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• January 3, 2021
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CUBES Math Strategy for Word Problems

The CUBES math strategy is a tool teachers use to aid students with problem solving. Do you have students that when faced with a word problem they seem to freeze and have no idea where to start?

The math CUBE strategy provides those students with a starting point, a set of steps to perform in order to solve a particular math word problem.

What is the CUBES strategy?

This strategy helps students break down word problems by creating five steps they must follow in order to solve. CUBES is an acronym that is easily remembered by students.

C – Circle the numbers

U – Underline the question

B – Box the key words

E – Evaluate and Eliminate unnecessary information

S – Solve and check

Why use the CUBES math strategy?

• It gives students a starting point when they are faced with word problems. We know many kids fear word problems and many times they have no idea where to start.
• It makes kids aware of what the problem is asking – this might seem simple but forcing kids to underline the question is a good way to make them read what is the problem asking me to do.
• It brings out all the numbers in the problem – sometimes word problems present numbers in numerical form, word form, or any other tricky form. Circling the numbers forces kids to look through the problem to find numbers in any form.

If you are looking for a digital way to use CUBES, I have created a set of Google slides where students can annotate the word problems, write an equation, and solve.

https://youtu.be/0iL3v7V6jVA

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Exploring the Power of the CUBES Math Strategy for Word Problems

Math problem-solving is one of the most challenging things we teach. The CUBES strategy is all about helping students tackle those tricky word problems with ease. Whether you’re dealing with pesky volume or area questions, or trying to figure out how many more apples Sally has than Timmy, the CUBES math strategy can be a great way to help those learners who struggle with word problems develop a systematic method to approach these problems. By breaking down the problem into smaller, more manageable chunks, you can quickly solve even the most complicated math problems.

So if you’ve ever found yourself scratching your head in frustration over your struggling learners’ battle with story problems, fear not! The CUBES math strategy is here to make your life a whole lot easier. Stick around to learn more about how this awesome strategy can help you help your struggling students become math problem-solving pros!

What is the CUBES Math Strategy?

The CUBES math strategy is a tool designed to help give students a systematic approach to breaking down and solving math word problems. The acronym C.U.B.E.S stands for:

• C ircle key numbers & units
• U nderline the question
• B ox math action words
• E valuate the problem
• S olve the problem & check your work

By breaking down the problem into these steps, students can better understand the context of the problem and effectively solve it.

Benefits of using the CUBES strategy in math word problems

While CUBES is not the ideal method for all math problem solving, especially as word problems become more complex, you can use the strategy as a starting point to guide struggling students in being more attentive and systematic when tackling word problems.

Many struggling learners struggle with executive functioning and need a clear-cut plan for tackling this next-level math skill, and incorporating a strategy like CUBES into your teaching can give them steps to approach word problems rather than leaving them overwhelmed and unsure where to begin. This can help students build confidence in their ability to successfully solve math story problems and prepare them to solve multi-step problems, ultimately enhancing their problem-solving skills.

Step-by-Step Guide to Using the CUBES Strategy

Implementing the CUBES strategy means teaching students the key steps and working through a gradual release process until they can effectively do this themselves. This systematic approach helps students understand the problem and empowers them to tackle word problems with confidence. Here’s a little more about each step your students will need to achieve:

C- Circle the numbers & units

C stands for “circle the key information.” This includes the numbers, units, and core information needed to solve the problem. This includes identifying math vocabulary that represents a number, such as “several,” “half,” or “a dozen.” Some questions may not involve numbers at all, in which case you would circle each instance of the word “none.” It is also important to identify units (such as feet, miles, or kilograms) and whether there is a decimal point.

While we don’t want students solely relying on keywords when faced with a word problem, it can be helpful for them to recognize which words are references to mathematical symbols. For example, “+” means addition, and “-” means subtraction.

U- Underline the question

After students read the problem and circle numbers/units, they must underline the question. While this may seem silly, if students aren’t attending to what is being asked, they won’t get the right answer. Helping students stay on target is a key component of the CUBES strategy for solving math problems.

Once your student has underlined the question and knows exactly what he or she needs to solve, it’s time to move on to step B: boxes and bullets.

B- Box math action words

Notice this doesn’t say keywords…Again, we don’t want students focused solely on using keywords for math problem solving. Research has shown time and time again this is an ineffective strategy once problems become more complex.

That said, students need to look at word problems through the lens of critical readers. What in the problem gives them a clue as to what they need to do to solve it?

Just like the author of a story gives us details to help us infer and get to the story’s resolution, the author of a word problem helps us find the path to the solution. We need to be critical readers to get there. This is where boxing key information can be helpful. Here are some common examples that are often viewed as keywords but are critical for students to attend to to solve problems accurately:

• Addition: add, added, both, sum, total
• Subtraction: difference between, less than
• Multiplication: times twice as many/much as of every
• Division: split equally among/between each share out of

E- Evaluate or Equation

At this stage, it’s time to implement your strategy to solve. For some students, this will be writing and solving the equation. Others may need to evaluate by drawing a picture or using manipulatives to model the problem.

Either way, by this stage your learners should have broken down the problem to the point that they feel confident implementing a method that will lead them to the final step – solving.

