# MAT Blog

YouTube is pretty awesome. YouTube videos have helped us fumble our way through countless tasks from how to build a staircase and put up drywall, to how to cook the perfect steak and make sushi. It has also helped us in the classroom when we needed to show our math students something rather than tell them about it.

While there are lots of useful math tutorials on YouTube, there’s also just as much rubbish, which makes sorting out the good stuff tedious and time consuming.

This morning we made an exciting new discovery—a video tutorial website called ThatTutorGuy. It’s run by a Stanford University graduate named Chris who is well-versed in anything from pre-algebra and analysis to trig, pre-calculus and physics. After watching several of his tutorials, we assure you that he’s the real deal.

While you will find several free videos on his site, you’ll have to become a subscriber to access all of them. For \$30 a month you’ll get 24/7 access to all the videos in all the classes on the site, to watch in whatever order you want, as many times as you want. As new classes are added, you'll get access to those as well.

If you’d like to try before you completely buy, Chris offers a seven-days-for-\$7 trial. There’s also a discounted, six-month plan for \$97 (that’s 46 percent off the regular subscription price).

To give you a sense for what his algebra tutorials are like, check out the video below.

“When will I ever use this?” It’s one of the most common questions math teachers hear from students. While there are lots of ways we can respond to this question, we believe the best answer comes from showing, rather than telling, our students why math is relevant to their lives.

Yummy Math is a web resource that will help you do this. All of the activities you’ll find on the site use real-world problems and scenarios that are not only familiar and engaging to students, but require them to use math to solve them.

Everything you’ll find on Yummy Math corresponds with the National Council of Teachers of Mathematics Process (NCTM) Standards and the Common Core State Standards (CCSS) for Mathematical Practice. Yummy Math is also in the process of adding CCSS correlation to every activity on the site. New lessons are added a few times a week and all of them are completely free.

Here are two examples of the types of activities you’ll find on the site:

Boorito
For Halloween 2013 Chipotle (a fast-casual Mexican restaurant chain) is offering \$3 burritos to any customer that comes in dressed in their Halloween costume after 4 p.m. Even better, Chipotle will donate up to one million dollars of the proceeds from the \$3 items to the Chipotle Cultivate Foundation. This foundation is dedicated to creating a sustainable, healthful, equitable food future.

• I wonder how likely it is that Chipotle will be able raise one million dollars in one evening? Take a couple minutes, first individually and then with a partner, to think about whether this goal is even reasonable? Write some of your observations and thoughts below.

•What information would be helpful to know in order to figure out the probability of Chipotle reaching their goal? Record your thoughts below.

Can you imagine sailing off to the West, into an empty looking ocean, to find what your captain believes is a good route to the Indian subcontinent?  This was a pretty risky navigational feat. Luckily the ships experienced good weather on their trip to the Caribbean.

These are only two amongst dozens of math activities you’ll find on Yummy Math, so be sure to stop by and browse their resource library.

Earlier this week, we shared a zombie-themed writing activity with you and we’re happy to say that there are more zombies where that came from. This morning we came across STEM Behind Hollywood, a cool new resource put together by Texas Instruments.

Here you’ll find three free, Hollywood-inspired math and science activities that model the transmission of a hypothetical zombie contagion.

These activities encourage students to engage with STEM concepts like the exponential growth of a zombie horde and how the growth turns into a characteristic “s” curve from limited resources as the infection begins to spread. Students will learn or review the basic functions of various parts of the human brain and discuss factors dealing with immunity and vaccines.

Unless you can recreate the activities on your own, you’ll need to download the TI-Nspire trial software; the good news is that it’s compatible with iPads and other Texas Instrument hardware like the TI-Nspire.

Websites housing worksheets tailored to meet the Common Core are a dime a dozen, but few—if any—are as comprehensive as CommonCoreSheets.com. Here you will find free downloadable PDFs for math, social studies, science and language arts. Each worksheet comes in 10 different versions. Preview each version or download all of them in one fell swoop.

What we particularly love about the PDFs we find on CommonCoreSheets is that there is an answer column on almost all of the worksheets, which makes grading quicker. And because of the convenient formatting, you can actually grade several papers at once.

