Elementary Curriculum for
Third Grade - Mathematics

Patterns, Relationships and Functions

Content Standard 1: Students recognize similarities and generalize patterns, use patterns to create models and make predictions, describe the nature of patterns and relation-ships, and construct representations of mathematical relationships.  (Patterns)

• Create, explain, extend and record simple numerical and geometric patterns.  (1.1)
• Represent, describe, record and interpret patterned relationships using graphs, tables and charts.  (1.2)
• Apply their experiences with patterns to help solve problems and explore new content.  (1.5)
   

Content Standard 2: Students describe the relationships among variables, predict what will happen to one variable as another variable is changed, analyze variation and sources of variability and compare patterns of change. (Variability and Change)

• Recognize change and variability when it occurs in a variety of settings.  (2.1)
• Recognize that change is often predictable, but variable, and that patterns emerge that help to describe the change.  (2.2)
• Use tables, charts, open sentences and hands-on models to represent change and variability.  (2.4)
• Begin to describe and differentiate between types of relationships, especially repeating, growing and shrinking patterns.  (2.5)
• Explore variability and change in a variety of contexts, investigations and problems.  (2.6)

Geometry and Measurement

Content Standard 1: Students develop spatial sense, use shape as an analytic and descriptive tool, identify characteristics and define shapes, identify properties and describe relationships among shapes.  (Shape and Shape Relationships)

• Describe attributes of 2D and 3D shapes.  (1.2)
• Compare, sort and classify familiar 3D shapes (rectangular prism, pyramid, triangular prism, cone).  (1.3)
• Able to draw and build familiar shapes.  (1.4)
• Explore ways to combine, dissect and transform shapes.  (1.5)
• Recognize parallel and perpendicular line segments and figures that have similarity and /or congruence.  (1.6)
• Use shape, shape properties and shape relationships to describe the physical world and to solve problems.  (1.7)
   

Content Standard 2: Students identify locations of objects, identify location relative to other objects and describe the effects of transformations (e.g., sliding, flipping, turning, enlarging, reducing) on an object.  (Position)

• Locate and describe objects in terms of their position, including front, back, inside, outside, right, left, over, under, next to, between, locations on the number line and locate ordered pairs on a map.  (2.1)
• Recognize objects according to their orientation (flip, etc.) recognize directions on a map, N-S-E-W.  (2.2)
• Use concepts of position, direction and orientation to describe the physical world and to solve problems.  (2.5)
   

Content Standard 3: Students compare attributes of two objects, or of one object with a standard (unit), and analyze situations to determine what measurements should be made and to what level of precision.  (Measurement)

• Compare attributes of objects using nonstandard and standard (metric) forms of measurement (weight, capacity, temperature, length and volume).  (3.1)
• Identify the attribute to be measured and select the appropriate unit of measurement (time, temperature, length, mass, money, perimeter).  (3.2)
• Develop strategies for estimating measures and compare the estimates to the results of the measurement; decide if an estimate is “a good estimate.”  (3.3)
• Explain the meaning of measurements and recognize that the number of units it takes to measure an object is related to the size of the unit.  (3.4)
• Explore scale drawings, models and maps and relate them to measurements of real objects.  (3.5)
• Apply measurement to describe the real world and to solve problems.  (3.6)

Data Analysis and Statistics

Content Standard 1: Students collect and explore data, organize data into a useful form and develop skill in representing and reading data displayed in different formats.  (Collection, Organization and Presentation of Data)

• Collect and explore data through counting, measuring and conducting surveys and experiments.  (1.1)
• Organize data using concrete objects, pictures, tallies, tables, charts, diagrams and graphs.  (1.2)
• Present data using a variety of appropriate representations and explain the meaning of the data.  (1.3)
• Identify what data are needed to answer a particular question or solve a given problem, and design and implement strategies to obtain, organize and present those data.  (1.4)
   

Content Standard 2: Students examine data and describe characteristics of a distribution, relate data to the situation from which they arose, and use data to answer questions convincingly and persuasively.  (Description and Interpretation)

• Read and explain data they have collected and organized themselves and progress to reading data from other sources.  (2.1)
• Describe the shape of the data using language.  (2.2)
• Draw, explain and justify conclusions, such as trends based on data.  (2.3)
• Formulate questions and problems, then gather and interpret data to answer those questions.  (2.5)
   

Content Standard 3: Students draw defensible inferences about unknown outcomes, make predictions and identify the degree of confidence they have in their predictions.  (Inference and Prediction)

