Algebra I Objectives from the Alabama Course of Study
SIXTH – EIGHTH GRADE OVERVIEW
Students in Grades 6-8 mature and progress at varied rates and are sensitive to peer perceptions; therefore, a supportive classroom environment where students feel comfortable sharing ideas is a priority. Classroom learning experiences are enhanced through interactions in which students learn to develop reasoning skills and evaluate their own thinking and the thinking of others.
The main focus of the mathematics program in the middle grades is to provide a coherent, integrated curriculum that enables all students in Grades 6-8 to recognize and apply mathematics in contexts outside the classroom. Middle school students acquire a solid foundation for high school mathematics by making a transition from concrete topics to abstract concepts. Through the use of manipulatives, social interaction, mathematical discourse, and a variety of technological tools, students engage in mathematical investigations, propose ideas and conjectures, and make generalizations. A challenging curriculum and a supportive environment encourage middle school students to be actively involved in their own mathematical learning. The mathematics program in Grades 6-8 plays a key role in preparing students for high school mathematics and further study. This curriculum integrates algebraic and geometric concepts into other mathematical topics. By enabling students to make connections between these topics, algebraic and geometric thinking skills are developed. Instruction focuses on rational numbers and algebraic, geometric, and proportional reasoning concepts in order to provide students with the necessary prerequisite skills for success in high school mathematics courses.
Embedded in the content standards of Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability are the important process standards of Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. These process standards are integrated throughout the middle grades curriculum to deepen students’ understanding of mathematical concepts. Students become good problem solvers with a mathematical foundation that allows them to choose problem-solving techniques appropriate for a situation, communicate the reasoning for these choices, and identify the methods used to determine the results. The teacher plays a key role in helping students develop the skills needed for reasoning and proof. Students are better able to make conjectures and arguments when they are encouraged to verbalize, illustrate, or record their mathematical thought processes. By listening to or reading the mathematical thinking processes of their classmates, students are encouraged to communicate and to learn from each other.
Mathematical discussion becomes more complex in the middle grades. Students are expected to use mathematical vocabulary as they explain their reasoning. Students who are taught the connectedness of mathematical concepts will learn to use these concepts to build upon their own mathematical knowledge, rather than attempt to memorize many isolated facts/formulas, an exhaustive and perhaps impossible task in the middle grades. Representing mathematical concepts in various ways allows students to use modeling to solve complex problems. When students realize that algebra makes the problem-solving process much more efficient, they see the interconnectedness of mathematics with the real world. Through this curriculum, middle-grades students form positive attitudes about mathematics that contribute to decisions to pursue further study of mathematics and ultimately enhance their life opportunities.
The content of the mathematics program for Grade 7, Grade 8, and Algebra I is significantly different from one grade or course to another. School systems may offer Algebra I in Grade 8. However, eighth-grade students taking Algebra I need an in-depth knowledge of the mathematical concepts taught in Grades 7 and 8. Careful consideration should be given before placing Grade 8 students in Algebra I rather than requiring them to complete the Grade 8 mathematics course.
ALGEBRA I
Algebra I is a formal, in-depth study of algebraic concepts and the real number system. In this course students develop a greater understanding of and appreciation for algebraic properties and operations. Algebra I reinforces concepts presented in earlier courses and permits students to explore new, more challenging content which prepares them for further study in mathematics. The course focuses on the useful application of course content and on the development of student understanding of central concepts. Appropriate use of technology allows students opportunities to work to improve concept development. As a result, students are empowered to perform mathematically, both with and without the use of technological tools.
Because of its importance in the development of mathematical empowerment, Algebra I is required for all students. The content is also a central component of formal state-level assessments at the secondary level. To better meet the needs of students of varying abilities, school systems may offer Algebra I (140 hours/one credit) or Algebra IA and IB (280 hours/two credits). If systems choose to offer Algebra I in the eighth grade, the course must include the minimum required content as prescribed in this course of study.
Number and Operations
1. Simplify numerical expressions using properties of real
numbers and order of operations, including those involving
square roots, radical form, or decimal approximations.
•1.1 Applying laws of exponents to simplify expressions,
including those containing zero and negative integral
exponents
Algebra
2. Analyze linear functions from their equations, slopes, and
intercepts.
•2.1 Finding the slope of a line from its equation or by
applying the slope formula
•2.2 Determining the equations of linear functions given two
points, a point and the slope, tables of values, graphs,
or ordered pairs
•2.3 Graphing two-variable linear equations and inequalities
on the Cartesian plane
3. Determine characteristics of a relation, including its domain,
range, and whether it is a function, when given graphs, tables
of values, mappings, or sets of ordered pairs.
•3.1 Finding the range of a function when given its domain
4. Represent graphically common relations, including x = constant,
y = constant, y = x, y = , y = x2, and y = .
•4.1 Identifying situations that are modeled by common relations,
including x = constant, y = constant, y = x, y = , y = x2,
and y =
5. Perform operations of addition, subtraction, and multiplication
on polynomial expressions.
•5.1 Dividing by a monomial
6. Factor binomials, trinomials, and other polynomials using GCF,
difference of squares, perfect square trinomials, and grouping.
7. Solve multi-step equations and inequalities including linear,
radical, absolute value, and literal equations.
•7.1 Writing the solution of an equation or inequality in set
notation
•7.2 Graphing the solution of an equation or inequality
•7.3 Modeling real-world problems by developing and solving
equations and inequalities, including those involving direct
and inverse variation
8. Solve systems of linear equations and inequalities in two variables
graphically or algebraically.
•8.1 Modeling real-world problems by developing and solving
systems of linear equations and inequalities
9. Solve quadratic equations using the zero product property.
•9.2 Approximating solutions graphically and numerically
Geometry
10. Calculate length, midpoint, and slope of a line segment when
given coordinates of its endpoints on the Cartesian plane.
•10.1 Deriving the distance, midpoint, and slope formulas
Measurement
11. Solve problems algebraically that involve area and perimeter
of a polygon, area and circumference of a circle, and volume
and surface area of right circular cylinders or right
rectangular prisms.
•11.1 Applying formulas to solve word problems
Data Analysis and Probability
12. Compare various methods of data reporting, including scatterplots,
stem-and-leaf plots, histograms, box-and-whisker plots, and line
graphs, to make inferences or predictions.
•12.1 Determining effects of linear transformations of data
•12.2 Determining effects of outliers
•12.3 Evaluating the appropriateness of the design of a survey
13. Identify characteristics of a data set, including measurement
or categorical and univariate or bivariate.
14. Use a scatterplot and its line of best fit or a specific line graph
to determine the relationship existing between two sets of data,
including positive, negative, or no relationship.
15. Estimate probabilities given data in lists or graphs.
•15.1 Comparing theoretical and experimental probabilities
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