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# M/J Grade 8 Pre-Algebra   (#1205070)

Version for Academic Year:
Course Number: 1205070
Course Path:
Abbreviated Title: M/J GRADE 8 PRE-ALG
Course Length: Year (Y)
Course Type: Core Academic Course
Course Level: 2
Course Status: Course Approved
Grade Level(s): 6,7,8

### GENERAL NOTES

Additional content addressed on the Grade 8 NAEP Mathematics assessment includes:

• Draw or sketch from a written description polygons, circles, or semicircles. (MAFS.7.G.1.2; include circles and semicircles)
• Represent or describe a three-dimensional situation in a two-dimensional drawing from different views. (MAFS.6.G.1.4)
• Demonstrate an understanding about the two- and three-dimensional shapes in our world through identifying, drawing, modeling, building, or taking apart. (MAFS.6.G.1.4, MAFS.7.G.1.3, MAFS.7.G.2.6)
• Visualize or describe the cross section of a solid. (MAFS.7.G.1.3)
• Represent geometric figures using rectangular coordinates on a plane. (MAFS.6.G.1.3)
• Describe how mean, median, mode, range, or interquartile ranges relate to distribution shape. (MAFS.6.SP.2.5c)
• Using appropriate statistical measures, compare two or more data sets describing the same characteristic for two different populations for subset of the same population. (MAFS.7.SP.2.3, MAFS.7.SP.2.4)
• Given a sample, identify possible sources of bias in sampling. (MAFS.7.SP.1.1)
• Distinguish between a random and nonrandom sample. (MAFS.7.SP.1.1)
• Evaluate the design of an experiment. (MAFS.7.SP.1.2)
• Determine the theoretical probability of simple and compound events in familiar contexts. (MAFS.7.SP.3.8a)
• Estimate the probability of simple and compound events through experimentation or simulation. (MAFS.7.SP.3.8)
• Use theoretical probability to evaluate or predict experimental outcomes. (MAFS.7.SP.3.6, MAFS.SP.3.7)
• Describe relative positions of points and lines using the geometric ideas of midpoint, points on common line through a common point, parallelism, or perpendicularity.
• Describe the intersection of two or more geometric figures in the plane (e.g., intersection of a circle and a line).
• Make and test a geometric conjecture about regular polygons.

English Language Development ELD Standards Special Notes Section:
Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL's need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:
http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf

For additional information on the development and implementation of the ELD standards, please contact the Bureau of Student Achievement through Language Acquisition at sala@fldoe.org.

Florida Standards Implementation Guide Focus Section:

The Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.

Major Clusters

MAFS.8.EE.1 Work with radicals and integer exponents.

MAFS.8.EE.2 Understand the connections between proportional relationships, lines, and linear equations.

MAFS.8.EE.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

MAFS.8.F.1 Define, evaluate, and compare functions.

MAFS.8.F.2 Use functions to model relationships between quantities.

MAFS.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software.

MAFS.8.G.2 Understand and apply the Pythagorean Theorem.

Supporting Clusters

MAFS.8.NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

MAFS.8.SP.1 Investigate patterns of association in bivariate data.

Additional Clusters

MAFS.G.3 Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Note: Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.

### VERSION REQUIREMENTS

In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

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 the 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 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.
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.
3. Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilation, 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 traversal 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.

Additional Instructional Resources:
A.V.E. for Success Collection: http://www.fasa.net/iTunesU/index.cfm

47 Course Standards