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.
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.
Squares, Triangles and Primes
- Consecutive Squares Review Classwork
a) Review Warm-Up: Four Corners Game
(Link to Puzzle Point instruction page)
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
A study of the patterns in triangular numbers.
This investigation is adapted to grade level from Jo Boaler’s “Squares to Stairs” activity on YouCubed.
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
6. Word Problems with Sharkey
Another entertaining question involving the adventures of Alpha, Beta, Gamma and Sharky. Good as a warm up.
7. Games We Like
Here is a link to our favorite game sources.
Games are proven to increase student engagement and learning. The most important requirements for a good math game are:
- 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!
- 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.
- Strategy is integral. Developing strategic thinking is a life skill!
Quiz #4 – What about Assessment?
Link to blog about the philosophy behind our assessments.