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51 Esti-Mysteries - Steve Wyborney's Blog: I'm on a Learning Mission.

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Ohio Department of Education and Workforce Server

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Supporting Students Who Are Gifted: Using Effective Literacy Practices

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Every year, the EngineerGirl website hosts a contest dealing with engineering and its impact on our world. The topic and detailed instructions for the contest are posted in September with a deadline for submissions on February 1st of the following year. Winners are announced in the summer.

The 2024 EngineerGirl Writing Contest asks students to write a piece exploring the lifecycle of an object that you use in your daily life.

Learn more about the 2023 EngineerGirl Writing Contest

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Every year, the EngineerGirl website hosts a contest dealing with engineering and its impact on our world. The topic and detailed instructions for the contest ...

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Higher-Order Thinking Questions for Reading.pdf

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The Multiple Menu Model for Developing Differentiated Curriculum* | Renzulli Center for Creativity, Gifted Education, and Talent Development | Neag School of Education | University of Connecticut

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Joseph S. Renzulli, Director The National Research Center on the Gifted and Talented University of Connecticut Overview The Multiple Menu Model emerged from…

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Empower Your Students with The 4 C's Learning Menu

YOU can empower your students with this 4 C's learning menu! If you've followed this blog for very long, you've probably noticed I'm a big fan of learning menus aka choice boards.

Student choice is empowering. Combine that with the power of the 4 C's, and you've got a supercharged lesson!
Student Choice + 4 C's = Supercharged Learning!
What is a Learning Menu?

Learning Menus are a form of differentiated learning that gives students a menu or choice of learning activities.

Want more examples? Check out my blog post: Interactive Learning Menus with G Suite and my Learning Menu Pinterest Board.

The 4 C's

The 4 C's are integral to dynamic learning, and every dynamic learning experience should include at least one of the 4 Cs.

Creativity: The use of imagination and original ideas to solve problems and create.

(Examples: Cultivate creativity and innovation with projects that require students to design original solutions, invent something new to solve a problem, or integrate art and design with room to fail.)

Communication: The ability to effectively and clearly communicate for a variety of audiences and using a variety of tools and mediums.

(Examples: Give students opportunities to interact with adult experts, authors, and real-world audiences. Let them experience speaking and presenting.)

Collaboration: Learning and working in groups or teams, locally and/or globally, to achieve a goal.

(Examples: Ensure there is a purpose to the collaboration and not just group work. Form partners and teams strategically with assigned leadership roles, include team-building exercises, establish collaboration guidelines and shared decision-making.)

Critical Thinking: The ability to conceptualize, analyze, synthesize, and evaluate information for the purpose of deeper understanding, problem solving, and guiding action.

(Examples: Create learning experiences, such as mock trials or debates, scientific investigations, interpreting events in history or literature, or design challenges.)

As you integrate the 4 C's in your classroom, you will easily see how they overlap and support each other.
In what ways are you already integrating the 4 Cs into your curriculum?
[Tweet "Student Choice + 4 C's = Supercharged Learning! #edtech #gsuiteedu #shakeuplearning"]

The 4 C's Learning Menu

This learning menu was openly designed using Google Slides so that it can easily be adapted for just about any grade level or subject area.

You can control and align this with your content, topics, and units of study.

The Teacher's Guide

I have also included a Teacher's Guide (slide 2 of the template) with tips to revise for your classroom needs. Use one idea or use them all. Totally up to you!

Download The 4 C's Learning Menu

Below are two choices to download. The template link allows you to preview and click the "use template" button, but these do not work as well on mobile devices. The "make a copy" link will prompt you to make a copy and add to your Google Drive. (Please do not request access.)

Catch the Podcast Episode on the 4 C's!

Listen to episode 2!

Want to learn more idea like this? You will love my new book!

Check out my new book, Shake Up Learning: Practical Ideas to Move Learning From Static to Dynamic.

About the Shake Up Learning Book

Technology is not a magic solution for education. It is an opportunity! An opportunity to shake things up, to connect and grow, and to create dynamic learning experiences for our students!

In this three-part book, you will explore WHY it's time to Shake Up Learning, WHAT changes we can make in our classrooms to support dynamic learning experiences, and HOW to plan meaningful lessons for your classroom.

Shake Up Learning is a powerful guide and planning tool to help educators at all grade levels make the most of technology. Educator and blogger Kasey Bell guides you through the process of using technology and proven techniques to make learning dynamic.

You'll discover . . .

Practical strategies to help move from static teaching to dynamic learning

Straightforward and easy-to-use templates for crafting engaging learning opportunities

Tips and tricks for fearless implementation of powerful lesson plans

Advice for moving from one-and-done activities to learning that evolves and inspires throughout the school year-and beyond!

