Learning Math: Patterns, Fractions and Algebra
Explores the “big ideas” in algebraic thinking, such as finding, describing, and using patterns; using functions to make predictions; understanding linearity and proportional reasoning; understanding non-linear functions; and understanding and exploring algebraic structure. The concluding case studies show you how to apply what you have learned in your own classroom.
Episode Descriptions
1. Algebraic Thinking
Covers describing situations through pictures, charts, graphs, and words; interpreting and drawing conclusions from graphs; and creating graphs to match written descriptions of real-life situations.
2. Patterns in Context
Explores the processes of finding, describing, explaining, and predicting using patterns.
3. Functions and Algorithms
Covers the importance of doing and undoing in mathematics, determining when a process can or cannot be undone, using function machines to picture and undo algorithms, and the unique outputs produced by functions.
4. Proportional Reasoning
Covers differentiating between additive and multiplicative processes and their effects on scale and proportionality, and interpreting graphs that represent proportional relationships or direct variation.
5. Linear Functions and Slope
Explores linear relationships by looking at lines and slopes. Using computer spreadsheets, examines dynamic dependence and linear relationships and shows how to recognize linear relationships expressed in tables, equations, and graphs.
6. Solving Equations
Looks at different strategies for solving equations. Topics include the different meanings attributed to the equal sign and the strengths and limitations of different models for solving equations.
7. Non-Linear Functions
Explores functions and relationships with two types of non-linear functions: exponential and quadratic functions. Reveals that exponential functions are expressed in constant ratios between successive outputs and that quadratic functions have constant second differences.
8. More Non-Linear Functions
Investigates more non-linear functions, focusing on cyclic and reciprocal functions. Explores situations in which more than one function may fit a particular set of data.
9. Algebraic Structure
Looks at "algebraic structure" by examining the properties and processes of functions.
10. Classroom Case Studies, Grades K-2
Explores how the concepts developed in Patterns, Functions, and Algebra can be applied at different grade levels. Observes what teachers do to develop students’ algebraic thinking and investigate ways to incorporate algebra into K-8 mathematics curricula. This video is for the K-2 grade band.
11. Classroom Case Studies, Grades 3-5
Explores how the concepts developed in Patterns, Functions, and Algebra can be applied at different grade levels. Observes what teachers do to develop students’ algebraic thinking and investigate ways to incorporate algebra into K-8 mathematics curricula. This video is for the 3-5 grade band.
12. Classroom Case Studies, Grades 6-8
Explores how the concepts developed in Patterns, Functions, and Algebra can be applied at different grade levels. Observes what teachers do to develop students’ algebraic thinking and investigate ways to incorporate algebra into K-8 mathematics curricula. This video is for the 6-8 grade band.
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