How Food Examples Illuminate Tough Math Concepts
When elementary students are struggling, there is frequently a food example that helps
I have been teaching math concepts for a long time.
First as a 2nd grade teacher, then a 4th grade teacher, and then as a mom.
Now I am back in classrooms again as an instructional assistant, and a lot of my job involves helping the kids who need extra help understanding the math concepts.
In every case, I have found that over and over again, food related mental pictures are what takes the student from being in the dark to the light going on in their eyes, and that brilliant moment where they can say with pride, “I get it now!”
I want to help every child’s light go on, even at schools that I am not a part of, and so I decided to share a few of these examples. I will take no offense if you already have perfect examples for all these concepts, but in the hopes that if there is a teacher out there, searching for just the right example to help “that student,” here are the mental food pictures I find to be the most helpful.
Cookies and “Mean Mom” to teach basic addition and subtraction
When I was starting to teach my kids about addition, I started with various versions of a simple concept. I would say imagine you have three cookies (or something else sweet), and I gave you one more, how many would you have?
Being kids with a sweet tooth, it was easy enough for them to imagine getting more of their favorite treat. I started simple, just going up by one, but as they got the concept, I could change the numbers and increase the difficulty.
Subtraction is a harder concept for many kids. For some reason, I find that when you say “take away” so many from the total, it is not intuitive to their young mind what exactly is happening.
So, I “eat” when we practice subtraction. In our car rides, my kids would get to say how many cookies (candy, brownies etc) they had on their imaginary plate. Then “mean mom” would sneak in and eat a certain number of them! I always said it very dramatically, and frequently got them to laugh at the mental picture of stealing and eating their sugary treats. But they understood.
When you take something away, there is still somewhat of a lingering concept of wondering if it is still around. But eating, that’s clear, and definite, and the food isn’t coming back.
My kids also liked to reverse it, where they were the “mean” one, who sneakily stole my food instead. But in both cases, they were the ones subtracting, and solving the problem.
I used this again last week at school, where one student was confused on the idea of subtraction, and I told her to imagine she had so many chocolates, and I sneakily ate some of them. She laughed at me, and even told her teacher how funny I was, but she also understood it. By the end of our little time together, she was accurately subtracting more often than not.
Multiplication and the cookie boxes
The crucial idea for multiplication is understanding “groups of” when they see the multiplication sign.
Typical word problems deal with desks in rows, or distributing stickers, etc. But my default is to cookie boxes.
A typical mental picture for 5x6 might be: Imagine you have five boxes of cookies, and each box has six cookies in it, how many cookies would you have?
In my experience, kids like the idea that each group is contained within the box, but you can count the items inside, and the idea that the more boxes you have the more you have that amount of cookies seems to resonate with them. It is also very easy to illustrate on paper by drawing rectangles with various amounts of circles with them.
Multiplying by one makes more sense. If you have one box, with however many cookies you put inside, it is easy to see that is the amount of cookies you have. You won’t be tempted to add one, because why would you add a box to your amount of cookies?
Multiplying with zero also makes more sense. A box with zero cookies in it is very sad. And it clearly means you have no cookies. It doesn’t matter how many empty boxes you have, you still have no cookies. The reverse is also true. It doesn’t matter how many cookies come in a box, if you have no boxes. You still have no cookies.
Dividing with Skittles (or M&Ms)
Division is a very hard concept for many kids. They are asked to do something vastly different from the addition or subtraction that they learned when they were younger. Multiplication as repeated addition is comparatively easy.
But division isn’t just repeated subtraction because it is about being fair.
The biggest take home we want for our kids with division problems is to know that you are taking the total amount, and distributing it the specified number of times so that all groups get an equal portion.
What makes sense to the kids is sharing a treat. Like Skittles or M&Ms. These treats come in a package with an unknown amount. They can easily imagine that they might have friends to eat these with.
So, say I was introducing the problem six divided by three. Many kids will tend towards the answer of 3. Why? Because they learned that 3+3=6, and that fact is entrenched in their brain.
At this point, I will say imagine that there are 6 Skittles, and three friends want to eat them. How many can each person have? If they still try out the number three, I pretend to start passing them out. Ok, the first person gets three, the next person gets three… and oh no, the last person doesn’t get any!
