Elementary Curriculum for
Second Grade - Mathematics

I.  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 relationships, and construct representations of mathematical relationships.  (Patterns)

• The learner will create, explain, extend and record simple numerical and geometric patterns.  (1.1)
• The learner will represent, describe and record patterned relationships using graphs, tables and charts.  (1.2)
• The learner will predict and identify missing elements of a familiar pattern in order to create 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 natural variation and sources of variability and compare patterns of change. (Variability and Change)

• The learner will recognize change and variability when it occurs in a variety of settings.  (2.1)
• The learner will recognize that change is often predictable, but variable, and that patterns emerge that help to describe the change.  (2.2)
• The learner will begin to describe and differentiate between types of relationships, especially repeating, growing and shrinking patterns.  (2.5)
• The learner will explore variability and change in a variety of contexts, investigations and problems.  (2.6)

II.  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)

• The learner will recognize and name and draw basic shapes (circle, triangle, square, rectangle).  The learner will recognize and name rectangular prism, pyramid and triangular prism.  (1.1)
• The learner will describe and identify attributes of familiar 2D and 3D shapes.  (1.2)
• The learner will compare, sort and classify familiar 2D shapes (curved and straight lines, rectangular prism, pyramid, triangular prism, cone).  (1.3)
• The learner will build/assemble and trace/draw familiar shapes, hexagon, octagon, trapezoid and parallelogram and 3D shapes (sphere, cone, cube, cylinder, rectangular prism, triangular prism) paper patterns and geoboards, etc.  (1.4)
• The learner will explore ways to combine, dissect and create shapes.  (1.5)
• The learner will 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)

• The learner will locate and describe objects in terms of their position.  (2.1)
• The learner will recognize symmetrical objects and identify their lines of symmetry.  (2.2)
• The learner will 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 measurement(s) should be made and to what level of precision.  (Measurement)

• The learner will compare attributes of objects using nonstandard and standard (metric) forms of measurement (area, weight, capacity, temperature, length, add and subtract lengths).  (3.1)
• The learner will identify the attribute to be measured and select the appropriate unit of measurement (tell and write time in five minute intervals, temperature, length in metric and standard measurement, weight, money, perimeter, capacity, read and write decimal notation).  (3.2)
• The learner will 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)
• The learner will apply measurement to describe the real world and to solve problems (duration of time and word problems).  (3.6)

III.  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)

• The learner will collect and explore data through counting, measuring and conducting surveys and experiments.  (1.1)
• The learner will organize data using concrete objects, pictures, tallies, tables, charts, diagrams and graphs.  (1.2)
• The learner will present data using a variety of appropriate representations and explain the meaning of the data.  (1.3)
• The learner will 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)

• The learner will describe the shape of the data using descriptive language.  (2.2)
• The learner will draw, explain and justify conclusions, such as trends based on data.  (2.3)

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)

• The learner will make and test hypotheses.  (3.1)
• The learner will conduct surveys, samplings and experiments to solve problems and answer questions of interest to them.  (3.2)

IV.  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)

• The learner will develop an understanding of whole numbers and read, write and count using whole numbers to 1,000.  Investigate basic concept of fractions.  (1.1)
• The learner will investigate and develop an understanding of the base 10 place-value system.  (1.2)
• The learner will develop an understanding of the properties of numbers.  (1.3)
• The learner will 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)

• The learner will represent whole numbers and fractions (with denominators 12 or less, halves) using concrete, pictorial and symbolic representations.  (2.1)
• The learner will explore and recognize different representations for the same number and explain why they are the same (up to 1,000, relate the number to quantities they represent).  (2.2)
• The learner will investigate ways numbers are used.  (2.3)
• The learner will explore strategies for estimating quantity and evaluate the reasonableness of their estimates.  (2.4)
• The learner will 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)

• The learner will compare and order numbers using “equal,” “less than,” or “greater than up to 1,000.”  (3.1)
• The learner will use part-whole relationships to explore numbers, develop number concepts and understand computation concretely, pictorially and symbolically (decompose numbers up to 100, equal groups).  (3.2)
• The learner will explore the classification of numbers as even or odd.  (3.3)
• The learner will apply understanding of number relationships in solving problems.  (3.5)

V.  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)

• The learner will 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 (numbers up to 2 digit).  (1.1)
• The learner will develop and apply the appropriate method of 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 (add and subtract fluently using algorithms, does not require regrouping).  (1.2)
• The learner will explore properties of operations (e.g., commutative properties) and give examples of how they use those properties).  (1.3)
• The learner will apply appropriate operations in solving problems (find the distance between two numbers on a number line, add and subtract fluently).  (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)

• The learner will solve open sentences and write stories to fit the open sentences.  (2.1)
• The learner will explore algebraic concepts with manipulatives such as balance scales, tables  (2.2)
• The learner will use analytic thinking to describe situations and solve problems.  (2.4)

VI.  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)

• The learner will compare events and describe them as “more likely” or “less likely.”  (1.2)
• The learner will 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)
   

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)

• The learner will use manipulatives and diagrams to explore problems and involving counting and arranging objects.  (2.1)
• The learner will explore sets and set relationships by sorting and classifying objects.  (2.2)
• The learner will explore situations in which they model and trace paths using figures consisting of vertices connected by edges.  (2.3)
• The learner will explore now-next patterns.  (2.4)
• The learner will explore, develop and invent their own algorithms to accomplish a task or to solve numerical problems.  (2.5)
• The learner will 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)