The Key to Helping a Child Become A Math Story Problem Solver
Check out these math word problem strategies that are easy-to-use and a critical step to understanding math story problems!
Picture this: a fourth grade child, let's call him Johnny, (fun fact, when I was a kid and would meet someone new, I would just call them Johnny instead of their real name) knows how to use the standard algorithm for multiplication, he has the conceptual understanding to know why it works and can use it efficiently. But then consider that Johnny comes across the following math story problem and is not sure what the problem is asking him to solve.
Joelle has 3 times as many marbles in her collection as Justin. If Justin has 18 marbles in his collection, then how many marbles does Joelle have in her collection?
Johnny might ask himself 'Do I need to find the total number of marbles? Do I need to find how many marbles one person has?' He wonders what the problem is asking him and is not sure where to begin the problem solving process. He could just grab two numbers from the problem and jump in with solving (and in this case, if they multiplied 3 x 18, it would be correct. But what if the question asked how many marbles do they have combined?) Wouldn't it be better for a child to have a tool to figure out exactly what the problem is asking? I think so, and I know many teachers that would agree.
This is where visual models come into the equation (no pun intended ha!). Visual models often get a bad reputation of being ‘slow’ strategies, taking too much time or not being efficient. Especially from the perspective of parents who typically learned one way to solve a problem, they wonder why on earth their children are spending time drawing ‘pictures’ in math. Check out these visual multiplication models from this awesome blog post by Room to Discover about using visual models in math!
Looking at those models, you might think, that is a LOT of work when you could just solve these problems using the standard algorithm. However, visual problem solving strategies are a critical first step in building conceptual understanding (which is necessary to develop procedural fluency). All of the models above help children understand what multiplication means, so that when they are ready for more efficient strategies, they actually understand why they work. But aside from that, visual models serve many different purposes.
That’s why Johnny needs a tool in his toolkit to UNDERSTAND what the problem is asking him to solve. Bar models(shown in the picture below)are great for this in all four operations. These types of models do not actually solve the problem for the child, but rather they help the child understand the structure of the story problem. So in the example below, you can't actually figure out the value of 3 x 18 by looking at the model, but you can understand that the problem is asking you to find out Joelle's total number of marbles. You could use this same model to represent a problem asking how many marbles they have combined by just changing the placement of the question mark. This is the foundation of algebraic understanding.
Once a child uses a bar model (or other visual model) to UNDERSTAND what they’re trying to solve, they can choose a tool for SOLVING (a strategy such as the distributive property/area model--a visual problem SOLVING strategy (left) or the standard algorithm--a more abstract problem SOLVING strategy (right) as seen in the picture below).
If Johnny jumped to solving before he understood the problem, then he might not get the correct answer—not because he doesn't have an efficient problem solving strategy, but because he didn’t take the time to understand the problem. This is especially important with multi-step word problems.
I used multiplication in my example to illustrate the importance of using both a tool for understanding and a tool for solving, but this same idea can (and should) be applied to other operations. Imagine you were given the problem: "Julio has 8 toy cars. Justine has 4 more toy cars than Julio. How many toy cars do the two children have all together?" This first grade problem (problem solving within 20) is a little more complicated than it might seem at first glance. First, a child would need to figure out how many toy cars Justine has. Then they would need to add that value, to the 8 cars that Julio has to find the total number of cars. Many children might just jump into this problem by seeing an 8 and a 4 and adding the two together (because sometimes children are taught to look for key words such as all together to recognize that it is an addition problem--nothing wrong with key words if they are used alongside another tool such as a bar model, but you can see how that might be tricky in this problem because the solution is not found by simply adding 8 and 4). So a child would need to use a tool to UNDERSTAND first, and then choose their solution strategy (to add 8 + 4 they might use counters, a ten frame, a number line, or 'just know' the sum. Then they would use a similar strategy to add 8 + 12 to find the total value).
You might be wondering, 'that is a lot of work and a lot of steps for a child to solve a story problem. And what if they have 10 (or more) story problems on their homework, or class work? How in the world would they solve all the problems if they're doing this every time! My recommendation is not for children to use these tools to understand every time, but rather to use them frequently at the beginning, and then keep them as a tool in their tool kit to use as needed. Once children use bar models for problem solving, they will start to recognize similar structure in story problems and they might think back to a similar bar model they made, and rather than draw it out, might be able to visualize it in their head. But at that point, they know how to create one of these models, and if they come across a problem that stumps them, they can pull this tool out and use it to build understanding. This helps children move past frustrational moments in math because they actually have a tool to use to build understanding. Because at the end of the day, isn't that what we want as parent/teachers? For our children to understand the math they're doing? I believe that understanding is at the core of everything we do in mathematics (it is one of the 5 strands of mathematical proficiency after all. But more on that in another blog post).
Looking for some math story problems to try with your child or your class? Check out my Math Story Problem resources on my TPT page for differentiated math story problems that are engaging, seasonal and perfect for trying tools to UNDERSTAND and tools to SOLVE!
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