Ditch the C.U.B.E.S. Strategy in Math

First of all, I want to acknowledge the tremendous impact of Robert Kaplinsky’s insights, which have resonated with many for years. His thought-provoking posts “Is Problem Solving Complex or Complicated?” and “Why Do We Have Word Problems?” are invaluable resources. Today, I want to not only express my appreciation for Kaplinsky’s work but also highlight an alternative strategy to the C.U.B.E.S. approach. We can broaden our problem-solving toolset by exploring new perspectives, and I believe this strategy will further enhance our problem-solving skills. Don’t miss out on the original posts: Is Problem Solving Complex or Complicated? and Why Do We Have Word Problems?.

This image shows what the acronym C.U.B.E.S. represents. Many teachers use this to teach an easy way for students can begin to tackle word problems. I, in fact, had an anchor chart displaying this very technique many years ago. As the saying goes, “Know better, do better.” I now know better and therefore do better. I know you might be asking yourself, “Okay, but I still don’t get why this isn’t ideal?”


Let’s consider the problem to the right. With our adult brains, we understand that it is a two-step problem. We understand we need to add the adults and children together and then subtract the number of males who were in attendance. Now imagine your 8-year-old self reading this and not yet having reading mastered let alone the comprehension skills to decode what is being asked. (Okay, maybe that was just me and my learning disability) You can see that I also went through the CUBES strategy. I circled the numbers, underlined the question, boxed keywords, and got rid of extra information. Arguably, the statement that everyone showed up might also be considered extra information to a young learner. An 8-year-old will start the CUBES process. They will look at the boxed words to find out what operation they need to use. And this is where we run into our first problem. It only says, “How many.” It doesn’t say, “how many more,” or “how many less.” Being around kids, we know that their default is to add. So what are they going to do? You guessed it, add 12, 25, and 15. Even if the question that is underlined is: How many females were there? chances are students are still going to add it all up because they are specifically looking for keywords like ‘in all’, ‘altogether’, ‘less’, ‘more’, etc.

Years ago, I used to teach my elementary students these strategies, as it was what I knew at the time. However, as I learned better strategies to help students, one of my favorite methods became the 3-Read Protocol. You can find more information about it in the blog post Mastering Mathematical Language Routine 6: Three Reads. This approach helps students concentrate on understanding the story, identifying units and quantities, and focusing on the question or task. By following the 3-Read Protocol, students can comprehend the context, which enables them to think critically instead of simply focusing on a procedure that may or may not work.

Finally, to help students effectively apply the information from the story, I highly recommend integrating MathReps into your classroom. MathReps are strategically practiced sets of skills that allow students to practice basic math concepts in similar skill clusters and receive immediate feedback. This approach promotes automaticity and fluency, freeing students to focus on what is needed rather than both what to do and how to do it. You can delve deeper into MathReps by reading a series of blog posts. I suggest starting with The Power of MathReps.

It Doesn’t Always Start Off Smoothly

When I first started attending tech and innovative teaching conferences, I felt completely overwhelmed. It’s common to feel this way when surrounded by so much new information and ideas. Many of us are eager to try everything at once, but then struggle to figure out where to begin and how it will all come together. I have to admit, I often wondered if I could even pull off some of the amazing things I saw. It took me far too long to realize that presenters, including myself now, tend to showcase only the very best. Starting something new is rarely a smooth process; in fact, it’s often quite messy and can even be painful at times. But embracing the challenges is all part of the journey. And that’s what this post is about.

Messy MathReps

When presenting on MathReps, I am very open and honest about the time it took my 5th-grade class to complete the first MathRep – 45 minutes, in case you were wondering. As a teacher, I am acutely aware of the learning curve involved in implementing MathReps. Some students may breeze through independently and accurately within three days, while others may require weeks of support. This variability is the inevitable, albeit messy, aspect of introducing MathReps or any new routine/learning opportunity.

Why do I bring this up? I understand the frustration of the messiness of beginning something new and wanting to revert back to a previous routine or way. The idea of starting something new after the school year has started can be daunting. There are pacing guides, expectations, benchmark assessments, and a million other tasks that weigh on us. We often hear that we should give it time, but all too often it doesn’t feel as if we have the time to give. But some things are worth spending time on.