AVAILABLE NOW ON AMAZON Be DYNAMIC and SHAKE UP LEARNING in Your Classroom This Year!
But wait...There's more!

With this book, I have also created several interactive resources, templates, and downloads, all available on ShakeUpLearningBook.com.

Get the FREE Shake Up Learning Quickstart Guide

An online community

Discussion Questions, Chapter Actions, and Embedded Resources for all 20 Chapters!

An interactive companion website to help you continue and deepen the learning

A lesson plan database (submit and search for dynamic lesson plans)

Tons of free resources, videos, templates, and downloads, all available on the website: ShakeUpLearningBook.com.

© Shake Up Learning 2022. Unauthorized use and/or duplication of this material without express and written permission from this blog's author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Kasey Bell and Shake Up Learning with appropriate and specific direction to the original content on ShakeUpLearning.com. See: Copyright Policy.

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Empower Your Students with The 4 C's Learning Menu

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YOU can empower your students with this 4 C's learning menu! If you've followed this blog for very long, you've probably noticed I'm a big fan of learning menus aka choice boards. Student choice is empowering. Combine that with the power of the 4 C's, and you've got a supercharged lesson!

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Choice menus (sometimes called Extension Menus or Choice Boards or fifty other titles) are a foundational technique for many teachers. Typically, they're a grid somewhat like a tic-tac-toe board that has different options students can choose from to complete some task or project. Just do a quick search and you'll see thousands of them.

I've taught teachers how to use them for years, and when my colleage Ian Byrd wrote about why he's totally over them, I realized I'd been leading teachers astray.

Now, I don't agree with Ian's conclusion (essentially that we should ditch them), but I do think we need to be better at creating them. To do that, we need to understand their true purpose and not fool ourselves into confusing quantity with quality.

If You're Doing This, You're Doing Menus All Wrong

Let's look at a few examples of Menus Gone Wrong so you can see what Ian's talking about.

Menu Gone Wrong #1

Look at the two choices in this section of a menu:
You already know how I feel about Accelerated Reader, so I'm not going to give a lecture on how much I hate it. For our purposes here, that's not the point.

The point here is the total disparity in the quality of the thinking required for these tasks.

Read a book and take a low-level quiz on it or research a topic and create a product based on that research. These tasks are connected how, exactly?

It's like saying, "Either take your car to the car wash or develop a new chemical formula for a superior cash washing soap." They're just not on the same playing field.

First, let's be honest: most of our students can pass the AR quizzes without even reading the books. So there's that.

Secondly, there is no way that a knowledge/comprehension task is the pedagogical equivalent of a research/create task.

It definitely offers the option for high ability learners to avoid a mind-numbing AR test, but just because a student can do higher-level work doesn't mean they'll want to. Your high-ability learners could just as easily pick reading a Puppy Place book (those are 2 AR points) that's four hundred points below their Lexile. And then where will you be? How is that really differentiation?

If Ian reads this, he'll be (metaphorically) bashing his head into a wall. This is exactly the kind of nonsense we see in menus.

It looks good because there are options, but it's not actually good.

Menu Gone Wrong #2

This is a book report menu. Students can choose any way to share their understanding of a book they read. There are really nine choices, but I'm just showing six because you'll be able to see what I mean from them.

I was going to leave the horrible clipart out of the discussion, but I really can't because it's part of the problem. The teacher is taking up space with pictures that could have been used for better instructions. You can make stuff look good - I believe there's real value in that - but not at the expense of pedagogy, and not for something ugly like this clipart.

1990s-era clipart aside, I have two real beefs with this menu.

First, it's dying on the hill of "I must have nine choices to be a menu." While you can only see six, you know what I'm saying. There's no magic in the number nine. The teacher could have accomplished the same idea of student choice with fewer choices that were better aligned in thinking level.

Secondly, there is not separate rubric, so the only information the student has about the task is what's in the little box. Look at the section called "Letter to the Author." There is nothing about the quality of the work. A student could write, "Dear Ms. Patterson, I hated your book because it ended sad. Why did you write such a sad book? What is your middle name? Do you like ice cream? Sincerely, Sidney Student."

This would fulfill the requirement as listed.

It would have been far better for this teacher to have fewer choices and have those choices more fleshed out to encourage quality thinking.

Menu Gone Wrong #3

Let's look at a math example. As you look at this, consider the different standards being covered here.

First, let me say that the options in the top of the menu are strong. I have no beef with that. The options on the bottom include concepts that must be mastered, no argument there. (This menu only had four options.)

Now that I've complimented it, I'm going to tell you what's wrong with it.

