Common Core Standards for mathematics require students to be proficient at applying the mathematics they know to solve problems that arise around them every day — in their personal lives as well as in the workplace. And this is for a good reason. According to a synthesis of math research created by the National Research Council:
“Studies in almost every domain of mathematics have demonstrated that problem-solving provides an important context in which students can learn about a number of other mathematical topics.”
The National Research Council goes on to say:
“Problem-solving ability is enhanced when students have opportunities to solve problems themselves and to see problems being solved. Further, problem-solving can provide the site for learning new concepts and for practicing learned skills.”
But no matter how important these math skills are, problem-solving with math applications can be a challenge for many students, and word problems are often a very intimidating element of any math curriculum.
In this hour-long, on-demand webinar from the Consortium on Reaching Excellence in Education (CORE), Dean Ballard, CORE’s Director of Mathematics, reviews research and resources related to mathematical problem-solving. He also models many proven techniques you can use to help students tackle math word problems on their own, without anxiety. Some of these strategies include:
In addition, Ballard provides several sample common core math word problem examples you can use to practice the techniques covered in the webinar and listed here. Watch the video above and read below for a preview of one of the math word problem examples Ballard introduces in the webinar: the Counting Trees activity.
This particular math word problem activity is from the Mathematics Assessment Resource Service (MARS). It is based off a 50 column by 50 row diagram, shown below, that depicts a forest or trees in a tree farm. The circles in the diagram represent old trees and the triangles in the diagram represent young trees.
When working through this activity with students, ask them to write down a quick estimate of how many trees of each type (old trees and new trees) there are in the diagram. Try this word problem yourself right now. What was your guess? How did you come to that conclusion?
In the webinar, Ballard will show you how to walk students through this and other sample math word problems modeling the many problem-solving techniques he covers in the webinar.
This activity is just one of many math word problem examples Ballard uses to model effective techniques for teaching students how to confidently solve math word problems. Be sure to watch the full webinar with CORE and Ballard for more sample math word problems coupled with proven strategies you can use to help students solve them.
Learn more high-leverage teaching practices to help improve students’ math performance and academic success in CORE’s math professional learning. CORE’s professional learning services for mathematics guide teachers, math coaches, and administrators in best practices for increasing the rigor of math instruction while using high-quality, evidence-based math instruction techniques.
Right. Now, the Common Core Math Practice Standards describe what and how students learn math and what they’re to do with the math while they’re learning it. Mathematical practice standard number four, which is shown on the screen here, indicates the importance of students applying math to solve math real-world problems and tasks, which word problems are a part. Students are to solve such problems from the early grades through the end of high school, so this standard is present really in almost all state standards in one form or another whether they’re using the Common Core anymore or not.
This one, is a quote from Adding It Up and take a moment to read that, so I’ll pause for a few seconds while you have a chance to read that over. Solving real world and math word problems are included now in state standards because research has emphasized the importance of applying math, creating mathematical models for problematic situations and using models via a graph, an equation, a diagram, or whatever, to solve a problem. This excerpt from the seminal work, Adding It Up, published by the National Research Council back in 2001, is just one example of synthesis of research around this.
Before we launch, however, into direct discussion on the techniques, I want to actually challenge you with a math problem, which I’ll use to illustrate some of those techniques. By the way, there is a PDF of this and of the handout on our website and Emily has just posted up in the chat area the URL for where you can get and download this problem and as well as another handout we’re going to have later on. You don’t need to go do it right now. You can just look at the problem on the screen and use that for reference, but it’s a resource that you can go to later on if you want.
This problem is called counting trees. This is from the Mathematics Assessment Resource Center, MARS or at MathShell.org, also known as the Mathematics Assessment Project. Throughout today’s session, I’ll use problems from a variety of sources, actually, such as MARS, Engage, Eureka… Engage New York, Eureka Math, Open Up Resources, and enVision Math, Ready Classroom and just by way of explanation, our team of math consultants at CORE provide support in schools for whichever program a school district has and it just so happens that over the last couple of years, these programs have popped up a lot in the schools we work with, so it’s really easy for me to pull problems from these particular ones. My purpose is not to advocate for any of these programs. I’m just letting you know what the resources are I’m using and giving credit where credit’s due. That’s all.
Again, I realize some of you may be rusty on some of the math and some of the problems. The problems are pulled from fourth grade up through middle school curricula. Don’t worry if that’s the case for you. Focus on the process or techniques being modeled, not so much on the actual math. All right, so back to the problem on the screen and it’s in that handout.
We have a diagram that represents a forest of some sort. The circles represent old trees and the triangles represent young trees. Really, you know with that, I wonder how many trees of each type there are in that diagram in this forest? I do know, I can already tell you, there are 50 columns and there are 50 rows, but exactly how many tress, how many of each kind, I don’t know at the moment, so I’d like you to feel free. I’d like you to look at it and write down a guess, a very quick estimate of how many old and how many young trees you think are in that diagram. Enter your guess in the chat window, as a matter of fact. You have 30 seconds from now to enter your guess. I’m not looking for any real statistical analysis at this point. You’re just like, “Gee, I think there’s a million.” Well, there’s not a million I’ll tell you right now, but some number between one and a million. All right? Go ahead and take your guess, put it in the chat window.