A clever, yet simple tool that helps our youngest mathematicians develop a sense of number is the number ring, which is introduced in kindergarten. The number ring provides concrete practice to help students compose and decompose numbers. Each ring has a set number of beads ranging from 3-10. A boy working on a ring with five beads can manipulate the beads to gain an understanding that 1 and 4 together makes 5 (composing). He will also be able to manipulate the 5 beads to be broken down into 2 and 3 (decomposing). As they practice with a variety of numbers, the boys begin to notice the relationship between them and start to see patterns. Boys also become fluent with number combinations, build automaticity of numbers and develop executive functioning skills as they organize their beads on the ring. This is one of the first activities that kindergartners do to explore numbers and what a great way to start as it builds math confidence and curiosity for the boys.
In Fourth Grade, every Friday is math game day in Sarah Luposello’s math class.
“Mr. Bellard and I want the boys to leave Fourth Grade with very strong multiplication skills,” said Fourth Grade Teacher Sarah Luposello. “To achieve this, I sought out ways for the boys to have fun with math as well as to apply what they have learned during the week more quickly. Playing math games has definitely meant the boys look forward to Friday math and at the same time they seem to be getting quicker with their math skills.”
“One of the games I’ve introduced is Prodigy, an online computer game. I like this one, because I can set the curriculum,” explained Ms. Luposello. “After the boys have played, I can assess where they are in terms of their skills and plan their challenges for the next round. What’s particularly nice is that they are competing against their classmates, even though they are playing at their own level.”
Ms. Luposello went on to say, “As well as Prodigy there’s Multiplication Grand Prix which tests math fluency. The faster you answer questions, the faster your car goes. Number Monsters is a game that is more old school, but the boys enjoy it all the same. Then there’s the Chip Game. Players count chips in 1’s, 10’s and 1,000’s. This game gives the boys practice with every math skill they’ve learned. Either way, all of the games offer the motivation piece – to go higher, faster or collect more, and the only way to do this is to learn the math skills.”
Fifth graders in Lisa Anderson’s math class found a way to combine math skills with charitable work. The boys were keen to organize a bake sale. So instead of simply holding a bake sale, the teachers asked the boys to come up with a business plan and pitch it via a PowerPoint presentation to Middle School Head Kim Kyte. The boys began by researching non-profits to narrow down to two organizations that would benefit from the sale. They worked out what percentage of the profits they would like to go to each of these organizations, learning the difference between gross and net profit. They set the price points for the baked goods, based on how much they wanted to make.
An end-of-year project for sixth graders asks them to formulate a personal budget. They are given a paycheck and must calculate the percent of the salary that one must pay for taxes, healthcare, and other expenses, and then to budget the net pay in order to cover their expenses. Seventh graders have fun creating a scale drawing of their “dream room” using proportions, scales and similar factors.
Upper School Math Teacher Robin Keats introduced equations, inequalities and graphing to his eighth grade math class through an interactive unit called Baker’s Choice. This multi-layered problem based on the premise that a couple own a bakery and have to maximize their profit given specific constraints uses an example that the boys can relate to as they attempt to grasp these complicated math concepts.
Each boy was required to come up with the name of his own consultancy and prepare a report from the consulting company to be presented to the bake shop. The report had to be written so the couple could easily follow it. The boys priced out two types of cookies, requiring different ingredients costing different amounts, and with varying prep times. Comparing different profits and graph lines using the constraints to maximize profit was part of the final proposal.
Raam Melvani ’20 walked through his proposal, which was made on behalf of his company, The Stepper Helpers. He explained that he began by identifying the four constraints—fixed pounds of icing, fixed pounds of cookie dough, oven space and prep time. He then assigned variables— ’p’ for the number of plain cookies in dozens and ’i’ for the dozens of iced cookies. Working through each of the constraints one by one, Raam graphed inequalities using the variables and information provided. After overlaying the lines from each of the graphs, Raam said he recognized that the answer would be a point in the multi-colored feasible region and plugged in points in his equation to get to the maximum profit.
For those boys who can’t get enough math as they move into the Six through Eighth Grades they have the option of joining the math team and work with Math Teacher Will Goss to challenge themselves even further, even competing in the MATHCOUNTS competition against hundreds of other students from public and private schools across Manhattan.