The menu has four different tasks with four *very* different standards. I was going to go look up all of the standards, but I don't think we need that. It's easy to see that they're so, so different. Place value and equivalency are not the same.

Why is this a problem? Why does it matter if the menu is a hodge-podge of standards?

Because it begs the question, what exactly are you trying to do here?

If you are doing this as a review, you'd need them to do all of it (unless you had some kind of pretest for the menu, which is not a bad idea at all).

This menu also suffers from a common issue: too little actual instruction. Look at the top left corner. Are you 100% confident you know what to write on the lines? Would your 4th-graders be?

The Mosaic activity and the "Find the Pairs" activities are both quality activities that deserve their own time. They don't need to be lost in a sea of other choices. They are at different thinking levels. Just let your mind rest f or a moment on the "Find the Pairs" activity and then on "What Number Is..." It only takes a few seconds to feel the difference in neural pathway involvement between the two.

If students can actually choose these, you could easily end up with students choosing tasks that will not stretch them at all.

Menu Gone Wrong #4:

This one is the one that really got me. I realized I'd done so many almost exactly like this, and I was making some critical errors. Do you ever want to go back and apologize to former students? Yeah, that's a thing.

There are a number of things that are fine with this menu. Giving lots of choice for basic practice is a valid use of menus. Here's what's wrong:

Having a pretest be a choice is a huge no-no. Everyone should pretest, and they're work should be adjusted as a result of that pretest. Having students take a pretest and then practice all of the words the same no matter how they did is ridiculous and a waste of time (both yours and theirs).

Typing words is not how the brain learns to spell, so that's another waste of time. I love fonts, but having students put the words in a funky font is an egregious misuse of technology that defies all we know about the neuroscience of learning.

Writing words in ABC order is trying to practice two skills simultaneously: alphabetizing and spelling. Kids who struggle to alphabetize will not gain the benefit they could have from another activity that didn't require mastery of alphabetizing to accomplish. This is a perfect example of how students with any kind of learning difficulty or deficit get a double whammy.

So, I've shared some examples of what can go wrong. Let's look at how to make it better.

Making Choice Menus Better in Five Steps

Choice menus are a useful tool in a teacher's arsenal, but only if they're done well. This is true of so, so many things! Here are five steps to making choice menus better.

1. Make the purpose of your menu clear.

Just having menus because you think you should is poor pedagogy. There is nothing inherently superior about letting kids choose their tasks. The tasks must be worthy of being chosen. I know this goes against the self-directed learning mantra being spouted everywhere right now, but I stand by it.

Choice alone is not adequate differentiation.

With menus, choice alone can never be the goal. It's insufficient.

What is a worthy goal of a choice menu? Here are a few possibilities:

I have students with disabilities and I want to include options for them without having them feel separate or excluded.

The students are going to be presenting their work, and I want to offer a variety of presentation modalities to keep the interest of the students who will be seeing the presentations.

I have several quality possibilities for demonstrating learning that I've used over the years, and I think students may have strong preferences for one over the other. I'm going to give them choice to decrease resistance to the assignment.

The content is new to students, and they need different types of exposures to it.

There are a number of steps in an activity, but they don't need to be done in order. I want to maintain student interest to the greatest extent possible by allowing them to choose the order they do them OR I don't want all of the students on the same step at the same time because it means they don't all need help at the same time.

I've pretested them, and I need different choices based on the results of the pretest.

They're at the point in the process of knowledge acquisition that they need lots of different kinds of practice, so I'm giving them lots of different kinds of practice opportunities.

This list is not exhaustive, but you get the idea: choice menus must be about more than just looking cute. There must be intention and deliberation behind them.

Teachers must be able to answer the question: In what way does this truly advance students' thinking/learning/experience in a way that a single opportunity would not have?

2. Keep the thinking foremost in your mind.

Ian and I have a mantra: It's not about what they're doing; it's about what they're thinking. Too often, menus are all about doing. Are they making a brochure or a poster? Are they making a crossword or a wordsearch?

Here's where Ian and I split: I would consider differentiation of product a type of differentiation. It's just not enough by itself.

Consider the spelling word menu above. I'm pretty sure this teacher did what I used to do: just think of a bunch of different things kids could do with words, and then make those the choices.

What would be better is to truly consider what activities actually help kids learn to spell. Which words are kids most likely to misspell? How can the menu make it more likely that students will acquire the knowledge they need?

Here's one idea: The research is clear that the practice of interleaving leads to better acquisition. Interleaving is when students can't answer a group of consecutive problems with the same strategy. It's research-speak for "mixing it up."

