# Mathematics

- Mathematics Content Standards
- Standards for Mathematical Practice
- Commentary and Elaborations for K-5
- Commentary and Elaborations for 6-8
Welcome to the Worcester Public Schools' Mathematics Curriculum web page. Here you will find information about the Math Curriculum for pre-K through high school and other math resources. |

## Pre-K Math

In preschool or pre-kindergarten, students' activity time will focus on two critical areas:

- developing an understanding of whole numbers to 10, including concepts of one-to-one correspondence, counting, cardinality (the number of items in a set), and comparison; and
- recognizing two-dimensional shapes, describing spatial relationships, and sorting and classifying objects by one or more attributes.

Relatively more learning time should be devoted to developing children’s sense of number as quantity than to other mathematics topics.

## Grade K Math

In kindergarten, students' learning time will focus on two critical areas:

- representing, relating, and operating on whole numbers, initially with sets of objects; and
- describing shapes and space.

More learning time in kindergarten should be devoted to number than to other topics.

## Grade 1 Math

In grade 1, students' learning time will focus on four critical areas:

- developing understanding of addition, subtraction, and strategies for addition and subtraction within 20;
- developing understanding of whole number relationships and place value, including grouping in tens and ones;
- developing understanding of linear measurement and measuring lengths as iterating length units; and
- reasoning about attributes of, and composing and decomposing geometric shapes.

## Grade 2 Math

In grade 2, students' learning will focus on four critical areas:

- extending understanding of base-ten notation;
- building fluency with addition and subtraction;
- using standard units of measure; and
- describing and analyzing shapes.

## Grade 3 Math

In grade 3, students' learning will focus on four critical areas:

- developing understanding of multiplication and division and strategies for multiplication and division within 100;
- developing understanding of fractions, especially unit fractions (fractions with numerator 1);
- developing understanding of the structure of rectangular arrays and of area; and
- describing and analyzing two-dimensional shapes.

## Grade 4 Math

In grade 4, students' learning will focus on three critical areas:

- developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends;
- developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers;
- understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

## Grade 5 Math

In grade 5, students' learning will focus on three critical areas:

- developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions);
- extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and
- developing understanding of volume.

## Grade 6 Math

In grade 6, students' learning will focus on four critical areas:

- connecting ratio and rate to whole number multiplication and division, and using concepts of ratio and rate to solve problems;
- completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;
- writing, interpreting, and using expressions and equations; and
- developing understanding of statistical thinking.

## Grade 7 Math

In grade 7, students' learning will focus on four critical areas:

- developing understanding of and applying proportional relationships;
- developing understanding of operations with rational numbers and working with expressions and linear equations;
- solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and
- drawing inferences about populations based on samples.

## Pre-Algebra

In this accelerated course for 7th graders, students' learning experiences include those in Math 7 as well as topics such as number theory (rational numbers), ratio and proportion, estimation, exponents and radicals, the rectangular coordinate system, sets and logic, formulas, and solving first-degree equations and inequalities. Students will experience an emphasis on readiness for Algebra-I.

## Grade 8 Math

In grade 8, students' learning will focus on three critical areas:

- formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation and solving linear equations and systems of linear equations;
- using functions to describe quantitative relationship;
- analyzing two- and three- dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

## Algebra I

For this 9th grade Algebra I course, students' learning will focus on four critical areas:

- deepen and extend understanding of linear and exponential relationships;
- contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions;
- extend the laws of exponents to square and cube roots; and
- apply linear models to data that exhibit a linear trend.

## Algebra II

For this 11th grade Algebra 2 course, students' learning will focus on four critical areas:

- relate arithmetic of rational expressions to arithmetic of rational numbers;
- expand understandings of functions and graphing to include trigonometric functions;
- synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions; and
- relate data display and summary statistics to probability and explore a variety of data collection methods.

## Geometry

For this 10th grade Geometry course, students' learning will focus on six critical areas:

- establish criteria for congruence of triangles based on rigid motions;
- establish criteria for similarity of triangles based on dilations and proportional reasoning;
- informally develop explanations of circumference, area, and volume formulas;
- apply the Pythagorean Theorem to the coordinate plan;
- prove basic geometric theorems; and
- extend work with probability.

## Pre-Calculus

For this 12th grade Pre-Calculus course, students' learning will focus on four critical areas:

- extend work with complex numbers;
- expand understanding of logarithms and exponential functions;
- use characteristics of polynomial and rational functions to sketch graphs of those functions; and
- perform operations with vectors.

## Algebraic Reasoning

This course for 12th graders is intended to accelerate student learning in Algebra where curricular gaps may exist; upon successful completion of this course the student will be prepared for entry-level college coursework. Part one of this course covers all basic operations of real numbers, linear and literal equations, graphing lines (using tables, x-and y-intercepts), the arithmetic of polynomial expressions including properties of exponents, solving and graphing linear inequalities, perimeters and areas of basic figures, scientific notation and intrasystem metric conversions. Part two of this course covers major topics in the study of algebra. Students learn to factor polynomials (common factor, grouping, difference of squares and trinomials), perform arithmetic operations on rational expressions and complex fractions, and solve rational, quadratic and literal equations. The course also covers applications including the use of the Pythagorean Theorem, understanding the definition of radical expressions, simplifying radical expressions containing numerical and variable radicands, graphing linear equations using slope-intercept concepts, and solving systems of linear equations.

## Advanced Topics Trigonometry

In this course, students will explore trigonometry and Algebra II topics, including right trigonometric and circular functions, inverses, and graphs; trigonometric identities and equations; solutions of right and oblique triangles; complex numbers; numerical tables; field properties and theorems; set theory; operations with rational and irrational expressions; factoring of rational expressions; in-depth study of linear equations and inequalities; quadratic equations; solving systems of linear and quadratic equations; graphing of constant, linear, and quadratic equations; and properties of higher degree equations.

## Advanced Quantitative Reasoning

In this course students will study concepts of algebra, geometry, statistics and probability in relevant, engaging contexts, emphasizing statistical and financial applications. Students will solve real-world problems and apply concepts of Algebra to decision-making through the analysis of data, modeling change, and mathematical relationships.

## Computer Science

In this course, students will solve problems by writing, running, and debugging computer programs; use commonly used algorithms and data structures; and develop and select appropriate algorithms and data structures to solve problems. Students will also code fluently in an object-oriented paradigm using Java. Furthermore, students will read and understand a large program consisting of several classes and interacting objects, showing an ability to read and understand a description of the design and development process leading to such a program.

## Financial Literacy

In this course, students will begin to develop the skills and strategies that promote personal and financial responsibility related to financial planning, savings, investment, and charitable giving in the global economy. Five broad topics will be the foundation of the course: college and career planning, money management, savings and investing, income, and spending. The course will teach students to search and assess college and career opportunities, identify and prioritize their personal money management goals, develop personal spending and savings plans, comprehend the impact of time on the value of money, understand the cost of using credit, and protect assets.

## Topics in Algebra and Geometry

In this course, students will study pre-algebra, algebra, and introductory geometry topics, including the study and applications of formulas, algebraic expressions, linear equations and inequalities; the rectangular coordinate system; area, perimeter, and volume of geometric figures; and properties of triangles and circles. Particular emphasis will be placed on concepts and skills necessary for success in Algebra II.