Clickable links from the lesson assignments in the Coursebook:

For help and extra practice with the concepts in this chapter:

- Estimation
- Rounding
- Pascal’s Triangle patterns
- Fully-worked example of the Four-Step Problem Solving Process

For more about Archimedes:

- To learn about the legend of Archimedes and his bathtub discovery of the solution to the problem of Hiero’s golden crown, watch this video.
- To find out about Archimedes’ design of the floating palace “Syracusa” and his discovery of the Principle of Buoyancy, watch this video.
- To learn what Archimedes meant by “Give me a place to stand, and I shall move the Earth,” watch this video.

For fun and deeper exploration:

- Books
*How to Solve It*by George Polya

- Logic puzzles and riddles
- River crossing problems
- Sudoku, KenKen, Kakuro
- Magic Square puzzles
- http://www.magicsquarepuzzles.com/
- Learn how to make your own Magic Square puzzles.

Real problem-solving in the news

- “Wikipedia-size maths proof too big for humans to check,” from
*New Scientist,*February 17, 2014.

Clickable links from the lesson assignments in the Coursebook:

- Dennis Wildfogel’s “How Big Is Infinity?” (TED-Ed)
- Numberphile’s “Infinity is Bigger Than You Think”
- The MacTutor History of Mathematics Archive

For help and extra practice with the concepts in this chapter:

- A great explanation of what sets are, definitions of set theory terminology, and examples
- Explanations and examples of how to solve word problems using Venn diagrams

For fun and deeper exploration:

- Infinite sets:
- A proof that some infinities are bigger than others
- A good explanation of infinite sets (also click through to the next page to continue the story)
- An excellent TED-Ed lesson on the Infinite Hotel Paradox

- Fibonacci numbers:
- Games involving set theory:
- SET, a fun and educational card game, is also available online and as an app

Clickable links from the lesson assignments in the Coursebook:

- James Tanton’s video, “Divisibility Rule for 7”
- Scishow’s video, “The Fibonacci Sequence: Nature’s Code”
- Cristóbal Vila’s short video, “Nature by Numbers”

For help and extra practice with the concepts in this chapter:

- Khan Academy has a good explanation of how to use the Sieve of Eratosthenes to find prime numbers
- Explanations and examples for the order of operations
- Rational and irrational numbers
- Khan Academy also has an entire section devoted to Scientific Notation
- Exponent rules explained
- Explanations and examples for arithmetic and geometric sequences

For additional inspiration for the Fibonacci Inspiration activity, check out these videos:

- Vi Hart’s “Spirals, Fibonacci and being a plant” video series (3 parts)
- Arthur Benjamin’s TED Talk

For fun and deeper exploration:

- Prime and composite numbers game
- Learn how Eratosthenes calculated the circumference of the Earth in Khan Academy’s article
- Learn more about that famous number, pi:
- To see what a million digits of pi really looks like, check out Numberphile’s “A Mile of Pi” video
- To hear a tonal representation of the digits of pi, check out Numberphile’s “Sounds of Pi” video
- To see artistic data visualizations of the digits of pi, check out Numberphile’s “Pi is Beautiful” video

Clickable links from the lesson assignments in the Coursebook:

For help and extra practice with the concepts in this chapter:

- Khan Academy’s Linear Equations and Inequalities section
- Proportions explanations and examples
- Video on direct and inverse variation

For fun and deeper exploration:

- For additional discussion to help you explore whether you believe mathematics was invented or discovered, check out PBS Idea Channel’s “Is Math a Feature of the Universe or a Feature of Human Creation?”

Clickable links from the lesson assignments in the Coursebook:

- Line of Best Fit tool on the NCTM Illuminations website

For help and extra practice with the concepts in this chapter:

- Graphing linear equations
- Explanation of function evaluation
- Explanation of scatterplots and regression lines
- Solving systems of linear equations
- Solving systems of linear inequalities

For fun and deeper exploration:

- Now that you know a bit about correlation, it’s important to understand that correlation does not imply causation. In other words, just because two variables are related does
*not*mean that one of the variables caused the other. This is a common logical fallacy that leads to invalid conclusions. Check out this*Los Angeles Times*article that makes the point that correlation does not imply causation. Then to drive the point home, visit the site that inspired the article, Spurious Correlations, to view a variety of amusing graphs showing two completely unrelated variables that just happen to be closely correlated.

Clickable links from the lesson assignments in the Coursebook:

- Vi Hart’s video, “Doodling in math: Spirals, Fibonacci, and being a plant (1 of 3)”
- Golden Spiral video

For help and extra practice with the concepts in this chapter:

- For help with factoring quadratic equations
- Solving quadratic equations using the quadratic formula
- Solving quadratic equations using the square root property
- Features of quadratic functions
- Graphing quadratic functions
- For a refresher on how to construct a square with straightedge and compass
- For a refresher on how to construction a line perpendicular to an existing line

For fun and deeper exploration:

- More on the legend of Newton and the falling apple
- Additional Vi Hart videos (part 2 and part 3 of the “Doodling” series)

Clickable links from the lesson assignments in the Coursebook:

For help and extra practice with the concepts in this chapter:

- Percents explanations
- Solving word problems with percentages
- Calculating simple and compound interest

For fun and deeper exploration:

Clickable links from the lesson assignments in the Coursebook:

*How to Lie with Statistics,*by Darrell Huff- Edmunds’ True Cost to Own

For help and extra practice with the concepts in this chapter:

For fun and deeper exploration:

- Learn more about personal finance for teens at The Mint
- Find out the real costs of owning a car as a teen

For help and extra practice with the concepts in this chapter:

- Khan Academy unit conversion section
- More on converting units

For more information on the history of the metric debate in the United States.

