Merry ConsumerismShopping Smart is a Gift

If the mayhem of Black Friday has taught us anything, it’s that people LOVE a bargain

! Willing to camp out on the concrete for the latest phone or coolest game, psychotic - just playing, I mean savvy shoppers venture out on Thanksgiving night in search of insane savings, prepared to throw bows over the latest iteration of

Elmo.But what if there was a better way?

A method by which gift-getters could set a budget, safely peruse the possibilities for those on their nice list, calculate discounts, markups, and tax, then purchase those items without having to miss the pumpkin pie!

There is!Catalogue shopping, and it’s a great way for students to practice adding, subtracting, multiplying, and dividing decimals – without a calculator. Learning to stick to a budget is also a valuable life-lesson, especially during holiday shopping.

*I decorated my classroom for Christmas before starting and wore a Santa hat and played holiday music during the activity, but this could be used with any theme as it’s always a good time to shop! 😊

I started by splitting the students into groups of three and gave them a $500budget. This can also be done inpairs with any amount you choose, some prefer to give the kids $1000 to work with.

Any catalogue will work though I find students’ interests are most peaked when working with a conceptthey find engaging.Could they practice these math concepts while pretending to purchase summer sausage and cheese? Sure. Would they be able the calculate the discount and tax skimming through a brochure on lawn equipment? Absolutely. Would they have this much fun and remained this focused on the task at hand?

No.

Which is why I gave them a

Toys R Us

catalogue and had them “shop” for

TOYS! Yes, I know that Toys R Us is closed now but many stores still give out paper catalogues, though you can also use electronic versions. Just be sure each group gets the same catalogue.

The Object

The object of the game is to spend all of the money – without going over– meaning the group that comes closest to spending the $500, after properly making all of the calculations

, wins. (No, it doesn’t mean you have to buy the winners the things they’ve chosen, but they will ask! 😊)

In addition to the catalogue, each group is given a worksheet on which to make their calculations:

You can work in any special math you choose:

• For all items that say “

Save $$”, you must find the

percent decrease.• For Hot Price items, Take 25% off

• For VIP Items, Add a 40% markupon the price

• After you find the Grand total, remember that Georgia tax is 8%.

Or rework the rules entirely:

The group that reaches $500 bypurchasing the fewest number of items wins

Round each item you buy to the nearest dollar. The group that makes exactly $500 wins

The group closest to $500buying only one of each item wins.

Be sure to also include a place for the students to show all of their work.

The students did a great job working together picking out trampolines, scooters, and bikes and now understand that even without Amazon, it’s possible to figure out how much they’re spending – and saving – while shopping.

In this day of constant credit and living beyond our means, a good old-fashioned consumer math lesson couldn’t come at a better time. Tying the lesson to a real-world activity – like shopping – makes the concept relatable and tangible to children. We’re raising the next generation of consumers, why not arm them with the curriculum to keep them clever in the face of corporate commercialism too?

]]>Interdisciplinary Transformation Day: It’s All Greek to Me

Everyone knows students believe - with every fiber of their being - that Halloween should be a school holiday. Just because it’s not, doesn’t mean we didn’t dress up, have a blast (treat,) and cram in a whole lot of learning! (Trick.)

Interdisciplinary instruction is comprised of methods used to teach a concept across different curricular disciplines, and the notion isn’t new. Combining two or more subjects, thus increasing understanding and retention

of the material, was first introduced in the 1920’s. The positive educational outcomes for students learning via an integrated curriculum, were extensively

reported in 1997.It doesn’t take a scholarly journal, however, to know that kids learn best when they’re interested in the subject and engaged in the approach.

Cue the Greek tragedy…

For this year’s school-wide Halloween transformation day, I teamed up with my friend and fellow teacher, Mr. Wilmer. Together, we taught a lesson rooted in Greek mythology containing both math

and social studies assignments.

Based in the

the students – dressed in their finest peplos and chitons – set to solving a series of impossible tasks in the hopes of overcoming the obstacles of forbidden love.

Task 1: Seed Sorting (Classifying Types of Numbers)

Just as Venus had Psyche sort a huge pile of seeds in a single night, the kids got busy classifying the

real number system.Broken into groups, students sorted into cups:

Natural NumbersWhole NumbersIntegersRational NumbersIrrational Numbers

Successfully completing the task, (with zero help from the ants) the students moved on to the next assignment.

Task 2: The Golden Fleece (Identifying the States of the Original 13 Colonies or Flags of Different Countries)

Venus next sent Psyche on the hunt for fleece of the Golden Sheep. The student groups earned their golden fleece by correctly identifying states in a booklet, then attaching pieces of fleece to the states of the original 13 colonies, (thankfully not under the threat of disembowelment by livestock.) The eight grade class were required to do something similar. They were asked to correctly identify the country based on the flag and then attach pieces of fleece to the countries that were a part of the middle east.

With the golden fleece collected, it was time to move on to the third and final obstacle standing in the way of immortal love.

Task 3: A Drop of Beauty (Logic Puzzles)

For her final task, Psyche had to travel to the underworld and convince Persephone to put a drop of her beauty in a box for Venus. Though successful, Psyche’s curiosity got the best of her and she opened the box! Instead of beauty, the box was filled with sleep, immediately rendering Psyche unconscious.

The students worked on opening the box

(

solving a logic puzzle

) and retrieving the key to the potion, thus waking up Psyche.

Thankfully, the students cracked the code,

revived Psyche (thus making her immortal,)

and she and Cupid lived happily ever after

with their daughter, Pleasure.

The day was a huge success,

and not just for Cupid and Psyche. The students enjoyed the costumes, stories, games, and activities allowing us to teach a lesson in Greek mythology utilizing skills in math and social studies.

Interdisciplinary teaching is an approach provento aid in the development of cognitive abilities and mental processes, though the kids just think it’s fun!

Remember, this integrated teaching style works with any lesson and any grade level.

Enjoy 😊

]]>Which of these was made to twirl? The hula hoop OR this gorgeous green floral ruffle dress from Free People? That’s easy- BOTH. Next question: What type of transformation would we need to use to make both our hula hoop and our runway model spin like a top? You guessed it… ROTATION. This rotation helps the hula hoop become magical, mathematical, and perfectly complement creative thinking. Allow me to explain…

The hula hoop is spinning, or to put it another way, rotation is occurring.

Rotation is a type of shape transformation or change in appearance. When a shape rotates, it moves around a fixed center point either clockwise or counter-clockwise. The shape remains the same, but its position within the space changes. Rotation is measured in degrees from 0 to 360. We use a positive or negative number to show whether the rotation is clockwise (negative rotation) or counter-clockwise (positive rotation)

What does this have to do with fashion, you ask? Well, take our math teacher on the runway, for example. We could ask her to turn to her left…

“Now turn to the left”

“What? Left?”

“Right… No, I mean correct.”

Or…

“Could you please rotate 270 degrees Dr. Jones?”

“…Sure… positive degrees means counter-clockwise… ?”

Aside from fashion, there are countless examples of rotation happening all around you, whether you realize it or not.

Just as in fashion, there will always be knock-off versions of the real thing. Can you “mathfashionistas

” spot the fake? Which of these two rides should genuinely be labeled “The Rotation Express” and which one is just not quite authentic?Did you spot the fake? Its the Ferris Wheel! While both of these rides show some characteristics of rotation:

Circular motion on a coordinate planeEqual distance from the center point (origin)Doesn’t resizeDoesn’t reflect

The carousel has those little details (like a great dress) that the Ferris wheel just forgot:

Entire figure rotates simultaneously

Orientation of the figure changes as it moves around the axisIf the Ferris wheel was a “genuine” example of rotational geometry, then the cars would be stuck in place, unable to move, and the unlucky passengers would be hanging upside down at the top! (can’t do that in a designer dress!) While the Ferris Wheel’s cars are all following a circular path around the origin, (the center of the wheel) the cars maintain their orientation throughout. No one is dangling upside down or sideways.

In contrast, picture the carousel from a drone’s camera hovering just above. Looking down at the carousel rotating, each horse stays stuck on its pole, so the rider moves with the whole carousel, facing lots of different views during their trip around the circle. The horses do not get to stare at the popcorn cart all the way around the circle. Their orientation changes as they rotate.

Just remember, in geometry, rotation simply means… SPINNING AROUND A POINT.

Another example of rotation is the agitation of a washing machine, sometimes it moves in a short, jerking motion others it’s spinning clock-wise or counter clockwise, but it’s never changing shape and it’s never changing distance from the center point. (Is it a real example or a fake?)

