# Illinois Common Core Math Standards

Instructor: Marissa Baranauskas

## Common Core Math Standards in Illinois

Illinois math classes have been following Common Core State Standards for Mathematics since the 2013-2014 academic year. Each standard includes skills practiced at every grade level, including considering ways to approach problems, thinking both abstractly and contextually, building and analyzing arguments, and using models. Students are also taught to use various mathematical tools, to apply precision and consistency, to discern patterns, and to use efficiency in solving math problems.

The Illinois standards outline specific concepts and skills that students should learn in each grade level for kindergarten through 8th grade. For high school, the standards are divided into categories. The math content students need to learn at key grade-level milestones and in high school classes are outlined below.

## Common Core Math Standards for 1st Grade

In the 1st grade, students learn to add and subtract numbers to find solutions to word problems. The standards require students to count to 120, add and subtract numbers up to 20, and use equations to demonstrate addition and subtraction. Students need to understand the ones and tens place value of two-digit numbers, and they should know how to combine multiples of ten to form numbers up to 100.

Additionally, students need to be able to compare the measurements of objects by placing them next to each other. In geometry, they should learn how to identify the characteristics of different shapes, combine two or more shapes, and divide circles and rectangles into sections. They should also be able to interpret and represent time on a clock to the nearest half-hour.

Teachers can find applicable lessons from the Math for Kids course to teach these concepts in an easy-to-understand way.

## Common Core Math Standards for 5th Grade

To meet the common core math standards, 5th grade students should learn how to use symbols in equations and algebraically explain patterns. They need to understand how to multiply numbers to the power of ten, interpret decimals to the thousandth place value, use operations with decimals to the hundredths place, and compare decimal quantities that are greater than, less than, or equal to each other. Previously learned multiplication and division concepts should be expanded to include division of a four-digit number by a two-digit divisor and multiplication of large numbers.

Students need to be able to apply strategies to perform operations on fractions and represent fraction amounts using graphs. They also need to know how to transform different units of measurement and solve problems that involve volume calculations and graphing points. In the subject of geometry, students should understand how to categorize two-dimensional shapes according to their characteristics.

Students in this grade can review and practice their math skills with the 5th Grade Math course.

## Common Core Math Standards for 8th Grade

In 8th grade, students should be introduced to the concept of irrational numbers. Math concepts should cover how to identify irrational numbers and estimate their quantities. Students should also learn to use exponents and their scientific notation in equations. They need to gain a basic understanding of functions, solve for up to two variables, and represent lines using linear equations.

The lessons in the 8th Grade Number System, 8th Grade Functions and 8th Grade Expressions & Equations courses offer valuable information to students to help learn these concepts.

Students need to understand the geometrical concepts of congruence, transformations, and the Pythagorean Theorem, and they should learn how to use volume formulas for cones, cylinders and spheres. Additionally, they'll be expected to be able to use scatter plots to model the relationship between two variables.

The 8th Grade Geometry and 8th Grade Statistics & Probability courses can help students understand the common core math concepts and can be used by teachers to help with lesson plans, classroom instruction and homework assignments.

## Common Core Math Standards for High School Students

### Number and Quantity

High school students should expand their knowledge on exponents, rational numbers, and radicals to meet the common core math standards. They need to be able to select and describe the use of units of measurement in math problems. Students should also be introduced to the methods for graphing and solving equations that contain complex numbers. Furthermore, they should learn concepts related to polynomial functions, the quadratic equation, matrices, and vectors.

The High School Number and Quantity course includes instruction for all common core standards in this area. The lessons can be used to help students grasp difficult concepts and by teachers to use as visual aids in class or assign for homework.

### Algebra

At the high school level, students need to be introduced to complex numerical expressions. Lessons should further develop their reasoning skills for problem solving, and they should be able to translate words into mathematical expressions, and solve polynomial equations and inequalities.

High school students can go over these concepts using the Algebra High School Standards course, and teachers can use the lesson quizzes as well as chapter and course exams to ensure students have learned these essential math concepts.

### Functions

High school students need to learn how to build functions to demonstrate relationships and quantity. They should be able to apply the ideas of domain and range, and learn the proper notation for functions. Students should encounter linear, exponential, quadratic, and trigonometric functions.

The High School Functions course covers all of the material teachers and students need to meet the common core standards.

### Geometry

Students in high school need to build on their previous knowledge of plane geometry to develop proper definitions of terms and learn about proving geometrical theorems. They should be able to perform various transformations of shapes on a graph, demonstrate the principle of congruence, and build complex geometric shapes and objects. Students should also become familiar with applying modeling to geometry and proving theorems with algebra.

The High School Geometry course can help students understand geometric concepts covered by the common core standards.

### Statistics and Probability

At the high school level students should be introduced to classifications of data and variables, and they should use statistical concepts to make judgments. They also need to be able to use principles, such as probability and linear representation, to demonstrate events and predict outcomes.

The High School Statistics & Probability course is an excellent tool to help teachers cover these topics in the classroom or for students to use on their own to better understand complex concepts.

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