Functions, Linear Equations, Geometry & Data

Objectives

• D05.S1.08.01 Distinguish rational and irrational numbers and approximate square roots by locating them on the number line.
• D05.S1.08.02 Use integer exponents and scientific notation to represent and compare very large and very small quantities, such as distances in space or the size of cells.
• D05.S2.08.01 Define, evaluate, and compare functions and use function notation to describe how one quantity depends on another.
• D05.S2.08.02 Solve linear equations in one variable and analyze a pair of simultaneous linear equations by graphing.
• D05.S3.08.01 Describe translations, rotations, reflections, and dilations, and use them to show congruence and similarity.
• D05.S3.08.02 Use the Pythagorean theorem to solve problems about right triangles and distances.
• D05.S4.08.01 Construct and interpret scatter plots for two related variables and describe patterns of association.
• D05.S4.08.02 Fit a line informally to data to model a relationship, evaluate the fit, and explain that association does not prove causation.

Essential questions

• How do I tell rational from irrational numbers and use scientific notation to hold the very large and the very small?
• How do functions describe how one quantity depends on another, and how do I solve and graph linear equations?
• How do transformations and the Pythagorean theorem describe shape and distance, and how do scatter plots model without mistaking association for cause?

Big ideas

• Numbers extend beyond the rational, and scientific notation lets one quantity hold distances in space and the size of a cell.
• A function is a precise way to say how one quantity depends on another, and linear equations and their graphs are its first full language.
• Transformations describe congruence and similarity, the Pythagorean theorem measures distance, and a line fit to data models a relationship without proving causation.

Lessons

1. 1 Numbers, Dependence, Shape, and Data: Opening the Year 50 minutes
2. 2 Rational and Irrational Numbers 50 minutes
3. 3 Approximating Square Roots on the Number Line 50 minutes
4. 4 Scientific Notation: Holding the Very Large and Very Small 50 minutes
5. 5 Functions: How One Quantity Depends on Another 50 minutes
6. 6 Solving Linear Equations in One Variable 50 minutes
7. 7 Two Equations at Once: Solving Systems by Graphing 50 minutes
8. 8 Transformations: Moving Shapes, Proving Congruence and Similarity 50 minutes
9. 9 The Pythagorean Theorem: Right Triangles and Distance 50 minutes
10. 10 Scatter Plots and Association 50 minutes
11. 11 Capstone: Lines of Fit, and Why Association Is Not Causation 50 minutes

Assessment plan

Observation of a learner distinguishing rational from irrational numbers, using scientific notation, and solving and graphing linear equations; a functions notebook, transformation and Pythagorean-theorem work, and a scatter-plot-with-line-of-fit investigation that names association without claiming cause as portfolio artifacts.