Mathematics

jump to 1st, 2nd, 3rd, 4-5th, Middle School

Kindergarten

The goal of the math program is to encourage discovery and to develop an understanding of mathematical
patterns and concepts through the use of concrete materials. The child’s understanding of concepts progresses
from free exploration to working at a connecting level with symbols, and finally to working with
equations at an abstract level.

Skills that are introduced and developed in kindergarten encourage the students to:

NUMBER AND NUMBER SENSE
• Given sets, identify and describe one set as having more, fewer, or the same number of members using
the concept of one to one correspondence.
• Write numerals through 20 and recognize numerals though 100.
• Count forward to 100 by 1’s, 2’s, 5’s, and 10’s and count backward from 20 by ones.

COMPUTATION AND ESTIMATION
• Add and subtract whole numbers up to 10 with concrete items.
• Give a reasonable estimate when given a number of objects up to 25.

MEASUREMENT
• Recognize a penny, nickel, dime and quarter.
• Measure and/or compare two objects according to length, height, and weight.
• Begin to tell time to the hour using an analog or digital clock.

GEOMETRY
• Identify and describe circles, triangles, squares, and rectangles.

PROBABLY, STATISTICS, AND DATA
• Gather data relating to familiar experiences by counting and tallying.
• Gather objects and information, using object and pictorial graphs and tables.

PATTERNS, FUNCTIONS AND ALGEBRA
• Identify, describe and extend a repeating pattern.

PROBLEM SOLVING
• Sort and classify objects according to a variety of attributes.
• Use concrete materials to illustrate the answer to a simple addition or subtraction problem, and to write
a simple equation that corresponds with the word problem and his or her solution.

First Grade

The goal of the mathematics program is to develop an understanding and insight into the patterns of mathematics through the use of concrete materials. The activities are designed to help young children see relationships and interconnections in mathematics and to enable them to deal with mathematical ideas and concepts. Children are encouraged to question, investigate, hypothesize, discover, and communicate their findings.

Skills that are introduced and developed in first grade encourage the students to:

NUMBER AND NUMBER SENSE
• Recognize and write numbers 0-100.
• Given a number, count forward and backward from the number.
• Identify the place value of each digit in a three-digit numeral, using numeration models.

COMPUTATION AND ESTIMATION
• Recognize fact families (e.g., 2+3=5, 3+2=5, 5-3=2, 5-2=3).
• Recall basic addition facts, sums to 18 or less, and the corresponding subtraction facts.
• Write and solve story and picture problems using basic addition and subtraction facts.
• Add and subtract two-digit numbers without regrouping.

MEASUREMENT
• Use standard units to measure length and weight and a calendar to record day and month.
• Tell time to the hour and begin to tell time to the half hour and quarter hour using an analog or digital clock.

GEOMETRY
• Draw and describe triangles, squares, diamonds, hexagons, rectangles and circles.

PROBABILITY, STATISTICS, AND DATA
• Use a graph to compare, count, add and subtract.
• Interpret information displayed in a graph using the vocabulary of more, less, fewer, greater than, and
less than.

PATTERNS, FUNCTIONS, AND ALGEBRA
• Sort and classify concrete objects according to one or more attributes.
• Recognize, describe, extend and generate a wide variety of patterns.

PROBLEM SOLVING
• Use appropriate strategies to solve mathematical problems, including counting on or back, doubles and
reverse, doubles plus 1 and reverse, 10 as a base and reverse, magic nines, compare and contrast, and looking
for patterns.

Second Grade

Our students encounter a rigorous and exciting math program. It engages our multi-dimensional students by using manipulatives in a spiraled curriculum, touching upon many topics several times a year. We place a strong emphasis on problem solving to develop higher level thinking skills and encourage the application of mathematical understandings. By using a wide variety of resources, we meet each student’s individual needs.

Skills that are introduced and developed in second grade encourage the students to:

NUMBER AND NUMBER SENSE
• Compare whole numbers between 0 and 999 using symbols and words.
• Describe multiplication as repeated addition.
• Describe division as separating objects into subsets and repeated subtraction.

COMPUTATION AND ESTIMATION
• Recall multiplication and division facts through the nines table.
• Recognize and describe related facts that represent and describe the inverse relationship between addition
and subtraction.
• Use estimation to determine reasonableness of answers in math problems.

MEASUREMENT
• Estimate and then measure length, volume, and weight using standard and non-standard units of measure.
• Tell and write time to the nearest five minutes.

GEOMETRY
• Compare and contrast plane and solid geometric shapes.

PROBABILITY, STATISTICS, AND DATA
• Read, construct, and interpret a simple picture and bar graph.

PATTERNS, FUNCTIONS, AND ALGEBRA
• Identify, create, and extend a wide variety of patterns using symbols and objects.

PROBLEM SOLVING
• Use appropriate strategies to solve a given mathematical problem.