Why Is MathReps Worth It?

MathReps is undeniably worth the investment due to the proven effectiveness of repetition in skill acquisition. As with any new skill, whether it is teaching, riding a bike, or knitting, initial proficiency is typically lacking. Through consistent practice and the repetition of key actions, one can develop heightened confidence, risk-taking, and greater speed. Similarly, MathReps specifically aims to provide students with ample opportunities for repetitive practice, thereby enabling mathematical skills to become second nature. Once proficiency is achieved, students can then apply their knowledge in varied contexts, such as solving word problems. Without this foundational knowledge, tackling word problems becomes an overwhelming task. For instance, even if a student knows that they need to multiply a two-digit number by a three-digit number, without understanding the process of multiplication, they are left unable to proceed effectively. It is akin to attempting to walk before mastering the skill of crawling. Through consistent practice and the connections facilitated by MathReps, students are empowered to enhance their confidence, adaptability in thinking, and fluency in their mathematical abilities.

More 2nd-grade MathReps on Wipebook

After sharing my post about the amazing NBT standards on Wipebook, the response has been incredible! So many people have reached out, eager to discover what other fantastic MathReps are available on this innovative platform. And guess what? I’ve got another gem for you – skip counting! This incredible resource delves into three NBT.A standards, making it an essential tool for mastering mathematical concepts. Let’s dive in and explore this MathRep on Wipebook and the standards found on it!

  • 2.NBT.A.1: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases
  • 2.NBT.A.2: Count within 1000; skip-count by 5s, 10s, and 100s.
  • 2.NBT.A.3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form
  • 2.OA.C.3:Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends

Bonuses of Using MathReps on Wipebooks

  • Concept Connection: Using MathReps allows students to make connections between concepts, helping them master the skills necessary to access higher thinking skills.
  • Reusable Surface: MathReps on Wipebooks provides a reusable surface, allowing students to practice multiple repetitions in one go.
  • Student Engagement: Teachers who have implemented MathReps on Wipebooks have found great success, with students cheering when asked to complete them.

Watch the video below that explains how to implement MathReps in your classroom.

2nd Grade NBT MathRep

The captivating world of MathReps is even more exciting with this second-grade MathReps on Wipebook! What sets this apart is its eco-friendly design that saves paper, its reusable surface allowing for multiple reps in one go, and its seamless integration with a scanning app. Not to mention, it covers three of the four NBT standards in second grade. Be sure to check out the accompanying video for a closer look at this game-changing MathRep on Wipebook!

Magic School – UDL Choice Board

Earlier today, I had the pleasure of meeting with a fantastic group of teachers from Plymouth-Canton Community Schools in Michigan. Our main focus was on incorporating more EduProtocols and technology into math classes. During our discussion, we touched upon the topic of what students can do once they have demonstrated mastery using MathReps. Specifically, if students show mastery on their weekly assessment for two consecutive weeks, I no longer require them to do the daily practice in the following week. To provide an alternative avenue for these students, I suggested the use of a Choice Board, allowing them to delve deeper into the skills they have mastered. This idea sparked a conversation about the UDL Choice Board creator in Magic School. Intrigued by this resource (see previous post), I decided to explore this component further, and I must say, I was not disappointed.

After finding the Choice Board (UDL), I chose the grade level and input the standards. For my purposes, I chose all of 5.NBT. I gave the tool minimal parameters.

The output was okay:


Choice Board: Place Value and Decimals

AssignmentDescription
  1. Place Value Detective| Create a comic strip showing how a digit’s value changes based on its position in a multi-digit number.
  2. Decimals in the Real World| Research and create a slideshow presentation showcasing examples of decimals in everyday life.
  3. Powers of 10 Exploration| Design a poster explaining patterns in the number of zeros when multiplying or dividing a number by powers of 10.
  4. Decimal Number Line| Construct a number line using decimals and demonstrate how to compare decimals using greater than, less than, and equal to symbols.
  5. Rounding Riddles| Create a set of riddles where students need to round decimals to a specified place value to find the answer.
  6. Decimal Art Gallery| Use various art materials to represent decimals visually. Label and display your artwork in a mini gallery.
  7. Interactive Place Value Game| Develop a board game that involves using place value understanding to round decimals. Include instructions and game pieces.
  8. Decimal Number Chef| Write a step-by-step recipe using decimals for a favorite dish. Include appropriate measurements and conversions.
  9. Decimal Reflection| Write a reflective journal entry explaining the importance of understanding place value and decimals in real-world applications.