S- Solve & Check

Once the strategy has been chosen, guide your students through the process of solving the problem. This may involve writing out the equation, solving for the unknown variable, and checking their work to ensure they have found the correct solution.

Encourage your students to show their work and explain their reasoning as they solve the problem. This will not only help them understand the process better but also allow you to provide feedback and support if needed.

It’s important to emphasize the importance of checking their work to ensure they have found the correct solution. This may involve plugging the solution back into the original problem to verify it or checking their work for errors in calculations.

Once your students have successfully solved the problem, congratulate them on their hard work and encourage them to reflect on the process. Ask them questions such as what strategies worked well for them, what challenges they encountered, and how they can apply what they have learned to similar problems in the future.

By guiding your students through the process of problem-solving and encouraging them to reflect on their work, you are helping them develop essential critical thinking skills that will serve them well in all areas of their education and beyond. 

Tips for Implementing the CUBES Math Word Problem Strategy

Whenever you’re preparing to implement a strategy with your struggling learners, it can be helpful to get some tips from teachers who have been there. In asking for advice from colleagues, here’s what they had to say.

To teach the cubes strategy, you should:

• Teach the strategy as a whole. Because this is such a visual strategy, it’s useful to provide multiple examples of how to solve problems with CUBES on a poster or anchor chart. You can use the chart below as an example of what to include.
• Use a standard problem as an example. Before having students practice on their own, have them watch and listen as you model how to use the CUBES strategy on the board using a Problem of the Day or by writing in student journals. Visual learners will appreciate watching you write out each step and manipulate your complex number sentence cube.
• Use anchor charts you make together in class. Then transfer that knowledge into modeling one or two more examples with students using cubes they create out of construction paper, or if necessary, manipulatives like buttons or dry beans.
• Don’t fall into the trap that the standard algorithm is the only way to solve once the strategy has been used. Let students draw pictures, use manipulatives, make number lines, or whatever other strategies you’ve taught. The CUBES math strategy is to help them break up the problem. It isn’t the guiding principle of the math calculations.
• Students can use CUBES to filter out irrelevant details and focus on the essential details needed to solve the problem. By guiding students to evaluate the problem systematically, you can help students make informed decisions and tackle complex math challenges. It is great for learners who might get bogged down in all the details.

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Posted on Nov 2, 2016 in Classroom Management , STEM

CUBES: A Mnemonic Strategy for Word Problems

It stands for: C = Circle the Numbers U = Underline the Question B = Box the Key Words E = Evaluate and Draw S = Solve and Check

Math Problem-solving Strategies that were seen in the video

• Number Line

Helpful Links

• Video on CUBES for direct student instruction.
• Attention-Getters in Whole Brain Teaching
• Essential Question
• TeachLogic in-classroom microphone system for Teachers and Students

Related Front of the Class Videos

• Distributive Summarizing
• Using the RAISE and SAC Rubric for Written Responses

This video was filmed at W.B. Simpson Elementary School .

© 2017 The Office of Attorney General Matt Denn, State of Delaware. All rights reserved.

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Maneuvering the Middle

Student-Centered Math Lessons

Math Problem Solving Strategies

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem?  For me, the answer is too many to count.  Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for .  There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

1. C.U.B.E.S.

C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.  

• Why I like it: Gives students a very specific ‘what to do.’
• Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem.  None of the steps emphasize reading the problem but maybe that is a given.

2. R.U.N.S.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence. 

• Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence.  This is a great strategy to teach when you are tackling various types of problems.
• Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

• Why I like it: I love that there is a check step in this problem solving strategy.  Students having to defend the reasonableness of their answer is essential for students’ number sense.
• Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

Here is the strategy that I adopted a few years ago.  It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

• Know: This will help students find the important information.
• Need to Know: This will force students to reread the question and write down what they are trying to solve for.
• Organize:   I think this would be a great place for teachers to emphasize drawing a model or picture.
• Work: Students show their calculations here.
• Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

Ideas for Promoting Showing Your Work

• White boards are a helpful resource that make (extra) writing engaging!
• Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
• Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work. 

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more. 

Students who plan succeed at a higher rate than students who do not plan.   Do you have a go to problem solving strategy that you teach your students? 

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

Problem Solving Posters (Represent It! Bulletin Board)

Check out these related products from my shop.

Reader Interactions

18 comments.

October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

Great idea! Thanks so much for sharing with our readers!

October 8, 2017 at 6:51 pm

LOVE this idea! Will definitely use it this year! Thank you!

December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

September 2, 2019 at 11:18 am

Going off of your idea, Natalie, how about the following?

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

March 16, 2020 at 4:44 pm

I’m doing this one. Love it. Thank you!!

September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

(502) 895-9500    |    [email protected]

CUBES: Who is Doing the Thinking?

Written by vmillerbennett.

A search on the internet for “CUBES math strategy” yields about 36 million results. Seeing a bright, cheery, and colorful CUBES poster on display in mathematics classrooms is a typical occurrence. Elementary and middle school mathematics teachers who are familiar with the Common Core State Standards for Mathematics (CCSSM) or their state’s version of CCSSM might know that the phrase “solve word problems” shows up 20 times in the grades kindergarten through grade seven standards, signaling its importance (National Governors Association, 2010).

