## Penguin Math: Elementary Problem Solving 2nd Grade

The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to reason their way through math problems? I must help my students develop the ability to translate “real world” situations into mathematical language.

In a previous post, I analyzed two problem-solving tools we can teach our students: algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Now I want to demonstrate these problem-solving tools in action with a series of 2nd grade problems, based on the Singapore Primary Math series, level 2A. For your reading pleasure, I have translated the problems into the universe of one of our family’s favorite read-aloud books, Mr. Popper’s Penguins.

## Elementary Problem Solving: The Tools

[This article begins a series rescued from my old blog. Moving has been a long process, but I’m finally unpacking the last cardboard box! To read the entire series, click here: elementary problem solving series.]

Most young students solve story problems by the flash of insight method: When they read the problem, they know almost instinctively how to solve it. This is fine for problems like:

There are 7 children. 2 of them are girls. How many boys are there?

As problems get more difficult, however, that flash of insight becomes less reliable, so we find our students staring blankly at their paper or out the window. They complain, “I don’t know what to do. It’s too hard!”

We need to give our students a tool that will help them when insight fails.

## Are You Smarter than a 3rd-6th Grader?

Here are a few challenging word problems from Singapore:

I did fine on the 3rd-grade problems, but I stumbled a bit on the 4/5th-grade “How much sugar…” problem. The toy cars were tricky, but manageable. I misread the problem with the chocolate and sweets at first — I think of chocolates as a sub-category of sweets, but in this problem they are totally different. (Perhaps “sweets” are what I would call “hard candy”?) Finally, I had to resort to algebra for the last two Grade 6 questions.

How many can you solve?

## Solving Complex Story Problems

[Dragon photo above by monkeywingand treasure chest by Tom Praison via flickr.]

Let’s play around with a middle-school/junior high word problem:

Cimorene spent an afternoon cleaning and organizing the dragon’s treasure. One fourth of the items she sorted was jewelry. 60% of the remainder were potions, and the rest were magic swords. If there were 48 magic swords, how many pieces of treasure did she sort in all?

[Problem set in the world of Patricia Wrede’s Enchanted Forest Chronicles. Modified from a story problem in Singapore Primary Math 6B. Think about how you would solve it before reading further.]

How can we teach our students to solve complex, multi-step story problems? Depending on how one counts, the above problem would take four or five steps to solve, and it is relatively easy for a Singapore math word problem. One might approach it with algebra, writing an equation like:

$x - \left[\frac{1}{4}x + 0.6\left(\frac{3}{4} \right)x \right] = 48$

…or something of that sort. But this problem is for students who have not learned algebra yet. Instead, Singapore math teaches students to draw pictures (called bar models or math models or bar diagrams) that make the solution appear almost like magic. It is a trick well worth learning, no matter what math program you use.

## Percents: Key Concepts and Connections

[Rescued from my old blog.]

Paraphrased from a homeschool math discussion forum:

“I am really struggling with percents right now, and feel I am in way over my head!”

Percents are one of the math monsters, the toughest topics of elementary and junior high school arithmetic. Here are a few tips to help you understand and teach percents.

## Number Bonds = Better Understanding

[Rescued from my old blog.]

A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part.

Number bonds let children see the inverse relationship between addition and subtraction. Subtraction is not a totally different thing from addition; they are mirror images. To subtract means to figure out how much more you would have to add to get the whole thing.