Rotation is near and dear to your heart, in fact, it’s near and dear to everyone’s heart! The opening and closing of your heart valves to control blood flow is another example of rotation. (Is it a real example or a fake?)

Now that you know rotation is a matter of life and death 😍 try to come up with some real-world examples of your own.

]]>GET THIS LESSON PLAN BY CLICKING HERE!

Looking for a way to spark your students’ interest in math? Check out this lesson that I taught for the

#RockYourSchool event sponsored byGet Your Teach On! On September 20th, teachers from coast to coast taught unique and innovative lessons to jumpstart student engagement and set the tone for an exciting school year. These lessons rocked… literally.

I joined 30,000 educators from around the world for the Get Your Teach: On Rock Your School event. More than 1 million students were impacted by creative, outside-the-box lessons designed to encourage a life-long love of learning. This invitation gave teachers the opportunity to shape educational experiences in an active, engaged, and meaningful way resulting in enhanced understanding, retention, and self-esteem.

Regardless of grade level or subject, students learn best when they’re having fun and the lesson revolves around their areas of interest. Could I teach ratios, congruence, and dilation by having the kids knit sweaters? Yes. Would they enjoy the lesson and remain engaged? Probably not. The lesson must fit their interest. My students actually love to play games!

According to the Encyclopedia of Early Childhood Development, play-based learning results in better outcomes in math, literacy, and science - regardless of demographic – than standard drill and testing methods. So I found a way to make my lesson fun through game-based learning.

Right after the first quiz of the year, I used my Rock Your School lesson to do quiz corrections and review before the students received their grade. I connected each part of the lesson to a different concept from the quiz, then pulled out the board game.Get a copy of the written materials I used in this lesson here!

Board Not Bored Games

We all know students love to play board games, but this game was exponentially more awesome. I aligned a board game to content from my first quiz. We used the multi-faceted game Dropmix to multiply engagement during the quiz review. This game combines a physical card game with a bluetooth-enabled magical box of wonders. The game allows players to mix, layer by layer, an infinite number of song combinations from favorite pop artists.

Easily found atTargetor Walmart, Dropmix comes with cards containing different artists and musical components.

Used in conjunction with a free smartphone app, players collect cards and place them in slots which then play sounds. Combining different cards creates different songs.

Teachers should provide repeated opportunities for students to play games, then let the mathematical ideas emerge as students notice new patterns, relationships, and strategies. This, according to an article by theNational Council of Teachers of Mathematicswhich also states, games are an important tool for learning as they:

Encourage strategic mathematical thinkingSupport development of computational fluencyPresent opportunities for student practice and teacher observation/assessmentHelp develop familiarity with the number system, encourage engagement in computation practice, and build a deeper understanding of operationsSupport a school-to-home connection

The Dropmix Lesson

✔ Setup: Here’s how I aligned the different parts of the quiz to the Dropmix game.

First, I chose the artists I wanted to use for the drums and aligned them with different problems from the section on decimals.

For piano and trumpet, I aligned artists with the different classifying numbers questions.

For guitar and extra, I aligned artists with the complex fractions section of the quiz.

For vocals, I aligned the artists to the order of operations and the absolute value problems.

💡 Remember: This game can be used with any subject and any grade level to create a fun, engaging, and rigorous lesson aligned to your content!

How to Play

After dividing the students into teams, I gave them song lyrics. The answers to the problems were embedded in the song lyrics in red ink.

The red indicated answers from different sections of the quiz:

DrumsTrumpetGuitarExtraVocals

The students had to use the red answers to determine which music card to place on the dropmix game. Once they figured out the answers, they could create a song complete with drums, trumpet, guitar, vocals, and extras. I knew they were correct when the right song played from their device.

Answers

After identifying the correct cards, they placed them on the board and listened as their calculations created acrazy remix!

We did a total of five songs and the kids were focused, engaged - and having fun – while learning math. As stated in the research study, The Impact of Early Child Development and Experience on Later Outcomes, early childhood learning experiences can have a powerful impact on children’s later life outcomes.

In all honesty, I had as much fun as the kids! I truly enjoyed creating this experience and watching the students get so excited over a lesson. To see this lesson explained in more detail, follow me on instagram (@Dr_VCJones) and check out the highlight called ROCKMATH.

Why use this method to teach the same old math concepts? Interest-driven learning, such as this, has been shown to have long-term impact on student achievement. Studies show that students who play math games in class display higher mathematics productivity than those who learn through conventional paper-and-pencil activities. Additionally, English language learners who may be reluctant to participate in class discussions are more likely to participate in a game, where they gain access to structured social interactions as well as mathesteem. Whatever your subject area, here’s the perfect opportunity to subtract the “bored” from “board game” and kick it up another level with this radical lesson!

Better bring your A game though, ‘cuz this teacher DOES play! 😃

References:

]]>Looking for an eccentric way to weave geometry into the fabric of real life for you students? This project is sure to silence the “coplanars” and their age old question, “When will I ever use this?” The Geometry in Real Life project applies geometry skills with a new angle: architecture.

Don’t be obtuse! Every angle is the right angle when wearing acute dress! (Math humor. 😊)

Now, while I’d love to talk only about this gorgeous piece from the Gabrielle Union collection, fashion isn’t the only area into which we’re delving. (Ha! Did it again 😂)

Understanding area and surface area are very important, especially if you’re going into the fields of construction or architecture. All three-dimensional structures begin with, at least, a plane, (a flat, two-dimensional surface.) Throughout history, the circle, triangle, square, and rectangle have been manipulated to create astonishing, functional designs; the first being the pyramid.

To prevent collapse in the building being constructed - behind me in the photo – the architects and engineers had to figure out how to create a three-dimensional structure from a two-dimensional drawing. Oh, and they had to do it for each piece – each window, each support column, and each small part that makes a whole – like the squares inside the rectangles making up the perimeter of the large rectangular frame. One miscalculation and disaster could strike!

Finding the area of a rectangle, or square, is quite easy! Just multiply the length by the width, that’s it. Area is always measured in square units; inches, meters, feet - whatever the unit - it’s squared.

Modern architecture is where things start to get extra cool! Think of engineers and construction workers as really big, really lucky kids with enormous Legos, that can mold to any shape their artistic pal (the architect) can dream up! To build this fantastical, futuristic high-rise they need to know how to find the areaof a triangle, like the one I’ve created in the picture.

The area of a triangle is one-half base times height. Just make sure you know which triangle you’re dealing with; right-angled, acute or obtuse. (Ahhh, see, now my joke makes sense! 😊)

To best understand, picture I’ve taken down the cylindrical water tower in the photo and flattened it into two circles (the top and bottom) and one rectangle (the “body” unrolled.)

We’ve previously learnedthat to get the circumference of the circles, we multiply pi by radius squared. Because we have two circles, we multiply two times pi times radius squared. After finding the area of the rectangle, remembering we also need the height, because the rectangle “wraps” around to sit on and support the circles:

area = 2 π r(squared) + 2 π r h

We add those two up and voila! Surface area!

Bonus points if you can explain why it looks like I’m able to grab the cylinder in the picture! 🏆

Photographer: @jaxonphotogroup

]]>GET THIS PROJECT PLAN BY CLICKING HERE!

Looking for a way to put the “rad” back in quadratic? Here’s a crazy-fun and creative way to help your students take ownership in learning and teaching this difficult concept. Anyone can write a catchy jingle to remember prepositions or U.S. states, but when was the last time you heard the word “quadratic” in a song, much less the whole formula?

In the Quadratic Formula Project, each student taps into their “roots” working individually to create their own song, spoken word piece, or monologue that helps students memorize the quadratic formula. Students become “x-perts” by using all their talents to express this difficult concept in a way that builds camaraderie through the shared experiences of challenge and accomplishment. And while there may be a little song and dance, this is no “X-Factor” talent show!

Each student’s content-rich project must include:

A chorus or stanza that only contains the quadratic formula

Typed lyrics or script for the entire presentation submitted in a creative wayA 1-2 minute live presentation including costumes and/or propsMusic set to either a student’s own original rhythm or an instrumental version of a popular songAt least one verse describing how to use the quadratic formula to solve problems

Step-by-step typed explanations for at least two original problems solved using the quadratic formula completely worked out with answers

The use of songs to teach difficult concepts (from elementary to college level) has been widely associated with higher student performance as well as more favorable student attitudes about content and instruction. The potential benefits of students creating their own content-rich songs extend far beyond those of a simple mnemonic device. They include:

Enhancement of RecallReduction of StressMulti-Modality DeliveryIncreased EnjoymentIn Depth Exploration of Content

Can a worksheet deliver outcomes that “x-traordinary?” Download the full rubric for this project HEREand help your students discover the revelation that the quadratic formula can do more than just feed baby parabolas!