For fun and deeper exploration:

Clickable links from the lesson assignments in the Coursebook:

- Math is Fun Reflectional Symmetry page
- Math is Fun Rotational Symmetry page
- Dr. James Tanton’s “Generating Pythagorean Triples” video
- Escher Gallery
- Tessellation Creator tool at the National Council of Teachers of Mathematics’ Illuminations site
- Platonic Solids tool from the National Council of Teachers of Mathematics’ Illuminations site
- Platonic Solids Models from Math is Fun

For help and extra practice with the concepts in this chapter:

- Khan Academy Geometry section with dozens of applicable videos
- Math is Fun main Geometry page with dozens of links to topic-specific articles
- Graphing circles

For fun and deeper exploration:

- If you enjoyed the Platonic Solids activity, explore the duals of the Platonic Solids with these videos
- For more on tessellations, visit here, or try this app

Clickable links from the lesson assignments in the Coursebook:

- TED-Ed video by Yannay Khaikin
- TED-Ed lesson, “The last banana – a thought experiment in probability,” by Leonardo Barichello
- Ron Clarke’s Monty Hall problem video
- Horizons’ Monty Hall problem video
- Stay or Switch simulation tool
- Marilyn vos Savant’s “Game Show Problem” solution and criticism from the public

For help and extra practice with the concepts in this chapter:

- Watch video explanations and try practice problems with the Khan Academy Probability and Combinatorics lessons
- Practice figuring out which counting method to use and try your hand at some problems with the Counting Methods Review and Self-Test

For fun and deeper exploration:

- Try challenging counting methods problems at Brilliant.org
- Try challenging probability problems at Brilliant.org
- Play some probability games here and here
- Learn about the origins of Probability as discovered by Blaise Pascal and Pierre de Fermat in solving the Problem of Points

Clickable links from the lesson assignments in the Coursebook:

For help and extra practice with the concepts in this chapter:

- Videos on descriptive statistics, including the mean, median, mode, range, quartiles, and standard deviation
- Explanations of the Normal Distribution and z-scores

For fun and deeper exploration:

- To hear more from Hans Rosling about world statistics, watch his 2014 TED talk, “How Not to Be Ignorant About the World.”

Learn how statisticians contribute to our world by watching the video “Improving Human Welfare in 2013 International Year of Statistics,” presented by Worldofstatistics.org.

Clickable links from the lesson assignments in the Coursebook:

- “Guide to Common Fallacies Playlist” by PBS Idea Channel
- Your Logical Fallacy
- Colm Kellehar’s TED-Ed lesson, “Zeno’s Dichotomy Paradox”:
- Codebreaker game
- Internet Encyclopedia of Philosophy’s fallacy page
- Puzzle Baron’s Logic Puzzles
- Puzzle Baron’s logic puzzle generator

For help and extra practice with the concepts in this chapter:

- Math Goodies has a list of articles explaining various topics in symbolic logic from this chapter
- Truth tables video explanation by ProfessorSerna
- Activity A help: Additional worked example of a Lewis Carroll logic puzzle, as well as more challenging puzzles
- Activity B help: Khan Academy logic videos and exercises. The validity and fallacy videos, in particular, may be helpful.

For fun and deeper exploration:

- Lewis Carroll
- Lewis Carroll’s Paradox
- Lewis Carroll’s book,
*Symbolic Logic*(full text available online through Project Gutenberg) - The books
*The Mathematical Recreations of Lewis Carroll: Pillow Problems and a Tangled Tale*by Lewis Carroll and C. L. Dodgson and*Lewis Carroll’s Games and Puzzles*by Lewis Carroll and Edward WakelingBrain teasers and puzzles - Brainden.com has several fantastic pages with brain teasers and logic puzzles. The river crossing puzzles tend to be a student favorite. Try this and this to start, but be sure to explore some of the other pages. Answers are hidden until you click them. Don’t peek until you are sure you are ready to know the answer!
- Challenge puzzles and problems: Brilliant.org has a section with questions for all levels of logic. Quiz yourself on topics ranging from symbolic logic to games of strategy.

- Grid-based logic puzzles
- Solve grid-based logic puzzles online or on an app
- Create your own customized logic puzzle grid and clues

- Learn about Euler’s Konigsberg Bridges Problem

An interview with Andrew Wiles, the mathematician who finally solved Fermat’s Last Theorem in 1993.

Recommended sites for general math help and practice (in no particular order):

Recommended sites for students ready for an additional challenge:

*Return to curriculum resource links.*