Third Grade

The goal of the math program is to instill a feeling of joy for mathematics while guiding students toward developing a solid conceptual foundation, accuracy with basic arithmetic skills, and an appreciation for patterns and relationships. We provide opportunities to apply prior knowledge and construct new knowledge through hands-on, exploratory, and open-ended activities. Students are encouraged to use problemsolving skills and to look for mathematical connections. Students demonstrate understanding by building, viewing, or showing a problem in several ways. In addition to homeroom math activities, students participate in a math explorations class. In this setting, students are encouraged to discover the rules and algorithms of mathematics while connecting and integrating mathematics with other subjects. Studying topics such as the relationship between math and art, mathematical patterns, and probability give students the opportunity to enhance visual understanding while developing high level thinking and problem-solving skills.

Skills that are introduced and developed in third grade encourage the students to:

NUMBER AND NUMBER SENSE
• Explore the general pattern of number systems through building and notation using other bases.
• Read and write seven-digit numerals and identify the place value for each digit.
• Read, write, represent, and identify decimals and fractions.

COMPUTATION AND ESTIMATION
• Estimate and find the product of two whole numbers using estimation and paper and pencil.
• Estimate and find the quotient of two whole numbers when the divisor is a one-digit number.

MEASUREMENT
• Estimate and measure length, volume, and weight using metric and customary units.
• Tell time to the nearest minute.

GEOMETRY
• Identify and describe congruent, similar, and symmetrical two-dimensional figures.

PROBABILITY, STATISTICS, AND DATA
• Collect data on a topic and construct a bar graph showing the results.
• Determine the probability of a simple given event, using concrete materials.

PATTERNS, FUNCTIONS, AND ALGEBRA
• Analyze a given pattern formed using concrete objects and pictures and then create a pattern with the
same attributes.

PROBLEM SOLVING
• Use appropriate strategies to solve a given mathematical problem.

back to K-3 Curriculum

Grades 4 and 5

The aim of the mathematics program is to establish and maintain a joy of mathematics and an appreciation for the breadth of the subject. Mathematical ideas are presented in a variety of ways in order to spark the interest and extend the skills of each child. By approaching mathematics with wonder and curiosity, students can manipulate mathematical rules, formulas, and algorithms with understanding, accuracy, and confidence. In the fourth grade, the mathematics program is characterized by the study of upper elementary arithmetic from a number system point of view, with emphasis on exploring order of magnitude and formulating equations. In fifth grade, the mathematics program continues to explore upper elementary arithmetic. In addition, proportionality, percentage, and the generalizations that lead to Algebra are introduced.

Skills that are introduced and developed in fourth and fifth grade encourage the students to:

NUMBER AND NUMBER SENSE
• Identify factors of single numbers, common factors of number pairs, and greatest common factors of number pairs.
• Identify multiples of a single number, common multiples of number pairs, and least common multiples of number pairs.
• Recognize and express fractional numbers, mixed numbers, the components of fractions, and decimals to the hundredths.
• Complete number sentences using inequalities.
• Recall basic arithmetic facts and use facts to find multiples and factors of a given number.
• Read, write, compare, and order whole numbers; read and write Roman numerals.
• Find equivalent and lowest term fractions; compare and order fractions and mixed numbers.

COMPUTATION AND ESTIMATION
• Solve addition and subtraction problems from basic facts through four-digit sums.
• Multiply 2- and 3-digit factors by 1- and 2-digit factors and divide by 1-digit divisors and 2-digit multiples of 10.
• Add and subtract fractions with like denominators and decimals to the hundredths.
• Multiply 1-, 2-, and 3-digit factors; divide by 1-, 2-, and 3-digit divisors.
• Find sums and differences of fractions with like and unlike denominators; find products and quotients of fractions
and mixed numbers.
• Round decimals and estimate sums, differences, products, and quotients; find decimal and fractional equivalents.

MEASUREMENT
• Explore basic units of length, weight, volume, and temperature in English and metric units.
• Use appropriate tools such as rulers, protractors, and compasses for purposes of measurement.
• Express equivalent measures in a variety of metric units.
• Add, subtract, and convert units of time.

GEOMETRY
• Compute perimeters of various polygons.
• Recognize basic geometric figures (triangle, square, and rectangle) and their corresponding area formulas.
• Compute the volume and surface area of rectangular prisms.
• Recognize and use basic geometric units: points, lines, line segments, rays, and angles.
• Identify congruent figures and draw lines of symmetry.
• Identify and classify polygons according to sides and angles.
• Identify and draw diameter, radius, chord, arc, and central angle.
• Find perimeter, circumference, area, volume, and surface area of various polygons and regions.

PROBABILITY, STATISTICS, AND DATA
• Interpret and construct bar graphs as a means of analyzing and depicting data.
• Identify the mean, median, mode, and range of sets of data points.
• Calculate theoretical probabilities of events.
• Interpret and construct bar, line, circle, and pictographs.
• Identify the mean, median, mode, and range of sets of data points.
• Identify possible outcomes of a simple event and compute their corresponding probabilities.

PATTERNS, FUNCTIONS, AND ALGEBRA
• Search for function rules underlying arithmetic and geometric sequences.
• Recognize percent as a proportion to 100; find the percent of a number.
• Write equivalent ratios, fractions, decimals, and percents.