References:

]]>Oh man! It looks like our math teacher has become a true scientist and mastered the ability to clone herself! Either that, or she's just changing personalities as she's sliding down the chairs, (and some of them aren't very nice!) Translation: Mean Girls! LOL. No, there aren't really five impeccably dressed mathematics educators playing musical chairs; just one chic, shy, bored, rude, floored fashionista translating across them all.

A quick look in the mirror before you leave your house for the day holds a secret that you can unlock through the great mystery of math. Your reflection in the mirror is simple flip of an image over the line of reflection. Everything that you see is a reflection of light bouncing into your eyes. Reflection is everywhere!

You may look at this picture and think you are seeing double. And you’re right! Looking a little closer, this picture exhibits so many forms of reflection than a double image. Thanks to reflection, you are actually seeing quadruple! The very design on this Chiara Boni LA Petite Robe Color block Jersey Sheath Dress allows you to see how reflection works as the design is flipped on the mirror image at the line of reflection. You can find this dress here. Reflection is very common in all things fashion; not just my dress! Beautiful patterns on fabrics often show reflections in the design. Fashion designers need to have a good grasp on the concept of reflection to create amazing masterpieces that we all can enjoy! Who says you can’t find math in fashion? The concept of reflection in this image is simply mesmerizing.

Translation is a term used in geometry, describing how an object changes location without changing size or direction.

Imagine kicking a soccer ball back and forth with your dad. There’s only one ball and it maintains its size and shape the entire time. When you kick the ball, it travels from the point where you’re standing in the yard in the direction of your father stopping against his foot, until he kicks it back. As the ball glides across the yard, that’s translation.

Have you ever been on the monorail at an airport? All the passengers pile into the train and it travels back and forth between two terminals. There’s only one cabin-car per track, it never changes size or shape, and it only travels in one direction before stopping. Inside the monorail, you are being translated between terminals. Translation: Very Cool!

The image of the teacher above is a translated "like" image. Because Dr. Jones is arranged in different positions, but she is not identical, she is not truly being translated. In translation, the shape of an object or image:

Doesn't rotateDoesn't resizeDoesn't reflect

AND every point of the shape:

Must move the same distanceMust move in the same direction

Just remember, in geometry, translation simply means…MOVING

Photographer: @jaxonphotogroup

]]>GET THIS PROJECT PLAN BY CLICKING HERE!

Looking for another way to make math More Than A Worksheet? Wondering how to make “interdisciplinary learning” more than a buzzword? With this project, you can do both! The Math Spanglish Fiction Book integrates a full quarter of Spanish and math concepts into one concrete and creative demonstration of real-life application!

Each student creates a tangible children’s book which is bound, illustrated, and indexed with Spanish vocabulary and math explanations. The student chooses the setting, plot, and characters that match their interest. What could be more engaging than finally casting your little hermano as the villain in print for all to read? Te gusta shopping? Be the Super-Senorita who solves the mystery of the actual sale price after discounts, coupons, and tax! Whatever their interests, this project offers students a rare, student-directed opportunity to impart real-life significance to the seemingly unlikely amigos- math and Spanish.

Check out this sample project and consider how much critical thinking, active investigation, and ownership went into fully understanding, and then teaching, the mathematical concepts integrated into the plot! (Keep in mind this is not a perfect example- this student work was graded using the rubric).

Some of the requirements for this interdisciplinary project include:

10 pages minimumColor and IllustrationsAn explanation of mathematical technique, concept, or rule embedded into the storyFive math problems incorporated into the story with solutionsSpanish words embedded into the storyVocabulary word index (or both Spanish and Math)

Aside from being FUN and practical, interdisciplinary projects such as this have been associated with MASSIVE effects on student outcomes including:

Better school attendanceMore positive attitudes about schoolFewer discipline problemsLower drop-out rateHigher GPAHigher ACT scoresEngagement of students who are at risk of being marginalized in traditional disciplinary programs

And yes… I know that we, as teachers, often like to teach alone in the safety and security of our classroom bubbles, where we can do everything our own way… but can we just take a second to recognize that our students will enter a knowledge-based economy where communication and collaboration are required, rather than optional? Part of teaching our students to be problem-solving team players with diverse perspectives is actually modeling being a problem-solving team player with a diverse perspective! Take, for example, my colleagueMiss Maestra, the amazing Spanish teacher who collaborates with me on this project! (Check out her fun online Spanish classes at www.missmaestra.com) Partnerships like hers are what makes interdisciplinary learning possible to begin with! Who could you collaborate with on this project to take your first step toward interdisciplinary learning for your students? Its yet another way to make math More Than A Worksheet!

References:

]]>Did you notice the circles the first time you viewed this picture? Yes! No- just me? Well, by the end of this blog, I hope you will start to see more math terminology in every structure you encounter:) You can find some unique art pieces along Atlanta's Beltline and this circular lamp post a great example! Standing on a platform on the eastside trial, this piece is a replica of a circular antique street light.

Now the teacher's dress is from Badgley Mischka. See how the coral ruffle goes all the way around her shoulders? It’s a circle! If you have ever watched Project Runway, then you know that a circle pattern was used to cut out the fabric for this dress. Let’s break down how the designer incorporated the side-less shape into this fashionable frock.

Taking into consideration the way the ruffle should look in relation to the sheath and straps of the dress, the folks at Badgley Mischka had to make calculations about each part of the circle it formed. The most important thing to remember about a circle is that it’s just a set of points equidistant (the same distance) from the center point; the center is the original starting point of the circle.

And that's how they made this dress as pretty as Pi!

Let’s walk through the parts of the circle they calculated to ensure the ruffle is neither too big nor too small. Imagine we’ve removed the ruffle from the dress and laid it flat on a table; we are now looking at a very stylish circle.

After identifying the center, also called the origin of the circle, we can measure the radius.

The radius is the distance from the center to any other point on the circle. All the points on the circle are equidistant from the center.

Measure the distance all the way around the circle and you now know the

circumference of the circle.

Draw a line straight through the center of the circle, from one point to another, and you’ve just found the diameter- the distance across the circle.

By now you might be thinking, “Okay, but what does this have to do with PIE?!” Nothing, because we’re talking about Pi!

Often denoted by the Greek symbol, the value of Pi is an irrational number (a number with decimal digits that never repeat nor end.) The actual value of Pi is:

3.141592653589793238…………………………

So, we usually just round it to 3.14

What is Pi really? Well, if you took the diameter of a circle and decided to wrap it around the outside of the circle itself, it would take three whole diameters. But that still would not be enough. There would be a fraction more needed to complete the wrapping and that piece equals about 0.14159265... and so on. So for any circle it would take "pi" diameters to wrap completely around the circle. Hence, on a circle, Piis the ratio of the distance around the circle (circumference) to the distance across the circle (diameter). The coolest thing is that no matter how big or small the circle, Pi always equals 3.14!

Now, it’s easier to envision a seamstress measuring the parts of our fabric circle before cutting it down to perfectly adorn our math teacher’s dress!

Fashion is far from the only instance understanding the parts of a circle can come in handy!

If you’ve ever gone to the fair and played games in the hopes of bagging an enormous stuffed bear - only to walk away empty-handed and angry - you may have been duped by diameter! Whether it’s the ring toss or shooting hoops, if the circumference of the ring or ball is too small and the circle is not able to fit over the bottle top or pass through the basket, the carnies have done their homework!

Architecture is another industry that heavily relies on dismantling the parts of a circle. Looking back at the picture of our math teacher, we find numerous examples of circles in the city design like the bulbs on the lamp post, the base of the pole, and even the center of the painted flower in the background.

Understanding the parts of a circle may just come in handy at home, too.

The next time your sibling tries to take more than his or her share of the pizza, bust out your newfound circle knowledge and lay down the law with the lingo:

A chord is a line that connects two points on a circle.

(The diameter is always the longest chord.) A sector is the "pie-slice" shaded region.

While your sibling tries to figure out what language you’re speaking, you can make off with the largest sector of pizza pie!

🍕 Math is delicious!

