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    8th grade
    Mathematics Curriculum at Ola Middle School

    Grade 7

     

    The Common Core Georgia Performance Standards (CCGPS) specify what students are expected to know and be able to do by the end of the school year. Three distinct sections comprise the 7th grade mathematics CCGPS:  Content Standards, Process Standards, and a Reading Standard.  These standards can be viewed at https://www.georgiastandards.org/Georgia-Standards/Pages/Math-6-8.aspx

     

    NUMBER AND OPERATIONS

    Students will further develop their understanding of the concept of rational numbers and apply them to real world situations.

    M7N1. Students will understand the meaning of positive and negative rational

    numbers and use them in computation.

    a. Find the absolute value of a number and understand it as the distance from

    zero on a number line.

    b. Compare and order rational numbers, including repeating decimals.

    c. Add, subtract, multiply, and divide positive and negative rational numbers.

    d. Solve problems using rational numbers.

    GEOMETRY

    Students will further develop and apply their understanding of plane and solid geometric figures through the use of constructions and transformations. Students will explore the properties of similarity and further develop their understanding of 3-dimensional figures.

     

    Line and rotational symmetry

    Surface area and volume

    Ratio as a representation of quantitative relationships

    M7G1. Students will construct plane figures that meet given conditions.

    a. Perform basic constructions using both compass and straight edge, and

    appropriate technology. Constructions should include copying a segment;

    copying an angle; bisecting a segment; bisecting an angle; constructing

    perpendicular lines, including the perpendicular bisector of a line segment; and

    constructing a line parallel to a given line through a point not on the line.

    b. Recognize that many constructions are based on the creation of congruent

    triangles.

    M7G2. Students will demonstrate understanding of transformations.

    a. Demonstrate understanding of translations, dilations, rotations, reflections, and

    relate symmetry to appropriate transformations.

    b. Given a figure in the coordinate plane, determine the coordinates resulting

    from a translation, dilation, rotation, or reflection.

    M7G3. Students will use the properties of similarity and apply these concepts to

    geometric figures.

    a. Understand the meaning of similarity, visually compare geometric figures for

    similarity, and describe similarities by listing corresponding parts.

    b. Understand the relationships among scale factors, length ratios, and area ratios

    between similar figures. Use scale factors, length ratios, and area ratios to

    determine side lengths and areas of similar geometric figures.

    c. Understand congruence of geometric figures as a special case of similarity:

    The figures have the same size and shape.

    M7G4. Students will further develop their understanding of three-dimensional

    figures.

    a. Describe three-dimensional figures formed by translations and rotations of

    plane figures through space.

    b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and

    prisms.

    ALGEBRA

    Students will demonstrate an understanding of linear relations and fundamental algebraic concepts.

    M7A1. Students will represent and evaluate quantities using algebraic expressions.

    a. Translate verbal phrases to algebraic expressions.

    b. Simplify and evaluate algebraic expressions, using commutative, associative,

    and distributive properties as appropriate.

    c. Add and subtract linear expressions.

    M7A2. Students will understand and apply linear equations in one variable.

    a. Given a problem, define a variable, write an equation, solve the equation, and

    interpret the solution.

    b. Use the addition and multiplication properties of equality to solve one- and

    two-step linear equations.

    M7A3. Students will understand relationships between two variables.

    a. Plot points on a coordinate plane.

    b. Represent, describe, and analyze relations from tables, graphs, and formulas.

    c. Describe how change in one variable affects the other variable.

    d. Describe patterns in the graphs of proportional relationships, both direct

    (y = kx) and inverse (y = k/x).

    DATA ANALYSIS AND PROBABILITY

    Students will demonstrate understanding of data analysis by posing questions, collecting data, analyzing the data using measures of central tendency and variation, and using the data to answer the questions posed. Students will understand the role of probability in sampling.

    M7D1. Students will pose questions, collect data, represent and analyze the data,

    and interpret results.

    a. Formulate questions and collect data from a census of at least 30 objects and

    from samples of varying sizes.

    b. Construct frequency distributions.

    c. Analyze data using measures of central tendency (mean, median, and mode),

    including recognition of outliers.

    d. Analyze data with respect to measures of variation (range, quartiles,

    interquartile range).

    e. Compare measures of central tendency and variation from samples to those

    from a census. Observe that sample statistics are more likely to approximate

    the population parameters as sample size increases.

    f. Analyze data using appropriate graphs, including pictographs, histograms, bar

    graphs, line graphs, circle graphs, and line plots introduced earlier, and using

    box and- whisker plots and scatter plots.

    g. Analyze and draw conclusions about data, including describing the

    relationship between two variables.

