Seventh Grade Mathematics
SDE Course Code: 0706
MNPS Course Code: MTH4007Y
Course Description
The seventh grade mathematics curriculum deals with deepening students’ understanding of problem solving and of operations using rational numbers. Students apply appropriate techniques, tools, and formulas to determine measurement of two- and three-dimensional geometric figures. Patterns, data, graphs, relations, words and algebraic symbols are used to analyze mathematical situations. Students are expected to communicate logical thinking using correct terminology and multiple forms of representation.
Course of Study
· Understand numbers, ways of representing numbers, relationships among numbers, and number systems
○ Recognize the place value of a given digit
○ Develop meaning for perfect squares (e.g., 1, 4, 9, 16)
○ Develop meaning for square roots
○ Use exponential notation
○ Use a variety of models to demonstrate the relationships within the real number system (e.g., Venn diagrams, webs)
○ Use real numbers to represent real-world applications
○ Represent equivalent numbers using a variety of forms (i.e., whole numbers, fraction, decimals, percents)
○ Compare fractions, decimals, percents, and integers using the appropriate symbol (i.e., <, >, =)
○ Use mathematical notation appropriately
○ Connect whole numbers, fractions, decimals, percents, and integers to locations on the number line
○ Develop meaning for percents greater than 100 and less than one
○ Understand and use ratios and proportions to represent quantitative relationships
○ Develop meaning for opposites, reciprocals, and integers
○ Use concrete, pictorial, and symbolic representations for integers
○ Apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime)
○ Demonstrate an understanding of the subsets, elements, properties, and operations of the rational number system
· Understand operations and how they relate to one another
○ Understand the meaning and effects of arithmetic operations with fractions and decimals.
○ Use models to demonstrate meaning and effects of arithmetic operations with integers
○ Communicate the concepts and strategies being used in estimation, measurement, and computation
○ Apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals
○ Apply order of operations when computing with whole numbers, decimals, and fractions
○ Understand and use the inverse relationships of addition and subtraction and multiplication and division to simplify computations and solve problems
○ Demonstrate an understanding of division involving zero
○ Connect physical, graphical, verbal, and symbolic representations of absolute value
· Solve problems, compute fluently, and make reasonable estimates
○ 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)
○ Analyze procedures for computing with fractions, decimals, and integers
○ Demonstrate an understanding of the relative size of rational and irrational numbers
○ Connect physical, graphical, verbal, and symbolic representations of rational numbers
○ Use strategies to estimate the results of rational number computations in real-world situations
○ Judge the reasonableness of the results of rational number estimates and computations
○ Solve two-step real-world problems involving whole numbers, fraction, decimals, and percents
○ Develop methods for solving problems involving proportions (e.g., scaling, finding equivalent ratios)
· Understand patterns, relations, and functions
○ Represent, analyze, and extend geometric and numerical patterns
○ Develop understanding for arithmetic sequences
○ Use tables, graphs, and symbolic rules to generalize patterns in data
○ Apply and create function rules
○ Analyze mathematical patterns related to algebra and geometry in real-world problem solving
· Represent and analyze mathematical situations and structures using algebraic symbols
○ Demonstrate understanding of different uses of variables
○ Represent mathematical statements and real-world situations using symbols
○ Translate one-variable verbal and written expressions into algebraic expressions
○ Evaluate algebraic expressions given the value of two or more variables
○ Connect formal and informal methods to solve one-step linear equations
○ Identify whole numbers that satisfy a given one-variable inequality
○ Model algebraic equations with manipulatives, technology, and pencil and paper
○ Solve real-world problems involving one-step linear equations
○ Explore relationships between symbolic expressions and graphs of lines
○ Solve problems in number theory, geometry, probability and statistics, and measurement and estimation using algebraic thinking
· Use mathematical models to represent and understand quantitative relationships
○ Create a scatterplot to represent data presented in tabular form
○ Describe the relationship between two quantities represented in a scatterplot
· Analyze change in various contexts
○ Describe how changes in one quantity or variable result in changes in another
○ Use unit rates to solve problems (e.g., miles per hour, words per minutes)