Most of the time, just to drive home the idea of fairness, I will have the person who gets zero be the child doing the problem. They definitely don’t want to divide in a way that keeps them from having a treat. So they try again, until I can give each friend the same amount.
The more I use Skittles with a group learning division, the more they catch on, and I even hear them going through to themselves, “if I have ___ and this many people want to eat them ___, then we each get ____.” This is a great moment as a teacher, because it shows they understand what the numbers on the page are truly asking.
Again, the concept of dividing by one makes more sense. However many Skittles you have, if you only have to share them with yourself- then you get to eat that many.
Regrouping concepts- Legos (I know, not food), Fun-sized Skittles, and cakes
My primary concept for regrouping in addition is Legos. I know Legos aren’t food. But I might as well share while I am taking the time to divulge all these math tricks. For this example, ones are separate bricks. Every time you get ten, you get to make a tower, and they get connected. Then, they go in the pile of other towers of ten that you have made.
For subtracting, I recently used Fun-Size Skittles to teach my daughter about regrouping.
I had her imagine that every Fun-sized bag of Skittles had ten Skittles in it. She was given permission to eat however many Skittles were being subtracted in the ones column. But if she didn’t have enough Skittles “out of the bag” from the ones in the number being subtracted from, she had to “rip” open the package and add those ones to the ones she already had before she could “eat” the number being subtracted.
When we subtracted in the tens, the bottom number was the number of bags that “dad wanted”, subtracted from however remaining bags that were not ripped.
The fifth graders I worked with this week had a completely different form of regrouping to solve. Subtracting fractions from mixed or whole numbers when there wasn’t enough to subtract from the fraction.
Their problems were complicated subtraction problems like 3 and 1/4 minus 1 and 5/6.
The number being subtracted (one and five sixths) was the order placed at the bakery. In this case, one whole pie and then 5 slices of a pie cut into sixths.
So, with three whole pies “in the back” you could easily serve this order to customers… but you have to take one of your pies, that aren’t sliced yet, and slice it to order.
It is technically regrouping, but it makes a lot more sense for why and how you can “magically” change the number 1 to 6/6 as needed to subtract. When you put it in terms of a pie being sliced, it seems very logical.
Decimals- a ten slice pizza, a hundred slice pizza and a thousand slice pizza
When kids are asked to compare decimals, it can be very difficult to convince them that .1 is much greater than .05 and that even that is greater than .009.
They see the digit, ignore the place value, and think that the greater the digit, the greater the number.
Then I break out the imaginary pizza examples.
The .1, I remind them is the same as 1/10. So this is a person who gets one slice of a pizza cut into ten slices. Very possible in the real world.
Meanwhile the .05 means 5/100. This is a pizza that has been cut into a hundred slices. Sure, you get five of them. But they are five very small slices, that added together are not even as big as the friend who got one of the ten slices from the first pizza.
Finally, the .009 means 9/1000. Some crazy person decided to cut this pizza into a thousand teeny tiny slices. You are the proud owner of 9 hairline thin slices of pizza, if you can even see them. You almost have the same as one of the hundred slices… but not quite.
After this somewhat strange explanation, the comparisons go a lot easier. More is always better with pizza, and the kids learn quickly to look at these strange numbers with a dot next to them differently.
To sum up- go to a real world food example when your kiddos are stuck.
To keep from going on endlessly, I will summarize with the idea that none of these are particularly mind blowing examples. These all came through trial and error, trying to help kids understand and picture what these abstract numbers on the page really mean.
Not every math concept has a real world example, or a food example in particular, but many of them do. Even multiplying by a fraction makes sense in baking. If I want to make a half recipe of something that calls for a 1/2 cup of something, yes, in the real world, I will use a 1/4 cup instead. 1/2 times 1/2 equals 1/4, but in a very practical sense you can understand that you need something smaller than a half to actually reduce the recipe.
Teachers, as a group, are very creative when it comes to teaching kids, and if you think about it, you can probably come up with some great food (and non-food) real world examples as well.
Let’s keep having those light bulb moments in math!