Photographer: @jaxonphotogroup

]]>Looking for a fun way to get to know your new students this year? You could always take attendance and ask them to write out what they did over their summer vacation… Or you could try this super creative math autobiography project!

GET THIS PROJECT PLAN BY CLICKING HERE!

Let them introduce themselves with a burst of creativity and pride that will instantly abolish the notion that “math is boring.” In the mathematical autobiography project, students are given creative freedom in describing their formative experiences, favorite memories, and overall attitudes about math- both inside and outside the classroom. This is demonstrated in three parts:

Live Presentation

This is where each student’s creativity and personality has the opportunity to really shine beyond the confines of a poster board! Students can choose the most meaningful form of expression and tell their story in their own unique style. This could take the form of a rap, a poem, the construction of a model, or even a funny skit. Students can perform live in class or alternatively, they can record a video or audio clip to share in class, which can help empower introverted students without the pressure of an in-person performance. The student decides what, why, where, when, and how to present their math autobiography to the class. And yes, creativity counts! (Click HERE to get the rubric for this project!)

Written Explanation

In addition to the class presentation, students compose a one-page written explanation of their math autobiography. Students can mix and match from a list of sample questions or create their own questions and answers to help them chronicle their math journey (whether fairytale, horror story, or thriller!) Some of the sample questions provided include:

When do you first remember doing math?What is your proudest math moment?What is your most embarrassing math moment?What are your math experiences, both good and bad?How do you feel about math and why?How do you think math will affect you in your future profession?

Visual Depiction

The third and final piece of the math autobiography is a visual depiction of the student engaged in some sort of mathematical activity. This could be an illustration, photograph, or even a video clip. But more important than choosing the media, is the student’s analysis of all the tasks in which they personally (and probably unknowingly) utilize classroom math concepts in their every day lives. I dare you to find a student who doesn’t have an interest in SOMETHING that utilizes math! From cooking to music, athletics to video gaming, your students are using math, not just on paper, but in real life! Helping them to recognize their use of math and the mastery they already possess can boost their mathesteem for the next challenge they will master!

With the new school year upon us, why not take this first easy step toward a more project-based approach? Starting the year off with the math autobiography can help you empower your students as stakeholders in their own learning. There is increasing evidence to support the effect of providing choices upon student motivation. A project-based approach that accommodates different learning styles, provides choices, and teaches to the student’s strengths has been shown to not only reduce procrastination in junior high math students, but also leave a lasting impact on their intrinsic motivation! Can a worksheet do that? Another great way to show that math is "More than a Worksheet."

References

]]>Uh oh, looks like our teacher has tessellated on the floor! Luckily, this isn’t a bad thing as the floor is tessellated too! Before you reach for a mop and bucket, let’s talk tessellation!

Tessellation is the use of a single shape, to cover an area, with no gaps or overlaps.

Notice how the teacher’s dressis really made up of three colored rectangle-like shapes, while the floor is completely covered in triangles, this is tessellation.

Tessellation has always been an art and fashion favorite, though can sometimes be hard to detect.Tessellation is a favorite of fashion designers because it relies on symmetry - two or more pieces of the same object being identical, balanced and proportionate – much like the human body.

There are four types of symmetry that can create tessellation, (while lending on-trend traction to your wardrobe!)

Translation – a shape that does not turn or flip, but glides.

Reflection – a shape that’s been flipped at an angle, horizontally, or vertically.

Rotation – a pattern of shapes that appear to rotate around a certain point

Glide Reflection – a pattern created using translation and reflection.

Look at Sam Kerr’s tessellation picture made entirely of rabbits.Remembering that there can be no gaps or overlaps and that the pattern must repeat, you might be wondering how this is even possible. It all begins with one simple shape. Each of Kerr’s rabbits starts as an equilateral triangle to which he makes symmetrical adjustments until they all fit together like puzzle pieces!

Tessellation also occurs in nature. The patterns of a snake’s skin and a turtle’s shell are examples of tessellation, as are fish scales and honeycombs.

Both artists and mathematicians are fascinated by tessellation as it seamlessly combines a clear set of mathematical rules with infinite creative possibilities, resulting in one visually stimulating piece.

In the grand scheme of things, it all makes sense: People are drawn to beauty; people feel most comfortable when surrounded by order - yet art is inherently chaotic. Tessellation is the best of both worlds, lending imagination to computation!

Think of tessellation as the couture of calculations.😎 Thinking about math in relation to other interests, (like fashion) is a great way to internalize the concept and raise your mathesteem!

Can you think of any other real-world examples where you’ll see tessellation?

Photographer: @jaxonphotogroup http://www.jaxonphotogroup.com

]]>GET THIS PROJECT PLAN BY CLICKING HERE!

Do you love to dance to the beat of your own drum? What about to the beat of the mathematical concepts rotations, translations, dilations, and reflections? When rhythmic motion and math collide, there is an explosion of knowledge just waiting to happen. Everyone loves to move their body to the beat of a good song. Throwing in a little math can spice things up to be both fun and educational. Who knew? The Transformation Dance Project is a fun way to get kids engaged and learning math in a new way. Click here to get the rubric for this project!

There is a huge misconception that certain aspects of math cannot be applied to real life. It’s time to shatter those notions and deliver a dance to remember! Did you know that rotations, translations, dilations, and reflections can be found just about everywhere in real life? A simple photo can demonstrate how a dilation functions when you order a package of wallet size pictures verse the larger size of 8”x 10”. Mirrors can be used as an amazing representation of a reflection in that an image is flipped over a given line. Rotation happens as you ride on a carousal and wheels spin on an axis. Translation is like a slide from one place to another.

Now that you can easily see how these concepts apply to real life, it’s not hard to see how dance can be incorporated to create a new learning experience in math. You can use popular dance moves like “The Shoot” and “Millie Rock” not only on the dance floor, but also in the classroom to visually showcase various math concepts. Adding a few extra movements to these popular dances can take the rhythm to the next level. Throw in a few props and costumes and you’ve got yourself a dance party to remember!

In the transformation dance project, students will create an original dance to a piece of music using rotations, translations, dilations, and reflections. Transformations are used to demonstrate movement using the entire body. Students work in groups of 4 or less to create a dance between 1 - 4 minutes. The dance must be performed live for the class. Students are also required to create an instructional video of the choreography and how it applies to mathematics.

Doing your own Transformation Dance Project can be a fun way to try something new in the classroom and build mathesteem within your students. Blending pop culture and education appropriately can turn something drab into an amazing experience that will give pupils better retention of the information. It is always fun to make math activities more than a worksheet! Going to math class can be something to look forward to every day by reaching out to students on their level and fueling their brains with knowledge and enjoyment.

]]>GET THIS PROJECT PLAN BY CLICKING HERE!

Everything is related to math, it just depends on the “angle” you look at things- LOL! See what I did there :). Angles are really everywhere, lines too. What better way to investigate these topics than by using your own neighborhood!

In the street map project, students apply their knowledge of special lines and angles to the street map of the neighborhood in which they live. Once the map has been developed, students identify, define, and label key math concepts. Then finally, the students design a creative way to display their map unrelated to a street or neighborhood. It has been so wonderful to see the amazing ways the students have re-imagined their map into something completely different. Click here to get the rubric for this project!

The best thing about this project is that you begin to see math terms everywhere! For example, let’s take a look at a normal Saturday:

You take a trip to the mall, and you want to get from H&M to Build A Bear, how will you find the way? You’ll go to the directory…which is just a BIG MAP! While you plan your route, you’ll have to calculate the angles: Will you walk parallel to the H&M window display, turn 90 degrees at Auntie Anne’s Pretzels, and walk perpendicular to the store? Or will you have to make a total 180 degree turn and head back from where you came? Your plan of action relies on math concepts of different lines and angles.

But you aren’t always at the mall. Where else can you find angles? Well, when you come home from the mall, you’ll want to hang the new strand of lights you got at Urban Outfitters above your bed. It’s going to look so cute! You get the ladder from the garage. Here’s the thing: when the ladder rests against the wall, you’ve inadvertently made an angle. Not only that, but you have to calculate what degree is the most stable for you to climb the ladder and hang your lights. Hint: Acute angles are your friend here.

It’s been a great day. First the mall, then your new bedroom décor, and now you’re headed to the Yoga Studio to get your sweat on. From Warrior Pose to Child’s Pose, you’re using angles to get the best lines and stretches from your body. Your guru knows the difference between an acute and obtuse angle, and that’s why she comes over to help you reposition during Downward Facing Dog. Just don’t fall asleep when you utilize a straight angle during Corpse Pose. After your Yoga sesh, you indulge in a smoothie bowl with your bestie. You both notice the parallel lines of kiwis, coconut flakes, and chia seeds running over the top of your bowl.

