MACOPIN MIDDLE SCHOOL
Mathematics 7
Syllabus
I. COURSE TITLE
Mathematics 7
II. TEXTBOOK
Connected Mathematics 2. Glenda Lappan, James T. Fey, et al. Prentice Hall, Boston, MA, 2006.
III. COURSE DESCRIPTION
The Connected Mathematics Program, 2nd revision, aims to expand student knowledge to prepare them for algebra beyond symbolic manipulation and to offer opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. Eight units that focus formally on pre-algebra instruction emphasize reasoning and communication while constructing and reinforcing mathematical concepts through practice and application. The Connected Mathematics curriculum is the beginning piece of a comprehensive long-range plan stimulated by New Jersey’s participation in the American Diploma Project, designed to bring larger numbers of students to Algebra II in the high school at a more accelerated pace.
IV. COURSE OBJECTIVES
A. Number Sense and Operations: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.
1. Extend understanding of the number system by constructing meanings for rational numbers, percents, and whole numbers with exponents.
2. Demonstrate a sense of the relative magnitudes of numbers
3. Understand and use ratios, proportions, and percents in a variety of situations.
4. Compare and order numbers of all named types.
5. Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.
6. Understand that all fractions can be represented as repeating or terminating decimals.
7. Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with pencil-and-paper, mental math, and calculator.
8. Use exponentiation to find whole number powers of numbers.
9. Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.
10. Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.
B. Geometry and Measurement: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena.
1. Understand and apply properties of polygons.
2. Understand and apply the concept of similarity.
3. Use logic and reasoning to make and support conjectures about geometric objects.
4. Understand and apply transformations.
5. Use coordinates in four quadrants to represent geometric concepts.
6. Use a coordinate grid to model and quantify transformations.
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7. Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.
8. Develop and apply strategies for finding perimeter and area.
9. Recognize that the volume of a pyramid or cone is 1/3 of the volume of the prism or cylinder with the same base and height.
C. Patterns and Algebra: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.
1. Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.
2. Graph functions, including equations involving two variables, and understand and describe their general behavior.
3. Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.
4. Use patterns, relations, symbolic algebra, and linear functions to model situations.
5. Use graphing techniques on a number line.
6. Solve simple linear equations informally, graphically, and using formal algebraic methods.
7. Create, evaluate, and simplify algebraic expressions involving variables.
8. Understand and apply the properties of operations, numbers, equations, and inequalities.
D. Data Analysis, Probability, and Discrete Mathematics: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.
1. Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).
2. Make inferences and formulate and evaluate arguments based on displays and analysis of data.
3. Interpret probabilities as ratios, percents, and decimals.
4. Model situations involving probability with simulations.
5. Estimate probability and make predictions based on experimental and theoretical probabilities.
6. Play and analyze probability-based games, and discuss the concepts of fairness and expected value.
7. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems.
8. Apply the multiplication principle of counting.
V. COURSE CONTENT OUTLINE
A. Variables and Patterns
1. Recognize problem situations in which two or more quantitative variables are related to each other
2. Identify quantitative variables in situations
3. Describe patterns of change between two variables that are shown in words, tables and graphs of data
4. Construct tables and graphs to display relations among variables
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5. Observe relationships between two variables as shown in a table, graph, or equation and describe how the relationship can be seen in each of the other forms of representation
6. Use algebraic symbols to write equations relating variables
7. Use tables, graphs, and equations to solve problems
8. Use graphing calculators to construct tables and graphs of relations between variables and to answer questions about these relations