Put away your calculator or sliding scale and simply refer to the built-in scoring rubrics on the bottom of each sheet.

What’s the catch? There isn’t one. Everything on CommonCoreSheets is completely free, no registration required.

In school, we depend on language to convey ideas. The teacher walks up to the board, writes words, uses words to ask and answer questions; the students receive books with words and are assessed with tests using—you got it—words. Even when it comes to assessing math literacy, we depend on words. This dependence on language is precisely what TED Talks speaker Matthew Peterson—Chief Technical Officer and Senior Scientist at the MIND Research Institute—addresses in his eight-minute lecture, Teaching Without Words. Sounds crazy, doesn’t it?

Words, words, words…do we need them to teach math literacy?

Interrogating our dependence on language starts to make sense, however, when we consider states like California where 25 percent of students are English language learners, 15 percent have language learning difficulties and 20 percent fail language comprehension tests. Is Peterson suggesting that reading proficiency is not a priority? Not at all. He is simply suggesting that it may be necessary to find new ways to teach students for whom language is still a barrier. He’s also suggesting that we may not need language to teach math literacy.

In addition to watching his brief lecture (which you’ll find below), we recommend stopping by MIND Research Institute’s website to learn more about Peterson’s spatial-temporal approach to teaching K-5 mathematics. The software he and his team have designed to teach math literacy does not use language, numbers or symbols; instead, it teaches students to visualize and focus on interactive problem solving.

It’s curious that math and art have traditionally been placed on opposite sides of the spectrum, especially when you consider that they share many common features. Artists, like mathematicians, are problem solvers; they know how to improvise with raw materials, and look at their environment and their world in new and innovative ways. Both must be able to communicate, collaborate, think critically and approach their palate from perspectives other than their own. That’s why we are so stuck on arts integration—that is, bringing math into the art classroom and art into the math classroom.

Last week, we shared two of our favorite arts integration activities from Caren Holtzman and Lynn Susholtz’ book Object Lessons: Teaching Math through Visual Arts. Readers were enthusiastic about it, so we’re sharing one more lesson plan with you:

Arts Integration in the Elementary Math Classroom: Venn Sihlouettes
This activity is called Venn Silhouettes and, as you may have guessed from the title, it asks students to work with a Venn diagram and a silhouette. This could work for older students, but it is most appropriate for grades 3-5.

Here’s what you’ll need to get started: An overhead projector, markers, colored pencils or crayons, large white paper and tape.

Before you begin the activity, your students should be familiar with the following vocabulary words: Venn diagram, silhouette, overlap, same, different, compare, contrast, survey, graph, certain, equally likely, unlikely, impossible, profile.

Once you’ve familiarized your students with these vocabulary words, pair them up in groups of two. Have them tape their piece of paper to the wall opposite the projector; then have them take turns tracing each other’s silhouette on the same sheet of paper. If you look at the picture to the right, you’ll see that the silhouettes overlap but are facing opposite directions.

Next, have your students discuss things they have in common and things that make them unique from each other. Their task is to use colored pencils to either draw or use words to illustrate what makes them unique in the sections of their faces that do not overlap. After this, they should use the markers to write or illustrate those things they share in common.

Once they are finished, it’s up to you to decide where you want to take the activity. If it is still early in the school year, this is a great ice-breaker; it’s also a great way to spruce up your walls and create a student gallery.

Should you choose to create a student gallery, you can build on the activity by having your students conduct a “gallery walk” where they garner ideas and think about new things they could add to their own silhouettes. This activity is useful for triggering what Holtzman and Susholtz call “I wonder” questions: “Does John have a younger sister like I do? How long did Kelly live in Germany and why?” This will prompt students to interact and communicate with one another to find answers to their questions.

If you want to take the activity further, ask your students to collect data from the entire class; they can convert their findings to percentages and create graphs.

If you are like most educators, you’re on the prowl for new ways to engage your students. That's why Marygrove's Master in the Art of Teaching program continues to add  free downloadable guides to our website. If you find our resources to be helpful, you should know that this is only a small portion of the forward-thinking career and professional development ideas you’ll encounter at Marygrove College.