Thinking about the world in terms of math concepts might seem daunting at first, but once you realize that the concepts are practical, it becomes a piece of cake (which, incidentally, is an acute angle). For instance, building and studying a map helps you master the concepts of lines and angles. The project has students explore vertical angles, adjacent angles, linear pairs, and the special eight angles formed from a transversal hitting across parallel lines. Learning in this real world way helps the material become real. The kids learn that math is “More than a Worksheet” and more than something only done in a classroom. Plus, you’ll always remember these concepts because it’s easier to remember that one time you pulled a muscle in Yoga class (from the improper use of angles) than a nondescript worksheet.

]]>Wouldn’t it be wonderful to shrink your math teacher, pop her in your backpack, and take her to your house for homework help? Yes, but only if she remained the same, only smaller; her brain may be filled with math content, but her head should still stay proportionate!

The process by which we transform a proper-sized professor – adorable dress and all - into a magical mini math teacher, is called dilation. We use dilations to reduce or enlarge an object, proportionally. Most commonly, you may hear this term used in a doctor’s office. When the doctor dilates your eyes, they are widening the pupils of the eyes in order to allow more light to reach the retina. In this image, the life-size teacher is the preimage, and the resulting petite instructor is the dilation image.

Sometimes small children see an architect’s model and think it’s a dollhouse, though it’s really a scaled down – yet proportional – representation of an actual development. (Please don’t rearrange the landscaping or you may have a tree growing out of your pool! 😊)

The tiny townhomes (shrunken skyscrapers and miniscule malls – complete with pint-sized people and pets) architects use to represent new communities are created using scale factor. To find the scale factor of an actual hotel to the model, the architect divides the length of each of the corresponding sides (length, width, and height) by the same number. Architects often use scales as crazy as 1:2400!

*******

Math modeling is another great way to figure out real-wo

rld problems using the language of mathematics! Let’s say we want to figure out which Eva Mendez dress on the New York & Company site is the cutest; we’ve already completed the first step by determining what we want to know!

Next, make some assumptions; in this case, what is cute? Length? Cut? Pattern? By assigning value, you begin to define consistent factors that impact outcome. Now it’s time to figure out what you really know and what you don’t. After researching and gathering data on hashtags, social media posts, customer reviews and fashion blogs, you define your variables and figure out a solution!

Now it’s time toanalyze and asses your model. Does it make sense? Has it solved the problem? Is the answer reasonable? Prove it by validating the model. Now that your creation is complete, report the results - you know which dress is the cutest – shout it from the ceiling, sister!

Your findings should summarize the problem, methods, and results in addition to explaining why you chose this problem along with your approach. (Because fierce fashionistas need to know!) Be sure to lay out your entire process, cite sources and explain your conclusion.

See, math is always in style! 😊

Photographer: @jaxonphotogroup http://www.jaxonphotogroup.com

]]>Getting kids engaged in STEM can be a challenge - especially if they don’t have great math-esteem just yet. By using popular culture (superheroes in particular) teachers and parents can get their children involved in complex problem solving without breaking a sweat. A few years ago, physics professor, Jim Kakalios, contributed to an articleto the PBS News Hour website which discussed this very topic. Professor Kakalios turned his love of comic books into fun ways to find the math and science behind our favorite superheroes powers.

In this blog, I’d like to share one of my most recent lessons based on the new Avengers Infinity War movie

. If you’re not familiar with

The Avengers, they are a superhero team (also called “the world’s mightiest heroes”) who have teamed up to fight evil and save the world. You can find out more about them and their story here.In this lesson, my class joined the Avengers in their quest to protect all six Infinity Stones. I played Gamora from the Guardians of the Galaxy and presented the Avenger Math Challenge to my 7th grade class. Students competed in groups to try to secure the Infinity Stones before the villain, Thanos, could use them to destroy half the world’s population!

Here is the information about each station the students had to complete:

1) The Space Stone Challenge (The Tesseract)

The Space Stone gives the user power over space. Anyone holding the Space Stone can create a portal from one part of the universe to another. In the Marvel films, the Space Stone

is hidden inside a blue cube called the Tesseract. The Tesseract makes its first appearance in “

Captain America: The First Avenger”. The only thing powerful enough to move space and lift Thor’s hammer is liquid vibranium. The first challenge in this lesson was to figure out how much vibranium was needed to raise Thor’s hammer. Students had to problem solve to determine the volume of the container with and without the hammer in place. Once the group determined the volume of vibranium needed, the answer would release the space stone.

In the next challenge, the students’ navigated their way through the angle measurements embedded in Spider-Man's web.

2) The Mind Stone Challenge (Loki’s scepter)

The Mind Stone allows the user to control the minds of others. We first see it as a blue orb in Loki’s scepter in 2012’s The Avengers. Whenever Loki touched someone with the scepter, he could control what they do. Thanos gave the Mind Stone to Loki, a hilarious but not particularly accomplished villain. Weird decision, Thanos.

In this challenge, students used the power of their mind to help Spider-Man find as many angle measurements as possible in his web. Students helped Spiderman activate the correct angles to create the perfect web to trap Thanos.

Continuing on, the powerful and kind-hearted T’Challa - ruler of Wakanda presented the next challenge.

3) The Power Stone

The Power Stone bestows upon its holder a lot of energy—the sort of energy that you could use to destroy an entire planet. Star Lord (Chris Pratt) accidentally discovers the stone in Guardians of the Galaxy. Ronan the Accuser steals it from him and threatens to wipe out an entire race.

In this third challenge, T’Challa feels as though there may be an epic power battle on his land in the near future and wanted to build more castles for protection. To earn the power stone, students had to use a merge cube to create a hologram model of this castle as a blueprint. The correct calculation released the stone. The merge cube app used for this task was called Dig. It is a free app that is compatible with the merge cube technology.

In the next challenge, the students discovered the surface area needed to dress Baby Groot.

4) The Reality Stone

The Reality Stone grants the user the power to manipulate matter. In Thor: The Dark World, the villain, Malekith (Christopher Eccleston), wanted to use dark matter called Aether to complete evil deeds.

In this challenge, Baby Groot wanted use the matter to create a new outfit made out of geometric solids. Students needed to determine the exact amount of matter in square centimeters that it would take to create clothes for Baby Groot.

Now, we can’t forget Iron Man! He was in the next challenge. Tony Stark is all about technology. But you can’t save the world if your measurements are off and your suit doesn’t work, can you?

5) The Soul Stone

We haven’t seen the soul stone in prior movies. The Soul Stone’s powers in the comics are somewhat vague and ever-changing. Basically the Soul Stone allows the user to control others “souls,” both living and dead. Soul Stone users have previously trapped souls in other dimensions and have brought dead people back to life.

For this task, Iron Man needs to train for his battle against Thanos. He constructed new gloves for his suit that used laser technology and Iron Man planned to used them to destroy his enemy. Before he attempted to test the gloves, he needed draw the outside boundary of the region on the ground so he could discover the exact spot to shoot from. Hitting the correct target would release the stone.

The last challenge of the lesson involved Ant-Man and our last stone, the Time Stone.

6) The Time Stone

The Time Stone grants its owner the power to rewind or fast-forward time. Stephen Strange discovered it in the Eye of Agamotto pendant in the library of Kamar-Taj, where he trained in the mystic arts in Doctor Strange.

To release the Time Stone, the students needed to help Ant-Man create a scale model of his two-story house out of legos. This way he could train, sleep, and eat in his home no matter what size he was and no matter what time interval (present, past, or future) he was sent into.

Needless to say, my class had a blast! Use math and you too can be a Guardian of the Galaxy! Building math esteem comes from getting students motivated and building their confidence. We are meeting kids on their turf, using their world to interact, and using fun to build their cognitive strength. That gives students confidence - and THAT builds their Math Esteem! And that’s what it’s all about!

If you’d like a copy of this lesson plan to save or print for your classroom, simply

Happy world-saving, superheroes in training!

]]>With the release of the blockbuster movie Ready Player One, we have another super opportunity to reach math students in one of their favorite environments: VIDEO GAMING!

The Story Line

Ready Player One is a story set in 2045, in a dystopian world that is harsh and almost unbearable. People spend most of their time inside a virtual reality simulator known as Oasis.

