or set.
Currency can be represented and compared as fractional parts.
Measurement tools can show fractional parts of a whole.
Estimates represent reasonable but not exact measurements.

Skills
Represent numbers in expanded and regrouped forms in the base ten place value system.
   1.)       Use models and expanded and regrouped forms to represent 2- and 3-digit numbers.
   2.)       Locate, label, compare and order whole numbers to 1000, including multiples of 10 and 100 using place value models, number patterns and the number line.
   3.)       Name and state the value of pennies, nickels, dimes, quarters and half-dollars and show different ways to make a given amount.
   4.)       Determine and compare the values of sets of coins and write the values using decimal notation up to $100.
Recognize that a fraction with the same numerator and denominator represents the whole object or an entire set.
   1.)       Use models and pictures to represent fractions and label the parts with words and fraction symbols.
   2.)       Identify a whole as a fraction with the same numerator and denominator.
   3.)       Use counting and grouping of objects to find equal parts of a set of objects and use models and number patterns to identify amounts such as 2/3 of 12 is 8.  
Use fractions to measure and to represent points on a ruler or number line.
   1.)       Estimate fractional values and measure to the nearest half unit with the aid of number lines and rulers.   
Use strategies that involve place value patterns and algebraic properties to estimate, add and subtract.
   1.)       Identify 10 and 100 more and less than a number.
   2.)       Compare and round numbers to the nearest 10 and 100.
   3.)       Use commutative and associative properties to solve problems.  
Approximate solutions to story problems involving computation through the use of efficient methods.
   1.)       Estimate, add and subtract with 2- and 3-digit numbers using a variety of strategies.
   2.)       Use estimation strategies to determine and justify the reasonableness of a computational answer.
   3.)       Recognize when an estimate is appropriate and determine whether an estimation strategy will result in an over or underestimate.  
Solve multiplication and division problems using rectangular arrays, number patterns, skip counting and repeated addends.
   1.)       State the multiplication and division facts with factors of 1, 2, 3, 4, 5, and 10.
   2.)       Explore division problems with and without remainders.
   3.)       Write and solve multiplication and division story problems and match to number sentences (equations).
   4.)       Use models and pictures of sets and arrays to represent multiplication and division of 2- and 3-digit numbers by 1-digit numbers.
   5.)       Solve real-world multiplication and division problems using a variety of methods.
Compare fractions, identify equivalent fractions, add and subtract fractions with like and unlike denominators using models and pictures.
   1.)       Construct and use models to compare and order fractions with like and unlike denominators of 2, 3, 4, 5, 6, and 8 and to identify equivalent fractions.
   2.)       Identify patterns with equivalent ratios such as 3 out of 6 crayons are red or 4 out of 8 crayons are red is the same as 1 out of 2 crayons is red.
   3.)       Construct and use models to add and subtract fractions with like and unlike denominators and write fraction sentences to match the models.
   4.)       Write and solve story problems that involve fractions.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
Polygons can be classified, compared, analyzed, and measured using various attributes.
Units of time can describe the duration and sequence of events.

Skills
Classify and compare polygons and solids using various attributes.
   1.)       Sort polygons and solids through using characteristics such as the relationship of sides (parallel, perpendicular), kinds of angles (acute, right, and obtuse), symmetry and congruence.
   2.)       Describe similarities and differences of two- and three-dimensional shapes in the environment using physical features such as number of sides, number of angles, lengths of sides and straight and curved parts.
   3.)       Investigate ways to tile or tessellate a region or shape using various polygons.
Represent location on simple maps.
   1.)       Draw and interpret simple maps using coordinate systems and shapes or pictures.
Plan events and make schedules.
   1.)       Tell time to the minute, suing analog and digital clocks, and identify AM and PM.
   2.)       Use calendars and clocks to plan and sequence events.  
Determine and use different tools and units appropriate for specific measurement tasks.
   1.)       Develop and explain strategies for using nonstandard and standard referents to estimate measurements of length, area, weight, temperature, volume and capacity. 
   2.)       Explore strategies for estimating and measuring the perimeters, areas and volumes of irregular shapes and solids.
   3.)       Describe and use estimation strategies that can identify a reasonable answer to a measurement problem when an estimate is appropriate.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
Probability can be represented numerically and graphically.
Degree of probability determines fairness.

Skills
Design surveys for the collection of data and justify conclusions drawn from the data.
   1.)       Pose questions and use a variety of ways to collect, organize, and analyze data from samples and surveys.
   2.)       Display, read, interpret and draw conclusions from data that is represented in a variety of ways including tables, charts, lists, diagrams, line plots and graphs.  
Analyze data to identify a typical element or event.
   1.)       Describe trends in data using range and mode.  
Use samples and simulations to determine probability, and to make and test predictions.
   1.)       Make predictions and test them by conducting probability experiments and recording results.
   2.)       Explore the fairness of games involving a variety of spinners and dice.