In elementary mathematics education, problem-solving strategies like CUBES (Circle, Underline, Box, Evaluate, Solve) and keyword approaches have been staples in the toolkit of teachers aiming to guide young learners through puzzling mathematical tasks also known as story problems. According to the National Assessment of Educational Progress (NAEP) report , “the average fourth-grade mathematics score decreased by 5 points and was lower than all previous assessment years going back to 2005. The average eighth-grade mathematics score decreased by 8 points compared to 2019 and was lower than all previous assessment years going back to 2003. In 2022, fourth- and eighth-grade mathematics scores declined for most states/jurisdictions as well as for most participating urban districts compared to 2019” (NAEP, 2022).

This alarming trend again underscores the need for comprehensive reforms in mathematics education across the United States, emphasizing teaching methodologies grounded in research, increased support for educators, and targeted instruction to address learning gaps and promote mathematical proficiency among all students.

Structured and procedural methods, like CUBES, that are often offered as support to students as they solve word problems need to be eradicated. The ability to think critically and independently is essential for all students. In this blog post, we’ll explore why reliance solely on CUBES and keyword strategies may hinder the development of cognitive skills and why it is imperative for teachers to prioritize teaching students how to think instead.

The Pitfalls of Structured Strategies

Structured problem-solving strategies may offer a sense of security and direction for both students and teachers. However, such scaffolds come with inherent limitations that can impede genuine understanding and hinder the cultivation of critical thinking abilities. Recipe-like directives also prevent students from engaging in tasks that are of high cognitive demand and collaborative, for example.

1. Rote Memorization Over Conceptual Understanding

Structured strategies often encourage students to follow a predetermined set of steps without truly grasping the underlying concepts. This can lead to a surface-level understanding based on rote memorization rather than conceptual understanding and opportunities for making connections, seeing patterns, and thinking mathematically, in general.

2. Lack of Flexibility and Adaptability

While CUBES and keyword strategies may be effective for certain types of problems, they can be restrictive when faced with more complex or unconventional scenarios. Students may struggle to apply these rigid frameworks outside of the specific contexts they were taught, limiting their ability to adapt their problem-solving skills to novel situations. Powell, Namkung, and Lin (2022) analyzed 747 high-stakes released items across grades 3, 4, 5, 6, 7, and 8. Keywords were identified and then matched to the implied or commonly associated operation. The correct solution to routine problems was found less than 50% of the time when following the method implied by the keyword. The rate of success was less than 10% of the time with multistep routine word problems. Elementary and middle school students are asked to solve word problems categorized as directive, routine, or nonroutine. (Powell & Fuchs, 2018).

3. Stifling Creativity and Exploration

By providing a formulaic approach to problem-solving, structured strategies leave little room for creativity, exploration, and divergent thinking. Students may become accustomed to following prescribed procedures rather than engaging in the exploration and experimentation essential for developing innovative problem-solving skills. Keyword strategies such as CUBES remove opportunities for students to think while at the same time fostering the act of pulling numbers from the task and simply operating. The well-known example problem of the shepherd’s age illustrates this. When presented with the problem “There are 120 sheep and 5 dogs in a flock. How old is the shepherd?”, a common response of “125” is given. The correct response is “There is not enough information”. For more on this task, see “Informing the Need for Critical Thinking in Mathematics” by Vardeh (2020).

The Case for Teaching Students to Think

In contrast to the confines of structured strategies, nurturing students’ ability to think critically empowers them to tackle problems with depth, insight, and flexibility. Here is why prioritizing student thinking is paramount.

1. Building a Strong Foundation for Lifelong Learning

By focusing on cultivating critical thinking skills, educators lay the groundwork for students to become lifelong learners who can adapt to the challenges of an ever-changing world. Rather than simply providing answers, teachers equip students with the tools to analyze, evaluate, and solve problems independently.

2. Fostering Resilience and Confidence

When students are encouraged to think critically and grapple with challenging problems, they develop resilience and confidence in their abilities. They learn to persevere in the face of difficulties, knowing that they have the skills and resources to overcome obstacles.

3. Encouraging Deep Conceptual Understanding

Critical thinking goes hand in hand with deep conceptual understanding. By engaging students in meaningful explorations of mathematical concepts, educators foster a profound understanding that transcends memorization and enables students to make connections across various domains of knowledge.

Strategies for Cultivating Critical Thinking

How can teachers shift their focus from structured strategies to nurturing critical thinking in their students? Here are a few practical approaches:

1. Inquiry-Based Learning

Embrace inquiry-based learning approaches that encourage curiosity, exploration, and discovery. Provide students with open-ended questions and real-world problems that invite them to investigate, analyze, and propose solutions.

2. Incorporate Reading Comprehension Strategies

Visualizing, retelling, making connections, and asking questions are established reading comprehension strategies that teachers of all grade levels can use to support students in making sense of the context of any type of word problem. Many students learn these strategies in language arts classes and can easily apply them to mathematics problem-solving as well (Gallagher, Ellis, & Weiland, 2021).

