Authentic Math

 Math Congress is a mathematics instructional strategy developed by Fosnot and Dolk (2002). Preparation for and participation in a Math Congress occurs over two lesson periods. The purpose of the congress is to support the development of mathematicians in the classroom learning community, rather than fixing mistakes in the children’s work or getting agreement on answers. A congress enables the teacher to focus the students on reasoning about a few big mathematical ideas derived from the mathematical thinking present in the students’ solutions.

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_communication_Mathematics.pdf

Ontario educators were gifted with a new math curriculum this fall. There wasn't any time to prepare for it and for other teachers (like me) who are completely new to teaching this grade, this can be somewhat problematic as the textbooks and traditional resources no longer match the expectations. I am using the long range plans provided by the Ontario Ministry of Education but I find that there is very little time to accomplish what I need to in the time allotted. For instance, I have 10 days (2 weeks) to address the following expectations (and these are just for Grade 5).

Attributes and Numbers

B2.2 = recall and demonstrate multiplication facts from 0x0 to 12x12 and related division facts

B2.3 = use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths and explain the strategy used

B1.1 = read, represent, compose and decompose whole numbers up to and including 100 000, using appropriate tools and strategies, and describe various ways they are used in every day life

B1.5 = read, represent, compare and order decimal numbers up to hundredths, in various contexts

C1.4 = create and describe patterns to illustrate relationships among whole numbers and decimal tenths and hundredths

C1.1 = identify and describe repeating, growing, and shrinking patterns, including patterns found in real life contexts

E1.1 = identify geometric properties of triangles, and construct different types of triangles when given side or angle measurements

I'm on Day 6 of 10 and have only started B1.1. Colleagues have told me it's more important to go deep rather than wide and to ensure understanding before rushing on, but it makes me nervous that I'm not "getting to everything". The one reprise is that there are no longer 5 math marks to provide (one for each strand) but instead there is a single math mark to include all math work.

An opportunity arose that I shoehorned into our examination of "big numbers" (as well as our new letter-writing language unit) and I feel like it was worth the detour.

Since we no longer hang our coats on hooks outside the classroom for COVID safety reasons, we bring all our items in the class. We wondered how we'd handle the indoor-shoe / outdoor-shoe routine. I didn't care much about changing shoes but the students felt it was important. 

The school library is currently undergoing renovations - new carpet squares and a few tiled sections replace the old carpet. I put a note on the library door to see if we might be allowed to have some of the old carpet to use as shoe mats in the class.

The workers said yes, and they wanted to know how many pieces and what size. This was a chance to involve the class in some authentic math. I called it a Math Congress, but it technically wasn't a Math Congress because it doesn't match all the parameters.

The students, in mixed-grade pairs, really took the task seriously. I hadn't yet taught area so I provided them with the formula. We spent half of the day on Thursday measuring, calculating, and debating. We collected everyone's basic recommendations and then narrowed it down. We chose squares over rectangles because we thought it'd be easier for the workers to measure and cut, and would save some material. (We didn't know how much leftover carpet existed, although we were told "4 feet" and that led to a discussion about translating inches and feet to centimeters.) Choosing the dimensions was tricky. In the end, we decided to go with a length that was big enough to fit the largest shoe size with a smidge extra to include the difference between boots and shoes, but not too large so that the mats would become unwieldy and take up too much space. We wrote our recommendations on a note that I pinned to the library door and by the next morning, our 30 mats (upped because the HSP class wanted some too) were ready for us!

We took a "field trip" to the library to chat with the carpenters who were in charge of the library makeover and see the changes. We gathered their names so that we could write a thank you letter to them for cutting all those squares for us. I also spent a large part of Saturday afternoon taping the edges with duct tape so they wouldn't fray. Too bad I didn't estimate / calculate how much duct tape I'd need, because I had to go to four different Dollaramas before I found one more roll of blue duct tape to finish the job.

I'm pretty pleased with how engaged the students were as they determined the best shape and size for our shoe mats. Our next debate will involve where they go in the class. I look forward to hearing their opinions.