○ Demonstrate an understanding of rates and other derived and indirect measurements
· Analyze characteristics and properties of two- and three-dimensional geometric figures
○ Determine congruence of line segments, angles, and polygons by direct comparison of given attributes
○ Compare and classify triangles by angle size and length of sides
○ Compare and classify polygons by properties
○ Use appropriate mathematical language to describe similarity and congruence
○ Analyze relationships among corresponding parts of similar or congruent geometric figures
○ Apply the Pythagorean Theorem in problem solving
· Specify locations and describe spatial relationships using coordinate geometry and other representational systems
○ Plot a given set of points on the coordinate plane
○ Communicate position using spatial sense with two-dimensional coordinate systems
○ Apply transformations and use symmetry to analyze mathematical situations
○ Relate symmetry and congruence to reflections about a line
· Use visualization, spatial reasoning, and geometric modeling to solve problems
○ Use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, angle measure)
○ Demonstrate understanding of the properties and construction of geometric figures, including angles, parallel lines, perpendicular lines, triangles, circles, and quadrilaterals
○ Build a three-dimensional object from a two-dimensional representation (net) of that object and vice versa
○ Use visualization and spatial reasoning to solve real-world problems
· Understand measurable attributes of objects and the units, systems, and processes of measurement
○ understand both metric and customary systems of measurement
○ convert from one unit to another within the same system
○ understand, select, and use units of appropriate size and type to measure angles, perimeter, areas, surface area, and volume
· Apply appropriate techniques, tools, and formulas to determine measurements
○ Use a variety of strategies to estimate length, perimeter, circumference, area, and volume
○ Select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision
○ Use concepts of length and area to estimate and solve real-world problems
○ Apply measurement concepts and relationships in geometric problem-solving situations
○ Use estimation to make predictions and determine reasonableness of results
○ Choose appropriate techniques and tools to measure quantities in order to meet specifications for precision and accuracy
○ Demonstrate and understanding of pi
○ Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles
○ Apply geometric properties, formulas, and relationships to solve real-world problems
○ Develop strategies to find area of complex shapes develop strategies to determine the surface area and volume of selected prisms and cylinders
○ Construct tables and graphs to represent rates of change
○ Model real-world phenomena using graphs
○ Use inductive reasoning to make conjectures
· Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions
○ Formulate questions, design studies, and collect real-world data
○ Construct, interpret, and use multiple-bar graphs, multiple-line graphs, and circle graphs displaying real-world data
· Select and use appropriate statistical methods to analyze data
○ Find, use, and interpret measures of center and spread (e.g., mean, interquartile range)
○ Recognize misleading representations of data
○ 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)
○ Choose, construct, and analyze appropriate graphical representations for a data set including pie charts, histograms, stem and leaf plots, and scatterplots
○ Apply appropriate technology in data collection and analysis
· Develop and evaluate inferences and predictions that are based on data
○ Make conjectures and predictions based on data
○ Make conjectures to formulate new questions for future studies
· Understand and apply basic concepts of probability
○ Connect the symbolic representation of a probability to an experiment
○ Construct a tree diagram to determine all possible outcomes of a simple event
○ Apply theoretical and experimental probability to analyze the likelihood of an event
○ Use simulations to estimate probability
○ Analyze the validity of statistical conclusions and the use, misuse, and abuse of data
○ Apply counting principles of permutations and combinations using appropriate technology
Standards:
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm
Textbook:
Basal: Larson, et al, McDougal Littell Middle School Math, Course 2, 1st Edition, 2004, McDougal Littell
Online Textbook:
http://www.classzone.com/books/msmath_2/
Recommended and/or required resources:
· TI 83+ graphing calculator, scientific calculator, or four-function calculator
· TCAP Item Sampler - http://www.state.tn.us/education/tsachsamp.htm
· Manipulatives: graph paper, rulers, protractors, two-color counters, fraction bars, centimeter cubes or snap cubes, geoboards, miras, pattern blocks, base ten blocks, color tiles, Cuisenaire rods, tangrams, algebra tiles, meter sticks, etc.