WEEKS 9 – 10

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Link to video by Andy Clark about the value of visualization. The first problem in his video is similar to our first lesson — consecutive squares — but the whole video highlights the usefulness of visualization.

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Seeing Patterns

Patterns are intrinsically visual, intrinsically accessible to anyone willing to look. The first time a class sees (because they built it) that every square number is the sum of that many consecutive odd numbers, we ask for silence and whisper conspiratorially, “Did you feel it? … That was a goosebumps moment!”, and rub our forearms in pleasure. Because such patterns truly are amazing, artistic and just so universally true.

1. Consecutive Squares Review Classwork

a) Review Warm-Up: Four Corners Game

(Link to Puzzle Point instruction page)

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Optional Activity: PRIME CLIMB

2. Sums of Consecutive Squares Investigation

Optional: An excellent investigation from New Zealand: “Looking for Patterns in Consecutive Squares”

3. Triangular Numbers

Follow up discussion – Use this animated video, and ask students to put it into words.

4. Primes and Squares

If students have not been exposed to prime numbers, this video does a good job of helping you introduce the concept.

5. Squares in a Chessboard

Teacher’s Notes

6. Word Problems with Sharkey

Another entertaining question involving the adventures of Alpha, Beta, Gamma and Sharky. Good as a warm up.

Games are proven to increase student engagement and learning. The most important requirements for a good math game are:

1. Games should NOT be speed-based. Rather, look for games with one element of luck, and one element of strategy. Lopsided games (ones based on speed) are not fun for at least half of the players!
2. Games should have at least some concrete/visual component. Instead of fraction cards with symbols (1/2) , make fraction cards with pictures, bars, pizzas. Play strategy games with blocks, strips, dice, pattern blocks. Instead of decimal numbers, use visual decimal squares. Use the classroom floor as a game board, or hide cards for a treasure hunt.
3. Strategy is integral. Developing strategic thinking is a life skill!