Tennessee Department of Education

Seventh Grade Math

Number and Operation

Content Standard 1.0 The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.

Learning Expectations:

1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1.2 Understand operations and how they relate to one another.

1.3 Solve problems, compute fluently, and make reasonable estimates.

Accomplishments

7.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

    1. recognize the place value of a given digit;
    2. develop meaning for perfect squares (e.g., 1, 4, 9, 16);
    3. develop meaning for square roots;
    4. use exponential notation;
    5. use a variety of models to demonstrate the relationships within the real number system (e.g., Venn diagrams, webs);
    6. represent equivalent numbers using a variety of forms (i.e., whole numbers, fraction, decimals, percents);
    7. compare fractions, decimals, percents, and integers using the appropriate symbol (i.e., <, >, =);
    8. connect whole numbers, fractions, decimals, percents, and integers to locations on the number line;
    9. develop meaning for percents greater than 100 and less than one;
    10. understand and use ratios and proportions to represent quantitative relationships;
    11. develop meaning for opposites, reciprocals, and integers;
    12. use concrete, pictorial, and symbolic representations for integers;
    13. apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime).

7.1.2 Understand operations and how they relate to one another.

    1. understand the meaning and effects of arithmetic operations with fractions and decimals;
    2. use models to demonstrate meaning and effects of arithmetic operations with integers;
    3. apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals;
    4. apply order of operations when computing with whole numbers, decimals, and fractions;
    5. understand and use the inverse relationships of addition and subtraction and multiplication and division to simplify computations and solve problems.

7.1.3 Solve problems, compute fluently, and make reasonable estimates.

    1. select and use appropriate methods and tools for computing with whole numbers, fractions, decimals, percents, and integers in problem solving situations (e.g., mental computation, estimation, calculators, computers, paper and pencil);
    2. analyze procedures for computing with fractions, decimals, and integers;
    3. use strategies to estimate the results of rational number computations in real-world situations;
    4. judge the reasonableness of the results of rational number estimates and computations;
    5. solve two-step real-world problems involving whole numbers, fraction, decimals, and percents;
    6. develop methods for solving problems involving proportions (e.g., scaling, finding equivalent ratios)

Seventh Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

7.1.spi.1. identify prime and composite numbers up to 50;

7.1.spi.2. compute efficiently and accurately with whole numbers, fractions, and decimals.

at Level 2, the student is able to

7.1.spi.3. represent numbers using a variety of equivalent forms (i.e., mixed numbers, fractions, decimals, percents, and integers);

7.1.spi.4. compare rational numbers using the appropriate symbol (<, >, =);

7.1.spi.5. identify the opposite and the reciprocal of a rational number;

7.1.spi.6. connect percents greater than 100 and percents less than one to real-world situations;

7.1.spi.7. apply order of operations when computing with whole numbers (no more than two parentheses and no exponents);

7.1.spi.8. solve one- and two-step real-world problems involving whole numbers, fractions, and decimals;

7.1.spi.9. use estimation strategies to select a reasonable solution to a computation involving rational numbers;

7.1.spi.10. select a reasonable solution to a real-world division problem in which the remainder must be considered.

at Level 3, the student is able to

7.1.spi.11. connect rational numbers to locations on the number line;

7.1.spi.12 use ratios to represent quantitative relationships.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

7.1.tpi.1. use concrete, pictorial, and symbolic representations for integers;

7.1.tpi.2. understand and use the inverse relationships of addition and subtraction and of multiplication and division to simplify computations and solve problems.

at Level 2, the student is able to

7.1.tpi.3. develop meaning for percents greater than 100 and percents less than one;

7.1.tpi.4. understand the meaning and effects of arithmetic operations with fractions and decimals;

7.1.tpi.5. use models to demonstrate meaning and effects of arithmetic operations with integers;

7.1.tpi.6. analyze procedures for computing with fractions, decimals, and integers;

7.1.tpi.7. develop methods for solving problems involving proportions.

at Level 3, the student is able to

7.1.tpi.8. develop meaning for perfect squares (< 100)

7.1.tpi.9. develop meaning for square roots of perfect squares;

7.1.tpi.10. use exponential notation for powers of whole numbers;

7.1.tpi.11. use a variety of models to demonstrate the relationships within the real number system (i.e., Venn diagrams, webs).

Algebra

Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Learning Expectations:

2.1 Understand patterns, relations, and functions.

2.2 Represent and analyze mathematical situations and structures using algebraic symbols.

2.3 Use mathematical models to represent and understand quantitative relationships.

2.4 Analyze change in various contexts.

Accomplishments

7.2.1 Understand patterns, relations, and functions.

    1. represent, analyze, and extend geometric and numerical patterns;
    2. develop understanding for arithmetic sequences;
    3. use tables, graphs, and symbolic rules to generalize patterns in data;
    4. apply and create function rules.