When the creator of Oasis died, he announced in his will an Easter egg, which could be found through a series of three challenges. The first person to find it would be the winner and would inherit complete control of Oasis and his immense fortune.

The movie is full of action and exciting special effects. The characters inside Oasis are Avatars, created as the digital portrayal of the player’s self-image. Throughout the story, the players have to play games, work through puzzles, and defeat enemies.

The characters have to use their wits, their minds, and learn as they move through the virtual universe. And these are exactly the kinds of things that we want our students to do while learning math concepts!

Through the use of educational video games, we can help students expand their minds. Playing edutainment games could build their knowledge and allow them to practice their mathematical concepts to mastery. And this all can occur while playing games and having fun!

Dimension U Games in the Classroom

For our math lesson based on Ready Player One, we used games on theDimension Usite and app.

Dimension U has interactive video games that follow common core standards for math and english, and these games are much like the ideas in the movie.

Players create their avatar and can collect coins to purchase powerups or superpowers. Similar to the first challenge in Ready Player One, Dimension U has a fun mathematical racing game called Velocity. Even the third challenge in Ready Player One on planet doom is similar to the Dimension U math game, Meltdown, it' just not as violent- LOL!

With all four games provided by Dimension U, students have to answer questions and work through problems as they move through each level of the game. Some of the challenges are thrown at the players in rapid succession, making the players have to answer questions quickly. Only when the players answer correctly do they attain the reward, up their level, or move on to the next challenge.

As a teacher, I can see each problem that the students encounter during game play. I can use this data to analyze results as a grade, a class, or an individual student. Teachers can select which standards each child will practice inside of the game. They can also determine the length of game play and exactly which of the four games the students will focus on. Similar to Ready Player One, students can work in a "clan", teams play, depending if that feature is selected.

Students have a blast with this infusion of video edutainment in math class. I love using this resource as a way to determine how much of the material has been mastered by each class. Dimension U also has the same features and games for English language arts.

You can check out some videos of the game play:

Research on the Benefits of Game Play

In December of 2013, American Psychologist Association published an article, “The Benefits of Playing Video Games”, by authors Isabela Granic, Adam Lobel, and Rutger C. M. E. Engels. The study examined and identified four areas of positive impact on their players: cognitive, motivational, emotional, and social.

This study explained how gamers can improve their brains’ functions, as well as, build confidence through playing games. They not only exercise and build the parts of their brains that are used to learn math, but they are being motivated to do so by the positive reinforcements built into the games. Players understand that learning a game takes practice and perseverance; they don’t give up just because they fail. Each time a gamer plays a game, he can learn something new, and improve his performance. He must accomplish one thing after another, incrementally.

We see examples of this through the characters in Ready Player One. This is a skill needed to learn math as well.

Another terrific source for reading about the benefits of gaming and summaries of some of the research is the website MindShift. The site has a number of articles focused on video games and the positive applications in learning.

Building Math Esteem

Video games definitely help our students get motivated - students love gaming, even if they learn while doing it! We are meeting them on their turf, using their world to interact, and using fun to build their cognitive strength.

That gives students confidence - and THAT builds their Math Esteem! And that’s what it’s all about!

]]>So, this week, I’d like to share with you one of my past lessons about Type of Numbers. Who knew numbers had types, right? LOL! :) Well, you teachers did, but for the kids we teach, this concept can be confusing.

Classifying Numbers

There are two main types of numbers I talked about in my lesson, but all of these numbers are part of the real numbers.Incorporating math into everyday things kids love is a great way to keep their attention and interest. The goal here is to change the “I stink at math” mindset that discourages and sets back so many bright students.

In the real numbers, you have rational numbers, and you have irrational numbers. I represented the rational numbers by using Iron Man, and I represented the irrational numbers by usng Captain America. There were some cool superhero nesting dolls that I used as a fun way to get the kids engaged. I have provided a link at the bottom of this blog if you’d like to purchase them for your classroom. Also, if you’re not familiar with the Marvel Universe characters, here’s a quick cheat sheet you might find helpful.

The reason I chose Iron Man is not just because I am a Marvel fan, but because after watching the movie, Captain America Civil War, I personally believed that Iron Man was rational in his decisions and Captain America was irrational in his decisions. A discussion on the definitions of “rational” and “irrational” would be a great start here for kids who aren’t yet familiar with these words.

Rational Numbers

Let's start with the rational Iron Man. So, rational numbers contain integers, represented by War Machine, and the whole numbers, represented by Black Panther. The counting numbers, or natural numbers, represented by Black Widow, and my example number was the number 1 represented by Vision.

I chose the number 1 as it is has positive connotations for most kids. Everybody wants to be number 1! All of these dolls fit inside of the other, which visually demonstrated how each set of numbers were connected together.

The counting numbers start with 1. Remind your students that when they’re counting, they don't usually start with zero. If they’re playing hide and seek, they don't count “0, 1, 2…” They start at 1. But if you want to include 0, it now becomes a whole number. Inside of the whole numbers doll are the counting numbers and zero. So, counting numbers do not have zero but the whole numbers do.

The whole numbers are zero plus the counting numbers. Next, we have the integers. The integers are the positive numbers, like the counting numbers, and they’re the negative numbers and zero. The whole numbers doll fits inside of the integers doll but it also includes the negative numbers. So, inside of the integers doll are the whole numbers plus the negative numbers.

Finally, we're dealing with rational numbers as an entire group. The integers doll fits inside of the rational numbers doll. All of these numbers are rational, but they also include fractions and decimals that end and repeat. Your kids will likely ask “what do you mean by that?” and sort of glaze over.

Here’s how I explained it:

The integers do fit inside the rational numbers, but they also include fractions like 4/5 or 1/3. All those fractions are considered to be rational because those fractions end or they also might repeat.

The next likely question might be “what do we mean by end? Well 3/4 is .75 and it's done! it ends. But, 1/3 is .333333 (forever!). It doesn't end, but the same number repeats over and over again. But, that's still okay to be a rational number. Any number that can be written as a fraction is rational and is part of Iron Man's team!

Irrational Numbers

Next, I talked about the irrational people. Captain America - he's an irrational number in this example. These dolls stay separate from each other and do not nest together. They're not a part of the same team as Iron Man (so sad!). Instead, the dolls illustrate examples of irrational numbers.

This is a great place to introducepi. I like to start with the fact that the most famous irrational number is pi (not pie - although that would be awesome too!) represented here by the Winter Soldier. So, pi would be considered to be irrational because it never ends. In fact, it's famous for never ending. All the numbers are different and they do not repeat. They are non-terminating because they don’t end.

Next, non-terminating decimals, represented byThe Falcon, show numbers that do not end or repeat are irrational. Other examples I used for irrational numbers were the square root of 3 (orHawkeye) and the square root of 2 (Ant Man). You can have your students put them in a calculator to see that they never end and they also never repeat! If you notice in my video below, I made sure our irrational superheroes were all separated from each other. They were not nested because one doesn’t fit into the other like our Iron Man rational number team does. It’s kind of irrational, just like they are! But, rational numbers and irrational numbers all make up the Real Number Universe just like the superheroes make up the Marvel Universe!

Check out these notes that one of my students created based on the video:

I love making and finding fun video lessons for my students. It is a great tool forflipped classrooms, but that is for another blog.:) But you gotta do whatever you can to promotemathesteemin your class!! If you’d like to purchase the superhero nesting dolls I used in my video, you can buy them fromAmazon. They are “super” fun (see what I did there? ;).

]]>Geometry can be a daunting subject for many students. Imagining shapes and figures and how they fit together in the physical world can be a tough thing to grasp. But if we can make it more concrete and help students wrap their hands, as well as their eyes, around it...we can help make geometry lessons easier to understand. We can help students actually enjoy and look forward to learning!

The hit movie, A Wrinkle in Time, based on the book of the same name by Madeleine L’Engle, has kids of all ages jazzed. The story has elements of family, love, friendship, mystery, danger, and even the fight against evil. All of those are wrapped up in a plot of science, technology, and a bit of the supernatural.

Travel Through Dimensions by Wrinkling Time

The book and the movie, Wrinkle in Time, has a bit of something for everyone! No wonder it’s such a long-standing favorite. The story takes our heroes into a world of travel outside of time and space, through a tesseract. Using a tesseract, the kids in the story are able to “wrinkling time”. They can travel through space without having to go the long way around. They can jump into the fifth dimension via the tesseract and travel through dimensions, visiting planets and accomplishing their missions.