     

    Terms/Symbols:

    natural number, whole number, sign, integer, opposite, negative, positive, absolute value, term, variable, commutative property, associative property, distributive property, algebraic expression, linear equation, direct and indirect proportions, constant of proportionality (y = kx), variation, polyhedron, translation, rotation, reflection, dilation, symmetry, bisector, parallel lines, perpendicular lines, cross-section, similar, congruent, point, line, plane, line segment, endpoints, intersection, ray, parallel lines, perpendicular lines, similar, similarity, rate, scale drawings, corresponding sides, corresponding angles, congruent, diagonal, algebraic expression, commutative property, associative property, distributive property, direct variation, inverse variation, inversely proportional, mean, median, mode, range, quartile, interquartile range, outlier, histogram, scatter plot, line plot, box-and-whisker plot, , ~, ≈, ||, ⊥, ∠.

    Process Standards

    The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

    M7P1. Students will solve problems (using appropriate technology).

    a. Build new mathematical knowledge through problem solving.

    b. Solve problems that arise in mathematics and in other contexts.

    c. Apply and adapt a variety of appropriate strategies to solve problems.

    d. Monitor and reflect on the process of mathematical problem solving.

    M7P2. Students will reason and evaluate mathematical arguments.

    a. Recognize reasoning and proof as fundamental aspects of mathematics.

    b. Make and investigate mathematical conjectures.

    c. Develop and evaluate mathematical arguments and proofs.

    d. Select and use various types of reasoning and methods of proof.

    M7P3. Students will communicate mathematically.

    a. Organize and consolidate their mathematical thinking through communication.

    b. Communicate their mathematical thinking coherently and clearly to peers,

    teachers, and others.

    c. Analyze and evaluate the mathematical thinking and strategies of others.

    d. Use the language of mathematics to express mathematical ideas precisely.

    M7P4. Students will make connections among mathematical ideas and to other

    disciplines.

    a. Recognize and use connections among mathematical ideas.

    b. Understand how mathematical ideas interconnect and build on one another to

    produce a coherent whole.

    c. Recognize and apply mathematics in contexts outside of mathematics.

    M7P5. Students will represent mathematics in multiple ways.

    a. Create and use representations to organize, record, and communicate

    mathematical ideas.

    b. Select, apply, and translate among mathematical representations to solve

    problems.

    c. Use representations to model and interpret physical, social, and mathematical

    phenomena.

     

     

    Reading Standard 

    After the elementary years, students are seriously engaged in reading for learning. This process sweeps across all disciplinary domains, extending even to the area of personal learning. Students encounter a variety of informational as well as fictional texts, and they experience text in all genres and modes of discourse. In the study of various disciplines of learning (language arts, mathematics, science, social studies), students must learn through reading the communities of discourse of each of those disciplines. Each subject has its own specific vocabulary, and for students to excel in all subjects, they must learn the specific vocabulary of those subject areas in context.

     

    Beginning with the middle grades years, students begin to self-select reading materials based on personal interests established through classroom learning. Students become curious about science, mathematics, history, and literature as they form contexts for those subjects related to their personal and classroom experiences. As students explore academic areas through reading, they develop favorite subjects and become confident in their verbal discourse about those subjects.

    Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

     

    MRC. Students will enhance reading in all curriculum areas by:

    a. Reading in all curriculum areas

    • Read a minimum of 25 grade-level appropriate books per year from a variety of subjects.

    • disciplines and participate in discussions related to curricular learning in all areas.

    • Read both informational and fictional texts in a variety of genres and modes of

    discourse.

    • Read technical texts related to various subject areas

     

    b. Discussing books

    • Discuss messages and themes from books in all subject areas.

    • Respond to a variety of texts in multiple modes of discourse.

    • Relate messages and themes from one subject area to messages and themes in another area.

    • Evaluate the merit of texts in every subject discipline.

    • Examine author’s purpose in writing.

    • Recognize the features of disciplinary texts.

     

    c. Building vocabulary knowledge

    • Demonstrate an understanding of contextual vocabulary in various subjects.

    • Use content vocabulary in writing and speaking.

    • Explore understanding of new words found in subject area texts.

     

    d. Establishing context

    • Explore life experiences related to subject area content.

    • Discuss in both writing and speaking how certain words are subject area related.

    • Determine strategies for finding content and contextual meaning for unknown words.

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