PROBLEM SOLVING
• Apply standard techniques to approach solving non-routine problems in an organized way.
• Solve word problems involving addition and subtraction of whole numbers, multiplication and division of
whole numbers, and simple fractions and decimals using logically structured methods.
• Apply arithmetic skills to practical problems.
• Apply specific problem solving strategies appropriately and effectively.

back to 4-5 Curriculum

Grades 6, 7, and 8

The curriculum highlights quantitative, spatial, and reasoning skills. We develop thoughtful students who are capable of appreciating mathematics and math applications to make sense of their world. Our students are given consistent opportunities for “saturation,” to discover and represent fundamental concepts in a variety of contexts so that they gradually become more “intuitive.” In the sixth grade the core curriculum emphasizes essential topics in pre-Algebra. In seventh grade the core
curriculum emphasizes essential topics in basic Algebra. And in eighth grade, the class takes a rigorous approach to the essentials and more challenging aspects of Algebra. Many of the tools and concepts students explore in eighth grade will be used throughout their study of higher mathematics. Examples may include topics such as truth tables from formal logic, trigonometry, and applications of higher order matrices. In addition to software applications such as Geometer’s Sketchpad,
materials such as blocks, computers, rubber bands, mirrors, string, calculators, drawings, folded paper or anything that can form a pattern or be arranged in space are fair game for study and extension in math class. Emphasis is placed on the heuristics of problem solving in spatial relations, topology, and pre-engineering drawing.

Skills that are developed in Middle School encourage the students to:

NUMBER AND NUMBER SENSE
• Apply base-10 place value concepts and other bases.
• Evaluate expressions using order of operations.
• Use exponents in expanded base-10 notation.
• Express whole numbers as products of primes.
• Write equations describing applied problems.
• Identify the union and intersection of two or more sets.
• Order and find the absolute value of integers.
• Use prime factorization to find Least Common Multiple and
Greatest Common Factor.
• Express quantities and perform calculations using scientific
notation.
• Distinguish rational and irrational numbers.

COMPUTATION AND ESTIMATION
• Recognize and find equivalent fractions, decimals, and percents.
• Estimate accurately using fractions, decimals, and percents.
• Find sums, differences, products, and quotients of fractions,
decimals, and percents.
• Write and determine equality of ratios.
• Write and apply multiple expressions in one unknown.
• Solve and graph inequalities involving one operation.
• Evaluate Algebraic expressions with fractions, decimals, or
percents.

MEASUREMENT
• Understand and perform calculations using measurement units.
• Apply decimal skills to metric units.

GEOMETRY
• Classify polygons and angles.
• Demonstrate basic construction skills.
• Specify faces, edges, and vertices in solids.
• Locate points using Cartesian coordinates.
• Find surface areas and volumes of solids.
• Find perimeter and area of polygons and circles.

PROBABILITY, STATISTICS, AND DATA
• Find the probability of single and ordered pair events.
• Find the range, mean, median, and mode of a data set.

PATTERNS, FUNCTIONS, AND ALGEBRA
• Substitute a number for a variable in an expression.
• Solve simple equations using +, -, *, /.
• Use proper written format to solve equations.
• Find sums and differences, products and quotients of integers.
• Find ordered pairs and graph simple linear equations.

PROBLEM SOLVING
• Apply specific problem solving techniques.
• Perceive underlying mathematical structure.

VARIABLES, EXPRESSIONS, AND EQUATIONS
• Write, simplify, and evaluate Algebraic expressions.
• Multiply using the distributive property.
• Solve compound first degree equations/inequalities.
• Solve for a given variable and evaluate a formula.

POLYNOMIAL AND RADICAL EXPRESSIONS
• Distinguish prime and composite monomial factors, and factor
monomials.
• Distinguish rational, irrational, and imaginary numbers.
• Add, subtract, and multiply polynomials.
• Find least common multiples of rational expressions.
• Factor quadratic trinomials.

QUADRATIC EQUATIONS
• Solve quadratic equations by factoring, completing the square,
and by using the quadratic formula.
• Use the discriminant to determine the number of solutions.
• Use quadratic equations in mixture and motion problems.

GRAPHS AND LINEAR EQUATIONS
• Determine the slope of a linear equation.
• Write the equation of a linear relation.
• Find system solutions by graphing, substitution, and by using
linear combinations.

INEQUALITIES AND ABSOLUTE VALUE
• Graph and solve disjunctions and conjunctions.
• Write inequalities to model practical problems.
• Solve equations involving absolute values.

RADICAL EXPRESSIONS AND EQUATIONS
• Multiply, divide, add, subtract, and factor radical expressions.
• Simplify radicands and radical expressions.
• Solve equations involving radicals.

RELATIONS AND FUNCTIONS
• Define functions, domains, ranges, and inverse functions.
• Graph linear and quadratic functions and find their inverses
graphically.
• Write and solve direct and inverse variation equations.

back to Middle School Curriculum