Topic outline
- General
- Topic 1This topic
Topic 1
Unit 1: Rational and Irrational Numbers
Know that numbers that are not rational are called irrational. Understand informally that every
number has a decimal expansion; for rational numbers show that the decimal expansion repeats
eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.Essential questions:
- How are sets of real numbers related?
- How can the value of an irrational number be approximated?
- Where do you see irrational values in the real world?
- Unit 2. Exponents and Scientific Notation
Unit 2. Exponents and Scientific Notation
Know and apply the properties of integer exponents to generate equivalent numerical expressions. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3= p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Use numbers expressed in the form of a single digit time an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Essential questions:
- In what kinds of situations would it be useful to express a value using scientific notation?
- How can expressions with integer exponents be simplified?
- How can numbers in scientific notation be added and subtracted? Multiplied and divided?
- What are some advantages to performing operations with numbers in scientific notation rather than standard notation? Disadvantages?
- Unit 3. Linear Relationships and Functions
Unit 3. Linear Relationships and Functions
In this chapter, students will learn how to graph lines, solve direct variation problems, and evaluate functions. They will
- graph linear equations using tables of values and point-plotting, intercepts, and slope.
- identify equations of horizontal and vertical lines.
- use graphs of linear equations to model and solve real-life problems.
- identify and evaluate functions.
Essential Questions:
- How can the slope of a line be found, and what does it tell you about the line?
- What makes a situation proportional or non-proportional?
- How can the rate of change be found from tables? Ordered pairs? Graphs?
- How can you determine if a table, graph or equation represents a functional relationship?
- What distinguishes a linear relationship from a non-linear relationship?
- What pieces of information are needed to write an equation for a linear relationship?
- How can you analyze a graph that compares an object’s distance with the time?
- Unit 4. Linear Equations
Unit 4. Linear Equations
- Students solve multi-step equations and equations with variables on both sides using inverse operations.
- Students solve more complicated word problems, with an emphasis on Distance, Rate, Time problems
- Students recognize equations that have non-standard solutions (equations with many solutions, no solutions, or a solution of zero). Students also solve a formula for a variable.
- Students learn what to do when there is more than one unknown value in a problem and apply the 4 Step problem-solving process to a variety of situations (translations, consecutive integers, rectangle geometry, age problems).
Essential questions:
- How can you expand an expression using the distributive property?
- What determines if terms are considered “like terms”?
- How can you distinguish an equation with “no solution” from an equation with “infinitely many solutions”?
- Unit 5. Linear Systems
Unit 5. Linear Systems
Students will learn how to solve systems of two linear equations and graph the solutions to systems of linear equations. They will:
- solve linear systems by graphing, substitution, and linear combinations
- use the linear system to model real-life situations
- determine the number of solutions to a linear system
Essential questions:
- How does graphing a system of equations help you find the solution to the system?
- What is meant by the “solution” to a system of equations?
- When is it easier or more beneficial to solve a system of equations by substitution?
- Unit 6. Angle Pair Relationships, Transformations and Pythagorean Theorem
Unit 6. Angle Pair Relationships, Transformations and Pythagorean Theorem
In this unit, students will discover the importance of understanding the language of geometry and will communicate mathematically making use of geometrical diagrams and related texts. They will learn about angles that are formed by transversals cutting parallel lines, construct angles and triangles, and apply their knowledge to find unknown measures of angles.
Essential questions:
Angle Relationships:
- What is significant about the angles formed when parallel lines are cut by a transversal?
- When might you see parallel lines cut by a transversal in real-life?
- How are the interior angles of a triangle related?
- How can interior angles of a triangle help you find an exterior angle measure?
- What do angle measures of triangles tell you about the similarity of the triangles?
Transformations:
- What is meant by a “rigid” transformation, and what are some examples of rigid transformations?
- Where do you see the various transformations in the real world?
- What are some key things to look for when trying to identify a transformation on a coordinate plane?
- What is the difference between the orientation of a figure and the orientation of a figure’s vertices?
Pythagorean Theorem:
- What are two different ways to determine which side in a right triangle is the hypotenuse?
- How are the side lengths of right triangles related?
- How can you visualize or draw a representation to explain the Pythagorean theorem?
- How can the Pythagorean theorem be used to find distances on the coordinate plane?
- Unit 7. Volume
Unit 7. Volume
In this unit, students will discover the importance of understanding the language of geometry and will communicate mathematically making use of geometrical diagrams and related texts. They will use exact methods to analyze 2-D and 3-D geometrical configurations and to select and combine known facts in solving geometrical problems related to real-world applications.
Essential questions:
- What is meant by the volume of a figure, and when might you need to calculate volume?
- How are the volumes of cones and cylinders related?
- What are the different variables in the formulas for the volume of cones and cylinders, and what do they represent?
- How is finding the volume of a sphere different than finding the volume of a cone or cylinder? How is it similar?