Translating the World into Math (Homework help alert!)

Math is about the world – the patterns we notice in it and the problems it presents us with. We don’t walk into a kitchen and see the equation “24 – 4 = X” shimmering in the air; we see the 2 dozen eggs we bought yesterday and that our spouse has used 4 of them, and we consider how many are left, so we can figure out if we need to go buy more.

That’s why word problems (also called story problems) are so important: they give our children practice in taking the problems that they’ll encounter in the world and figuring out how to solve them using math. Today I taught the students two steps in doing that – and they’ll be practicing it on tonight’s homework.

The first step is to read the problem and picture what’s happening in it. We tell the children to “make a movie in their minds.” Really picture the action! Then, tell the story of your “movie,” and as you do so, translate it into math and write it down as an equation, with an X standing in for what you don’t yet know. Underneath each number, and the X, jot down a reminder of what it means.

Let’s think about that problem with the eggs. “Ms. Audrey had 24 eggs. She used 4 of them to make a cake. How many does she have left?” Yes, these numbers are super easy – but this is about how to translate Life into Math! It’s easier to focus on that if the numbers are simple, at least when we start. I make a movie in my mind: “I’m picturing Ms Audrey looking at the egg carton. She sees 24 eggs.” (So we write 24 and underneath it, “eggs.”) “Then she cracks 4 of them into a bowl. They’re going away, so that’s subtraction.” (To the 24 we now add -4, and under the 4 we write, “used.”) “Now Ms Audrey is looking puzzled and wondering how many she has left” (and we finish off our equation with =X, and under the X we write “left”). That equation that “translates” the story into math is what I call a Plan. After you write the Plan, you go on to solve it. You might use the equation from the Plan, or you might use a different strategy.

Of course, many of our children can easily see how to solve simple word problems, even ones with larger numbers. So why bother with a Plan? Well, for students who get confused by word problems, it helps them really think about the math they need to do to solve the problem. However, for all students, much more complex story problems lie ahead in third grade (and beyond). Those problems will combine different operations and require multiple steps to solve them. Writing a clear and accurate Plan can help you see how to solve those complex problems, help you make sure that you kept track of all the steps, and can even give you ideas about the strategies you might use to solve them. Plans aren’t needed for easy problems – but we need to practice this step now so we’ll be comfortable with it as the math gets more complex.

Below are some examples of problems the class worked on today. (Thank you Hazel, Nathan, Aidan, and Rebecca for such beautifully clear work!)