B. Stretching and Shrinking
1. Identify similar figures by comparing corresponding parts
2. Use scale factors and ratios to describe relationships among the side lengths of similar figures
3. Construct similar polygons
4. Draw shapes on coordinate grids and then use coordinate rules to stretch and shrink those shapes
5. Predict the ways that stretching or shrinking a figure affect lengths, angle measures, perimeters, and areas
6. Use the properties of similarity to calculate distances and heights that can't be directly measured
C. Comparing and Scaling
1. Analyze comparison statements made about quantitative data
2. Use ratios, fractions, differences, and percents to form comparison statements in a given situation.
3. Judge whether comparison statements make sense and are useful
4. See how forms of comparison statements are related, for example, a percent and a fraction comparison
5. Make judgments about which statements are most informative or best reflect a particular point of view
6. Decide when the most informative comparison is to find the difference between two quantities and when it is to form ratios between pairs of quantities
7. Scale a ratio, rate, or fraction up or down to make a larger or smaller object or population with the same relative characteristics as the original
8. Represent related data in tables
9. Look for patterns in tables that will allow predictions to be made beyond the tables
10. Write an equation to represent the pattern in a table of related variables
11. Apply proportional reasoning to solve for the unknown part when one part of two equal ratios is unknown
12. Set up and solve proportions that arise in applications
13. Recognize that constant growth in a table is related to proportional situations
14. Connect unit rates with the equation describing a situation
D. Accentuate the Negative
1. Use appropriate notation to indicate positive and negative numbers
2. Locate rational numbers (positive and negative fractions and decimals and zero) on a number line
3. Compare and order rational numbers
4. Understand the relationship between a positive or negative number and its opposite (additive inverse)
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5. Develop algorithms for adding, subtracting, multiplying, and dividing positive and negative numbers and write mathematics sentences to show relationships
6. Write and use related fact families for addition/subtraction and multiplication/division to solve simple equations with missing facts
7. Use parentheses and order of operations to make computational sequences clear
8. Understand and use the Commutative Property for addition and multiplication of negative and positive numbers
9. Apply the Distributive Property with positive and negative numbers to simplify expressions and solve problems
10. Use positive and negative numbers to graph in four quadrants, model and answer questions about applied settings
E. Moving Straight Ahead
1. Recognize problem situations in which two or more variables have a linear relationship to each other
2. Construct tables, graphs, and symbolic equations that express linear relationships
3. Translate information about linear relations given in a table, a graph, or an equation to one of the other forms
4. Understand the connections between linear equations and patterns in the tables and graphs of those relations-rate of change, slope, and y-intercept
5. Solve linear equations
6. Solve problems and make decisions about linear relationships using information given in tables, graphs, and symbolic expressions
7. Use tables, graphs, and equations of linear relations to answer interesting questions
F. Filling and Wrapping
1. Understand volume as a measure of filling an object and surface area as a measure of wrapping or covering an object
2. Use flat patterns to visualize and calculate surface areas of prisms and cylinders
3. Develop formulas for the volumes of prisms, cylinders, cones, pyramids, and spheres either directly or by comparison with known volumes
4. Understand that three-dimensional figures may have the same volume but quite different surface areas or they may have the same surface areas but different shapes and volumes
5. Use surface area and volume to solve a variety of real-world problems
6. Understand how changes in one or more dimensions of a rectangular prism or cylinder affects the prism's volume
7. Extend students' understanding of similarity and scale factors to three-dimensional figures
8. Understand the effect on surface area and volume of applying a scale factor to a rectangular prism
G. Data Distributions
1. Apply the process of statistical investigation to pose questions, identify ways data are collected, determine strategies for analyzing data and interpreting the analysis in order to answer the questions posed
2. Compare the distributions of data using their related centers, variability, and shapes
3. Use the shape of a distribution to estimate the mean and median
4. Recognize that variability occurs whenever data are collected and use properties of distributions to describe the variability in a given data set
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5. Identify sources of variability, including natural variability and variability that results from errors in measurement
6. Decide if a difference among data values and/or summary measures matters
7. Understand and decide when to use the mean and median to describe a distribution
8. Make effective use of a variety of representations to display distributions, including tables, value bar graphs, dot or line plots, and bar graphs
9. Understand and use counts or percents to report frequencies of occurrence of data
10. Develop and use strategies for comparing equal- size and unequal-size data sets to solve problems
H. What Do You Expect?
1. Interpret experimental and theoretical probabilities and the relationship between them
2. Distinguish between equally likely and non- equally likely outcomes
3. Review strategies for identifying possible outcomes and analyzing probabilities, such as using lists or counting trees
4. Understand that fairness implies equally likely outcomes
5. Analyze situations that involve two-stages (or two actions)
6. Use area models to analyze situations that involve two stages
7. Determine the expected value of a probability situation
8. Analyze binomial situations
9. Use probability and expected value to make decisions
VI. EVALUATION OF STUDENT LEARNING
A. The evaluation of student performance is based upon tests, quizzes, assignments, alternate assignments, and class participation. Each student is responsible for daily preparation; i.e., pencil, notebook/binder, textbook, homework, etc. Homework is usually assigned daily. A minimum of 30 minutes should be spent at home each day preparing assignments and reviewing class work. Daily attendance is an important factor for the continuity of the course. Students are responsible for making up all work missed due to an absence from class. The student is expected to take an active role in the learning process by participating in class and by taking the initiative to seek extra help when difficulties arise.
B. Grade development
1. Tests, quizzes, and alternate assessment - 80%
2. Homework and class work - 20%
C. Comprehensive Final Exam (one-ninth of final grade)