presenting distance
Lili and Mackenzie teamed up last week with their bands to continue their exploration of estimating the distance from Brightworks to Dolores Park with a measurement unit of their choice. After some multiplication skill practice, the kids returned to the provocation to do some more math-y exploration, culminating in a presentation on Wednesday. Lili writes all about it below:
Each group used a map of the mission to count the number of long and short blocks between Brightworks and Dolores Park. Using the block the school is on as a sample block, students estimated how many of their units would make up a short block and how many would make up a long block. Some groups, looking for increased precision, used pieces of paper as makeshift "rulers" to decide that short blocks were ½ or ⅓ the length of long blocks, etc.
Each group employed different strategies to work out the math. Some added the number of units per block as they went along--creating long strings of complex addition problems. One group started by thinking about averages--estimating the average number of units in a given block and then doing the multiplication to get a rough answer before diving in with more specific numbers. Another group created an equation and learned how to cross-multiply. We made use of the base 10 manipulables to make long addition and multiplication more concrete for some groups who were struggling to visualize the arithmetic they were working out.
On Wednesday, when most groups had already worked out a lot of the math, we gave the students about an hour to create presentations for each other to describe the process they went through to arrive at an estimate. We emphasized the fact that the numerical answers would be different for each group because everyone started with a different unit. Especially without any define-able correct answer, our presentations would be the only way for us to understand each others’ methodology and eventual answer. It was lovely to remove the absolute from the mathematical process in this way. Everyone got a different answer based on the conditions they set up for themselves at the beginning of the project.
Clementine, Quinn, Ben, and Jacob solved the problem two different ways: they averaged the number of smaller and longer blocks, and counted the number of smaller and longer blocks and added the totals.
Bruno, Audrey, and Lukas measured the distance in sheets of paper - ten sheets of paper could fit in 3 paving stones, so they counted how many paving stones are in a city block, then used that number to figure out the total.
Natasha and Norabelle were thrilled about the chance to present their findings, and both handwrote and typed their spell-checked speech to make a confident presentation. They used Natasha's cubit (tip of finger to bottom of elbow) to determine the length of a copper pole, then used the copper pole to measure the block, and then added and added and added.
Oscar and Nicky used a long stick to measure and used multiplication and division to do their math work, measuring from the front door to the corner of the block. When prepping for their presentation, they found that they didn't show enough work during their figuring and needed to fill in the blanks before presenting. They learned that they actually do need to show their process in their work!
The presentations created further opportunities for a multi-modal approach to the project. Visual thinkers made diagrams and spent time designing and decorating their presentation boards. Tactile learners built structures with the base 10 blocks. Auditory learners talked through the steps of the project with peers and collaborators and got to shine during the actual speech-giving part of the process. Mathematical minds could attempt more precise estimations, making the project more challenging for those who were ready. Because the projects and presentations were so multifaceted, all different kinds of learners left feeling both accomplished and challenged by the work they had done.