Algebra I- Seventh Grade
Recommended Prerequisite: None
Grades Offered: 7
SDE Course Code: 0842
MNPS Course Code: MTH4017Y
Course Description
Algebra I provides students with a transition from thinking about patterns and operations using concrete quantities to their abstraction as variables, expressions, equations, inequalities, and functions Students should become adept at translating between verbal, symbolic, and graphical forms for representing algebraic ideas While most of the Gateway indicators will be covered in the first semester of this course, the second semester topics will provide the foundation for a student’s further study of mathematics Technology and manipulatives are used to develop and extend algebraic thinking and to engage student reasoning Students will take the Gateway Mathematics Test upon completion of this course
Course of Study
Number Sense & Number Theory
· The student will recognize, represent, model and apply real numbers and operations verbally, physically, symbolically, and graphically by …
○ Demonstrating an understanding of the subsets, elements, properties, and operations of the real number system
○ Demonstrating an understanding of the relative size of rational and irrational numbers
○ Articulating, modeling, and applying the concept of inverse (eg, opposites, reciprocals, powers and roots)
○ Describing, modeling, and applying inverse operations
○ Applying number theory concepts (eg, primes, factors, divisibility and multiples) in mathematical problem solving
○ Connecting physical, graphical, verbal, and symbolic representations of absolute value
○ Using real numbers to represent real-world applications (eg, slope, rate of change, probability, and proportionality)
○ Using a variety of notations appropriately (eg exponential, functional, square root)
Estimation/Measurement/Computation
· The students will apply appropriate tools and units of measurement; develop effective estimation and computation strategies for producing reasonable results; and calculate using appropriate tools such as mental mathematics, technology, manipulatives and pencil-and-paper by …
○ Selecting and applying an appropriate method (ie mental arithmetic, paper and pencil, or technology) for computing with real numbers and evaluate the reasonableness of the results
○ Communicating the concepts and strategies being used in estimation, measurement, and computation
○ Performing operations on algebraic expressions and informally justify the procedures chosen
○ Using concepts of length, area, and volume to estimate and solve real world problems
○ Selects & uses appropriate units of measures
○ Applying measurement concepts and relationships in algebraic and geometric problem-solving situations
○ Demonstrating an understanding of rates and other derived and indirect measurements (eg, velocity, miles per hour, revolutions per minute, cost per unit)
○ Using matrices with appropriate technology in real-world problem solving
○ Using estimation to make predictions and test reasonableness of results
Patterns, Functions, & Algebraic Thinking
· The student will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving by …
○ Recognizing, extending, and creating geometric, spatial, and numerical patterns
○ Analyzing mathematical patterns related to algebra and geometry in real-world problem solving
○ Using algebraic thinking to generalize a pattern by expressing the pattern in functional notation
○ Solving linear systems using a variety of techniques, including matrices, graphing, substituting, & elimination
○ Solving problems in number theory, geometry, probability, statistics, and measurement and estimation using algebraic thinking and symbolism
○ Communicating the meaning of variables in algebraic expressions, equations, and inequalities
○ Writes linear equations from:
■ Any 2 points (including integers)
■ Point (or intercept) & slope
■ One point & parallel or perpendicular slope to a given line
○ Identifying and representing a variety of functions
○ Applying the concept of rate of change
○ Analyzing graphs to describe the behavior of functions
○ Interpreting results of algebraic procedures
○ Applying the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities
○ Interpreting graphs that depict real-world phenomena
○ Modeling real-world phenomena using functions and graphs
○ Articulating and applying algebraic properties in symbolic manipulation
○ Identifying relationships which can and which cannot be represented by a function
○ Writes & graphs inequalities and interpret graphs of inequalities
○ Describing the domain and range of functions and articulating restrictions imposed either by the operations or by the real-life situations which the functions represent
○ Describing the transformation of the graph that occurs when coefficients and/or constants of the corresponding linear equations are changed
○ Solves equations & inequalities involving absolute values
○ Add, subtracts, & multiplies polynomials
○ Adds, subtracts, multiplies, & divides rational & radical expressions & functions
○ Simplifies algebraic rational expressions
Statistics and Probability (Data Analysis)
· The student will collect, organize, represent, and interpret data; make inferences and predictions; present and evaluate inferences and predictions; present and evaluate arguments based on data analysis, and model situations to determine theoretical and experimental probabilities by …
○ Collecting, representing, and describing linear and nonlinear data sets developed from the real world
○ Making predictions from a linear data set using a line of best fit
○ Interpreting a set of data using the appropriate measure of central tendency
○ Choosing, constructing, and analyzing appropriate graphical representations for a data set
○ Applying the Law of Large Numbers and the concept of randomness in sampling