3. Promote Metacognition

Encourage metacognitive reflection by asking students to articulate their problem-solving processes and strategies. Prompt them to consider why certain approaches were successful or unsuccessful and how they might approach similar problems differently in the future. Encourage dialogue among peers and provide opportunities for students to write or draw to represent their thinking.

In moving toward developing critical thinking in mathematics education, teachers should move beyond the constraints of step-by-step problem-solving strategies like CUBES and keyword approaches. By prioritizing the development of critical thinking skills, educators empower students to become resilient, confident, and independent learners who are equipped to tackle the challenges of the 21st century and beyond. If you are seeking valuable insights and strategies to enhance your teaching practices in elementary and middle school mathematics, I highly recommend “Elementary and Middle School Mathematics: Teaching Developmentally” (Van de Walle, Karp, & Bay-Williams, 2022).

Gallagher, M. A., Ellis, L., & Weiland, T. (2021). Making Word Problems Meaningful. Mathematics Teacher: Learning and Teaching PK-12, 114(8), 580-590. National Governors Association. (2010). Common core state standards. Washington, DC.

Powell, S. R., & Fuchs, L. S. (2018). Effective word-problem instruction: Using schemas to facilitate mathematical reasoning. Teaching Exceptional Children, 51(1), 31–42.

Powell, S. R., Namkung, J. M., & Lin, X. (2022). An investigation of using keywords to solve word problems. The Elementary School Journal, 122(3), 452-4.

U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2022 Mathematics Assessment.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2022). Elementary and middle school mathematics: Teaching developmentally. Pearson. One Lake Street, Upper Saddle River, New Jersey.

Vardeh, M. (2020). Informing the Need for Critical Thinking in Mathematics. Unpublished manuscript. Department of Mathematics, California State University, Turlock, CA.

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• by CAPCURRICULUM
• January 28, 2024

Solving math word problems can pose a significant challenge for students. While various processes and strategies exist for solving these problems, not all are equally effective.

There is, however, a strategy called R.I.E.D.S. that’s a game-changer when it comes to solving math word problems. I tried it out with my fourth-grade students, and in just six weeks, their problem-solving skills shot up by 22 percentage points, according to the school district’s benchmark assessment.

In my 20+ years as an educator, I’ve tried many word problem-solving strategies. I have also seen many implemented; some were effective, while others, not so much.

In all honesty, though, strategies are only as effective as the teacher’s implementation. I say this because I’ve seen teachers implement tried-and-true strategies ineffectively, and then blame the students or the strategy for the lack of success, instead of their implementation and execution.

Now, I know you don’t know anything about R.I.D.E.S, so I’m curious about the word problem solving strategy you’re teaching to your students.

If I had to guess, I’d say CUBES. Am I correct?

CUBES: A Popular Strategy for Solving Math Word Problems

Within the last decade (maybe a little longer), I’ve noticed that CUBES has become the go-to strategy for many teachers when it comes to teaching students how to tackle word problems.

CUBES isn’t a bad strategy it’s just that before you go teaching it to your students, you’ve got to tweak a few things.

So, what’s the problem? I had this ongoing debate with some fellow teachers about CUBES not being as effective when you stick too strictly to the steps.

Although there was much evidence suggesting that CUBES wasn’t working for their students, they were adamant that it was an effective strategy. But more than that, they were reluctant to try a new strategy.

I wanted to settle this collegial debate with a bit of outside-school evidence, so I threw a math word problem at my son to see his approach to problem solving.

I couldn’t believe what I was observing.

My Son Too!

Before even reading the word problem, my son began going through a routine. He started by circling all of the numbers.

The whole time he’s circling, I’m sitting there thinking…WTF!

After circling the numbers, he underlined the question. I knew where he was going next, so I stopped him. I couldn’t sit back and watch him reinforce a bad habit.

To confirm my assumption about the strategy he was using, I asked him why he circled the numbers first.

His response? “That’s what you’re supposed to do first. Circle the numbers.” 

I had to break it to him — circling numbers shouldn’t be the first thing you do.

Now, my son being the argumentative person he is, disagreed. He explained that he was following his teacher’s directions and that his work would be marked wrong if he didn’t stick to the steps.

So, I asked him flat out, “Are you using the CUBES strategy?”

“Yep!” he proudly responded.

Instantly, I thought about the teacher at my school who was emotionally attached to CUBES, despite it not working for her students.

Guess what? It wasn’t working for my son either.

As educators, we need to keep in ming — it’s not about what we like and our preferences; it’s about what works for our students.

A Directive to Stop Using Cubes

So, picture this: The math coordinator from the district swings by our school for a visit, doing the whole walkthrough and support thing. Afterward, during our debrief, she sings music to my ears and tells me that the CUBES posters plastered on the walls gotta go.

Turns out, she wasn’t a fan of CUBES either, echoing my sentiments. The minute she walked out the door, I made a beeline for every classroom with those posters and broke the news about the district directive.

Now, I get it, if you’re a teacher, you might be side-eyeing me for bossing other teachers around and reducing teacher autonomy. But hey, sometimes you gotta do what you gotta do.