Remember to be creative and have fun with your chosen assignment! Additionally, ensure that your work demonstrates your understanding of place value and decimals.


But not very user-friendly. So, I modified my request. Not exactly what I wanted but much better visually. I would prefer if it were a 3 x 3 grid. I did put in the request unfortunately, the tool wasn’t able to create it. But the output was still good and easier to read. And if I really wanted a 3 x 3 grid, I could simply copy and paste the components:


Sure! Here’s the choice board in a 3 x 3 table format:

AssignmentDescription
1. Place Value DetectiveCreate a comic strip showing how a digit’s value changes based on its position in a multi-digit number.
2. Decimals in the Real WorldResearch and create a slideshow presentation showcasing examples of decimals in everyday life.
3. Powers of 10 ExplorationDesign a poster explaining patterns in the number of zeros when multiplying or dividing a number by powers of 10.
4. Decimal Number LineConstruct a number line using decimals and demonstrate how to compare decimals using greater than, less than, and equal to symbols.
5. Rounding RiddlesCreate a set of riddles where students need to round decimals to a specified place value to find the answer.
6. Decimal Art GalleryUse various art materials to represent decimals visually. Label and display your artwork in a mini gallery.
7. Interactive Place Value GameDevelop a board game that involves using place value understanding to round decimals. Include instructions and game pieces.
8. Decimal Number ChefWrite a step-by-step recipe using decimals for a favorite dish. Include appropriate measurements and conversions.
9. Decimal ReflectionWrite a reflective journal entry explaining the importance of understanding place value and decimals in real-world applications.

I hope this format is helpful for you and your students! Let me know if there’s anything else I can assist you with.


Can this be improved? Definitely! Did I invest a lot of time fine-tuning the tool’s parameters? No. However, considering the minimal effort I put in, the output turned out to be surprisingly good. Without a doubt, I wholeheartedly recommend Magic School! I remain a fan of this remarkable tool!

Magic School AI

The world of AI tools is vast and ever-evolving. Amongst the sea of options, one particular tool has caught my attention: Magic School. With a focus on teachers and schools, it offers a unique approach that sets it apart from the rest. Its comprehensive range of categories opens up exciting possibilities for integrating AI into different educational contexts. The best part? It comes in both a free and paid version, tailored to suit varying needs. Allow me to share an image of its advantages from their official website. Get ready to dive into a world of innovative possibilities!

Compare subscription options for Magic School

On the home page, you will find 66 different categories. Some examples of these categories include Math Spiral Review, Standards Unpacker, Sentence Starters, Text Leveler, and IEP Generator, among many others. As I was curious, I decided to take a closer look at the Standards Unpacker category. What caught my attention was the fact that it addresses the specific skills that students need to succeed, provides clear Learning Targets, and summarizes the standard. However, I found the Instruction and Assessment Plan section to be somewhat vague. Nevertheless, one interesting aspect is that you can go back to the tool and use that initial plan as a starting point to create a more detailed and thorough plan.


Standard: 5.NBT.A.1

Break Down Standard:

Skills: Recognizing place value in multi-digit numbers
Knowledge: Understanding how the value of a digit changes as it moves to the left or right in a number
Concepts: Place value, base-ten number system, positional notation

Define Expectations:
In this standard, 5th-grade students are expected to understand the concept of place value in multi-digit numbers. They should recognize that each digit in a number has a specific value determined by its position. Additionally, they should understand that the value of a digit in one place is 10 times greater than its value in the place to its right, and 1/10 of what it represents in the place to its left.

Formulate Learning Targets:
By the end of this standard, students should be able to:

-Identify the place value of digits in multi-digit numbers.
-Determine the value of a digit based on its position within a number.
-Describe the relationship between the value of a digit and its position.

