By Katrina Maccalous, M.S. Ed.

Where it all began…

I began writing this article last school year as my students and I dived head first into what is easily the most important and most challenging standard for elementary (and honestly, all grade levels of math)…multi-step word problems!

There’s something about putting math into a “story” that makes children seemingly forget everything they know about math. The fact that they are no longer simply solving computations, but required to transfer reading skills to comprehend and compute, adds another layer of thinking students must problem-solve. They may have mastered strategies for addition, subtraction, multiplication and division, but put that in the context of a multi-step problem, and suddenly it’s like a foreign language! Solving word problems, and especially multi-step problems is a product (no, not the math kind) of a problem-solver and critical thinker…what we all want for our children! But teaching computation skills alone, is not enough to produce those qualities. It takes explicit instruction, modeling, plenty of resources and lots of practice and feedback to begin to develop that flexibility in thinking.

Hopefully, the ideas, resources, and strategies I have to share in these posts will be useful in some capacity for any teacher struggling with this concept, as they were for me. Check out these ideas below…and share your own in the comments!

Onto the Good Stuff…

• Operation Flow chart: I love this visual math flow chart! It takes a lot of modeling on how to use it along with many opportunities for guided practice, but it’s so worth it when students start internalizing the process. My version (which you can download for free) includes operation key words that can be used digitally or downloaded. The document also includes interactive math journal pages. You can also search for “strip diagram flow chart,” and you will find other examples.

• Strip diagrams: This model was new to me when I moved to Texas and it took awhile for me to appreciate it. They are sometimes called tape diagrams or thinking blocks. Drawing or acting out what is happening in a word problem is an effective way for students to visualize what path they need to take to solve the problem and strip diagrams are a great option for this. Each block is comprised of a single block or line that represents the total/largest value. The rest of the blocks or strips represent the parts. Depending on whether the parts are equivalent or not, as well as the relative sizes of the parts, helps create a visual of a problem. Below is an example of an activity I use in stations to have students practice matching a word problem, strip diagram and equation to each other. It’s also available as a digital resource on my TPT page!

• C.U.B.E.S.: This next strategy is one of the MOST important when helping students comprehend word problems. This excellent strategy aids students in internalizing the process of problem-solving is C.U.B.E.S., but it takes a LOT of modeling and practice to get them to use it successfully and independently. If you are unfamiliar with the acronym, C.U.B.E.S. stands for CIRCLE NUMBERS, UNDERLINE QUESTION, BOX IN CONTEXT CLUE WORDS (see below), EXAMINE THE PROBLEM (this is when I have students use the flow chart organizer process), and SOLVE. I start by having my students do a think-pair-share on strategies for solving word problems. Then we regroup, and share our ideas. After we’ve built some background knowledge, I pass out a graphic organizer with the acronym C.U.B.E.S. on it, and challenge the students to come up with what strategy each letter could stand for (get ready for some interesting thoughts, but also some ones that are right on target). Next, I share the anchor chart I’ve created and students copy the steps down on their organizer. This goes into their math resource folder or math journal for them to refer to as needed. After we’ve got our charts ready, I model the process, while they follow along, and they practice with guided support and independently (repeat the I do, we do, you do process as often as needed…for me, it’s often!) Check out my Pinterest Boards for some great examples created by other educators. This year I decided to create an organizer “plan” to support students. I use the organizer as a guide or plan for students to use to identify key information (or text evidence) that will answer the given question. Below is the organizer I have created to support my students.

• Look for Context/Operation Clues: One of the most challenging aspects of word problems is the VOCABULARY. Students need to understand the meaning behind a whole plethora of words to support them with comprehending the context of a given problem. Work with students to brainstorm context clue words (connection to reading comprehension strategies) and create a class chart for them to reference. Note: for these ideas to work, be sure to emphasize that the operation and pathway to solving (strategies) are not always one-in-the-same. A problem can ask for the difference (the amount/distance between given quantities), commonly identified as subtraction, but “counting up,” which is often associated with be adding can be the strategy used. Honestly, any activities you use in other content areas to learn vocabulary can be transferred to math! Another Note: In addition to operation context clues, students need exposure to reading numbers in written form (i.e. thirteen, fourteen, fifteen), as well as ordinal numbers (i.e. first, second, third).

• Practice, Practice, Practice in a Variety of Ways: One way for students to practice is first by trying to identify the operation(s). Give students a set of word problems with mixed operations and steps. Students sort by number of steps and then identify the operation(s). I don’t have students solve them for this part of the activity. My focus is on how to think through a word problem, not the computation yet. Have them practice creating their own word problems. Students can use the same sorting cards for this. They draw the number of steps, then operation. (Can be done with just one or the other too depending on students’ needs). Then they create their own problem for a partner to solve. With every practice we do, students are expected to use C.U.B.E.S. to make their plans and “find text evidence” to help them answer the questions.

• Be a Coach: They say that if someone can teach another how to do it, then they have a solid understanding of the concept. With this activity, students write or try and explain how to solve word problems to their peers. (Bonus: It’s great practice for procedural writing.)

• Task cards and lots of practice!: One way I have students practice is by sorting and matching equations, strip diagrams and word problems. We also engage in a daily thinking routine, where we analyze a different aspect of a word problem each day of the week. This can include: What is the problem asking? What information is important? What misconceptions do we need to watch out for? What connections can you make? What strategies could we use to solve this? How is this problem similar to other problems we’ve solved?

Additional Resources

I hope you find these strategies helpful, and please share your ideas in the comments. If you enjoyed this article, don’t forget to sign up for notifications, so you never miss out on a posting or resource! Happy Teaching!