7.2.2 Represent and analyze mathematical situations and structures using algebraic symbols.

    1. demonstrate understanding of different uses of variables;
    2. represent mathematical statements and real-world situations using symbols;
    3. translate one-variable verbal and written expressions into algebraic expressions;
    4. evaluate algebraic expressions given the value of two or more variables;
    5. connect formal and informal methods to solve one-step linear equations;
    6. identify whole numbers that satisfy a given one-variable inequality;
    7. model algebraic equations with manipulatives, technology, and pencil and paper;
    8. solve real-world problems involving one-step linear equations;
    9. explore relationships between symbolic expressions and graphs of lines.

7.2.3 Use mathematical models to represent and understand quantitative relationships.

    1. create a scatterplot to represent data presented in tabular form;
    2. describe the relationship between two quantities represented in a scatterplot.

7.2.4 Analyze change in various contexts.

    1. describe how changes in one quantity or variable result in changes in another;
    2. use unit rates to solve problems (e.g., miles per hour, words per minutes)

Seventh Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

7.2.spi.1. extend geometric and numerical patterns;

7.2.spi.2. apply function rules;

7.2.spi.3. extend rate charts to solve real-world problems.

at Level 2, the student is able to

7.2.spi.4. generalize patterns in data represented in tables and graphs;

7.2.spi.5. represent mathematical statements and real-world situations using symbols;

7.2.spi.6. evaluate algebraic expressions for a given value of up to two variables;

7.2.spi.7. solve one-step linear equations.

at Level 3, the student is able to

7.2.spi.8. solve real-world problems involving one-step linear equations;

7.2.spi.9. identify whole numbers that satisfy a given one-variable one-variable linear inequality;

7.2.spi.10. select the scatterplot that represents the data in tabular form;

7.2.spi.11. interpret graphs which represent rates of change.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

7.2.tpi.1. demonstrate an understanding of different uses of variables.

at Level 2, the student is able to

7.2.tpi.2. translate one-variable verbal and written expressions into algebraic expressions;

7.2.tpi.3. model algebraic expressions;

7.2.tpi.4. explore relationships between symbolic expressions and their graphical representation;

72.tpi.5. describe the relationship between two quantities represented in a scatterplot.

at Level 3, the student is able to

7.2.tpi.6. develop meaning of intercept and rate of change in real-world problems;

7.2.tpi.7. apply formulas in real-world problems.

Geometry

Content Standard 3.0 The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

Learning Expectations:

3.1 Analyze characteristics and properties of two- and three-dimensional geometric figures.

3.2 Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.3 Apply transformations and use symmetry to analyze mathematical situations.

3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.

Accomplishments

7.3.1 Analyze characteristics and properties of two- and three-dimensional geometric figures.

    1. determine congruence of line segments, angles, and polygons by direct comparison of given attributes;
    2. compare and classify triangles by angle size and length of sides;
    3. compare and classify polygons by properties;
    4. use appropriate mathematical language to describe similarity and congruence.

7.3.2 Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

    1. plot a given set of points on the coordinate plane.

7.3.3 Apply transformations and use symmetry to analyze mathematical situations.

    1. relate symmetry and congruence to reflections about a line.

7.3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.

    1. use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, angle measure);
    2. build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa;
    3. use visualization and spatial reasoning to solve real-world problems

Seventh Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

7.3.spi.1. identify the results of transformations of two-dimensional figures (i.e., turns/rotations, flips/reflections, slides/translations).

at Level 2, the student is able to

7.3.spi.2. classify triangles by angle, size, and length of sides;

7.3.spi.3. determine conguence of line segments, angles, and polygons;

7.3.spi.4. classify polygons by properties;

7.3.spi.5. use ordered pairs to describe given points in a coordinate system.

at Level 3, the student is able to

7.3.spi.6. determine the measure of an angle of a triangle given the measures of the other two angles;

7.3.spi.7. apply spatial reasoning and visualization to solve real-world problems.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

7.3.tpi.1. build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa.

at Level 2, the student is able to

7.3.tpi.2. relate symmetry and congruence to reflections about a line;

7.3.tpi.3. use appropriate tools and methods to draw geometric objects with specified properties, (i.e., side lengths, angle measure);

7.3.tpi.4. use models to explore relationships among angles (i.e., complementary, supplementary, interior, exterior, vertical, and corresponding, sum of angles of a triangle).

at Level 3, the student is able to

7.3.tpi.5. use coordinate geometry to investigate various polygons and to make conjectures about properties of polygons;

7.3.tpi.6. identify corresponding parts of congruent and similar triangles.

Measurement

Content Standard 4.0 The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

Learning Expectations:

4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.