○ Applying counting principles of permutations and combinations using appropriate technology
Spatial Sense and Geometric Concepts
· The student will investigate, model, and apply geometric properties and relationships by …
○ Applying geometric properties, formulas, and relationships to solve real-world problems
○ Using inductive reasoning to make conjectures
○ Applying right triangle relationships including the Pythagorean Theorem and the distance formula
Seventh Grade
The following skills are tested on TCAP and are prerequisites for Algebra
Number and Operations
· Determine the square root of perfect squares
· Work flexibly with fractions, decimals, and percents in word problems
· Compare and order fractions, decimals, and percents
· Locate and specify whole numbers, fractions, decimals, percents and integers on the number line
· Understand and use ratios and proportions to represent quantitative relationships
· Recognize and use exponential, scientific, and calculator notation to write large numbers in real-world situations
· Identify the opposites and reciprocal for an integer
· Identify the opposite of a rational number
· Use the distributive property to simplify computations with integers, fractions, and decimals
· Apply order of operations in computing with rational numbers
· Select and use appropriate methods and tools for computing with whole numbers, fractions, decimals, percents, and integers in problem-solving situations (eg, mental computation, estimation, calculators, computers, paper and pencil)
· Estimate the results of rational number computations in real-world situations
· Judge the reasonableness of the results of rational number estimates and computations
· Develop, analyze, explain, and use methods for solving problems involving proportions (eg, scaling, finding equivalent ratios)
· Calculate rates involving cost per unit to determine the best buy
Algebra
· Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible symbolic rules
· Relate and compare different forms of representation for a relationship
· Formulate multi-step equations that represent relationships and real-world situations
· Use symbolic algebra to represent situations and solve problems
· Recognize and generate equivalent forms for simple algebraic expressions
· Evaluate a first-degree algebraic expression given values for two or more variables
· Solve one- and two-step linear equations involving integers
· Use a variety of methods to solve real-world problems involving multi-step linear equations (eg, manipulatives, technology, pencil and paper)
· Apply given formulas to solve real-world problems
· Solve one-step linear inequalities
· Identify the graph of a linear equation and vice versa
· Interpret graphs that represent rates of change in real-world situations
Geometry
· Describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
· Identify and understand relationships among the angles (eg, complementary, supplementary, interior, exterior, vertical, corresponding)
· Solve problems using angle relationships (eg, complementary, supplementary, interior, exterior, vertical, corresponding)
· Determine the measure of an angle of a triangle given the measures of the other two angles
· Identify similar figures and apply relationships between the angles and side lengths of similar geometric figures, including triangles
· Demonstrate understanding of the Pythagorean theorem and use it to solve real-world problems
· Graph points in the coordinate system
· Use visualization and spatial reasoning to solve real-world problems
· Recognize and apply geometric ideas and relationships such as tessellations in areas outside the mathematics classroom (eg, art, science, everyday life)
Measurement
· Understand relationships among units and 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
· 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
· Apply formulas and/or other strategies to solve problems involving perimeter, circumference of circles, and the area of triangles, parallelograms, trapezoids, and circles
· Find area of complex and irregular shapes
· Solve problems involving rate/time/distance (ie, d = rt )
· Solve problems involving scale factors using ratio and proportion
· Solve real-world problems using the Pythagorean Theorem
· Construct tables and graphs to represent rates of change
Date Analysis and Probability
· Select, create, interpret, and use appropriate graphical representations of real-world data
(eg, histograms, box plots, scatterplots)
· Determine and interpret measures of center and spread (eg, mean, median, interquartile range)
· Discuss and understand the relationship between data sets and their graphical representations (eg, bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots)
· Make conjectures and predictions based on data
· Recognize misleading presentations of data
· Determine an appropriate sample and sample size to test a hypothesis
· Connect the symbolic representation of a probability to an experiment
Standards:
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://wwwstatetnus/education/ci/cistandards2001/math/cimathhtm
Gateway Mathematics Test Standards and Item Sampler:
http://wwwstatetnus/education/tssamplershtm
Textbook:
Basal: Larson, et al, McDougal Littell Algebra 1, 2nd Edition, 2004, McDougal Littell
Online Textbook:
http://www.classzone.com/books/algebra_1/index.cfm
Recommended and/or Required Resources:
· TI 83+ Graphing Calculator
· TCAP Item Sampler - http://www.state.tn.us/education/tsachsamp.htm
· A variety of manipulatives: graph paper, rulers, protractors, two-color counters, fraction bars, centimeter cubes or snap cubes, geoboards, miras, Cuisenaire rods, base ten blocks, tangrams, pattern blocks, algebra tiles, meter sticks, etc
· CBR or CBL with probes
· Test preparation book – Edwards, Merv. Tennessee Gateway Coach: Algebra I, New York, NY: Educational Design, 2002