And that’s why it is a fantastic theme for this math lesson:

calculating surface area and volume of 2D and 3D figures,

and changing dimensions using the calculations. Geometric shapes are full of dimension. A line is one-dimensional, a plane is two-dimensional, and a solid figure is three-dimensional. The fourth dimension is an extension of three dimensional object. It’s almost like cubing a cube but it is the dimension that some say would aid in time travel. This is why a tesseract is considered to be in the fourth dimension. Thus, the fourth dimension is referred to as the transition to the fifth dimension. So you see, the idea of traveling anywhere in time and space is based in math!The Lesson Plan

First, as a class we reviewed formulas for figuring perimeter, circumference, and area for 2-dimensional shapes. Then we reviewed the surface area and volume formulas 3-dimensional shapes. For example, I demonstrated how a 2-dimensional net consisting of 6 squares can be turned into a 3-dimensional cube, then we found the surface area and volume of the cube as a class.

To determine how much information the students retained, we worked through a group of activities. In the first activity, the students played a matching game electronically comparing 3D figures with their 2D nets. Next, the students worked in groups to hand draw the 3D shapes based on their 2D nets. Lastly, the students worked on problems determining the perimeter and area of 2D nets and then traveled to the third-dimension find the surface area and volume of 3D shapes.

After working through the calculations, the students got the chance to build their very own tesseract: the four-dimensional analogue of the cube. My students and I loved this part of the lesson most of all. They got to work as a team to conceptually visualize a tesseract and how to construct it. Team building is also one of the many themes from A Wrinkle in Time. To conclude the activity, the students found the surface area and volume of their own life-size tesseracts.

I hope you and your students have as much fun as we did learning about these shapes and building our tesseracts! Nothing is more thrilling than seeing students experiencing math, and then turning their knowledge into something fabulous! I always reach for more ways to motivate students, and help them build their confidence in math...so they can keep learning and grow Math Esteem even further!

Resources

Here are a variety of helpful and supportive videos you may also want to check out:

]]>Explaining math concepts with holograms & super heroes - Does it get more exciting than that?

That’s exactly what made this lesson on the concepts of holograms, scale factor, and the Pythagorean theorem so much fun!

The Black Panther was a hit movie this year, and it’s not a surprise. Movie goers loved all of the cool technology, fast-paced action, and awesome special effects! All of that fun wrapped up into a Marvel comic storyline, filled with mythological heroes and villains, made for a super-fun-filled, hands-on, kinesthetic math adventure!

As you’ll see in the video that explains the structure of the lesson plan, we studied several main ideas:

● Scale factor, the four transformations including translation, reflection, rotation, and dilation.

● Holograms, how they are made and how they work.

● Prisms, using the Pythagorean theorem to create trapezoids to create the “hologram” images.

The Story and the Tech

One of the amazing pieces of technology in Black Panther is the use of the Kimoyo Beads, a super-advanced communication tech that Wakanda developed. If you haven’t seen the movie yet, Wakandans is the home of Black Panther, king of the Wakandans. They use the Kimoyo Beads to carry the medical history of the wearer. The communication bead acts sort of like their mobile phones to talk to another Kimoyo Bead wearer. Another separate bead provides access to the Wakandan database through a holographic display. Those beads can be used to receive broadcasts, and those holographic images can be sized and used from large, projection screen-sized images to smaller, personal-use sized images.

These Kimoyo Beads and their tech formed the basis of this lesson.Scale Factor

The students learned all about scale factor, and we used a terrific video and comic book available on www.mathsnacks.com called Scale Ella. I had the students practice all of the lessons learned about scale factor and its effect on the coordinate plane using several activities throughout my .

Holograms

Our study of holograms centered around the cool tech that our heroes in Black Panther used to communicate. The kimoyo bead scaled down the hologram of the person sending a message. We talked about how holograms are made and how they could be hypothetically used to communicate like that.

What is a hologram exactly?

“Holography is a highly-specialized and technical photographic process. It allows one to record the light scattered by an object as it is subjected to a laser beam. The recording can then be presented in a form, known as a hologram, which makes it appear three-dimensional.” (https://wonderopolis.org/wonder/how-are-holograms-made)

Several videos are available on YouTube that explain holograms and how they work, so the students watched videos and discussed what they were learning.

Creating the Prisms and the Hologram:

We were ready to work towards the anticipated final activity: making our prisms and watching our holograms come to life! Now, we could not make true holograms with just an ipad, but we could create a "hologram-like" image to view in class.

After the kids scaled their images in Activity 1 and Activity 2 from the lesson plan, they were rewarded with being armed with everything they needed to create their own holograms! They worked through the process of created a clear bottomless trapezoidal prism. These prisms scaled to the correct scale factor were used to project the "hologram-like" images on ipad. This was Activity 3 from the lesson plan.

You can find several videos on YouTube by searching the term “hologram video.”

Using Math to Mimic Art

How exhilarating, to see the floating holograms, walking around, looking back at us, seemingly coming alive! What an accomplishment, and what a positive reinforcement for all of the learning and math that we did on this lesson!

This lesson was a hands-on and fun way to learn standards-based mathematics. My students related to the material and wanted to learn more for complete understanding.

As always, we are striving for lessons that keep students interested and motivated daily. And as I've talked about in other blogs, keeping students interested leads to retention, and ultimately success! Math success leads to students having a great math esteem, which then helps them continue to destroy any math anxiety!

And to me, that worth more than anything else!

]]>If Kinesthetic learning is based on creativity, then Math is a natural pairing!

Kinesthetic learning and Math go together like peanut butter and jelly. However, in most classrooms or in most settings you will come across children and adults alike who say: “Math is hard”, “Math is boring”, “I just don’t get math”. Maybe part of the reason for that is because educators are not adding their peanut butter (kinesthetics) to their jelly (math). Without the peanut butter, all you have is jelly on a slice of bread, and who wants to get just a jelly sandwich?!

Kinesthetic teachers are the movers and shakers of education!

Have you ever watched a presentation where the speaker is just standing behind a podium talking in a monotone voice? It is not fun and it is hard to pay attention to the information being given. In contrast, have you ever watched a keynote where the speaker is up moving around the room getting everyone involved in what they are saying. It is electric and the fun energy becomes contagious around the room! Math teachers should use movement, action, and excitement to make their lessons more engaging. Let's encourage student retention by using activities during instruction that make learning fun! Kinesthetic Learning is one of the three different learning styles popularized by Neil D. Fleming. A kinesthetic learner needs to be actively doing something while learning to comprehend the materials. Kinesthetic learners often struggle during classroom time due to sedentary structured learning, i.e. lectures, because the learner’s body does not compute that they are actually doing something when the student is listening. Generally, these learners need to get up and move to truly learn and understand.

It has been scientifically proven that incorporating kinesthetics into structured learning creates a better learning environment. We as educators should be adding exciting and fun methods that get our students up and moving! So why aren’t there more educators out there incorporating kinesthetics with math?!

Kinesthetic Learners Need to Move!

1. They wiggle, tap, swing their legs, bounce, and often just can’t seem to sit still. They learn through their bodies and their sense of touch.

2. They have excellent “physical” memory – they learn quickly and permanently what they DO as they are learning.

3. Kinesthetic Leaners are often gifted in athletics, dancing, and other physical activities.

4. They are generally very coordinated and have an excellent sense of their body in space and of body timing. They have great hand-eye coordination and quick reactions.

Incorporating Kinesthetic Learning Strategies for Educators

Students who learn kinesthetically are usually labeled restless, problematic, or hyper, simply because their bodies need to be in action in order to learn. For teachers, this can be difficult to manage without classroom disruption during a lecture. So, here are some strategies for teachers to help create a kinesthetic learning environment in the classroom.

Offer various methods of instruction – lectures, paired readings, group work, experiments, projects, plays, etc., so you'll keep the kinesthetic learners surprised and still be able to deal with the days you want to present material in a straight-forward manner.Incorporate kinesthetic activities during lecture time. Use cards, computer activities, dice, marbles, dominoes, fake money and coins for computation of units, physical clocks for telling time. Use anything that can transform abstract math concepts into concrete math activities.Engage students to perform movement tasks during lectures such as writing on desk to take notes, using songs and chants to remember key points, make certain hand signs and gestures to connect to key vocabulary words, or even rearranging desk locations.

In my last blog post, I discussed how to incorporate non-computational real-world connections into a learning environment for Math. Most of the ideas I discussed are perfect examples of kinesthetic learning involving Math such as: cooking, art, driving, music, and sports.