To add that research-based strategy into my menu, I can make sure that the students have to select options that don't allow for use of the same strategy over and over. I have to make sure the menu offers different types of thinking.

Here's another idea: I want students to identify patterns in their misspellings. It makes no sense for students to practice spelling words in isolation if the issue is actually a particular type of phonetic pattern. To do this, I must use the pretest and have students do some self-reflection of the pretest. I need to look at it as well. I need to know if missed words are part of an ongoing issue with "th" words or words with a silent letter. You get the idea.

While I've used a spelling example, what I say about this applies to all. We need to be thinking about thinking before we think about doing.

3. Two is a choice.

Let's abandon the idea that choice menus need to have nine choices. There are no choice menu police who are going to show up at your classroom and demand an explanation as to why you only offered two or three choices.

Additionally, as I mentioned before, I think choice is somewhat overrated. I don't let eight-year-olds choose everything they eat, and the idea that students with no training or experience are superior at pedagogy to trained teachers is somewhat silly.

If we think that our students know better than we do about what they need to learn, we don't know our students well enough. Enter more/better preassessment.

Giving a choice is great. Humans in general don't like to feel trapped, so choice can allow students to feel more autonomy. That's necessary for motivation. However, choice shouldn't trump quality pedagogy.

If you have two great activities that go with the learning goal, give a menu of two. If you have three, then use those. And if you have one solid activity, then use that and don't feel badly about it.

Only give the number of choices necessary to accomplish the goal, and only give the number of choices that you can offer while maintaining quality.

This will grow over time, so you may find that after a decade of teaching something, you have more activities than did. That's fine, too.

4. Don't skimp on the rubric.

If the menu choice offers more than just simplistic tasks (e.g., "Solve this problem and then create another similar problem that uses the same solving process."), you need to have a rubric available.

In the book report menu above, you can see exactly what I mean.

It is unlikely that there will be enough space in a choice menu to give students the information they need to do a full and delicious job on it.

Solutions include making the choice menu digital with links to rubrics for each choice or having the rubrics available on paper somewhere else.

You don't need to give every child a copy of every possible rubric. That's overkill. Just make sure they exist and are available. Not that I don't think my author letter was amazing...

5. Remember that it's not enough by itself.

As I mentioned earlier, choice alone is not sufficient differentiation.

Differentiation must involve adjusting learning to students' needs and strengths.

It does not require choice, but it does require appropriate thinking activities.

You can use menus as a method of accomplishing that, but you have to make sure that the menu choices offer options that accomplish that adjustment.

You can use colors, numbers, columns, rows, or other techniques to guide students to the choices that are appropriate for them. You can also have different menus for different students.

Consider, however, how much work that is. I'm not sure the benefits outweight the effort needed to accomplish that.

Wrapping Up:

While I'm not eager to throw menus out the window, I would say that they need to be reconsidered as necessary or even desirable. They are not inherently better, and if they're not done well, they are worse.

Like so much in education, we have to stop accepting techniques without challenging their true value.

We would expect that of our students, and we should expect no less of ourselves.

The bottom line is that menus can be great, but to make them so, they take a lot of time and thought.

That is true of excellent teaching in general.

Teachers should not feel badly about having one quality task. Doesn't it sound ridiculous to read that? Of course you shouldn't feel badly about having a quality task!

Use menus if they move students forward, and leave them alone if they don't. Use menus if they work for you, and don't feel badly if they don't.

You May Also Like:

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Making Choice Menus Better: Taking Extension Menus to the Next Level

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Making choice menus (extension menus) better benefits all students. You may be surprised at what you're doing wrong. Learn how to make it all right.

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POSSIBLE PROBLEMS THAT MAY BE ASSOCIATED WITH  CHARACTERISTIC STRENGTHS OF GIFTED CHILDREN

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The critical thinking tools introduced here were developed by Dr. Sandra Kaplan, USC under the auspices of OERI, Javits Curriculum Project T.W.O., 1996. Ideas presented here are also adapted from Flip Book, Too Dr. Sandra Kaplan and Bette Gould

The Depth and Complexity Icons are visual prompts designed to help students go beyond surface level understanding of a concept and enhance their ability to think critically. These critical thinking tools help students dig deeper into a concept ( depth) and understand that concept with greater complexity.

In fact, to truly understand something, one must be able to speak the language specific to that topic. One cannot have a critical understanding of that same topic without knowing the details, rules and patterns associated with it or understanding how it may have changed and the varied perspectives through which it is viewed.