Instruction and Assessment Strategies:
Use manipulatives, such as base-ten blocks, to help students visualize and understand the concept of place value.
Provide opportunities for students to explore and compare the values of digits in different positions within a number.
Use number lines and number charts to reinforce the concept and relationship of place value.
Engage students in problem-solving activities that require them to apply their understanding of place value.
Assess students' understanding through quizzes, worksheets, and real-life problem-solving tasks that involve place value.

Summarize:
In this standard, 5th-grade students are expected to develop a deep understanding of place value in multi-digit numbers. They should be able to recognize the value of each digit based on its position within the number and understand the relationship of each digit to its neighboring digits. Instructional strategies such as hands-on manipulatives, visual aids, and problem-solving activities can help students master this concept. Assessment strategies should include both formal and informal methods to gauge students' understanding and application of place value.

From my brief exploration, I believe that this tool has the potential to greatly assist teachers in working more efficiently. It eliminates the need for teachers to come up with learning objectives, develop grading criteria, and design lesson plans. Although AI should not replace all of a teacher’s work, it can certainly assist them in the more demanding tasks. Teachers will still have the ability to review and customize the generated outputs to suit their specific requirements. Overall, I am optimistic about the potential of this tool.

Winter Break Activities

Winter Break is just around the corner, bringing with it a well-deserved break from schoolwork. The question of whether to assign homework during breaks has always sparked debate. In my district, we are lucky enough to enjoy a generous three-week break. This extended period of downtime can be a blessing for students. To make the most of this time, I developed an exciting Winter Break Activity board and a Kindness Calendar, taking the opportunity to engage students in meaningful and enjoyable activities. It is important to note that these are optional.

  • Activity Board

As you explore the Activity Board, you’ll discover a variety of captivating activities that students can freely choose from. Completing just three out of the nine options is all it takes to participate! It’s important to note that these activities are not meant to be completed within a short 15-minute period. They are designed to be flexible, allowing students to engage either with or without the use of technology. Additionally, I’m thrilled to share that during the break, I received proposals from some students who were keen on pursuing alternative activities, and I happily accepted their ideas! When we reconvene after the break, I make sure to allocate dedicated time for students to showcase and present their remarkable projects.

The Kindness Calendar is a favorite among parents! I have received numerous expressions of gratitude from parents and guardians for this calendar. They particularly value the reminders to “clean your room” and “get along with your siblings ALL day.” Parents also appreciate the underlying concept of promoting kindness, gratitude, and appreciation. This calendar is really a gift for parents.

And did I mention that this is available in English and Spanish? Well, it is!

Template

Mastering Mathematical Language Routine 8: Discussion Supports

Looking back at the series of Mathematical Language Routines (MLRs) we have explored, we can see that their collective aim is to foster robust mathematical discussions and enhance language proficiency among students. These routines serve diverse purposes, such as refining ideas through structured conversation (Stronger and Clearer Each Time), stabilizing oral language as a reference (Collect and Display), refining written arguments through critique (Critique, Correct, and Clarify), promoting collaborative problem-solving through information sharing (Information Gap), empowering students to craft mathematical questions (Co-Craft Questions and Problems), facilitating comprehension and negotiation of math texts (Three Reads), and encouraging comparison and connection between various mathematical approaches and representations (Compare and Connect). Together, these MLRs not only elevate student participation and conversation but also cultivate meta-awareness of language, fostering a deeper understanding of mathematical concepts.

We conclude this series with Mathematical Language Routine 8: Discussion Supports. The goal is to foster inclusive discussions in math by combining multi-modal strategies that aid in understanding complex language, ideas, and classroom communication. These strategies encourage student participation, conversation, and awareness of language nuances. With continued modeling, the aim is for students to adopt these techniques independently, prompting deeper engagement among peers in discussions.

Having rich mathematical discussions can be challenging, especially when there are barriers that hinder effective communication. Recently, I encountered a situation where I was assisting a student with a math problem. The task was to determine the combination of rolls of coins needed to reach a specific amount. The problem provided information about the rolls of nickels and dimes, including the quantity each roll contained. However, during our discussion, it became evident that the student misunderstood the task. They believed they needed to determine the number of dimes or nickels in each roll, rather than finding the overall combination. To clarify this confusion, I decided to show them an image of a roll of coins and briefly discussed its concept, which helped them grasp the correct approach. This incident highlighted the importance of uncovering and addressing any gaps in background knowledge. It also underscored the significance of reflecting on the relevance of certain questions.

