Big Idea: In this unit, we will learn about reflections, rotations, and translations - how to DO each of these translations and what to KNOW about the resulting figures. We will work on both finding corresponding side lengths and angle measures as we develop an understanding of congruence.
Students will be able to:
Understand and Use Transformations:
Standard 1: Identify and describe a rotation, a reflection, and a translation on a figure.
Standard 2: Find the resulting coordinates for each type of transformation on a point or figure - a rotation, a reflection, and a translation.
Standard 3: Describe the sequence of rigid transformations that makes an image from a preimage.
Understand Congruence from Transformations:
Standard 4: Determine if two figures are congruent using an understanding of rigid transformations and congruence.
Standard 5: Identify, name, and find measures of corresponding angles and segments in congruent figures.
Apply Understandings from Transformations and Congruence:
Standard 6: Use transformations to find angle measures between intersecting lines.
Standard 7: Use the sum of the interior angles of a triangle to find missing angle measures.
Big Idea: In this unit we will add dilation to our understanding of transformations. Much of the work we did in Unit 1 will be similar to the work in Unit 2, but we will be extending that learning to include dilations. Throughout Unit 2 we will work on finding corresponding side lengths and angle measures and developing an understanding of similarity. Toward the end of this unit we will start to explore slope and use the similarity of slope triangles to gain an overall understanding of slope from different points on a line.
Students will be able to:
Understand and Use Dilations:
Standard 8: Identify and describe a dilation on a figure.
This includes finding corresponding side lengths for figures that have been dilated.
Standard 9: Find the resulting coordinates given a point or a figure.
Understand Similarity from Dilations:
Standard 10: Determine if two figures are similar using an understanding of transformations and similarity.
Standard 11: Find side lengths using similar figures.
Use Similarity to Calculate Slope:
Standard 12: Find the slope of a line on a graph.
Big Idea: In this unit, we will start to use our new understanding of slope to look at proportional and linear relationships. We will deepen our understanding of slope and learn to recognize connections among constant of proportionality, rate of change, and slope, as well as between linear and proportional relationships. By the end of this unit, students will be able to represent linear relationships with tables, equations, and graphs.
Students will be able to:
Use Slope to Understand Proportional Relationships:
Standard 13: Find the unit rate in a proportional relationship and describe what it means in the context of a given situation.
Standard 14: Use the unit rate to draw a graph or write an equation for a proportional relationship.
Standard 15: Compare proportional relationships given multiple representations including tables, graphs and equations.
Use Proportional Relationships to Understand Linear Equations:
Standard 16: Find the slope and y-intercept of a line given a graph, table, or two points on the line, and describe its meaning.
Standard 17: Explain why the slope is the same between any two points on a non-vertical line.
Standard 18: I can write the equation of a line, in slope-intercept form, given a variety of information.
Including a graph, table, two points on the line, or a real-world situation.
Standard 19: Identify and graph the solutions to an equation given a description or an equation in slope-intercept form.
Big Idea: To begin this unit, we will start to look for the solutions to equations and will develop an understanding of the graph as the set of all solutions that make the equation true. We will move into algebraically solving equations that have variables on both sides of the equation sign. We will take it a step further by exploring different solution types -- some equations have no solution or infinite solutions. We will build upon that understanding as we develop an understanding of a solution that makes two equations true -- the solution to a system of equations. In this unit we will learn to solve systems of equations algebraically and by graphing. We will write and solve systems of linear equations and interpret their solutions in the context of a word problem.
Students will be able to:
Solve Equations:
Standard 20: Solve multi-step linear equations with rational number coefficients.
Including those that involve the distributive property and/or combining like terms
Standard 21: Identify and write equations with each solution type - one solution, infinitely many solutions, or no solutions.
Solve Systems of Equations using Substitution and Graphing:
Standard 22: Graph a system of linear equations and identify the solution.
Standard 23: Solve systems of linear equations algebraically.
Standard 24: Identify systems with each solution type - one solution, infinitely many solutions, or no solutions.
This includes identifying solution types using graphs, slopes and/or y-intercepts, and by solving algebraically.
Standard 25: Interpret the solution to a system of equations in the context of a real-world problem.
