Welcome to the 8th grade Webpage!
This year, we will be using resources from the Illinois State Board of Education Model Mathematics Curriculum. Here are the key topics in mathematics this year:
Critical Area #1: Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/ x= m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m-A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.
Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane, these intersect, are parallel or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems
Critical Area #2: Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.
Critical Area #3: Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.
Our curriculum consists of 8 units that will be taught in the following sequence:
1) Real Numbers & Exponents: Unit 1 is a study of the differences between rational and irrational numbers. In this unit students apply what they have learned in previous grade levels about exponents to deepen their understanding of perfect squares and cubes and include square and cube roots.
2) Expressions & Equations: In Unit 2, students come to realize that, when solving equations, there may be a single solution, infinite solutions, or no solutions. Students solve real-world and mathematical problems using equations.
3) Congruence & Similarity: Unit 3 is an opportunity to study congruence and similarity through the lens of transformations. Students will informally prove that figures are congruent by identifying a sequence of rotations, reflections and/or translations or prove that figures are similar by describing the dilation of the original figure.
4) Functions: In Unit 4, students are introduced to Functions—learning that they describe relationships. They will compare and construct functions in various modes of representation.
5) Linear Relationships: Unit 5 is an opportunity to study linear relationships and slope (or rate of change) both graphically and algebraically. Students graph linear equations and systems of linear equations and discuss the representations with a single solution, no solution, and infinite solutions.
6) Pythagorean Theorem: Unit 6 is the introduction to and practice with using the Pythagorean Theorem to solve problems.
7) Volume: Unit 7 is the study of volume of circular figures. It is an opportunity for students to apply what they have learned about rational and irrational numbers and equations to geometry.
8) Patterns & Bivariate Data: Unit 8 is an opportunity to apply what students have learned about linear equations and graphing to statistics.
Our sequence of units has been carefully planned to prepare our students for success on the new PARCC assessments. These assessments have replaced the ISAT as the Illinois State Assessment, and will be given in March and in May of this school year. Students will practice many skills and concepts by revisiting them in daily routines and stations throughout the school year. We are looking forward to a wonderful experience in 8th Grade.
This year, we will be using resources from the Illinois State Board of Education Model Mathematics Curriculum. Here are the key topics in mathematics this year:
Critical Area #1: Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/ x= m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m-A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.
Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane, these intersect, are parallel or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems
Critical Area #2: Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.
Critical Area #3: Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.
Our curriculum consists of 8 units that will be taught in the following sequence:
1) Real Numbers & Exponents: Unit 1 is a study of the differences between rational and irrational numbers. In this unit students apply what they have learned in previous grade levels about exponents to deepen their understanding of perfect squares and cubes and include square and cube roots.
2) Expressions & Equations: In Unit 2, students come to realize that, when solving equations, there may be a single solution, infinite solutions, or no solutions. Students solve real-world and mathematical problems using equations.
3) Congruence & Similarity: Unit 3 is an opportunity to study congruence and similarity through the lens of transformations. Students will informally prove that figures are congruent by identifying a sequence of rotations, reflections and/or translations or prove that figures are similar by describing the dilation of the original figure.
4) Functions: In Unit 4, students are introduced to Functions—learning that they describe relationships. They will compare and construct functions in various modes of representation.
5) Linear Relationships: Unit 5 is an opportunity to study linear relationships and slope (or rate of change) both graphically and algebraically. Students graph linear equations and systems of linear equations and discuss the representations with a single solution, no solution, and infinite solutions.
6) Pythagorean Theorem: Unit 6 is the introduction to and practice with using the Pythagorean Theorem to solve problems.
7) Volume: Unit 7 is the study of volume of circular figures. It is an opportunity for students to apply what they have learned about rational and irrational numbers and equations to geometry.
8) Patterns & Bivariate Data: Unit 8 is an opportunity to apply what students have learned about linear equations and graphing to statistics.
Our sequence of units has been carefully planned to prepare our students for success on the new PARCC assessments. These assessments have replaced the ISAT as the Illinois State Assessment, and will be given in March and in May of this school year. Students will practice many skills and concepts by revisiting them in daily routines and stations throughout the school year. We are looking forward to a wonderful experience in 8th Grade.