Developing critical thinking skills with multi-step word problems

Our biggest goal as math teachers is to help our students become critical thinkers and problem solvers. I help my third graders develop critical thinking skills by using multi-step word problems in my math class every day.

Think about when you use math in your daily life

When you need to find how much fencing you’ll need for your dog pen… does a worksheet appear that says “Find the Perimeter” in a cute font?!

No!

When you are planning a party and want to make sure the amount of hotdog buns you purchased will be enough for every guest to have two… does a teacher tap you on the shoulder and remind you to multiply the number of guests times 2 to figure this out?

Nope

Math in the real-world

As adults we use math all the time. Except, we have to decide in the moment if we need to be using addition, subtraction, multiplication, division or a mixture. We are able to do this because of the teachers who taught us how to problem solve.

One way that we can encourage more thinking in math class is by utilizing multi-step word problems. I don’t mean word problems that contain answer choices A, B, C, or D. I mean open-ended, multi-step word problems where students have to do some thinking to arrive at the answer.

These word problems must encourage thinking and, beginning in 3rd grade, must be multi-step.

What are multi-step word problems?

Multi-step word problems are problems that require students to do more than one math operation before getting the answer to the problem. Introduction to these multi-step word problems should begin in third grade.

Here is an example:

Melissa has 48 marbles. John has 19 marbles more than Melissa. Tommy has the same amount of marbles as Melissa and John combined. How many marbles does Tommy have?

To solve this, you must first add 19 + 48 = 67. This answer is John’s total. Then, you add 67 + 48 to get Tommy’s total.

This differs from this one step problem: John has 19 more marbles than Melissa. If Melissa has 48 marbles, how many does John have?

Why teach problem solving skills?

There is more to teaching math than giving students a paper with directions that spell out exactly what needs to be done (ex: Add these three digit numbers, Find the perimeter of these shapes, etc.) Yes, this kind of stuff is absolutely needed, but not what this post is about.

Students need to be challenged with math situations daily. This type of brain work prepares them to be successful problem solvers as adults. It teaches them that there are multiple ways to solve problems and helps them see that math class has a real life purpose. Students will also learn to use multiple math process at the same time and to have perseverance to try multiple strategies until they are able to be successful.

Are you providing your students with daily experiences like this?

How this works in my third grade classroom:

Each morning when my students come in my classroom, they complete a multi-step word problem for morning work.

1. I project a problem on my ActivPanel from my 3rd grade multi-step word problem PowerPoint
2. Students solve it in their math composition books.
3. We begin math class by discussing the problem each day.

Here is a sample problem from my multi-step word problem PowerPoint:

The Problem Solving Mat

Friday mornings, I lay a printable word problem on their desks and they complete it and turn it in for me to see. I can use this to assess student understanding, look for common mistakes, and see where I need to go next with my problem solving instruction.

The Friday printable looks like this: (These are also included in my multi-step word problem product)

I really like the layout of this page because it walks students through the problem solving process.

Step 1: Picture.

It is important to start working by relating to the problem and understanding exactly what is being asked. One of the best ways to do this is by drawing a picture. A picture could mean a model, a chart, table, etc. Some type of drawing that helps them understand the information from the problem.

Step 2: Solve it.

This is where students “show their work” and do the necessary math to solve the problem.

Step 3: Answer.

I instruct my students to include a label with their answer. For example in the problem above, the answer is 236 seashells. Adding a label helps me ensure that my students know what the answer even means.

Step 4: Explain it.

My favorite & my students’ least favorite part (muahaha).

I think explaining the answer is very important. I teach my students to evaluate their answers and ask themselves “Is this reasonable?” For example, would it make sense that my answer for the above question would be 842? I know I need to add 111, 83, and 42. Knowing this, 842 would not be a reasonable answer.

I provide my students with a writing frame in the beginning of the year to help them put their math process into words.

If you need help implementing a daily word problem into your math instruction, check out my 100 Two-Step Word Problems product on Teachers Pay Teachers. These are the daily word problems that I use with my students. Every problem contains multiple steps and uses the 4 operations to solve.

With this download, you’ll get 100 word-problems presented in a few different formats. The same 100 problems are used in each of the different formats, this is so you can use them however you like. The different formats make this product adaptable to your classroom.

You can see each format below:

I am always looking for more ideas to help my students with problem solving. What have you found that works well in your math class?