I believe in teacher autonomy and buy-in, but not when it adversely impacts students’ learning. 

See, if a strategy isn’t cutting it for the students, no matter how much we like it, there are only two moves: either give it a makeover or kick it to the curb. Why? ‘Cause that’s what 1 thing highly effective teachers do .

Here’s the real reason why we had to ditch CUBES:

• It wasn’t working for our students – they problem skills were below grade-level.
• Teachers were clinging to it without giving it a facelift, stuck in their ways.
• There were more effective methods in the toolbox.

So, What is CUBES?

CUBES is a math word problem-solving strategy, with each letter representing an actionable step. 

If you search the web, you’ll discover several variations of CUBES. Some variations strengthen the strategy, but holes still remain. For example, the Caffeine Queen Teacher discusses CUBES in her blog titled How to Teach Math Word Problems – CUBES Math Strategy . She refined the strategy by adding a critical and necessary component: read to understand the problem. Everything else, though, stayed the same. After they read, they began circling numbers.

3 Holes in the CUBES Strategy

Issue #1 : The initial step instructs students to circle key numbers.

This poses a challenge because it’s impossible to determine which numbers are crucial without first reading the problem and pinpointing the question and/or task.

Problem #2 : CUBES advises students to circle, underline, and box various types of information.

This implies that students have to recall what to circle, underline, and box.

While it might not seem like a big deal, it results in inconsistencies in how students approach coding word problems. For instance, when I asked students in one class about the specific actions for each letter, they provided different responses.

Let me throw a scenario at you: Do students need to circle all numbers in the following word problem?

“Danielle had 5 red apples, 3 shirts, and 3 green apples. How many apples did Danielle have?”

No, they don’t—which is precisely why circling all numbers from the get-go is futile and a waste of time.

The Hole That Leads to Frustration

Issue #3 : When it comes to the “B” in CUBES, many teachers advise students to box key words and phrases (e.g., altogether, in all, and how many more) that suggest the operation to perform.

This becomes problematic because key words and phrases are not always present in word problems.

Consider this problem:

“Maria saw three yellow butterflies. She also saw eight orange butterflies. How many butterflies did Maria see?”

When students exclusively tackle problems containing key words, they face difficulties when approaching problems lacking them. This leads to frustration and a tendency for students to give up when they encounter unfamiliar scenarios.

Another snag with this strategy is that students often end up boxing irrelevant words.

Take this problem, for example:

“Justin baked two pies for his first baking contest. Unfortunately, the testers said the pies weren’t sweet enough, and he lost. The second time he entered the contest, he added 1 cup of lemon juice and twice the amount of sugar. How much sugar did he put in the first recipe if he put 4 cups of sugar in the second recipe?”

In such problems, I’ve observed students boxing words like “added” and “twice.” While “twice” is relevant and necessary to solve the problem, “added” is not. However, students box it because they perceive it as a math clue word, leading to unnecessary misconceptions.

A Better Strategy For Solving Word Problems: R.I.E.D.S.

As I mentioned earlier, R.I.E.D.S. is tried-and-true After giving it a shot for just six weeks, my students’ word problem skills shot up by 22 percentage points, soaring from 54% to a solid 76%.

Now, you’re probably curious about what sets R.I.E.D.S. apart from CUBES, right? Let me break it down.

First off, while reading might be implied in CUBES, R.I.E.D.S. explicitly tells students to read the problem for understanding. This is crucial because, from my experience, some students don’t dive into the reading until after they’ve already done the first three steps in the CUBES strategy, which is a gap in the strategy.

Only after students have read and fully grasped the problem should they start digging in.

Secondly, it’s not about boxing key words with R.I.E.D.S. It’s all about identifying the relevant info needed to crack the problem.

Thirdly, with R.I.E.D.S., students use the question or task in the problem to guide their decision-making, from spotting relevant details to figuring out which operation(s) to use.

Fourthly, R.I.E.D.S. calls out developing a plan, a crucial step to solving word problems. A step that engages students in metacognitive thinking

Solving Word Problems Using R.I.E.D.S.

R.I.E.D.S. is a simple five-step strategy for cracking word problems. Let me break it down for you:

Step 1: Read and Understand the Problem

The goal here is to get students reading and truly getting what the problem is about. We want them to explain the situation in the problem without diving into the numbers. For example, look at this problem:

“There are 15 cupcakes. The first-grade students ate 7 of the cupcakes. How many cupcakes are left?”

If your students tackle this problem, you want them to say something like, “There are some cupcakes, and the students ate some.”

Teachers often tell me that their students struggle with determining what operation is needed to solve the problem. When students focus on the situation instead of the numbers, the operation needed to solve the problem sometimes becomes obvious.

Just think about it. If there were some cupcakes and the students ate some, it’s obvious that the subtracting is the operation needed to solve the problem.

Step 2: Identify the Question/Task

This step is the engine of the whole process. It’s crucial that students pinpoint (box, underline, highlight, etc.) the question/task and understand what’s being asked.

Step 3: Extract Relevant Information

After identifying the question or task, students need to read and reread each sentence, grabbing the info they need to solve the problem. They should keep going back to the question/task, asking themselves: “Are there any details from this sentence that can help me solve the problem?”