4.2 Apply appropriate techniques, tools, and formulas to determine measurements.

Accomplishments

7.4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.

    1. understand both metric and customary systems of measurement;
    2. convert from one unit to another within the same system;
    3. understand, select, and use units of appropriate size and type to measure angles, perimeter, areas, surface area, and volume.

7.4.2 Apply appropriate techniques, tools, and formulas to determine measurements.

    1. use a variety of strategies to estimate length, perimeter, circumference, area, and volume;
    2. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision;
    3. develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles;
    4. develop strategies to find area of complex shapes;
    5. develop strategies to determine the surface area and volume of selected prisms and cylinders;
    6. construct tables and graphs to represent rates of change

Seventh Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

7.4.spi.1. apply formulas to determine the areas of rectangles and triangles;

7.4.spi.2. determine the distance between two points on the x- or the y-axis in Quadrant I.

at Level 2, the student is able to

7.4.spi.3. convert from one unit to another within the same system;

7.4.spi.4. select units of appropriate size and type to measure angles, perimeter, area, surface area, and volume;

7.4.spi.5. apply formulas to determine the area of parallelograms, trapezoids, and circles.

at Level 3, the student is able to

7.4.spi.6. estimate length, perimeter, circumference, area, and volume using a variety of strategies;

7.4.spi.7. find or estimate the area of irregular and complex shapes;

7.4.spi.8. solve problems involving scale factors using ratios and proportions.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

7.4.tpi.1. understand and use both metric and customary systems of measurement;

7.4.tpi.2. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision.

at Level 2, the student is able to

7.4.tpi.3. use a variety of strategies to estimate length, perimeter, circumference, area, and volume;

7.4.tpi.4. use a variety of manipulatives to develop formulas for area of circles and trapezoids;

7.4.tpi.5. develop strategies to determine the surface area and volume of selected prisms and cylinders;

7.4.tpi.6. use models and manipulatives to explore the volume of selected prisms and cylinders.

at Level 3, the student is able to

7.4.tpi.7. construct tables and graphs to represent rates of change.

Data Analysis & Probability

Content Standard 5.0 The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Learning Expectations:

5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

5.2 Select and use appropriate statistical methods to analyze data.

5.3 Develop and evaluate inferences and predictions that are based on data.

5.4 Understand and apply basic concepts of probability.

Accomplishments

7.5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

    1. formulate questions, design studies, and collect real-world data;
    2. construct, interpret, and use multiple-bar graphs, multiple-line graphs, and circle graphs displaying real-world data.

7.5.2 Select and use appropriate statistical methods to analyze data.

    1. find, use, and interpret measures of center and spread (e.g., mean, interquartile range);
    2. recognize misleading representations of data;
    3. discuss and understand the relationship between data sets and their graphical representations (e.g., bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, and scatterplots).

7.5.3 Develop and evaluate inferences and predictions that are based on data.

    1. make conjectures and predictions based on data;
    2. make conjectures to formulate new questions for future studies.

7.5.4 Understand and apply basic concepts of probability.

    1. connect the symbolic representation of a probability to an experiment;
    2. construct a tree diagram to determine all possible outcomes of a simple event

Seventh Grade Benchmarks

Performance Indicators State:

As documented through state assessment –

at Level 1, the student is able to

7.5.spi.1. interpret bar and line graphs to answer questions and solve real-world problems.

at Level 2, the student is able to

7.5.spi.2 interpret circle graphs displaying real-world data;

7.5.spi.3. determine the mean for a data set;

7.5.spi.4. determine the median for a data set;

7.5.spi.5. make predictions based on data;

7.5.spi.6. use a tree diagram or organized list to determine all possible outcomes of a simple compound event.

at Level 3, the student is able to

7.5.spi.7. connect data sets and their graphical representation (i.e., bar graphs, stem-and-leaf plots, box plots, and scatterplots);

7.5.spi.8. use proportional thinking to make conjectures about results of experiments and simulations;

7.5.spi.9. connect the symbolic representation of a probability to an experiment.

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

7.5.tpi.1. construct bar and line graphs to represent data from tables and real-world problems;

7.5.tpi.2. describe an appropriate sample to a given hypothesis.

at Level 2, the student is able to

7.5.tpi.3. recognize and discuss misleading representations of data;

7.5.tpi.4. suggest questions for future study to follow-up on experiments or studies;

7.5.tpi.5. identify appropriate data sources to address questions or hypotheses;

7.5.tpi.6. construct tree diagrams to determine outcomes of a simple compound event;

7.5.tpi.7. make conjectures to formulate new questions for future studies.

at Level 3, the student is able to

7.5.tpi.8. describe why or why not predictions can be made for a population based on survey results for a given sample;

7.5.tpi.9. communicate the difference in theoretical and experimental probabilities.