Mathematics

  • D15 Mathematics Curriculum

    The Mathematics Curriculum in District 15 is aligned to the Illinois Learning Standards, incorporating the Common Core. Based on this adoption of the Common Core, there are three major instructional shifts in mathematics from the previous 1997 Illinois Learning Standards. The shifts include greater focus, coherence and rigor. To read about these key math standard shifts, go to CoreStandards.org.

    Click here for the enVisionmath 2.0 Parent Guide K-6.

    Standards for Mathematical Practices

    All K-8 students are expected to develop appropriate expertise in the Standards for Mathematical Practice. These practices are longstanding important processes and proficiencies in mathematics education.

    Standards for Student Mathematical Practice

    Standards for Mathematical Content

    Students use the Standards for Mathematical Content, which are designated by grade level, in conjunction with the Standards for Mathematical Practices.

    Below are the major K-8 content topics covered per grade level.

    K

    • Know number names and the count sequences

    • Count to tell the number of objects

    • Compare numbers

    • Understand addition as putting together and adding to, and subtraction as taking apart and taking from

    • Work with numbers 11-19 to gain foundations for place value

    1

    • Represent and solve problems involving addition and subtraction

    • Understand and apply properties of operations and the relationship between addition and subtraction

    • Add and subtract within 20

    • Work with addition and subtraction equations

    • Extend the counting sequence

    • Understand place value

    • Use place value understanding and properties to add and subtract

    • Measure lengths indirectly and by iterating length units

    2
    • Represent and solve problems involving addition and subtraction

    • Add and subtract within 20

    • Understand place value

    • Use place value understanding and properties of operations to add and subtract

    • Measure and estimate lengths in standard units

    • Relate addition and subtraction to length

    3
    •  Represent and solve problems involving multiplication and division
    • Understand properties of multiplication and the relationship between multiplication and division

    • Multiply and divide within 100

    • Solve problems involving the four operations, and identify and explain patterns arithmetically

    • Develop understanding of fractions as numbers

    • Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects

    • Understand concepts of area and relate area to multiplication and addition

    4

    •  Use the four operations with whole numbers to solve problems
    • Generalize place value understanding for multi-digit whole numbers

    • Use place value understanding and properties of operations to perform multi-digit arithmetic

    • Extend understanding of fraction equivalence and ordering

    • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers

    • Understand decimal notation for fractions and compare decimal fractions

    5

    • Understand the place value system

    • Perform operations with multi-digit whole numbers and with decimals to hundredths

    • Use equivalent fractions as a strategy to add and subtract fractions

    • Apply and extend previous understandings of multiplication and division to multiply and divide fractions

    • Understand concepts of volume and relate volume to multiplication and addition

    6

    • Understand ratio concepts and use ratio reasoning to solve problems

    • Apply and extend previous understandings of multiplication and division to divide fractions by fractions

    • Apply and extend previous understandings of numbers to the system of rational numbers

    • Apply and extend previous understandings of arithmetic to algebraic expressions

    • Reason about and solve one-variable equations and inequalities

    • Represent and analyze quantitative relationships between dependent and independent variables

    7

    •  Analyze proportional relationships and use them to solve real-world and mathematical problems
    • Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers

    • Use properties of operations to generate equivalent expressions

    • Solve real-life and mathematical problems using numerical and algebraic expressions and equations

    8

    • Work with radicals and integer exponents

    • Understand the connections between proportional relationships, lines, and linear equations

    • Analyze and solve linear equations and pairs of simultaneous linear equations

    • Define, evaluate, and compare functions

    • Use functions to model relationships between quantities

    • Understand congruence and similarity using physical models or geometry software

    • Understand and apply the Pythagorean Theorem

Math Courses
  • Junior High Course Offerings

    Grade 7

    • 7th Grade Math—This course aligns to the 7th-grade Common Core State Standards with a focus on problem solving and application. The course topics include integers and rational numbers, proportional relationships and percent problems, equivalent expressions, equations and inequalities, sampling, probability, and basic geometry.

    • 7th Grade Accelerated Math—This course is a compacted curriculum of both 7th and 8th Grade Common Core State Standards which includes: number systems, rational number operations, ratios, proportionality, percentages, expressions, solving linear equations, inequalities, exponents and scientific notation, graphing proportional and non-proportional relationships, angles and angle relationships, circumference and area of circles, volume of cylinders, spheres, and cones, and the Pythagorean Theorem.
    • 7th Grade Algebra 1—This advanced 7th Grade algebra course introduces the fundamental principles of algebra. Course topics include linear equations, graphs and inequalities, systems of equations, exponents and scientific notation, simplifying and factoring polynomials, quadratic equations and functions, rational expressions, and introductory radical operations.

    For seventh-grade students who took Algebra 1 in sixth grade, these courses are also available:

    • Advanced Topics of Algebra 1 (see course description below)
    • Honors Plane & Solid Geometry (see course description below)

    Grade 8

    • 8th Grade Math—This course aligns to the 8th Grade Common Core State Standards with a focus on problem solving and application. Topics include the real number system, linear equations, modeling relationships using functions, bivariate data, identifying and solving systems of linear equations, transformations, solving problems including congruence, similarity, the Pythagorean Theorem, surface area, and volume.

    • 8th Grade Algebra 1—This advanced course introduces students to the fundamental principles of algebra. Algebraic symbolism, simplifying expressions, solutions to equations, the graphic representations associated with variables, and statistical variability are among the course topics. Additional points of emphasis include graphical representations, connection to related functions, and algebraic processes applied to word problems. Common Core State Standards provide the foundation for the course.
       
    • 8th Grade Advanced Topics of Algebra 1—This advanced course is designed to focus on problem solving, word problems and higher-order thinking. It incorporates previously learned concepts from 7th Grade Algebra 1 and delves deeper into the material and application process.
       
    • Honors Plane & Solid Geometry—This advanced 8th grade course is a comprehensive study of plane and solid geometry including constructions, formulas for measurement and formal proofs. It is based on the theorems and axioms that relate points, lines, planes, and solids. Topics are covered in great depth, especially area and volume of solids. Additional emphasis is placed on the integration of algebraic techniques in solving geometric problems.
    • Accelerated Algebra 2—This highly accelerated high school course is designed for students who have an excellent knowledge of algebra and geometry. M328 Accelerated Algebra 2 is provided at a high school location. The course briefly reviews concepts presented in earlier course work and then rigorously expands and applies them to other areas of mathematics. In addition, selected topics from pre-calculus are studied. Ideas presented in this course involve advanced techniques of graphing and solving equations and inequalities and prepares students to take Trigonometry/Calculus A. This course requires a graphing calculator.

    District-Required Achievement for the Advanced Program
    (2018-2019 Implementation in Grades 2, 3 and 4)

    Advanced Math

    enVision Math 2.0

    Contacts:

    Adrienne Bailey
    Curriculum Coordinator
    Phone: 847-963-3117
    Email: baileya@ccsd15.net