### Curriculum

#### The Goal

The goal in mathematics education is for students to:

• Develop fluency in basic computational skills.
• Develop an understanding of mathematical concepts.
• Become mathematical problem solvers who can recognize and solve routine problems readily and can find ways to reach a solution or goal where no routine path is apparent.
• Communicate precisely about quantities, logical relationships, and unknown values through the use of signs, symbols, models, graphs, and mathematical terms.
• Reason mathematically by gathering data, analyzing evidence, and building arguments to support or refute hypotheses.
• Make connections among mathematical ideas and between mathematics and other disciplines.

#### PreK and Kindergarten

Number Sense

• Students understand the relationship between numbers and quantities.
• Students understand and describe simple additions and subtractions.
• Students use estimation strategies in computation and problem solving that involve numbers that use the ones and tens places.
Algebra and Functions
• Students sort and classify objects.
Measurement and Geometry
• Students understand the concept of time and units to measure it; they understand that objects have properties, such as length, weight, and capacity, and that comparisons may be made by referring to those properties.
• Students identify common objects in their environment and describe the geometric features.
Statistics, Data Analysis, and Probability
• Students collect information about objects and events in their environment.
Mathematical Reasoning
• Students make decisions about how to set up a problem.
• Students solve problems in reasonable ways and justify their reasoning.

Number Sense
• Students understand and use numbers up to 100.
• Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.
• Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, and hundreds places.
Algebra and Functions
• Students use number sentences with operational symbols and expressions to solve problems.
Measurement and Geometry
• Students use direct comparison and nonstandard units to describe the measurements of objects.
• Students identify common geometric figures, classify them by common attributes, and describe their relative position or their location in space.
Statistics, Data Analysis, and Probability
• Students organize, represent, and compare data by category on simple graphs and charts.
• Students sort objects and create and describe patterns by numbers, shapes, sizes, rhythms, or colors.
Mathematical Reasoning
• Students make decisions about how to set up a problem.
• Students solve problems and justify their reasoning.
• Students note connections between one problem and another.

Number Sense
• Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.
• Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers.
• Students model and solve simple problems involving multiplication and division.
• Students understand that fractions and decimals may refer to parts of a set and parts of a whole.
• Students model and solve problems by representing, adding, and subtracting amounts of money.
• Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places.
Algebra and Functions
• Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction.
Measurement and Geometry
• Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured.
• Students identify and describe the attributes of common figures in the plane and of common objects in space.
Statistics, Data Analysis, and Probability
• Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations.
• Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways.
Mathematical Reasoning
• Students make decisions about how to set up a problem.
• Students solve problems and justify their reasoning.
• Students note connections between one problem and another.

Number Sense
• Students understand the place value of whole numbers.
• Students calculate and solve problems involving addition, subtraction, multiplication, and division.
• Students understand the relationship between whole numbers, simple fractions, and decimals.
Algebra and Functions
• Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships.
• Students represent simple functional relationships.
Measurement and Geometry
• Students choose and use appropriate units and measurement tools to quantify the properties of objects.
• Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems.
Statistics, Data Analysis, and Probability
• Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions.
Mathematical Reasoning
• Students make decisions about how to approach problems.
• Students use strategies, skills, and concepts in finding solutions.
• Students move beyond a particular problem by generalizing to other situations.

Number Sense
• Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.
• Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals.
• Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.
• Students know how to factor small whole numbers.
Algebra and Functions
• Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.
• Students know how to manipulate equations.
Measurement and Geometry
• Students understand perimeter and area.
• Students use two-dimensional coordinate grids to represent points and graph lines and simple figures.
• Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.
Statistics, Data Analysis, and Probability
• Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings.
• Students make predictions for simple probability situations.
Mathematical Reasoning
• Students make decisions about how to approach problems.
• Students use strategies, skills, and concepts in finding solutions.
• Students move beyond a particular problem by generalizing to other situations.

Number Sense
• Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.
• Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.
Algebra and Functions
• Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.
Measurement and Geometry
• Students understand and compute the volumes and areas of simple objects.
• Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures.
Statistics, Data Analysis, and Probability
• Students display, analyze, compare, and interpret different data sets, including data sets of different sizes.
Mathematical Reasoning
• Students make decisions about how to approach problems.
• Students use strategies, skills, and concepts in finding solutions.
• Students move beyond a particular problem by generalizing to other situations.

Number Sense
• Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.
• Students calculate and solve problems involving addition, subtraction, multiplication, and division.
• Students know the properties of, and compute with, rational numbers expressed in a variety of forms.
• Students use exponents, powers, and roots and use exponents in working with fractions.
Algebra and Functions
• Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.
• Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions.
• Students investigate geometric patterns and describe them algebraically.
• Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs.
• Students interpret and evaluate expressions involving integer powers and simple roots.
• Students graph and interpret linear and some nonlinear functions.
• Students solve simple linear equations and inequalities over the rational numbers.
Measurement and Geometry
• Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems.
• Students identify and describe the properties of two-dimensional figures.
• Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.
• Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale.
• Students deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures.
Statistics, Data Analysis, and Probability
• Students compute and analyze statistical measurements for data sets.
• Students use data samples of a population and describe the characteristics and limitations of the samples.
• Students determine theoretical and experimental probabilities and use these to make predictions about events.
• Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set.
Mathematical Reasoning
• Students make decisions about how to approach problems.
• Students use strategies, skills, and concepts in finding solutions.
• Students move beyond a particular problem by generalizing to other similar or new situations.