Our new math unit focusses on the critical concept of "rates." A rate (or ratio) is a change that occurs at a constant pace. Some examples: I can write my name 18 times per minute. The Herons can put out 180 chairs in 3 minutes. Three pounds of grapes cost $1.80.
The key tenant of rates is that we can extrapolate them. We can use what we know to find out what we don't know. This is the definition of algebra that we use with students and it certainly applies here. For example. If three pounds of grapes cost $1.80, then 6 pounds is $3.60 and 1 pound is $.60. This relationship can be graphed on an axis. It can also be written as $.60 x p = total price (where p is pounds of grapes). Graphing and equations are tools we can use so we don't have to compute all of the "in-betweens" as seen below:
Of course, initially, students do need to figure out the inbetweens to build their understanding. Otherwise, once they use the tool of a graph or equation, it seems disconnected from the real world. They only know it works to find an answer but they don't understand why it works.
Before we began this unit, we assessed students' current understanding of rates by asking them to answer a few questions and share their confidence with that type of problem. This helped us see if a child had little experience with the concept, was developing their understanding or was ready to tackle the idea of rates in a more complex way. Amy, Cathy and I set goals for each group of learners together and then individually develop and teach a curriculum to help students reach those goals.
As you can see above, a facility with basic multiplication and division facts makes this work much, much easier. We use this as an opportunity to explain to students, once again, why we feel strongly that they should master their basic facts. It's an authentic application. Kids who know without thinking that 3x6=18, instantly see a relationship in the above grape example that is missed by students who don't know that fact. It's a lot easier to use multiplication to extrapolate than to use repeated addition.
The next few weeks are a great time to explore rates at home with your Big Bird. Allowance, getting ready for school, cooking, gas mileage, and speed all afford great opportunities. I highly recommend The World in One Day by Russell Ash -- it uses stunning visual images to share rates for everything from the world's daily banana consumption to the heart rate of a blue whale. It's a great addition to any home library. As a staff, we've been discussing ways to make home numeracy work as easy as home literacy work -- rates is a great way to incorporate "math talk" into your family life.
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