Having sentence frames is not only helpful to me but also to the students. The above image is one that I created based on Illuminate Math‘s suggestions. These sentence frames can guide the class towards deeper thinking and understanding. As mentioned before, the main objective of this routine is to encourage students to take the lead in these discussions. Additionally, it is important to note that this particular routine can be integrated into any of the other Mathematical Learning Routines (MLRs).

This concludes our multi-part series on the 8 Mathematical Routines. I highly encourage you to start implementing these routines in your day-to-day math class. To further support you on this journey, I have gathered a variety of helpful resources, which you can access here. If you have any additional resources to share, please don’t hesitate to reach out. I will gladly add them to the collection and give you proper credit.

Mastering Mathematical Language Routine 7: Compare and Connect

In the previous Mathematical Language Routine (MLR) discussions, we explored a variety of essential skills. MLR 1 focused on enhancing our understanding by revisiting and reinforcing key concepts, making our knowledge “Stronger and Clearer Each Time.” We then moved on to MLR 2, where we delved into the crucial skill of “Collecting and Displaying” data effectively. Building on this foundation, MLR 3 emphasized the importance of “Critiquing, Correcting, and Clarifying” our models and methodologies for optimal results. In MLR 4, we explored the “Information Gap” and how to use this strategy to be thoughtful of the information needed to solve problems. Continuing this journey, MLR 5 introduced the skill of “Co-Crafting Questions and Problems” collaboratively to foster innovative approaches and insights. Finally, in MLR 6, we explored the technique of “Three Reads,” emphasizing the significance of multiple reads in order to enhance student understanding. Let’s now embark on our next MLR discussion, MLR 7 Compare and Connect.

MLR 7: “Compare and Connect,” has the purpose of fostering students’ meta-awareness in their exploration of different mathematical approaches, representations, concepts, examples, and language. Through this MLR, students are encouraged to reflect on and verbally respond to these comparisons. This involves analyzing why certain mathematical actions or statements are done in a particular way, identifying and explaining connections between various mathematical representations or methods, and pondering how one idea relates to others in terms of both concepts and language. To support this learning process, teachers should model their thinking aloud when addressing these questions. This routine allows students to engage in rich mathematical conversations. We will explore two ways in which to accomplish this.

Which one doesn't belong

Getting students to engage in discussions about math, make connections, and consider different perspectives can be quite challenging. I often encounter students who simply say, “It was in my brain” or “My brain told me the answer.” However, by modeling and encouraging metacognitive awareness, students can begin to make connections on their own. One effective routine that focuses on linguistic skills is called ‘Which One Doesn’t Belong‘. This activity can be done in groups, in pairs, or as a whole class. Students are presented with four images, equations, numbers, graphs, or geometric shapes, and they are asked to identify a commonality among three of them and explain their reasoning. The interesting twist is that any combination of three out of the four options can be correct. For example, in the orange example, one could argue that the three triangles go together and the hexagon is the odd one out. Alternatively, one could justify grouping all the white-filled shapes while excluding the shaded shape. This activity is both enjoyable for students and provides the opportunity to hear and consider different viewpoints.

Another interesting activity that aligns well with this MLR is the Math EduProtocol Sous Chef from The EduProtocols Field Guide Math Edition (Chapter 9, page 56). In this activity, students are grouped together to solve a problem using different approaches and then present their work to the class. For instance, if students were given the task of solving 4 x 6 in third grade, one student might use equal groups, another could opt for repeated addition, a third student may create an array, while the last student represents the equation with the area model. Through this activity, students can establish connections with previously learned concepts and broaden their understanding. There are numerous ways to implement Sous Chef, but the central focus remains on fostering connections among ideas and encouraging students to share their thought processes orally.

