Mathematics & Reasoning

Objectives

• D05.S1.09.01 Work with real numbers, roots, and radicals in expressions and equations, explaining which properties justify each step.
• D05.S1.09.02 Choose appropriate units and levels of precision when measuring and calculating, and interpret the results in context.
• D05.S2.09.01 Model real situations with linear and exponential functions and interpret slope and intercept in context.
• D05.S2.09.02 Solve quadratic equations using several methods and interpret what their solutions mean in real situations.
• D05.S3.09.01 Use rigid motions and coordinates to prove and reason about geometric relationships such as congruence.
• D05.S3.09.02 Prove and apply theorems about lines, angles, triangles, and parallelograms.
• D05.S4.09.01 Summarize and compare distributions of a single variable using plots and summary statistics.
• D05.S4.09.02 Use two-way tables and conditional relative frequencies to explore relationships between categories, including questions of fairness.

Essential questions

• How do real numbers, roots, and radicals behave in expressions and equations, and how do I choose units and precision that make my results meaningful?
• How do linear and exponential functions and quadratic equations model real situations, and what do their features and solutions mean in context?
• How do I prove geometric relationships, and how do data and two-way tables reveal relationships — including questions of fairness?

Big ideas

• Real numbers, roots, and radicals behave by justified properties, and choosing units and precision is what makes a calculation honest in context.
• Linear, exponential, and quadratic models describe real change, and their slope, intercept, and solutions must be read back into the situation.
• Proof through rigid motions and coordinates, and reasoning with distributions and two-way tables, are how mathematics questions fairness and finds structure.

Lessons

1. 1 Mathematics & Reasoning: Where We've Been, Where We're Going 50 minutes
2. 2 Real Numbers, Roots & Radicals 55 minutes
3. 3 Radical Equations: Justifying Every Step 55 minutes
4. 4 Units & Precision: Making Numbers Honest 55 minutes
5. 5 Linear & Exponential Models 55 minutes
6. 6 Slope & Intercept in Context 55 minutes
7. 7 Quadratic Equations: Several Methods 55 minutes
8. 8 Quadratic Solutions in Real Situations 55 minutes
9. 9 Rigid Motions & Coordinate Proof 55 minutes
10. 10 Theorems: Lines, Angles, Triangles & Parallelograms 55 minutes
11. 11 Comparing Distributions 55 minutes
12. 12 Two-Way Tables & Fairness 55 minutes

Assessment plan

Observation of a learner justifying each step with number properties and choosing appropriate units and precision; a linear-and-exponential modeling task read in context, a quadratic-equation interpretation, a geometric proof, a single-variable distribution comparison, and a two-way-table fairness analysis as portfolio artifacts.