Mathematics & Reasoning

Objectives

• D05.S1.11.01 Model and solve real problems with sequences and series, and interpret their meaning in financial or environmental contexts.
• D05.S1.11.02 Use vectors and matrices to represent and manipulate quantities with both size and direction or with several dimensions.
• D05.S2.11.01 Model periodic phenomena with trigonometric functions and interpret amplitude, frequency, and shift in context.
• D05.S2.11.02 Use logarithmic and exponential relationships to solve problems involving growth, decay, and large ranges of scale.
• D05.S3.11.01 Use the unit circle and trigonometry of general triangles to model periodic relationships in real phenomena.
• D05.S3.11.02 Reason about three-dimensional shapes, finding the volume and surface area of composite solids in real contexts.
• D05.S4.11.01 Use the normal distribution and standard deviation to describe data and reason about variability and outliers.
• D05.S4.11.02 Design and carry out a survey or experiment, and critique the sampling, bias, and conclusions it produces.

Essential questions

• How do sequences, series, vectors, and matrices model real financial and environmental problems?
• How do trigonometric, logarithmic, and exponential relationships model periodic phenomena, growth, decay, and large ranges of scale?
• How do the normal distribution, standard deviation, and a well-designed survey help me reason about variability, outliers, and bias?

Big ideas

• Sequences and series, and vectors and matrices, represent quantities with size, direction, and multiple dimensions in real financial and environmental contexts.
• Trigonometric functions model periodic phenomena, while logarithmic and exponential relationships describe growth, decay, and scale across many orders of magnitude.
• The normal distribution and standard deviation describe data, and a well-designed survey or experiment is judged by its sampling, bias, and conclusions.

Lessons

1. 1 Sequences: Arithmetic and Geometric 55 minutes
2. 2 Series: Summing with Sigma Notation 55 minutes
3. 3 Compound Interest and Debt: Series in Finance 55 minutes
4. 4 Environmental Accumulation: Series in the Living World 55 minutes
5. 5 Vectors: Size and Direction 55 minutes
6. 6 Matrices: Many Dimensions at Once 55 minutes
7. 7 Trigonometric Functions as Waves 55 minutes
8. 8 Modeling Periodic Phenomena 55 minutes
9. 9 Logarithms: Order, Growth, and Scale 55 minutes
10. 10 Exponential and Logarithmic Models in the World 55 minutes
11. 11 The Unit Circle and Radians 55 minutes
12. 12 Trigonometry of General Triangles 55 minutes
13. 13 Composite Solids: Volume and Surface Area 55 minutes
14. 14 The Normal Distribution and Standard Deviation 55 minutes
15. 15 Designing a Survey or Experiment 55 minutes
16. 16 Critiquing Sampling, Bias, and Conclusions 55 minutes

Assessment plan

Solved and reasoned sequence-and-series work interpreted in financial or environmental contexts; vector and matrix representation and manipulation; trigonometric models of periodic phenomena with amplitude, frequency, and shift; logarithmic and exponential solutions for growth, decay, and scale; unit-circle and general-triangle trigonometry modeling periodic relationships; composite-solid volume and surface-area reasoning; normal-distribution and standard-deviation analyses of variability and outliers; and a designed survey or experiment with a critique of its sampling, bias, and conclusions, gathered as portfolio artifacts.