Mathematics is a high-stakes subject, especially in light of recent educational initiatives like "Race to the Top" and "Educate to Innovate.” High stakes, however, doesn’t mean that math can’t be fun—or creative, for the matter. In fact, we might even argue that if math students aren’t taught to be creative, they may be unprepared to meet 21st century challenges.

Think about it: Your students’ future isn’t static. Regardless of their future profession, life will demand that they have a diverse skill set. The math-savvy artist, for example, is (most likely) going to have more opportunities than someone whose knowledge stops with their own palette. A rapidly-changing, global economy needs not only solution-oriented, but creative thinkers with a range of experiences and interests.

That’s why we’d like to talk about math and arts integration and offer 2 creative lesson plan ideas that will help you (and your elementary students) take two seemingly disparate subjects (math and art) and fuse them together without having to compromise rigor for good times.

Fac(e)ing Mathematics through arts integration
The human face is a perfect place to begin. Why? For Caren Holtzman and Lynn Susholtz—authors of Object Lessons: Teaching Math through Visual Arts—it’s simply because the face has it all: number, measurement, size, shape, symmetry, ratio and proportion. When you apply these concepts to the body, you not only give your students a new lens through which to view themselves, but you help them to also approach math in a new and exciting way.

Activity 1: Lessons in Symmetry
This activity teaches students to create two-dimensional symmetrical images by giving them a portrait that only has one side of the face and asking them to complete the other half. You can either find a picture online or, if you are tech-savvy, scan and edit a photo of the student. If you have Photoshop, you can simply erase one side of the face, print it out and make photocopies for each student. If you don’t have access to photo editing software, print out the photo, cut in half vertically, place on a blank piece of paper, and make as many photocopies as you need.

Lesson Objectives
The goal of this activity is to help students analyze the geometric attributes and congruence of the face. An added bonus is that it also forces them to use their spatial sense to identify and recreate the symmetrically-balanced features that are missing. Once they are finished, you’ll find another teachable moment by asking students to consider issues of symmetry, proportion, measurement and perspective.

Vocabulary
Symmetrical, congruent, balance, bilateral

Activity 2: Polygon Portraits
This is another activity that uses the human face. This time, however, students will use geometry to compare the attributes of two-dimensional shapes; they will also have to see how those shapes can be taken apart and realigned to create new shapes.

Vocabulary
Curved, straight, edge, polygon, regular, irregular, congruent, vertex, vertices, angle, plane

Here’s what you do:

• Define and compile a list of polygon shapes by drawing them out on the board. As you do this, have your students describe the attributes of each shape.
• To supplement this activity, you might show your students pictures of Pablo Picasso’s cubist portraits. Compare his work to more conventional portraits and have your students talk about the similarities and differences between the two. Ask them what the like/dislike about Picasso’s work and why.

• Next, hand out mirrors to each student and have them draw self-portraits in either black charcoal or pencil using only polygons.
• Once they’ve done this, have your students describe their portraits using their newly acquired vocabulary.

• There are innumerable spins you could put on this activity. For instance, you could limit the number of shapes your students can use—or you could require that each shape be a different color of pastel, charcoal or colored pencil. If you prefer, you could also have your students cut these shapes out of construction paper instead of drawing them.

• If you want to challenge your students, ask them to use a set amount of polygons. For example, tell them that they have to use six triangles, 4 decagons, 5 octagons, 2 quadrilaterals, etc.

If you like these lesson-plan ideas, check out Caren Holtzman and Lynn Susholtz’ book Object Lessons: Teaching Math through Visual Arts; this is only the tip of the iceberg.

Math games for teachers are a fun way to entertain your mathematical geniuses and inspire the students who are lagging behind. If you're looking for new ways to inspire your students to find the joy in fractions, decimals, and algebraic equations - look no further. Here are 10 FREE math games that can help you reinforce your current lesson plans, allow your students some computer time, and give them a break - of sorts.

10 Free Math Games for Teachers

1. Add Like Mad. This game gives students a target number and a huge board of number tiles. Students have to click the numbers in order to Add Like Mad until the numbers they have selected add up to the target number.