As you examine each icon, pay close attention to the design, as it will help to reveal its meaning. Keep in mind that our goal is not to teach the icons themselves, but rather to utilize them as visual "thinking" tools to help students gain a critical understanding of a topic or concept.
Depth Tool- Language of the Discipline
The meaning of this icon is pretty self-explanatory. The lips represent specialized language related to a topic or concept. This language includes key words, phrases, signs/symbols, figures of speech, abbreviations, and the like.
Depth Tool- Details
For example, to truly understand a concept in mathematics, one must speak the "language of math". A student being asked to add and subtract would need to understand not only terms such as "sum" and "difference", but also be able to understand mathematical sentences which often include symbols: 27 + (16 - 5) =
In the study of the American Revolution, students would need to know the meaning of "Redcoat" and realize that it isn't something one can purchase in a store!
Depth Tool- Patterns
As you consider the design of this icon, think about the details of the flower and how each part (flower petals, etc.) make up the whole flower. Details contain the information that enhance understanding. They act as supporting information to a big idea or concept (main idea). Details include: parts, factors, attributes, traits, and variables.
Depth Tool- Rules
If we go back to our earlier math example: 27 + (16 - 5) = the details are the numbers themselves (the parts that make up the equation). Being able to discern important details of a story is key to one's ability to critically analyze that text. While we can concede that one of the pigs in the story, The Three Pigs is wearing a red shirt, we can agree that the color of the shirt is extraneous and doesn't lead to a deeper understanding of the story.
Depth Tool- Big Idea
There's no surprise that this icon represents patterns (note the circle, line, circle, and zig-zag pattern). If one were asked, it would be a fairly simple task to continue the pattern. Patterns are recurring elements or factors in ideas, objects, stories, and events. They are predictable, repetitive and ordered.
Depth Tool- Ethical Issues
We see patterns in math: number lines, geometry; literature: "Little pigs, little pigs! Let me come in..." ; social studies: patterns in movement and settlement, behavior. The list goes on... Being able to move beyond simple identification of patterns to defining the cause and effect of a pattern or identifying relationships among patterns is rigorous and requires the ability to think critically.
Depth Tool - Trends
Rules are the organizational elements that create structure. This concept is an easy one for students, as they are surrounded by rules (at home, school, in sports, etc). Rules provide structure and represent organization and hierarchy. The meaning is reflected in the design of the icon, which itself has a clear structure.
Depth Tool- Unanswered Questions
This icon is often seen in science when looking at classifications. Students may encounter it when examining the structure of a text (compare and contrast, main idea and details, and the like). They may also be asked to apply mathematical rules (formulas) to solve a problem or utilize spelling and grammar rules in writing.
Complexity Tool- Multiple Perspectives
The Big Idea indicates a generalization, principle or theory about the curriculum being studied. It often represents the focus of study or a learning task.
Complexity Tool- Change Over Time
For example, the big idea of a science lesson might be the water cycle. The Big Idea design works well to help students organize the main idea of a story or paragraph (in the roof), which is then supported with evidence (pillars supporting the roof). Students use this with universal themes and generalizations.
Complexity Tool- Across Disciplines
This element of Depth and Complexity represents moral principles (possible rights or wrongs). An easy way to remember the meaning: "Black and white/ right and wrong". It represents conflicting points of view on events, ideas or issues and involves bias, values, or judgments.

Students will most likely encounter this dimension when analyzing literature or studying social studies. For example, students might be asked to consider ethical issues surrounding Spanish colonization and the establishment of missions along the California coast or to examine ethical issues surrounding a character's behavior in a story.

This is the icon I about which get the most questions. Trends represent the general direction of change. CHANGE is the key word here.

Trends can be explained by external factors or influences that contribute to the change. This icon is represented well by the line graph. Each spike and dip in the graph was caused by something (external factor or influence). Think cause and effect here. One example I like to use is the trend in schools to move away from hardback text books to e-books. What caused the change to go from one to another? Context is huge here! In this case, one reason the trend was caused was the availability of technology
This is different from simple change over time, because for a trend to occur, one thing has to replace, or compete with, another. It's important to not only examine the "why", but also the "so now what?" questions. What are the consequences, both intentional and unintentional?

These are questions about anything is is unsolved, unclear, or unproven. These can be ideas that have yet to be explored, are unresolved, or that have missing components (incomplete). Unanswered questions are good!

These are questions we need to pursue. Having said this, many students will be content with simply asking a question and leaving it at that. As educators, we need to push students to pursue the answers to these questions. These are typically questions that are not answered quickly and sometimes they aren't answerable (yet), but they do have the potential to generate some good thinking and discussion.

This icon basically represents different points of view on ideas, events, people, and issues.