In conclusion, incorporating this MLR into your math class will greatly benefit your students. It will help them enhance their meta-awareness, make connections between different concepts, and foster a deeper understanding of the subject. While we have explored two approaches to this MLR, there are numerous other equally powerful techniques available. In our next discussion, we will delve into MLR 8: Discussion Supports, which focuses on stimulating rich and meaningful conversations in the classroom.

Mastering Mathematical Language Routine 6: Three Reads

In our recent posts, we have explored various Mathematical Language Routines (MLRs) that aim to foster language development in the math classroom. We have covered MLR 1: “Stronger and Clearer Each Time,” MLR 2: “Collect and Display,” MLR 3: “Critique, Correct, Clarify,” MLR 4: “Information Gap,” and MLR 5: “Co-Craft Questions and Problems.” Each of these MLRs has offered valuable insights into different aspects of language acquisition in mathematics, be it written and oral expression, oral language proficiency, or the comprehension of tasks and word problems.

MLR 6: Three Reads

Building upon these discussions, let’s now delve into our next MLR, MLR 6: “Three Reads.” This routine plays a crucial role in enhancing reading comprehension and developing meta-awareness of mathematical language. By engaging in this exercise, students get the opportunity to practice navigating the intricacies of math-related questions, which often pose challenges for them. Through multiple readings, they can better understand the unique ways in which math concepts are presented and effectively plan their strategies for problem-solving. MLR 6: “Three Reads” serves as an important tool for supporting students’ grasp of mathematical language and equips them with the skills needed to tackle word problems with confidence.

The Three Reads protocol is a powerful tool designed to enhance students’ understanding of mathematical word problems. Its main purpose is to break down complex problems into manageable steps that students can comprehend, analyze, and solve successfully. This protocol is particularly beneficial for multilanguage learners and students with academic disabilities who often struggle with comprehending mathematical texts.

The Three Reads protocol begins by encouraging students to focus on the meaning of the problem. Instead of rushing to perform calculations, students are prompted to truly understand the context and situation described in the word problem. This initial step allows students to connect with the story or situation presented and reflect on its implications.

After gaining a solid understanding of the problem’s context, students move on to the second read. Here, they concentrate on identifying the units and quantities involved in the problem. By focusing on these key components, students can make sense of the mathematical concepts and relationships embedded within the word problem.

Finally, during the third read, students shift their attention to the specific tasks or questions asked in the problem. By this stage, students have already engaged deeply with the problem’s meaning and mathematical content. They are now able to formulate a plan of action and approach the problem in a strategic manner.

The Three Reads protocol supports not only reading comprehension but also sense-making and meaningful conversations around mathematical texts. By emphasizing understanding and meaning before diving into calculations, students are given the opportunity to reflect on different presentation styles, negotiate interpretations, and explore multiple solution strategies.

Let’s explore an example that demonstrates how to implement the protocol of co-crafting questions with students. In this example, Mateo’s M&Ms, the quantities are initially hidden to allow students to focus on comprehending the story. Once they grasp the concept that Mateo has a bag of M&Ms with different colors, the quantities are revealed. At this point, students can create a T chart to organize the quantities and their corresponding units. Although the units are the same in this particular example, it’s important to note that it may not always be the case in every word problem. Utilizing the T chart helps students effectively organize the information. Moving on, the final phase of this example involves students creating their own questions, reminiscent of MLR 5. By allowing students to differentiate and choose their own questions, they are encouraged to tackle more challenging problems rather than opting for the easy way out. This approach also fosters open-ended questions that lead to a variety of possible solutions. It’s a wonderful way to introduce this routine. Additionally, another teacher in my district, Nicole Garcia, and I have developed a recording sheet to assist students in organizing their thoughts and work. It’s worth noting that it’s also practical to address problems that already come with pre-established questions. In these cases, steps 1 and 2 of the protocol remain the same. However, in step 3, students formulate a plan to answer the provided question. Once again, reading the story multiple times allows students the necessary time to grasp and organize the given information.

In summary, the Three Reads protocol encourages students to engage actively with mathematical questions, reflect on presentation styles, and negotiate meaning. By following this routine, students can develop a deeper comprehension of word problems, improve their mathematical reasoning skills, and ultimately enhance their overall problem-solving abilities.