This post was prompted by looking at Aviva Dunsiger‘s Twitter stream – she is working on patterns with her students. I would like to engage with her 6th-grade class on Skype (my students are in 2nd grade) so we can do some Math together.
I am briefly outlining our inquiry into patterns last year so do not expect a “great” blog post. It was written in half an hour!
I had 4 groups of students (red, blue, etc.) and gave each group a set of 3 photos.
Question: What do these have in common?
Students realized they were about patterns despite the fact that the photos were extremely different (houses, animals, umbrellas etc.)
VIDEO – Fibonacci Sequence
The students were in awe at the beauty of mathematics and intrigued by how easily you can find it in nature! Some students were able (late in the unit) to crack this sequence…
Have a jigsaw group and assign 1 question for each and one specific color (so that you know what group contributed what ideas). Clap hands (or another signal) to swap the question papers.
1. WHAT is a pattern? How do you know? Students – things that repeat themselves, grow or change in a special way.
2. HOW do patterns work? Students – they repeat themselves, they grow longer and longer (or get smaller); a shape or a color or an object that repeats or grows up.
3. What patterns do you know in REAL LIFE?
Students – animals, clothes, music, language (rhyming words), weather, art, furniture etc. *They also pointed to their own clothes, furniture in the room, our rugs (with line patterns) etc.
4. WHY is it important to understand patterns?
Students came up with lots of answers (e.g. animals- to camouflage, music – to make songs etc.)
3. CREATING patterns
a) hands-on (using any tools in class – pencils, erasers, notebooks, math counters etc) students make patterns in pairs; discuss with class their patterns (difficulties, errors etc.)
b) drawing /writing / online applications
4. IDENTIFYING patterns
– explore school for patterns (rooms, tiles etc.) ; students take photos and discuss
– natural objects (leaves, flowers etc.)
– letter patterns
– geometric patterns
– number patterns
a). Simple number patterns (e.g. 12, 22, 32, 42…)
b). Story problem patterns (where they see a shape pattern that will grow and are asked to write values for, say, 3 consecutive days then PREDICT, based on the number pattern in the chart they write, what the 20th shape will be like).
5. CHALLENGING each other
– students create 1, 2 3 (or more)-function patterns
E.g. 12, 13, 15, 18, 19, 21, 24… (a 3-function pattern: +1, +2, +3)
Obviously, they worked with 1, 2 or more digit numbers depending on their ability. Also, the patterns could have been created using addition , subtraction, multiplication and/or division.
6. Identifying ERRORS in a pattern
This is quite tricky and it requires a lot of thinking – it’s easier to CREATE a pattern than ANALYZE one!
*Below is a simple one.
7. PASCAL’s Triangle
Have kids identify the pattern and then extend the triangle based on it.
*I don’t remember all activities but these would be the most important ones. Other mini-inquiries ran along practice as they were engaged with various pictures of patterns or came across interesting patterns. It was an engaging inquiry and kids came up with interesting questions and brought their own pictures, drawings, observations (see below).
*Other videos that the students viewed were Patterns in Nature and Math in Nature
Have you heard the following “puzzle” (that’s not really the right word). Here is a sequence of numbers: 2,4,6.
You have 3 experiments to work out the rule governing this sequence. Each experiment consists of three numbers. You tell me your numbers, I’ll say “yes” or “no”, depending on whether it fits the rule or not. After your three experiments, you tell me what you think the rule is.
If you like, we could do this on twitter, you tweet me your first experiment, I twee back my answer, and so on.
I loved it when I heard it. Of course, that’s because I got it wrong!