References:

https://www.thoughtco.com/the-kinesthetic-learning-style-3212046

https://sciencing.com/math-activities-kinesthetic-learners-12179525.html

https://www.edutopia.org/blog/kinesthetic-learning-new-model-education-kirin-sinha

https://child1st.com/blogs/resources/113559047-16-characteristics-of-kinesthetic-and-tactile-learners

]]>Can you believe that to some math is considered to be a subject needed only to graduate???

To these people, math is never to be used again after school is finished. This limited view destroys one’s math esteem. I hear this point a view from several adults that I encounter and I pray that this thinking is not passed on to students. So, I try to focus on ways to boost math esteem on a regular basis. I especially like to use non-computational approaches more than just going to the store or telling time.

Incorporate “non-computational” real world connections by showing others how math is used in life on a consistent basis.

Math is used in art

. Art is probably not the first thing you’d think of that contains math but art production involves the use of angles and symmetry. Whenever I walk through an art exhibit hall, all I see is an explosion of Geometry! In fact, I love collaborating with visual artists to showcase the connection between math and art in my classroom. In my Art in Math project, my students walked through the Atlanta BeltLine looking for joined shapes in street graffiti and determined the combined area and perimeter of the composite shape.

Math is used in music. In music, the rhythm danced to is a pattern of beats and the pitch is the frequency of vibration. Fractional notes help determine the tempo. In fact Pythagoras, known as the father of math, classified math based on a hierarchy of dimensions starting with arithmetic and ending with music. In my Math in music project, students learn how to create their own beats using fraction addition and time signature.

Math is used in sports. Math is used when computing the statistics sports enthusiasts so love. It is used when figuring out the probability on which team will win a series. The NBA Draft Lottery uses combinations and factorials. You can even compute the velocity at a certain angle that a player must shoot a ball so that the basket is made. With the help of the quadratic formula, a player can determine the perfect arc to angle a basketball into a hoop for a free-throw shot.

Math is used in cooking. Eating is something everyone does, especially when the meal is delicious. Part of what makes that cake so yummy or that meal taste so well is based on mathematics. Math is used in being able to convert from cups to ounces using multiplication and division, adjusting the ratios on whether you need to feed more or less people, and measuring the ingredients in the proper proportions so that the meal tastes well. This year for Halloween my students learned how to make a circular piecrust of a specific diameter to be used as the bottom and top of their dessert.

Math is used when driving. Driving, something we all look forward to, involves being able to make calculations in timing and speed. It involves being aware of the miles per gallon of gasoline. Being able to calculate how much gasoline you will need for the distance you are going so you don’t run out of gas and arrive at your destination safely. When I took my students to Lego world, the class was split into teams tasked with creating their own racing cars. Each team worked hard to determined the best mathematical design to build the fastest car. Factors included air resistance, weight, and dimension.

These are just a few examples of the ways math is used every day.

The list can go on and on, from budgeting, to decorating to gardening to building houses to do-it-yourself tasks around the home. Teaching students by applying math to real world circumstances causes math to become concrete, better understood, and there by boosts student’s math esteem. So, the next time you walk through the park or look at your cell phone GPS, think of ways that you can discuss the math you see with others around you!

]]>We are always looking for new ways to engage students and keep them interested in learning.

Generation Z learners (a/k/a Millennials) have been born into the digital age. Because of this, they want to actively participate, share, and learn from each other in- and out-side of the classroom. These young people are tapped into the world in an entirely different way. They want to be an integral part of the process - to know that what they are learning and sharing is in part, created by them.

Merging technology into instruction directly is a great way to appeal to and engage these students! Playing web games and using apps are just a couple of fun ways to engage students. Let's elevate it and infuse our lessons with technology! From my personal experience, the best program to use for an immersive technology experience is ClassFlow.

I find that using ClassFlow takes away some of my students’ math anxiety because it creates a safe space for effort.

Math anxiety is built on the fear of constantly being wrong. Even though research has shown that mistakes are good things because they make your brain grow, the fear of being incorrect can shut students down and prevent them from even trying.

When I use ClassFlow during class, I can send questions, images, and videos to my students and get instant feedback. In fact, all of my students’ responses are sent to my board in real-time and from there, I can select any of them to investigate further with the class.

The best part for students is that it hides the students' names so the class doesn't know who sent what question or gave what answer. This anonymity creates a safe space for discussions about everyone’s thinking process. This allows the class several opportunities: to see multiple representations; we can use error analysis without calling anyone out; students learn from each other; and classroom culture becomes supportive versus combative or accusatory. In addition to the students' benefits, there are benefits for the teacher! For instance, all of the data captured during instruction is saved in my account so I can review it later and find more ways to better serve each learner.

My students and I bleed #ClassFlowLove! I encourage each of us to find new ways to integrate technology in the classroom - boost #MathEsteem by meeting your students where they are!

]]>When you walk into a foreign language class for the first time, most likely, you are not fluent in that language. After the first week, you may only know a few phrases and vocabulary words. The ability to read and speak that language is built over time by practicing - hearing, writing, conversing - using the new information in a variety of ways. No one expects to go from new learner to translator overnight, or even in a year.

Why then, don't we treat learning math the same way?

Math is expected to be mastered the day, week, or year after being introduced to a concept. Typically, it is not allowed to be developed over time because many do not consider it to be a language. But, I’ll let you in on a little known secret:

math is a language

, it is not solely computation. In fact, computation is only one small part at mathematics. And once you can “speak math" you can problem solve in any situation.If we truly want students to understand the language of math, it starts with the teaching and learning of math vocabulary. Students must be able to "use their words" when working to comprehend mathematics. The majority of students are unaware of this and end up treating math as a purely computational subject. They spend time trying to memorize equations, routines, and methods of problem solving - the "what" - instead of using the language of math to understand the “why.”

Once students know and believe that math is a way of communicating relationships and structure, they can make connections that lead to real, long-term, conceptual understanding. I always say “If you can speak math, then you can do math.” The language of math should not be considered foreign.

]]>“I can’t do math.”

“I hate math because I can never get it right.”

“You better pay attention in class and take good notes, because I can’t even help you with this math homework.”

“Wow, you’re a math teacher? Whew, thank goodness for ya! I could never do math.”

As a math teacher, there is nothing more disheartening than hearing these feelings about math. When students hear this (especially from adults) they begin to think, “It’s okay if I don’t try, no one else can do this either" and it lessens the importance of learning math over time.

During the summer of 2016, I read Mathematical Mindsets by Jo Boaler. It confirmed my belief of how one’s mental approach to math dramatically affects one's performance. Several studies have been conducted about mindset in relation to mathematical achievement. Results were dramatic in showing that academic achievement increased as students worked on developingpositivemindsets in math (Blackwell et al. 2007).

It was this research that inspired me to create a youth math camp designed to focus primarily on building the math esteem of each student. The plan: to dissolve fixed mindset thinking, develop growth mindsets,and create an excitement for learning math.

The goal: to help change the way people think about math.

From “I can’t do math."

To “ I can do math but I prefer some math topics over others.”

From “I hate math because I can never get it right.”

To “I can always improve. I’ll keep trying to work with math.”

From “You better pay close attention in class and take good notes, because I can’t even help you with this math homework.”

To “When you work on your homework, write down specific questions you have. Then, review your notes and see what strategies or approaches you can take to solve the problems.”

From“Wow, you’re a math teacher? Whew, thank goodness for ya! I could never do math.”

To “You're a math teacher? Wow, cool! I respect that!”

Changing our perceptions of math as a society is critical to #MathEsteem. People are so comfortable openly "hating" certain subjects without realizing the affect it has on the youth.

Campaigns like With Math I Canflood my timeline and I am overjoyed! With programs like this and more government funding going into math programs, we are making strides in changing the perception of math.

But even more than exposure to math, we have to implement programs to address "mathitude" -- the math growth mindset -- for everyone, not just those interested in STEM. Similar to slogans like Reading is Fundamental or The More You Know, the program could be called: Critical Thinking Makes Me Grow or The More You Problem Solve. Okay- lol, those examples are awful. But you get the idea. 😉

#MathEsteem #ItsALifestyle #DJMath

Suggestions? Please leave them in the comment section below. Want more information about my future math esteem camps? Subscribe to the mailing list by filling out the box on the bottom of the home page.

Boaler, J. (2015). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. San Francisco, CA: Jossey-Bass.

Dweck, C. (2006). Mindset: The new psychology of success. Random House.

Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child development, 78(1), 246-263.

]]>