Step 4: Develop a Plan

During this step, students think about how to tackle the problem, considering different problem-solving strategies, such as make a table, work backwards, use logical reasons, find a pattern, solve a simpler problem , etc.

It’s crucial that students are exposed to a variety of problem solving strategies and given opportunities to solve problems that require the use of various strategies.

Step 5: Solve

This step is straightforward; students simply record their answer.

Recommendations for Success

To help your students master this strategy and become skillful at solving math word problems, I have a few recommendations for you:

• Devote Dedicated Time: Set aside a chunk of your math block specifically for problem-solving, around 10-15 minutes. For real proficiency, students need daily chances to dive into problem-solving, tackling at least two problems each day.
• Diversify Word Problems: Mix it up! Ensure that the word problems your students tackle cover various types, such as take-away, add-to, end unknown, change unknown, etc. When all problems involve the same operation, things get too predictable, and the critical thinking needed takes a hit. Check out this link for a variety of word problem types to keep things fresh.
• Reasoning Matters: Ask your students to explain why they chose certain details to help them solve the problem. Spend time discussing why those details matter in the context of the problem.
• Start Simple, Go Gradual: Kick off with single-step problems before diving into the complexity of multiple-step word problems.
• Gradual Release and Think Aloud: Use the gradual release model until students begin showing mastery with the strategy and various types of word problems. When modeling problem-solving, think aloud. Let your students in on your thought process. It’s like giving them a backstage pass to your brain.
• Teach Strategies and Foster Thinking: Equip your students with problem-solving strategies. Encourage them to ponder the methods they could use to crack a problem, supporting both flexible and metacognitive thinking. These are key skills for becoming adept problem-solvers.

Remember, to ace many word problems, students need a plan before they dive into computation. So, expose them to a variety of problem-solving strategies – it’s the roadmap to success!

How Did R.I.E.D.S. Come About?

Here’s how R.I.E.D.S. came into the picture.

Back in the 2008-2009 school year, we got our fall benchmark scores and were handed the mission to pick a standard to boost student achievement by the next benchmark assessment. I went with a math standard: solving word problems using the four operations.

Now, once I committed to leveling up my students’ word problem-solving game, I needed something that actually worked. I had tried two problem-solving strategies (I don’t recall their names), but they just weren’t cutting it.

So, I started thinking about the way I personally tackled word problems and wondered, “How can I turn this into a step-by-step, kid-friendly process?” And that’s when the magic of R.I.E.D.S. started brewing.

Word Problems and End-of-Grade Assessments

Let me tell you about our End-of-Grade state math assessment here in Georgia – it’s like a word problem marathon.

They don’t just throw isolated computations at our students. Nope. It’s all about diving into word problems.

Now, picture this – even if your students can crunch numbers like math wizards, without a solid strategy for tackling word problems, they might just miss the mark on that math assessment.

And that’s where R.I.E.D.S. comes in.

It’s the key to unlocking math success in the world of word problems.

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Free worksheet – addition and subtraction word problems strategy.

Free word problem comprehension strategy teaches students to apply reading comprehension strategies using CUBES or CUBED method – FREE!

This easy-to-use CUBES word problem strategy provides your students with the tools to solve addition and subtraction word problems. This strategy works because students are given a solid, concrete method to organize information.

Math word problems are always a bug-a-boo to teach – but they don’t have to be when students break the problem down into smaller pieces.

Concrete Strategy for Addition and Subtraction Word Problems

I’ve tried several different math word problem strategies for teaching students to truly understand story problems. However, CUBES or CUBED is the one method that I keep returning to year after year.

Plus, with these worksheets, students learn to apply the strategies they learn in reading class to their math problems – this brings REAL results!

Keep reading for a FREE SAMPLE!

Solving multi-step problems is difficult for students, and using either the CUBES or CUBED strategy helps break down the steps. A straightforward, easy-to-understand method also promotes confidence and provides a consistent strategy to follow.

Each page lists either the CUBES or CUBED procedure in a checkbox format. Most teachers are already familiar with CUBES, and with CUBED, the  “D”  stands for  “Draw a picture.” Students are encouraged to draw a picture to help promote comprehension and problem-solving.

I love the twist on CUBES – drawing pictures helps visual learners make the story problem concrete enough to visualize and solve .

Want to learn more about CUBES and CUBED?

To learn more about CUBES and CUBED math word problem-solving strategies, you’ll like the article Struggling with Math Story Problems? CUBES to the Rescue!

To learn more about steps to solve math word problems in general, you’ll like the article How to Teach Math Word Problems – CUBES Math Strategy .

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Android Police

Google's pixel strategy is officially a mess, but i know how to fix it.

The company’s strategy surrounding the 8a is downright awkward, but all is not lost

Last week, I highlighted Google’s issues with its Pixel lineup and, more specifically, its A-series devices, explaining how the phones are constantly hamstrung by the company’s poor marketing and pricing strategies. Instead of talking about the Pixel 8a’s merits, the tech community harped on its price, with many arguing it's simply better to wait for the Pixel 8 to go on sale again . We’re not talking about Samsung buyers or iPhone users declining to pick up the new Pixel; these were Pixel fans who enjoy Google products, deciding to wait because the company can’t seem to get out of its own way.

