Week 4 Task 1: Multiplication models bingo

My kids really loved this multiplication poster. I ordered it and had it in a corner and they keep unrolling it to look at it. They have mainly focused on the fractals, mentioning when they see something that has a fractal quality. The array and number line are others they are becoming familiar with. The others were newer and we are keeping a math journal with notes, photos and drawings to continue finding these models in our everyday lives.

We have the poster of the models so I sat the girls in front of it (they have looked at it briefly before) and we talked about the different ways of thinking about multiplication. Some were very familiar by now (fractals, mirror books) but others they seemed unfamiliar with. We went out and had a look to see what examples we could find.

They were pretty focused on finding fractals, and immediately zeroed in on various weeds in the back yard, some which were more fractal-y than others. My oldest tried to claim that a worm she saw was an example of multiplication because it had 6 and then 4 stripes, so you could multiply 6 by 4. I suggested this should rather be addition, and she was a bit offended, so we moved on... I find it hard to be enthusiastic about all their ideas while staying accurate, just need to practice ways to approach their observation in a manner that brings out the potential multiplication. Of course now after the fact I can think of some!

I tried to interest them in some of the other models, as they were beginning to assign fractal-hood to anything with a vaguely interesting pattern. We talked a bit about arrays, amply illustrated by a Rubik's Cube that happened to be nearby. After talking about that arrays seemed to be everywhere, on book covers, peg boards, those iron-together bead things, the calendar...

We also noticed some sets, two scooters with two wheels each, and a broken chair seat with 4 rows of 8-bump springs.

The kids were not super focused on this activity to be honest. I think partly it was just happenstance, and partly the task seemed a bit overwhelming for them - so many models! Zooming in on a couple definitely helped us find a way in, I can see in retrospect that this is what they were doing with the fractal obsession.

Now that we seem to have a good handle on two or three, I am going to try and bring these up with them day to day, and gradually increase the models we notice as they get more familiar with the concepts.

We did this together yesterday in the house.

Array-- decorative squares on on our door

Sets per each-- four people, two feet each

Fractals-- one of the pipe cleaner ones we made earlier in the course

Area-- the rug

Skip counting-- five petals on four flowers

Combinations-- three large dolls pair up with three little ones. My daughter was interested to find this did not equal six pairs, which was her initial guess

Scaling and stretching- my four year old very excitedly showed us this with a rubber band

Folding and splitting-- what would happen if we kept cutting their muffin for snack into halves?

Repeated addition- with Lego blocks, which led to doing symmetry, number lines with the same

Money-- how much did we pay for the splash park at two dollars a person?

Looking forward to getting our big chart!

My students enjoyed looking at the chart - I don't think any of them actually realized that multiplication is more than repeated addition, despite all the activities we've been doing over the weeks! I had the 4 girls go around the house and look for examples of each model. They found and understood most, but weren't really sure about area. I don't think we had an activity specific to that in this course, unless I missed it. Each student had brought a camera in anticipation of the next activity, and each took a photo of this chart to take home. I'll email their parents the info about the poster!

Here's what our family came up with. We did a photo scavenger hunt. It was surprising how many of these examples we were able to find around our house. My kids have been saying this all week--"Math is EVERYWHERE!"

I introduced all the models right before a family trip this week, so it was fun to look for these models in contexts and locations that were out of our daily routine. We found many, some in very surprising places we had never thought of before. The thing that struck us was finding multiplication all around us everywhere! Here are only some examples:

Array: tic-tac-toe game on a playground.

Area: floor tiles at the airport.

Number line: the speedometer of a taxi cab.

Sets, per each: number of people, pairs of shoes, number of shoes.

Skip counting: 5 minutes per unit on a clock, 60 minutes per hour.

Folding and splitting: splitting our breakfast toast into pieces.

Repeated addition: counting by fives to see how many fingers we have all together.

Symmetry: looking into a kaleidescope and seeing images multiplied by 6.

Fractal: trees.

Scale and stretching: measuring relative sizes of toy plush animals.

Time and money: currency conversions. $1USD=¥6CNY, $1USD=30THB, ¥1CNY=5THB.

It's amazing to me how just over two to three weeks, my daughter's ability to observe and "find" math all around her has multiplicatively increased!

This is going to be a really fun ongoing project with the kids. It was so interesting to see different kids connecting with different models. My 12 yr old is having fun making symmetry models with mirrors.

We played around with pictures on the internet and looking around our house & outside to come up with real life ideas for each area.

For arrays: Rubik cubes, chess board, muffin pan, egg cartons

For number line: airport runways, thermometers, measuring tape, yardstick, meter stick

http://www.mathsisfun.com/numbers/number-line-zoom... has a zoomable number line

For fractals: trees, ferns, peacocks, flowers

For area: solar panels, roof shingles, bricks on a building/tower

For set: book sets, boxed sets, deck of cards

For combinations: puzzles, Lego projects, abacus

For symmetry: snowflakes, balls, Ferris wheel, wheels, butterflies, flowers

For Scale: maps, sheet music, graphs, house plans, models of real life structures in Legos or Minecraft, model cars or trains

For time & money: clocks, watches, money in piggy bank, change counting machines

For repeated addition: sidewalk squares, counters, stepping stones, parking lot spaces

For skip counting: calculator math games (repeatedly hitting +2, +3, etc.), math charts for 2's, 5's, 10's, etc.

For Folding & Splitting: car/truck seats, origami, folding sheets/blankets/papers,

My son got more into this activity this time around now that he is has been doing daily activites of finding math in anything.

So appreciating “Becoming Invisible.” (Bob Kaplan)

“It is necessary for the teacher to guide the child without letting him feel her presence too much, so that she may always be ready to supply the desired help, but may never be the obstacle between the child and his experience.” Maria Montessori

“The most difficult thing to make clear to the new teacher is that because the child progresses, she must restrain herself and avoid giving directions, even if at first they are expected; all her faith must repose in his latent powers.” Maria Montessori