It often represents an "expert" viewpoint, and is dependent on time and place. This icon falls under the "complexity" section of the Depth and Complexity framework. This icon is easy for students to remember because glasses have lenses through which one must look to see something clearly. Multiple perspectives combines nicely with the other icons. For example, one could look at the different perspectives on rules or on details. One really couldn't get a good understanding of a conflict without first looking through the different perspectives involved.

This icon prompts students to explore a concept, event, or person as it relates to time (past/present/future).

Change is inevitable. This powerful tool facilitates a more complex exploration and can easily be applied across disciplines and combined with all the other Depth and Complexity Tools. Consider having students examine how and why rules change over time. How do changing perspectives impact changes in rules? For a different approach, consider having students explore why things haven't changed.

This icon also falls under the complexity section of the framework.

The Across Disciplines icon prompts exploration of connections within, between and across subject areas. Although not used as often as some of the other tools, this icon supports understanding of how something relates to multiple disciplines. For example, students can examine natural resources across science, economics, history, etc. Questions students might explore - How does the California Gold Rush relate to science, economics, and history? Through what disciplines might we better understand the presidential election?

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Understanding Depth and Complexity - Envision Gifted

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Understanding Depth and Complexity and Content Imperative Tools. Resources and ideas for teachers to use with gifted and advanced learners.

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The Depth and Complexity icons are eleven tools that act as lenses, prompting students to look at a topic in a new way. They will help you to take your students deeper into grade-level material rather than moving them onto a new topic.

Sound too good to be true? Read on!

Get It All Via Email

Hey, if this long article is way too long you can take it in more leisurely through the Depth and Complexity Mailer. You'll get an email every week introducing a couple of the prompts. It's free!
Get Free Depth and Complexity Ideas
Onward!

Table of Contents

The Back Story

The overarching goal of Depth and Complexity is to move students towards expert knowledge of content. Bette Gould and Sandra Kaplan looked to understand how an expert understands their field differently from a layperson. Through interviews, they saw that these experts knew things like repeating patterns, required rules, ethical dilemmas, changes over time, and essential vocabulary within their field.

They identified eleven of these traits and assigned a name and a symbol to each. The idea is that students can move closer to an expert's level of understanding by thinking through these same lenses.

A Quick Example

The prompts of Depth and Complexity will sharpen your questions - and your students' answers.

See the sharpness in action:

"Compare and contrast Lincoln and Washington"

"Contrast the ⚖️ ethical dilemmas Lincoln and Washington faced."

"Compare the 🚦 rules Lincoln and Washington created as presidents."

See how broad and vague that first question is? It invites surface-level thinking. Using a prompt of Depth and Complexity raises expectations.

About Those Icons

Each tool is represented by an icon that gives students a visual shortcut to expert thinking. The tools' icons especially benefit younger students or those learning English. They unlock access to higher levels of thinking than those students' vocabulary would otherwise support. But their use should not be limited to just those students.

Even as a grownup, I use the icons when I take notes. If I spot an interesting dilemma, I'll sketch a little ethics icon to call it out. When I see a student draw an icon on their work, I know that they're calling out a certain way of thinking.

A final note about the graphical icons: beware relying on pretty clip art or professionally designed images. It sets the bar too high. Instead, draw the icons by hand as you teach. Encourage students to do the same. The Depth and Complexity prompts are ultimately students' tools, and students should feel empowered to use their tools whether they have access to specific clip art or not.
Sidenote: Read about why I use emoji for depth and complexity icons when using devices. They're free and easily accessible anywhere.
Depth and Complexity Basics

Here are the eleven prompts of Depth and Complexity along with a teeny explanation and a link to full articles.

❓
Unanswered Questions
Perhaps the most under-used of the prompts. It's so much more than "What questions do you have?" Instead, push students towards what we don't yet know about this topic. Or what can't we know? Consider questions that are truly unanswered to humankind.

📚
Across Disciplines
How does this topic represent an intersection of other fields? How do language arts and math appear within this topic?

📈

Trends

How a topic is currently changing and what forces are causing those changes? Trends is the prompt I'd most like to get rid of.

So that's the eleven prompts of Depth and Complexity. Yeah, there are a lot! But there's no need to use them all at first. Get comfy with, like, four. Plus, you'll be surprised how quickly you start to pick them up.

Want to get a series of emails explaining each Depth and Complexity prompt? Sign up for free here!

The Biggest Problem with Depth and Complexity

Without a doubt, the biggest problem people make with Depth and Complexity is: pairing an icon with a low level of Bloom's Taxonomy.

Look at these three tasks and think about what the level of thinking that each requires:

Identify the rules in this math problem.

List the important details about George Washington.

What are the patterns in the solar system?

Do you see it? ☝️ Every one of those questions requires merely a list as an answer. Even though I might be taking the content deeper, I'm still asking super low-level questions. I'm at the bottom of Bloom's - despite using depth and complexity.