2. Aquarium Fish. Little ones will enjoy this counting game. Count the Aquarium Fish and select the number that reflects the accurate total. At the end of the game, the computer tells you how many attempts it took to get the answer right, which can be a helpful assessment for teachers.

3. Math Man. The game Math Man is based on Pac Man. Need we say more? First Math Man has to eat the ?, then he has to eat the ghost that solves the math equation. You can use it to reinforce multiplication, division, and rounding numbers.

4. Digit Drop. Students practice addition, subtraction, multiplication, and/or division in Digit Drop. Simply drop the correct number from a big number batch to finish the equation. Students can practice, play, and select their level.

5. Calc. Students do the calculation in their heads and type the correct answer. The better they do, the faster and harder it gets. Your geniuses can even start at the "genius" level.

6. Counting Money. This is one of the best games for teaching students how to count money, make change, and do money-based word problems. Money Counting Basic states a specific dollar amount and students click on the money drawer to put the appropriate amount of change in the "hand."

7. Genius Defender. Holy moly. Where was Genius Defender when we were learning to add and subtract decimals? Cute little men and women defend their fort as the "invaders" - holding decimal problems - mount an attack. When students type in the correct answer to an attacker's decimal problem, the defenders eliminate him. The goal is to answer all equation attackers accurately before they invade the fort. It's addictive.

8. WMD2. Weapons of Maths Destruction involves shooting targets and tanks to receive a math equation. Easy equations deal with simple addition and subtraction skills. Harder ones move into the algebraic realm.

9. More or Less? Help students make comparisons by determining whether there are More or Less of certain objects in the squares. By selecting the least populated, most populated, or evenly populated squares, students learn to compare quantities.

10. Space Match Geo. Space Match Geo is great for beginning geometry students, helping them learn lines, rays, acute angles, etc. by playing a memory game. They flip over the icons to reveal a shape or a vocabulary term and have to match them appropriately.

These 10 math games for teachers are just a sampling of all that MathNook has to offer. They can be used to reward students who are doing well, as a fun way to work with students who are struggling with certain concepts, or as a Friday Fun Day. However, we do recommend that students use head phones so you can remain sane during the learning process.

Math is the perfect time to reinvent the wheel. Children in elementary school should be given every opportunity to explore mathematical concepts with manipulatives, pictures, and other visuals so that they have a firm grasp of a concept before leaping into the memorization of an algorithm.

Many times, students figure out what they need to do to solve an equation before an adult needs to step in and tell them. Especially when students have difficulty with math, they need to be able to see what is happening. Once they do, they are less likely to make an error in the process because they can reason through the problem if they get stuck.

Just telling your children that they are “moving over 10” when regrouping in subtraction is probably not enough information; they need to actually see the base 10 blocks being traded in. It is all the better if your learners have the chance to break the blocks apart themselves. Keeping them active during the lesson not only keeps them focused, but deepens their understanding.

Here is one of my favorite ways to engage children in math with multiplication facts:

Two, five, and 10 multiplication facts are usually the first facts memorized. I want the children to see that by memorizing three sets of facts, they can quickly learn the rest. My students arrange single-colored manipulatives (base-ten cubes, poker chips, etc.) and create arrays of a given multiplication fact (let’s say 3x2).

Next, my students place another 3x2 array right next to the first, but in a different color. Now they have 3x4.  After a couple of examples, the children begin to see that when the array is doubled, the product is also doubled. They now have doubled the number of facts they know, and will know the four-facts and eight-facts.

We practice a similar method while learning the three-facts. When the children are learning 3x6, I have them build an array of 3x5, a fact they should know. Then they just add on one more group of three.  Rather than memorizing an entire list of multiples, they can quickly figure the five-fact and add one more group to get the six-fact. Of course, eventually quick recall of facts is necessary, but early on, helping your students see these patterns is crucial to developing a strong math foundation.

Math is fun to teach and should be fun to learn. Math instruction should not be a time for memorization of processes without first giving ample opportunity to try out the concepts on their own. Eventually, yes, children need to buckle down and rehearse algorithms, but not on day one! Give your students a chance to see the interrelation of numbers and they will learn to love math.

-Patricia Guest, M.Ed