Last Math Monday: Counting Patterns
This last Monday we played games that involve making and counting patterns, using pennies and other objects around the house. It sounds simple, but it’s an important and richly creative activity that many teachers repeat daily as a warmup (look up “counting collections” for details). And it’s a fun thing to do with young kids — there are so many things around the house to count! The key is to not just count things one at a time, but to group things so they are easier to count — counting by 2s or 5s makes it go faster, and is called “skip counting”.
- Here’s the slideshow from the event, including instructions for games you can play at home.
- And here’s a video replay of the event.
Activity: Counting and Grouping
Here’s the basic exercise, so you can play along at home.
- Get a bowl of 20 to 40 identical small objects, such as pennies, beans, checkers, or buttons.
- Put a bunch of the objects on a sheet of paper, placemat, or tray.
- Estimate the number of objects, and write it down.
- Count the exact number of objects, and write it down. How close were you? The more you play this the better you’ll get at estimating.
- Now try dividing your objects into some number of equal piles. Start by seeing if you can divide your objects into 2 equal piles. If that doesn’t work, try dividing the objects into 3 equal piles. Keep trying until you find a number that works.
- If you CAN’T find a number that works, then congratulations, your number is PRIME, which is the name for a number that can’t be divided evenly into smaller groups. For instance, 7, 11, 13, and 20,988,936,657,440,586,486,151,264,256,610,222,593,863,921 are prime numbers (this last example is the largest prime number found without the use of a computer).
- If you CAN find a number that works, then congratulations, you number is COMPOSITE, meaning it can be composed of smaller numbers multiplied together. For instance, 10 is a composite number because it can be divided into 2 equal groups of 5 (10=2×5).
- And if you CAN divide your number even into smaller groups, trying then dividing each of your smaller groups into yet smaller groups. For instance, 12 is 2x2x3, and 100 is 2x2x5x5, which can be visualized as:
Links and resources
Last Math Monday we watched these movies:
- The Black Diamond Precision Drill team (12 athletes marching in recombining patterns): https://youtu.be/thmn21wkFGY
- Watch the mesmerizing Factor Conga (counting from 1 to infinity one dot at a time) at: http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
You might also enjoy:
- Dan Finkel’s superb Counting Collections lesson https://mathforlove.com/lesson/counting-collections/
- The Julia Robinson Math Festival Game of the Week http://jrmf.org