Mathematics |
Middle School
Course Information
This is an advanced course for 7th graders that covers the 7th and 8th grade curriculum at a faster pace. Most students will advance to Algebra 1 in 8th grade. Students will be exposed to mathematical concepts in five domains: Number System, Expressions and Equations, Ratio and Proportional Relationships, Geometry, Statistics and Probability. Students will focus on problem solving and critical thinking to learn these concepts.
| Subject: | Mathematics |
| State Number: | 000 |
| Course Credits: | |
| Course Options: |
|
| NCAA: | N/A |
- Sem 1
- Unit 1: Probability & Statistics (7.DSP.A.1-2: Use random sampling to draw inferences about a population; 7.DSP.B.3-4: Draw informal comparative inferences about two populations; 7.DSP.C.5-7: Develop, use, and evaluate probability models; 7.DSP.C.5 & 8: Develop, use and evaluate probability models.)
- Unit Overview: You will learn about Populations and Samples. You will build upon your knowledge of probability by studying probability of random events, including how to calculate the chances, or probability, of an event happening or not happening with or without conditions. Lastly, you will learn how to calculate and determine the probability of multiple events, known as compound events.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Use random sampling to draw inferences about a population.
- Understand that statistics can be used to gain information about a population by examining a sample of the population.
- Analyze and interpret data in a real world setting.
- Compare two sets of data using box plots.
- Analyze real-world data in numerical and graphical forms.
- Compare populations using samples and their statistical measures.
- Compare 2 sets of data using their statistical measures and graphs.
- Determine the probability of simple events.
- Explain that the probability of chance events is a number that falls between 0 and 1.
- Predict outcomes using theoretical probability.
- Perform experiments that model theoretical probability.
- Compare theoretical and experimental probabilities.
- Use probability models to determine probabilities of events.
- Use a probability model and observe frequencies in data generated from a chance process.
- Determine the probability of simple events.
- Represent the sample space of a compound event.
- Calculate the compound probability of two probabilistic events.
- Calculate the compound probability of independent and dependent events.
- Unit 2: Integers & Rationals (7.NS.A.1-3: Apply and extend previous understanding of operations to add, subtract, multiply and divide rational numbers.; 7.NS.A.1-3: Apply and extend previous understandings of operations to add, subtract, multiply, and divide rational numbers.)
- Unit Overview: You will analyze the many ways in which humans use signed numbers to accomplish a variety of tasks, including measuring temperature, managing a bank account, and communicating with friends in different time zones. You will also learn mathematical strategies and rules for adding, subtracting, multiplying, and dividing signed numbers. You will describe the many ways in which rational numbers are used in daily life, define a rational number, and solve problems with rational numbers.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Discuss with your peers how to use signed numbers in the real world.
- Use absolute value and additive inverse to add and subtract integers to achieve a sum/difference of zero.
- Use signed numbers to represent transactions and calculate net gain/loss.
- Discuss with Peers how you used signed numbers to play a game.
- Solve Problems by adding and subtracting signed numbers.
- Use multiplication of signed numbers to solve a real life problem.
- Solve problems by multiplying and dividing signed numbers.
- Discuss with peers the types of numbers that are rational.
- Explain how rational numbers are used in real-world situations.
- Unit 3: Real Numbers (8.EEI.A.1-4: Know and apply the value and compare the size of irrational numbers and approximate their locations on a number line; 8.NS.A.1: Explore the real number system; 8.NS.A.2: Estimate the value and compare the size of irrational numbers and approximate their locations on a number line; 8.EEI.A.2a: Solve equations of the form x2=p and x3=p, where p is a positive real, rational number; 8.EEI.A.2b: Evaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes less than or equal to 1000; 8.EEI.A.2c: Recognize that square roots of non-perfect squares are irrational
- Unit Overview: In this unit, you will explore exponents that are fractions and different ways you can represent them. You will come to some conclusions about taking the square and cube roots of different kinds of numbers. You will also learn and practice converting from fractions to decimals and decimals to fractions. You will end this unit by classifying numbers as rational and irrational.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Define what it means to take the square root of a number and how to represent it
- Find the roots of square numbers and cubic numbers
- Solve equations involving exponents
- Convert fractions to decimals
- Covert different kinds of decimals to fractions
- Classify square roots and other real numbers as rational or irrational
- Find or approximate the value of square roots and irrational numbers
- Describe the real number system
- Locate or approximate the locations of different numbers on a number line
- Unit 4: Exponents (8.EEI.A.1-4: Work with Radicals and Integer exponents.)