And, now that I'm aware of it, I see it everywhere. Do a search for "depth and complexity worksheets" and spot all of the low-level questions out there. It's almost impossible to find any examples where the icons paired with high levels of Bloom's Taxonomy.

So please make sure to pair depth and complexity with high levels of thinking:

Compare/Contrast: How is Poe's 👄 language different from Lewis Carrol's?

Evaluate: Which author most effectively uses 👄 language to create their tone?

Synthesize: What would happen to the tone if we used some of Carrol's 👄language in The Raven.

See how we can go beyond "list the vocabulary words" and really get kids thinking?

Depth and Complexity Resources

Ok! Let's take a break here and I'll point you to a few Depth and Complexity resources that I've had a hand in creating:

If you'd like to continue on, I have an article about how to introduce depth and complexity to students.

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Depth and Complexity Icons: Everything You Need to Know!

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The dimensions of depth and complexity are a great first step towards a classroom differentiated for gifted learners. Learn the basics of these thinking tools and begin incorporating them into your lessons tomorrow!

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with Madam Bedazzle

Bedazzle: to confuse by a strong light. 2 : to impress forcefully, especially so as to make oblivious to faults or shortcomings: : enchant.

Madam Bedazzle is an esteemed deck dealer from Kaffeklubben Island, a highly-intuitive, card reader of The Halls™ Deck, used by skilled practitioners of the Arts and Crafts coterie to interpret, forecast, and crochet symbols, motifs, and typography into affirming messages.

Bedazzle practiced as an iffy intuitive for the last 23 years, and in a variety of seasonal, remote positions since COVID hit. She has a passion for ant farming and giving cliché advice. You may find some of her foundation work in Legend, Sagacious, and Halcyon? questionably rollicking.

She looks forward to astounding imaginations and asks that you take in her readings in whichever Kaffeklubben accent suits you best. She also welcomes recommendations for new hard candy flavors.

Legend of The Halls™ Deck

Existing in the Northern Hemisphere at least since the 14th Century, the highly-intuitive and suggestive Halls™ Deck is used by skilled practitioners of the Arts and Crafts coterie to interpret, forecast, and crochet symbols, motifs, and typography into affirming messages.

Expectedly, in a Deck the Halls fashion, skilled dealers pull a card and weave an interpretive reading into a sitter's tapestry of wishes and desires - gently nudging towards a productive direction. At one time, readings were only given during the wintertide Christmas season, but now with flexible work schedules can happen year-round.

Some creatives fear when certain cards are pulled and never want to get 'a bad deal.' Bedazzle assures that even ominous-appearing cards have two sides and four edges, so there's plenty of opportunities to turn them around.

Tarotble Card Readings

Deal 6: Dual states of being from potentiality to actuality.

Deals 4 & 5: This card pair encourages a game of optimistic one-upping in front of rolling stones.

Deal 3: Finding the state of halcyon in the midst of pelting interrobangs?

Deal 2: Wisdom to not to give in to the urge to change your creative work too quickly.

Deal 1: A sweet interpretation of what may be coming towards you.

Dynamic Apps

Use the power of the present and sit with the words that conjur up just for you. Oh, the places you'll grow!

Easter Eggs/Ongoing Themes

"The Halls Deck" is a rearrangment of "Deck the Halls", as MB first materialized in character during the Christmas Advent.

Red Skittles® are MB's favorite candies, which often are present during her deck deals. Why this particular candy? Pure chance.

Even though MB card readings are called "terrible", they are filled with much wisdom and thesaurusisms which you can benefit from if you pay close attention.

MB is purely authentic. No ChatGPT or other AI is involved in the creative content surrounding and eminating from MB. She doesn't make a single penny from her work, so AI won't profit from replacing her.

If you think MB's readings are lame, you can only blame yourself for wasting your time on them. You've been warned they are "tarotble."

If you keep finding nonsensical and convoluted reasoning around MB, you're definitely on target.

Don't be surprised if you also find half fini

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madam bedazzle card readings the halls deck

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Madam Bedazzle - Tarotble Deck Deals, Card Readings, Humor Apps / Creativity-Portal.com

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Educators! Learn how to use Pixton in the classroom. Set up your classroom and begin teaching any subject in minutes through the super-power of comics.

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Mindful Breathing Exercises for Children | Guided Meditation For Kids

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New Horizon - Meditation & Sleep Stories

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Guided Meditation for Children | ONE PERFECT MOMENT | Mindfulness for Kids

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Mindful Meditation for Kids: 1-Minute Deep Breathing Relaxation

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Guided Meditation for Kids: BODY SCAN - Mindfulness for C...

