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Unit | Timeframe | Big Ideas | Major Learning Experiences |
Unit 1 Rigid Transformations and Congruence
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September |
Rigid transformations (translations, rotations, and reflections) of polygons on the plane are explored.
Rigid transformations of two-dimensional figures and angles preserve properties of congruence.
| Students will: Translate, reflect and rotate polygons on a coordinate grid using geometry software (Desmos and Geogebra) and physically with graph paper and transparency paper. Use coordinates to describe the effects that rigid transformations have on two-dimensional figures in a coordinate plane. Prove that two figures are congruent by describing a sequence of rigid transformations that maps one figure onto the other. Create a geometric picture that involves using all three rigid transformations. Apply their understanding of rigid transformations to make important discoveries about the angle relationships inside and outside of a triangle; as well as, the angles formed when parallel lines are cut by a transversal.
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Unit 2 Dilations, Similarity and Introducing Slope | October |
A dilation produces a similar figure with congruent corresponding angles, and side lengths that are proportional.
Similar triangles can be used to prove that the slope between any two points on a non-vertical line is the same. | Students will: Understand that two-dimensional figures are similar if the image is obtained as a result of a rotation, reflection, translation, and/or dilation. Describe the characteristics that are preserved and/or changed when a figure is dilated. Describe the sequence of transformations that produce similar figures. Find the missing side lengths for similar figures. Discover and apply the angle-angle criterion for similar triangles. Use similar triangles to prove that the slope between any two points on a non-vertical line is the same.
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Unit 3 Linear Relationships | November |
Slope is a measure of the steepness of a line, and is a representation of the rate of change of a linear relationship.
The equation y = mx + b can be used to express all linear relationships, including proportional relationships, where m gives the slope of the line and b gives the y-intercept. | Students will: Graph proportional relationships and write equations to represent the relationship. Identify the slope in a proportional relationship as the unit rate, and compare the slope represented in different ways (table, graph, equations and words). Connect their understanding of a proportional relationship y = mx, to the linear relationship y = mx + b, by performing a translation. Graph a line in the form y = mx + b, and understand that m is the slope and b is the y-intercept. Model real world linear relationships by creating a scenario, writing an equation, creating a table, and graphing the line.
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Unit 4 Linear Equations and Systems of Linear Equations |
December - January | Linear equations and systems of equations can have zero, one, or infinitely many solutions. These solutions can be analyzed both graphically and algebraically and have a specific meaning within the context of a problem.
| Students will: Solve a multi-step linear equation with rational number coefficients, including equations requiring expanding and combining like terms. Identify examples of linear equations in one variable that result in one solution, infinitely many solutions, or no solutions. Determine whether a system of equations will result in one solution, no solutions, or infinitely many solutions. Solve systems of linear equations in two variables graphically and algebraically, using substitution and elimination. Apply their understanding of systems of equations to compare real world situations and make informed decisions.
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Unit 5 Functions and Volume |
February |
A function is a relationship between two quantities that assigns one output for every input. Linear and nonlinear functions have structures that can be explored and connected across multiple representations.
The formulas for the volumes of cylinders, cones, and spheres are related to each other and can be used to solve mathematical and real-world problems. | Students will: Define what a function is and identify if a relationship is a function when it is represented graphically, in a table, in an equation or in a mapping diagram. Write a function rule to represent inputs and outputs from a table of values. Describe the properties of a function that is represented as an equation, a table of values, a graph, or a verbal representation. Compare the properties of two functions that are represented in different forms (tables, graphs, equation, or verbal representation). Model real world situations by writing a function and interpret the meaning of the rate of change and the initial value of the linear function. Explore the differences between non-linear and linear functions. Describe the context of a distance-time piecewise function (including when the function is increasing/decreasing, and the rate of change).
Discover the volume formula for cones, cylinders, and spheres by investigating how they are related. Apply their understanding of volume to solve real world problems.
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Unit 6 Pythagorean Theorem and Irrational Numbers |
March
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The Pythagorean Theorem describes a special relationship among the sides of a right triangle, which can be used to solve mathematical and real-world problems involving right triangles.
| Students will: Explore lengths of sides that create right triangles, and investigate the special relationship between these sides. This special relationship is called the Pythagorean theorem. Determine if a triangle is a right triangle using the converse of the Pythagorean theorem. Apply the Pythagorean theorem to determine unknown side lengths in right triangles in order to solve real-world and mathematical problems. Use the Pythagorean theorem to determine the distance between two points in the coordinate plane. Learn about square roots and irrational numbers to approximate the length of any side of a right triangle, as side lengths are not always perfect squares. Approximate the location of irrational numbers on a given number line.
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Unit 7 Exponents and Scientific Notation
| March - April |
Exponents and scientific notation can be used to describe and compare very large and very small quantities.
| Student will: Discover and apply exponent rules. Represent a large quantity or a small quantity as a number written in scientific notation and standard form. Perform operations with two numbers expressed in scientific notation, including problems that include a combination of standard form and scientific notation. Apply their understanding of scientific notation to solve problems about the solar system, cells and atoms, population growth and environmental impact.
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Unit 8 Associations in Data |
April - May | Two attributes of a population may be associated with each other, and these associations can be revealed through the display and mathematical analysis of the data.
| Students will: Gather, organize, and display bivariate quantitative data in tables and in graphs. Describe patterns in bivariate quantitative data, including clustering, outliers, positive or negative association, and linear or nonlinear association. Determine the equation of a line of best fit to model a set of data. Use a linear model to make predictions about future data. Analyze bivariate categorical data in a two-way table and summarize the data, including the relative frequency. Create their own surveys to learn more about their classmates and analyze the results using a bivariate table.
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