- Unit Overview: In this unit, you will use several interactive tools to explore how to rewrite expressions with exponents. As you multiply and divide different expressions, you will look for patterns. The patterns will help you discover the rules for simplifying exponential expressions. You will then determine if these rules still work when the exponent is negative or zero.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Discover and explain the rules for exponents
- Write equivalent expressions using the rules for exponents
- Solve real-world problems using expressions that contain negative exponents
- Write numbers with negative exponents in different forms
- Unit 5: Ratios & Proportions (7.RP.A.1-3: Analyze proportional relationships and use them to solve problems.)
- Unit Overview: You will describe the many ways in which rational numbers are used in daily life, define a rational number, and solve problems with rational numbers.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Use rates to solve real-world problems
- Find unit rates and use them to solve real-world problems
- Build and use scale models in real-world problems
- Identify graphs of proportional relationships
- Understand different representations of ratios
- Compute percent of change
- Identify proportional relationships and identify or compute the constant or proportionality
- Unit 6: Expressions (7.EEI.A.1-2: Use properties of operations to generate equivalent expressions; 7.EE.I.B.3-4: Solve Problems using numerical and algebraic expressions and equations.)
- Unit Overview: You will evaluate the different ways in which equivalent expressions can be used in everyday life, and determine how to write and solve equations and inequalities that include more than operation.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Determine whether a quantity is fixed (constant) or variable.
- Use algebraic expressions to represent real-world situations.
- Write and use algebraic expressions to solve real-world problems.
- Unit 7: Equations & Inequalities (7.EE.I.B.3-4: Solve Problems using numerical and algebraic expressions and equations.)
- Unit Overview: You will evaluate the different ways in which equivalent expressions can be used in everyday life, and determine how to write and solve equations and inequalities that include more than operation.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Solve multi-step problems posed with rational numbers.
- Write and solve linear equations with 1 variable.
- Write and solve linear inequalities with 1 variable.
- Unit 8: Functions (8.EEI.B Understand the connections between proportional relationships, lines and linear equations; 8.F.A Define, evaluate and compare functions; 8.F.B: Use functions to model relationships between quantities)
- Unit Overview: In this unit, you will use several interactive tools to explore how to rewrite expressions with exponents. As you multiply and divide different expressions, you will look for patterns. The patterns will help you discover the rules for simplifying exponential expressions. You will then determine if these rules still work when the exponent is negative or zero.
- Missouri Learning Standards/Major Instructional Goals: You will know you have achieved the learning goal when you can:
- Graph proportional relationships, and identify that the unit rate is the slope of the graph
- Determine the slope of a line between two points
- Determine the equation of a line given a verbal description, table, or graph
- Define a function in terms of input and output and represent it in multiple ways
- Describe key features of linear functions and understand positive slope, negative slope, zero slope, and undefined slope
- Use the equation to represent a linear function
- Work with Radicals and Integer exponents
- Unit 1: Probability & Statistics (7.DSP.A.1-2: Use random sampling to draw inferences about a population; 7.DSP.B.3-4: Draw informal comparative inferences about two populations; 7.DSP.C.5-7: Develop, use, and evaluate probability models; 7.DSP.C.5 & 8: Develop, use and evaluate probability models.)
-
- Sem 2
- Unit 9: Linear Relationships (8.F.B Use functions to model relationships between quantities.)
- Unit 10: Linear Systems (8.EEI.C Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations.)
- Unit 11: Bivariate Data (8.DSP.A Investigate patterns of association in bivariate data.)
- Unit 12: Congruence & Similarity (8.GM.A.1-4: Understand congruence and similarity using physical models, transparencies or geometry software.)
- Unit 13: Intersecting Lines & Angles (8.GM.A.5: Explore angle relationships and establish informal arguments)
-
- Unit 14: Triangles & The Pythagorean Theorem (7.GM.A.1-4: Draw and describe geometrical figures and describe the relationships between them; 7.GM.B.5 & .6: Apply and extend previous understanding of angle measure, area, and volume; 8.GM.B.6-8: Understand and apply the Pythagorean Theorem.)
- Unit 15: Circles (7.GM.A.3: Draw and describe geometrical figures and describe the relationships between them; 7.GM.B.6: Apply and extend previous understanding of angle measure, area, and volume.)
- Unit 16: 3D Geometry (Surface Area & Volume) (7.GM.A.3: Describe the two-dimensional cross sections of pyramids, prisms, cones, and cylinders; 7.GM.B.6: Apply and extend previous understanding of angle measure, area, and volume; 8.CM.C Solve problems involving volume of cones, pyramids and spheres.)