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In this Guided Meditation you will perform a gentle body scan... This Mindfulness practice is designed to bring your awareness to the present moment: a place of peace, calm and relaxation. You can find many more Sleep Stories and Meditations by downloading our app for Free: https://www.newhorizo...

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Bubble Bounce! Mindfulness for Children (Mindful Looking)

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Rainbow Relaxation: Mindfulness for Children

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Curipod - Spark curiosity with interactive lessons

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Free ready to play interactive lessons that sparks your students curiosity in the classroom

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We have a variety of prompts to help you lesson plan and do administrative tasks with GenAI chatbots like ChatGPT, Claude, Bard, and Perplexity.

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Wordwall - Create better lessons quicker

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Need a fresh teaching resource that fits your class and teaching style? Create a customized pack of interactive and printable activities in just one minute.

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MagicSchool.ai - AI for teachers - lesson planning and more!

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Join over a million teachers saving hours of time using the #1 AI Platform for Education, MagicSchool, to help lesson plan, differentiate, write assessments, write IEPs, communicate clearly, and more!

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A Three-Act Task is a whole-group mathematics task consisting of three distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

Why would I use this strategy?

To provide an engaging context for the use of mathematics and the development of mathematical understanding.

To reduce the literacy demand.

To add engagement. Students wonder what will happen next.

To create low barriers to entry, allowing the teacher to scaffold as necessary.

To provide an opportunity for estimation and reasonableness.

To provide opportunities to talk about mathematics.

To provide opportunities for reflective thought.

To build new knowledge from prior knowledge.

To encourage multiple approaches.

To honor diversity.

To create situations which require students to engage in mathematical modeling.

To build relational understandings among mathematics concepts.

To shift student ideas about justification of thinking and answers.​

How do I use this strategy?
​
ACT 1: Engage and Perplex

In Act 1, the teacher sharing with students an image, video, or other situation that is engaging and perplexing.

Students discuss what they notice and wonder. They generate question to ask about the situation.

Students decide on a question to answer and make estimates about the likely solution.

ACT 2: Seek Information and Solutions

In Act 2, students work on finding solutions to their problems.

They use information they have and ask for more information as needed.

The teacher supplies more information as requested by students.

They may adjust their question as they work.

​ACT 3: Reveal, Discuss, Extend!

In Act 3, students share their work, their thinking, and their solutions.

There is a reveal by the teacher of a solution, and the discussion that ensues may take many directions:

Students might compare their solutions to each others and to the reveal.

Students might compare their solutions to their estimates and discuss the comparison.

Students might discuss the assumptions that were made in the work.

Students might think of other questions they could pursue next

The teacher helps students connect their work to the core math of the task.

The design of a 3-Act Task is meant to help students see that the math they learn is power rather than punishment. Each of the 3 steps is critical:

1. Invite students to try a task that is intuitive, but inefficient or inaccurate.

2. Help them understand some math.

3. Invite them to re-try the task and see that with math it's more efficient and accurate.

More Resources for 3-Act Tasks:

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A Three-Act Task is a whole-group mathematics task consisting of three distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and...

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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National Library of Virtual Manipulatives

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A digital library containing Java applets and activities for K-12 mathematics

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Printing the PDF files from Acrobat Reader reproduces the Challenges much better than simply printing from within your browser.

Caution: If you are printing on a color printer, you may want to set your printer to black & white or gray as the Challenges use significant amounts of color. (Or just download the black & white versions below.)

Note : It may be necessary to scale your page setup to 85% or select "Fit to Page" to print entire page on a single sheet of paper.

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Figure This! Math Challenges for Families - Download and Print the Challenges

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Printing the PDF files from Acrobat Reader reproduces the Challenges much better than simply printing from within your browser. Caution: If you are printing on a color printer, you may want to set your printer to black & white or gray as the Challenges use significant amounts of color.

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DIY traditionally means Do-It-Yourself and refers to the culture of building or creating things that can be bought. At DIY.org, we give DIY a slightly broader definition.

Our mission is to build a safe online community that kids can use independently, without parental supervision - a place where they can "do it themselves". Within this community, we encourage them to create, share, and interact with each other over shared interests, without the fear of negativity, bullying, or predatory behavior limiting them. To us, DIY means empowerment. Through our free site and app, we hope to empower millions of kids around the world to become creators, builders, and, most importantly, responsible global citizens.

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Let's honor Math- the king of reason and logic! Rules: Fill in the missing numbers. The missing values are numbers between 1 and 9. Each number is only used once. Each row is a math equation. Each column is a math equation. Remember that multiplication is performed before addition and subtraction.