Earlier this week on Late Night with Seth Meyers, guest and comedian Patton Oswalt joked about the panic he experiences when helping his daughter with her Singapore math homework.
Hearing about his guest’s struggles, Meyers commented on math education: “I can’t believe how ignorant I am that it never occurred to me there would be a different way to teach people the same stuff.”
Oswalt responds, “Exactly… Now the “new math” that you and I grew up on is old. And there’s something called Singapore math? And there’s something called the bar method? There are all these new methods. I have no idea what to do!”
He’s not alone! There’s a lot of unplanned homeschooling going on right now (and plenty of terrifying math memories being relived). If you’re a math-averse parent who could use some guidance, please make full use of our at-home learning resources.
Now, onto “something called the bar method…”
What Oswalt is referencing is bar modeling, an essential Singapore math tool, and something you’ll keep close in your math arsenal once you discover its powers.
Bar modeling is a visual problem solving technique that deals with parts and wholes. It’s an intuitive way of picturing quantities and understanding relationships between numbers. Bar models appear throughout the entire elementary Singapore math education, from addition and subtraction through fractions and ratios. A bar model looks as simple as it sounds, with rectangles or bars representing known and unknown numbers.
Let’s get a sense for how bar models are used.
Lola has 5 chocolate chip cookies. She has 3 more rainbow sprinkle cookies than chocolate chip cookies. How many sprinkle cookies does she have?
Bar modeling supports the Concrete, Pictorial, Abstract (CPA) approach. It is one of the tools used in the pictorial phase. With bar models, students move on from counting tangible objects to visualizing those objects on paper. In the simple problem above, students are no longer using manipulatives or actual cookies to count, and are a step closer to more abstract thinking about quantities.
Nina is selling cookies at a farmers market. One-third of the cookies are chocolate chip. One-quarter of the remaining cookies are sprinkle cookies. The other 24 cookies are peanut butter. How many cookies are for sale?
As you can see, bar models help with increasingly complex situations. They make multi-step word problems digestible and prime students for algebra. When kids eventually make it to an equation like 7b + 9 = 37, they aren’t daunted because they’re already used to thinking in terms of parts, wholes, knowns, and unknowns.
We love bar modeling because it’s versatile and no-fuss. It’s a technique that doesn’t require anything more than pencil and paper, and can be applied widely. Once you’ve been introduced to the concept, bar models seem totally obvious. When they’re introduced to kids early in their math lives, they support true math fluency.