Seventh Grade

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:

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

at Level 2, the student is able to

at Level 3, the student is able to

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

at Level 2, the student is able to

at Level 3, the student is able to

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:

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

at Level 2, the student is able to

at Level 3, the student is able to

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

at Level 2, the student is able to

at Level 3, the student is able to

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:

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

at Level 2, the student is able to

at Level 3, the student is able to

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

at Level 2, the student is able to

at Level 3, the student is able to

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:

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

at Level 2, the student is able to

at Level 3, the student is able to

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

at Level 2, the student is able to

at Level 3, the student is able to

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:

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

at Level 2, the student is able to

at Level 3, the student is able to

Performance Indicators Teacher:

As documented through teacher observation –

at Level 1, the student is able to

at Level 2, the student is able to

at Level 3, the student is able to