Big Idea: In this unit, students are introduced to the concept of a function -- a study topic that appears throughout high school mathematics. We will learn to identify functions from tables, graphs, mapping diagrams, and equations. As we build our understanding of functions, we will work on interpreting a graph, as well as drawing a graph that correctly displays information given. Our study of functions will also lead to new learning about linear vs. nonlinear functions, which we will identify from graphs, tables, and equations. In our study of nonlinear functions, we will look at new functions, called piecewise functions, that are sometimes used in interpreting trends in data.
Students will be able to:
Understand and Interpret Functions:
Standard 26: Interpret the functional relationship between two quantities given a description or graph.
This includes finding the constant rate of change and noting increasing/decreasing/constant, linear or non-linear, and continuous or discrete.
Standard 27: Sketch a graph of a function given a variety of information.
Standard 28: I can explain why a relation is or is not a function.
This includes descriptions, mapping diagrams, tables, equations, and graphs.
Compare Functions:
Standard 29: Compare two functions represented in different ways.
This includes making comparisons between linear and nonlinear functions.
Standard 30: Create or identify examples of a nonlinear function as a list of points, table, graph, equation, or verbal description.
Standard 31: Identify the slope and the x- and y-intercepts from an equation, graph, or table and interpret their meaning in the context of a given situation.
Standard 32: Evaluate a function at a given input.
Big Idea: Information on this unit will be added at a later date.
** This unit was abbreviated this year, due to timing and the need to get through more content. These standards are not numbered, because we did not assess them on a traditional test. **
Students will be able to:
Construct and Interpret Scatter Plots:
Construct a scatter plot using data points.
Interpret a scatter plot to identify clustering and outliers.
Interpret a scatter plot to identify a linear or non-linear relationship and a positive or negative association.
Analyze Data Using a Line of Best Fit:
Construct a line of best fit to model trends in a scatter plot and explain why it is an appropriate trend line.
Write the equation for the line of best fit and interpret the meaning of the slope and y-intercept for a given situation.
Use the equation for the line of best fit to solve problems.
Use Two-Way Tables:
Construct and interpret a two-way table summarizing data.
Big Idea: Now that we've started to build an understanding of functions and data that are nonlinear, this unit introduces the idea of nonlinear patterns. In this unit we start to look at exponential patterns -- patterns of multiplication. We start with an understanding of repeated multiplication and quickly move into exponent rules that include positive, negative, and zero exponents. In the second half of the unit we apply our understanding of exponents to the base-ten system, which is useful in scientific notation. We will learn to convert between standard notation and scientific notation, as well as to add, subtract, multiply, and divide when numbers are given in scientific notation.
Students will be able to:
Simplify Expressions Using Exponent Rules:
Standard 33: Simplify an expression that contains multiplication of terms with exponents.
Including only those with the same base or the same exponent.
Standard 34: Simplify an expression that contains a power raised to another power.
Standard 35: Simplify an expression that contains division of terms with exponents.
Including only those with the same base or the same exponent.
Standard 36: Simplify an expression that contains a negative or zero exponent.
Interpret and Use Scientific Notation:
Standard 37: Convert between standard notation and scientific notation.
Standard 38: Determine whether a number in scientific notation will be greater or lesser than the original factor based on the exponent given.
Standard 39: Apply all 4 operations to scientific notation and write my answer in scientific notation.
Standard 40: Compare values, with or without context, including problems where both decimal and scientific notation are used.
Big Idea: Information on this unit will be added at a later date.
Students will be able to:
Identify and Approximate Irrational Numbers:
Standard 41: Identify rational and irrational numbers.
Standard 42: Convert between fractions and decimals.
Standard 43: Estimate the value of irrational numbers using perfect squares and cubes.
Standard 44: Locate rational and irrational numbers on a number line.
Solve Equations Using Square Roots
Standard 45: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p.
Standard 46: Use the Pythagorean Theorem to prove that three lengths make a right triangle.
Standard 47: Use the Pythagorean Theorem to determine unknown side lengths in right triangles.
This includes both solving when given a triangle and solving problems in a 3-dimensional context.
Standard 48: Use the Pythagorean Theorem to find the distance between points on a graph.