It is finally here, our last unit of the year and I have to say I am so excited to make it to Growth Patterns! Before we did some reorganization of units due to CCSS shifts, I could never get to this unit, however now having fewer units, I finally make it to the end!
If you have never looked at this Investigations unit before, here is a brief description:
This unit is really a beautiful culmination of all of the pattern noticings my student do all year long.
Being the end of the year, I know I am going to miss constantly having a class to try out my ideas on during the course of the summer, so I am making the most of the time I have left to test some different number routines. After reading through this unit, two things jumped out at me that could potentially be incorporated into our number routine work before the lesson: predicting nth terms and relationships between two sets of numbers. So, I thought it may be interesting to do some counting and then think about relationships between our sets we make.
I first had a student count by 3’s four times: 3,6,9,12…. I asked the 10th term and everyone looked at me like I was crazy because this seemed too simple and said “30.” I asked how they knew and immediately thumbs went up and they all agreed that 3 x 10 = 30.I asked for another way you could get there? Next I got, “If you add one more 3 and get 15, you can just double it because it is doing the same thing all the way.” I wrote (12 + 3) x 2 = 30. Another student said, “You can double/half and do 5 x 6 = 30.” Me, “How does double/halving look here?” Silence for a minute, so I asked them to chat with a neighbor and then they came to thinking about jumps on a number line and explained that you were doing jumps twice as big so you need half as many.
Next I did the same process with 4’s: 4, 8, 12, 16 and I got much of the same as above. I asked if we could make any connections to the first set. I had an idea this one may be tough (but I had a plan for it in the next set), however I did have two students who noticed it was one more every time you counted by 4’s, so by the time you counted 10 times, you would have to add 10 to your total, 30+10=40.
The third problem, I wanted to give them the chance to make some connections to the 3 and 4 counts, so I did 12’s: 12, 24, 36, 48… Again, I got many of the above strategies, but then they made some connections to doing “3 times as many jumps of 4 in 12” and “4 times as many jumps of 3 in 12” and adjusting their 10th terms.
Because some students were really comfortable moving between the sets of numbers, others were still staying within one set of numbers in describing the 10th term, I gave them two sets to go back to their journal to reflect on: 2’s: 2, 4, 6, 8…. and 2/3’s: 2/3, 4/3, 6/3, 10/3….
I asked them to either talk about how they could arrive at the 10th term or make a connection to one of the previous sets of numbers…
It was interesting to see their connections between the sets, but I think for next time I need to think more about either the predictions of future terms or comparing two sets, this was a bit too much at once. Next time I may have them look at sets with constant change but not starting at a multiple of that number….and then as I was typing that, I think it would be cool to come up with a set with a missing number at the end that could be varying numbers depending on how they see the pattern, then give a term after the missing number and narrow it down to which pattern it actually is….hmmmm…have to think more about this one…
RE: “and then as I was typing that, I think it would be cool to come up with a set with a missing number at the end that could be varying numbers depending on how they see the pattern, then give a term after the missing number and narrow it down to which pattern it actually is”
A nice example (the “niceness” depending on the audience) is just to begin with 1, 2.
As a few examples:
It could continue with a 4 (e.g. doubling).
It could continue with a 3 (e.g. counting).
Okay, how about 3. …But what comes next?
If it is a 4, then we may be a bit more confident in the counting.
If it is a 5, then we have: 1, 2, 3, 5.
Maybe next is an 8 (e.g. adding consecutive terms to make Fibonacci proud).
Maybe next is a 7 (e.g. avoiding multiples – i.e. the non-composites: 1 and the primes).
And so forth.
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I love this Maya!! Thanks! So much to think about and play around with here. This is where planning is so fun, right? Playing around w/the possibilities and the places the students can go with it!
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Beautiful ending for your school year.
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I just wish I had you guys to teach me math at school. I feared it, hated it, and quit it. In that order. I am just rediscovering what fun it can be… at the raw young age of 45! LOL! way to go guys… keep doing this.. love y’all!