There has never been a good time to buy a Pixel

But as I and so many AP staffers are Pixel fans, I didn’t want to leave things on such a negative note. There’s no Empire Strikes Back here; it’s all Return of the Jedi. Besides, you’re either part of the problem or part of the solution, so I decided to pick up a shovel and see if there aren’t some ways to help Google be a little less awkward and make future Pixels a more attractive purchase from the start.

Christmas only comes once a year

You don’t have to reinvent the wheel.

A simple solution to Google’s Pixel lineup quagmire would be to release all of its new phones at the same time. Typically, Google releases its flagship Pixel phones in the fall, followed by the A-series in the spring. Instead, Google should unveil the flagship Pixels and the A-series on the same day. For example, this October, when the company announces the Pixel 9, 9 Pro, and the rumored 9 Pro XL , it should add the 9a to the list.

Unfortunately, Google wouldn’t be able to carry the same spec sheet we’ve come to expect from the Pixel A-series phones, as it would restart the cycle of confusion, only in reverse. We’d be balking at the Pixel 9, arguing it's better to buy a Pixel 9a if we get the same chipset for $300 less. Google would have to take a page from OnePlus’ playbook and put last year’s processor in the 9a. Like the OnePlus 12R sports the Snapdragon 8 Gen 2, the Pixel 9a would need a Tensor G3.

Sure, it would be awkward at first, and you’d have comparisons to the Pixel 8a, but that’s where some savvy marketing would come into play. Google could develop a plus version of the Tensor G3 with more AI features or overclocking. Even though an overclocked Pixel would need liquid nitrogen cooling, you get the idea; there are ways to sell us on last year’s processor if it means saving money.

Moreover, it solves the calendar problem. The Pixel 8 could be discontinued on the same day, eliminating the series from the site. The company would still have old stock and renewed devices to contend with. However, that’s nothing compared to selling a compelling alternative on your site for similar money — the scenario playing out between the Pixel 8 and 8a. The Pixel 9a would be a year newer than the 8, naturally dampening sibling comparisons.

A back-to-basics approach

It didn’t used to be like this.

If Google wants to maintain a staggered release schedule, it should go back to basics with the Pixel 9a. When the Pixel 3a was released, no one considered it a flagship killer. It was relatively underpowered, with an inexpensive build and only 4GB of RAM. The Pixel 3 shipped with a Snapdragon 845, more than enough horsepower to run laps around the Pixel 3a, eliminating concerns that the Pixel 3a would eat into Pixel 3 sales.

Still, the Pixel 3a had an identity and a purpose in the marketplace. I still remember Google’s site when the 3a came out. It had an entire page dedicated to Night Sight on the Pixel 3a, showing how much better low light photography was on the device compared to the outrageously more expensive iPhone XS. It was simple, straightforward, and effective: the Pixel camera you love at a price you’ve never seen before. You didn’t have to be Don Draper to appreciate the message.

Best budget Android phones in 2024

Similarly, Google could go back to basics with a hypothetical Pixel 9a, taking away the rumored metal frame, wireless charging, and 120Hz refresh rate to return the value to the A-series. At $399, a Tensor G3 with Gemini Nano and Google’s computational photography suddenly becomes interesting. As the company did with the camera years ago, it could play up AI functionality on a device under $400. It would give the A-series an identity of its own again and prevent it from being considered a nerfed flagship.

The first step is admitting you have a problem

The second step is actually solving it.

I don’t think it’s my imagination when I say that Google sometimes seems blissfully unaware. But if Mountain View is serious about staying in the smartphone game — as it appears to be — Google must make changes. Sometimes, a new coat of paint does wonders, and the company would benefit from sitting down and drafting a coherent plan for its Pixel lineup. Google’s hardware is in the best place in years, and with a little Marketing 101, Pixels could be allowed to shine.

Now, if we could only get Google to release Pixels in more countries and not act like a fledgling startup making phones out of its basement. Turns out you have to crawl before you can walk.

Google Pixel 8a

The Pixel 8a wants you to forget the Pixel 8 ever existed. With some crucial upgrades over its predecessor, including a brighter display, faster processor, and larger battery, Google's latest mid-range smartphone is the perfect combo of speed and AI smarts. And with seven years of OS upgrades, it's the longest lasting $500 smartphone you can find today.

These science-based tips can help you manage conflicts in relationships

Direct communication as well as cooperative and constructive problem-solving are key.

Key takeaways

Summary is AI-generated, newsroom-reviewed.

• Conflicts in relationships are not inherently bad and can foster growth.
• Effective conflict management involves direct communication and mutual understanding.
• How couples initiate these difficult conversations also matters.

Did our AI help? Share your thoughts.

Conflicts are inevitable even in the most loving of relationships.

Goals, needs and interests will differ on matters great and small — parenting styles, delegation of chores, whether the toilet seat should be up.

Contrary to popular belief, though, conflicts in and of themselves are not a sign that there’s something wrong with the relationship, experts say.

