Pre-Algebra 8 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.
EIGHTH GRADE
(Pre-Algebra)
Students in Grade 8 are independent thinkers. They can apply prior knowledge to new situations but may need to be guided through the learning process by continuing the use of hands-on materials, mathematical discourse, and technology. These students have the ability to take ownership of their own mathematical learning and need opportunities to explore and investigate mathematical concepts. Students in Grade 8 also need to be provided with instruction that includes a balance between skill development and mathematical understanding.
The major focus of the eighth-grade curriculum is the integration of new and prior knowledge to solve problems dealing with all mathematical strands, with particular emphasis on algebra, geometry, and proportional reasoning. This curriculum offers a more in-depth study of algebraic concepts than in years past. Therefore, this course is subtitled Pre-Algebra. Students who successfully complete the eighth grade have a thorough knowledge of the skills and concepts necessary for the study of Algebra I. High school credit may not be awarded for this course.
Number and Operations
1. Use various strategies and operations to solve problems
involving real numbers.
•1.1 Using alternative representations of rational numbers
•1.2 Applying GCF, LCM, and prime and composite numbers,
including justification for the reasonableness of results,
when working with rational numbers
•1.3 Applying proportional reasoning
•1.4 Using vocabulary associated with sets, including union and
intersection
•1.5 Determining whether a number is rational or irrational
•1.6 Demonstrating computational fluency with operations on
rational numbers
2. Simplify expressions containing natural number exponents by
applying one or more of the laws of exponents.
•2.1 Writing numbers using scientific notation
3. Use order of operations to evaluate and simplify algebraic
expressions.
•3.1 Applying the substitution principle
•3.2 Applying the properties of operations on rational numbers
to evaluate and simplify algebraic expressions
Algebra
4. Graph linear relations by plotting points or by using the slope
and y-intercept.
•4.1 Determining slopes and y-intercepts of lines
•4.2 Calculating the slope of a linear relation given as a table
or graph
•4.3 Exhibiting conceptual understanding of various uses of
variables
5. Solve problems involving linear functions.
•5.1 Identifying functions from information in tables, sets of
ordered pairs, equations, graphs, and mappings
•5.2 Determining the rule that defines a function
•5.3 Classifying variables in a function as independent or
dependent
•5.4 Classifying relations as linear or nonlinear by examining
tables, graphs, or simple equations
6. Solve multi-step linear equations, including equations requiring
the use of the distributive property.
Geometry
7. Solve problems using the Pythagorean Theorem.
•7.1 Applying the Triangle Inequality Theorem
•7.2 Verifying the Pythagorean Theorem
•7.3 Applying the Pythagorean Theorem to determine if a triangle is
a right triangle
•7.4 Applying the Pythagorean Theorem to find the missing
length of a side of a right triangle
•7.5 Calculating distances on the coordinate plane using the
Pythagorean Theorem
8. Compare quadrilaterals, triangles, and solids, using their properties
and characteristics.
•8.1 Developing mathematical arguments about the relationships
among types of quadrilaterals and triangles
•8.2 Identifying angle bisectors, perpendicular bisectors, congruent
angles, and congruent figures
•8.3 Constructing congruent and similar polygons, congruent
angles, congruent segments, and parallel and
perpendicular lines
Measurement
9. Determine the measures of special angle pairs, including adjacent,
vertical, supplementary, and complementary angles, and angles
formed by parallel lines cut by a transversal.
10. Find the perimeter and area of regular and irregular plane figures.
11. Determine the surface area and volume of rectangular prisms,
cylinders, and pyramids.
•11.1 Estimating surface area and volume of solid figures
•11.2 Determining the appropriate units of measure to describe
surface area and volume
•11.3 Developing formulas for determining surface area and
volume of rectangular prisms, cylinders, and pyramids
12. Determine the lengths of missing sides and measures of angles in
similar and congruent figures.
•12.1 Applying proportional reasoning
•12.2 Using dilations on the coordinate plane to determine
measures of similar figures
•12.3 Finding the ratios of the perimeters and areas of similar
triangles, trapezoids, and parallelograms
Data Analysis and Probability
13. Interpret data from populations, using given and collected data.
•13.1 Representing the data with the most appropriate graph,
including box-and-whisker plot, circle graph, and scatterplot
•13.2 Making predictions by estimating the line of best fit from a
scatterplot
•13.3 Comparing data sets involving two populations
•13.4 Determining the measure of center that is the most
appropriate for a given situation
14. Determine the theoretical probability of an event.
•14.1 Calculating the probability of complementary events
and mutually exclusive events
•14.2 Comparing experimental and theoretical probability
•14.3 Computing the probability of two independent events
and two dependent events
•14.4 Determining the probability of an event through simulation
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