• Make and test hypotheses.  (3.1)
• Conduct surveys, samplings and experiments to solve problems and answer questions of interest to them.  (3.2)
• Formulate and communicate arguments and conclusions based on data and evaluate their arguments and those of others.  (3.3)
• Number Sense and Numeration

Content Standard 1: Students experience counting and measuring activities to develop intuitive sense about numbers, develop understanding about properties of numbers, understand the need for and existence of different sets of numbers, and investigate properties of special numbers.  (Concepts and Properties of Numbers)

• Develop an understanding of whole numbers and read, write and count using whole numbers.  Investigate basic concept of fractions.  (1.1)
• Investigate and develop an understanding of the base 10 place-value system.  (1.2)
• Develop an understanding of the properties of numbers.  (1.3)
• Apply their understanding of number systems to model and solve problems concretely, pictorially and symbolically.  (1.4)
   

Content Standard 2: Students recognize that numbers are used in different ways such as counting, measuring, ordering and estimating, understand and produce multiple representations of a number and translate among equivalent representations.  (Representation and Uses of Numbers)

• Represent whole numbers and fractions using concrete, pictorial and symbolic representations.  (2.1)
• Explore and recognize different representations for the same number and explain why they are the same.  (2.2)
• Investigate ways numbers are used.  (2.3)
• Explore strategies for estimating quantity and evaluate the reasonableness of their estimates.  (2.4)
• Select appropriate numbers and representations in order to solve real world problems.  (2.5)
   

Content Standard 3: Students investigate relationships such as equality, inequality, inverses, factors and multiples and represent and compare very large and very small numbers.  (Number Relationships)

• Compare and order numbers using “equal,” “less than,” or “greater than.”  (3.1)
• Use part-whole relationships to explore numbers, develop number concepts and understand computation concretely, pictorially and symbolically.  (3.2)
• Classify numbers as even or odd and explore concepts of factors and multiples.  (3.3)
• Apply understanding of number relationships in solving problems.  (3.5)

Numerical and Algebraic Operations and Analytical Thinking

Content Standard 1: Students understand and use various types of operations (e.g. addition, subtraction, multiplication, division) to solve problems.  (Operations and their Properties)

• Use manipulatives to model operations with numbers; develop their own methods of recording operations; and relate their models and recordings to standard symbolic expressions and algorithms.  (1.1)
• Develop and apply the appropriate method of computation from among mental computation from among mental computation, estimation, paper-and-pencil or calculators; explain why they are choosing a method and how they know which operations to perform in a given situation.  (1.2)
• Explore properties of operations (eg., commutative and distributive properties) and give examples of how they use those properties.  (1.3)
• Apply appropriate operations in solving problems.  (1.4)
   

Content Standard 2: Students analyze problems to determine an appropriate process for solution, and use algebraic notations to model or represent problems.  (Algebraic and Analytic Thinking)

• Write and solve open sentences and write stories to fit the open sentences.  (2.1)
• Explore algebraic concepts with manipulatives such as balance scales and tables.  (2.2)
• Find replacements for the variable(s) in open sentences.  (2.3)
• Use analytic thinking to describe situations and solve problems.  (2.4)

Probability and Discrete Mathematics

Content Standard 1: Students develop an understanding of the notion of certainty and of probability as a measure of the degree of likelihood that can be assigned to a given event based on the knowledge available, and make critical judgments about claims that are made in probabilistic situations.  (Probability)

• Explain the difference between chance and certainty and give examples to illustrate their understanding.  (1.1)
• Compare event and describe them as “more likely” or “less likely.”  (1.2)
• Conduct experiments with concrete objects to explore concepts and develop an intuitive understanding of how the conditions of the experiment can affect the outcome.  (1.3)
• Conduct experiments, record the outcomes, examine those outcomes to determine if they make sense and search for explanations of the outcomes.  (1.4)
• Conduct probability experiments and simulations to model and solve problems.  (1.5)
   

Content Standard 2: Students investigate practical situations such as scheduling, routing, sequencing, networking, organizing and classifying, and analyze ideas like recurrence relations, induction, iteration and algorithm design.  (Discrete Mathematics)

• Use manipulatives and diagrams to explore problems and involving counting and arranging objects.  (2.1)
• Explore sets and set relationships by sorting and classifying objects.  (2.2)
• Explore situations in which they model and trace paths using figures consisting of vertices connected by edges.  (2.3)
• Explore now-next patterns.  (2.4)
• Explore, develop and invent their own algorithms to accomplish a task or to solve numerical problems.  (2.5)
• Use discrete mathematics concepts as described above to model situations and solve problems; and look for whether or not there is a solution (existence problems), determine how many solutions there are (counting problems) and decide upon a best solution (optimization problems).  (2.6)