If managed well, conflicts provide “the opportunity to enhance and grow in our relationships,” said Nickola Overall , a professor of psychology at the University of Auckland specializing in the science of relationships.

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“It’s not about conflict resolution,” since many problems that couples fight about may never fully go away, but about “conflict management,” said Julie Gottman , who researches relationships along with her husband, John Gottman .

But if conflicts are not properly managed or are avoided, they can result in negative consequences for the health of both partners and their relationship. Research shows that while partners in satisfying relationships live longer and have fewer health problems than their single or dissatisfied counterparts, strain and conflict are common. Conflict is especially potent in romantic relationships and associated with worse mental health symptoms , unhealthier patterns of the stress hormone, cortisol, and diminished immune and cardiovascular health .

Avoiding or withdrawing from conflict deprives partners of the opportunity to improve the situation and potentially signals a lack of engagement in the relationship, leading to reduced satisfaction. “You can really use conflict to understand your partner at a much deeper level than you may already know your partner,” Julie Gottman said.

But both partners need the motivation to address the problem and the ability to take their partner’s perspective, Overall said.

And perhaps the most difficult thing: “I think we have to be brave enough to really communicate how we feel and what the underlying issues are,” she said.

Direct communication is key to conflict management

Relationship researchers and clinicians study how conflicts affect relationships by bringing couples into a laboratory, videotaping their interactions while they discuss an intractable problem and analyzing those interactions. They consistently find that unhappy couples are more likely to express greater disagreement, hostility and criticism while happy couples are more likely to express greater validation, affection and humor.

But surprisingly, relationship research has also shown that couples expressing anger and hostility toward one another during arguments could sometimes be predictive of positive relationship outcomes over time.

Conversely, more positive interactions during conflicts — such as agreement and use of humor — could help the relationship in the short term but fail to produce change for the underlying problem in the long run.

These counterintuitive findings suggest that whether interactions are more positive or negative is just one factor in how conflicts turn out. How direct we are in our communication of the issues also matters.

In one study of recorded interactions of 61 romantic couples, Overall and her colleagues found that more direct communication strategies — both negative and positive — were associated with greater success in addressing the problem 12 months later and predicted increased relationship satisfaction even if they were initially perceived as relatively unsuccessful.

By contrast, indirect strategies — positive or negative — did not predict later change in the underlying problem.

Emotions such as anger and hostility can be useful to a conflict and to the relationship, Overall said. They can help convey “that a problem is serious and that the problem needs to be changed, and that the partner needs to do something about helping to resolve this problem,” she said. It also indicates an investment in the relationship.

But these emotions need to match the context of the situation.

In a 2020 longitudinal study of 268 couples, Overall found that while an increase in average levels of hostility and criticism is associated with worsening problems and decreasing satisfaction, it was associated with better outcomes if this expression of hostility was more variable.

But if someone gets upset about everything, “then the information signal gets lost and instead you’re just informing the partner that you’re negative all the time,” Overall said. Then “the potential benefits of expressing negativity and anger and hostility lose its power because it becomes nondiagnostic of the problem,” she said

Cooperative, constructive problem-solving

Constructive problem-solving — through reasoning, negotiations and solution-oriented discussions — can convey the salient pieces of information needed to manage an ongoing conflict: that the issue is important, that the partners are committed to resolving it and that they care about the relationship.

Direct communication is “good for minor problems. It’s good for serious problems,” Overall said. And it doesn’t carry the negative side effects of the negative emotions.

In their recent book, “Fight Right: How Successful Couples Turn Conflict Into Connection,” the Gottmans recommend an intervention they call the “ Dreams Within Conflict ,” which postpones solving the problem and instead has each partner ask the other questions about their values about the issue, why it is important, their feelings about the issue and what their ideal dream is for it.

“The goal is mutual understanding,” John Gottman said. In their couples workshops, the Gottmans have found that this strategy helps 87 percent of couples “move from gridlock on an issue to dialogue,” he said.

How we initiate these difficult conversations also matters because it can predict not only how the conversation will go, but also indicate how the relationship will go, Julie Gottman said.

The Gottmans recommend what they call a softened start-up: First, describe yourself and the situation, not your partner, and then a positive need “that gives your partner a chance to shine for you,” Julie Gottman said. For example: “I’m really worried. There’s the feeling that the bills haven’t been paid on time. Would you please pay the bills tonight?”

Remaining flexible in how we respond to our partner’s specific needs is important since becoming overly strategic in solving problems can have some costs, Overall said. “When the emotions are completely taken out and you’re just trying to be very rational and reasoning, you’re actually taking away the emotional connection and what makes us human,” she said.

The emotion — be it anger, warmth or sadness — also conveys important information about how much we care about our partner and the relationship, she said.

Expressing gratitude or laughing about yourself or together can also be very powerful in a relationship and in a conflict, John Gottman said.

These strategies for more effective conflict management may help to clearly communicate what matters — our partner, our relationship and our facing challenges together.

“It’s about how can I express, how can I be brave enough to engage in constructive ways when it matters,” Overall said.

Do you have a question about human behavior or neuroscience? Email [email protected] and we may answer it in a future column.

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