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:
Target 1: Identify and describe a rotation, a reflection, and a translation on a figure.
Target 2: Find the resulting coordinates for each type of transformation on a point or figure - a rotation, a reflection, and a translation.
Target 3: Describe the sequence of rigid transformations that makes an image from a preimage.
Understand Congruence from Transformations:
Target 4: Determine if two figures are congruent using an understanding of rigid transformations and congruence.
Target 5: Identify, name, and find measures of corresponding angles and segments in congruent figures.
Apply Understandings from Transformations and Congruence:
Target 6: Use transformations to find angle measures between intersecting lines.
Target 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:
Target 8: Identify and describe a dilation on a figure.
This includes finding corresponding side lengths for figures that have been dilated.
Target 9: Find the resulting coordinates given a point or a figure.
Understand Similarity from Dilations:
Target 10: Determine if two figures are similar using an understanding of transformations and similarity.
Target 11: Find side lengths using an understanding of similar figures.
Use Similarity to Calculate Slope:
Target 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:
Target 13: Find the unit rate in a proportional relationship and describe what it means in the context of a given situation.
Target 14: Use the unit rate to draw a graph or write an equation for a proportional relationship.
Target 15: Compare proportional relationships given multiple representations including tables, graphs and equations.
Use Proportional Relationships to Understand Linear Equations:
Target 16: Find the slope and y-intercept of a line given a graph, table, or two points on the line, and describe its meaning.
Target 17: Explain why the slope is the same between any two points on a non-vertical line.
Target 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.
Target 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:
Target 20: Solve multi-step linear equations with rational number coefficients.
This includes equations that involve the distributive property and/or combining like terms.
Target 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:
Target 22: Graph a system of linear equations and identify the solution.
Target 23: Solve systems of linear equations algebraically.
This includes solving using substitution and solving using elimination.
Target 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.
Target 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.
This unit also touches on a study of geometry, as surface area and volume are both functions. We will focus on extending our understanding from earlier grades to now include finding the surface area of a pyramid, as well as the volume of pyramids, cones and spheres.
Students will be able to:
Understand and Interpret Functions:
Target 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.
Target 27: Explain why a relation is or is not a function.
This includes descriptions, mapping diagrams, tables, equations and graphs.
Target 28: Sketch a graph of a function given a variety of information.
Compare Functions:
Target 29: Compare two functions represented in different ways.
This includes making comparisons between linear and nonlinear functions.
Target 30: Create or identify examples of a nonlinear function as a list of points, table, graph, equation, or verbal description.
Target 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.
Target 32: Evaluate a function at a given input.
Geometry:
Target 33: Calculate the surface area of a pyramid.
Target 34: Calculate the volume of pyramids, cones and spheres.
Big Idea: In this unit we will extend our understanding of linear patterns by examining real world situations that lead to scatter plots. We will learn about the line of best fit -- how to write the equation and how to use the equation to make predictions. This will also give us another chance to look at and interpret data that is non-linear. While most of the data we work with will be numerical, we will also study categorical data, which is best organized in two-way tables instead of scatterplots. We will practice completing and interpreting two-way tables and calculating frequencies from categorical data.
Students will be able to:
Create and Compare Scatterplots:
Target 35: Construct a scatter plot using data points.
Target 36: Interpret a scatter plot to identify patterns.
This includes clustering, outliers, linear or non-linear relationships, and positive or negative associations.
Line of Best Fit:
Target 37: Construct a lien of best fit to model trends in a scatterplot and explain why it is an appropriate trend line.
Target 38: Write the equation for the line of best fit and interpret the meaning of the slope and y-intercept in a given situation.
Target 39: Use the equation for the line of best fit to solve problems.
Two-Way Tables:
Target 40: 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 could be nonlinear, this unit tunes into numerical patters that are exponential rather than nonlinear. 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 a mix of scientific notation and standard notation.
Students will be able to:
Simplify Expressions Using Exponent Rules:
Target 41: Simplify an expression that contains multiplication of terms with exponents.
Including only those with the same base or the same exponent.
Target 42: Simplify an expression that contains a power raised to another power.
Target 43: Simplify an expression that contains division of terms with exponents.
Including only those with the same base or the same exponent.
Target 44: Simplify an expression that contains a negative or zero exponent.
Interpret and Use Scientific Notation:
Target 45: Convert between standard notation and scientific notation.
Target 46: Determine whether a number in scientific notation will be greater or lesser than the original factor based on the exponent given.
Target 47: Apply all 4 operations to scientific notation and write my answer in scientific notation.
Target 48: Compare values, with or without context, including problems where both decimal and scientific notation are used.
Big Idea: After building a stronger understanding of exponents in unit 7, this unit asks students to understand "undoing" an exponent. As we learn about square and cube roots, and apply that learning with Pythagorean Theorem, students will recognize that not all numbers have a "nice" square root or cube root. This leads us into a study of irrational numbers to conclude our year.
Students will be able to:
Approximate Irrational Numbers:
Target 49: Approximate the value of irrational numbers and locate them on a number line.
Use the Pythagorean Theorem:
Target 50: 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.
Target 51: Use the converse of the Pythagorean Theorem to prove that three lengths make a right triangle.
Target 52: Use the Pythagorean Theorem to find the distance between points on a graph.
Identify Irrational Numbers
Target 53: Identify rational and irrational numbers.
Target 54: Convert between fractions and decimals.