Thinking Outside Traditional Presentations.

The other night on my way home, I got to thinking about ways to explore transitioning from one topic to another in Math.  In other words, what are some ways students can present information showing how things are related.  For instance, I now have a textbook that actually discussed congruent shapes are just a pre-image and the image after being transformed while similar shapes have undergone some sort of dilation.

So think about having students create animation showing this concept using shapes with a voice over to explain or throw in sound effects with text the transitions in and out instead of a voice over.    This could be used as a final project for the section on geometric transformations.

For a real life application of geometric transformations, one might have students work in groups to produce the blueprint of a housing development with streets, houses that are flipped over a street, or along the fence lines.  Some are translated along the streets.  Most housing developments have a set number of basic floor plans buyers get to choose from.

Present the students with the challenge of explaining how substitution method is similar to composition of functions or explaining how dilations are responsible for similar shapes in 30 seconds via flip grid, animate, or other video program.  30 seconds may not sound like much but for students who dislike talking, that amount of time is going to be longer than they like but it is doable.

Another possibility is giving students a set number of slides in google slides or other presentation tool to explain a concept.  The idea is that they create this presentation so each slide remains up before moving to the next one within a set time limit.  Each slide has it's own picture and the person provides the talk to accompany the slides which for math means a quick explanation.

I keep thinking about having students create short commercials where they "sell"a concept like how to show visually prime numbers so people understand why there are only two factors, or how distributive property works visually.  They could also create news casts where they show the connections between the math taught in school with how it is actually applied in real life.  This has students doing the research.

These shorter videos and presentations allow students to be creative while keeping the assignment doable and the final product short enough to finish easily.  Let me know what you think, I'd love to hear.  Have a great day.

Reading comprehension and Math

Yes, I realize we expect students to arrive in high school being able to read at grade level, have a good vocabulary, and have an equally developed comprehension in reading.  Unfortunately, that isn't always true.

It is also known that just because a student is able to decode words well, it does not mean their comprehension level are the same.  Over the past few years, researchers have discovered it is important to have a good reading comprehension level to do well in math.

In general students with who do well in reading comprehension may not always be able to apply it to a wide variety of material unless their have developed a wide background knowledge and vocabulary. When reading normal books, writers leave out certain details with the understanding their readers will fill in the missing details based on their prior knowledge and experience but if they don't have the background knowledge they will have trouble relating to the material. I've noticed here in Alaska, students understand going to the store to shop but they don't understand taking a bus to get to the shopping mall because in their village the local store will have clothing and to get their you ride a ATV or snow machine.

There is research indicating that students who are on grade level with their reading, writing, and language skills do better in math and science because there appears to be a connection between certain types of linguistic skills and math skills.  On the other hand,  it has been found that students who have poor oral skills have difficulty learning material that is presented verbally regardless of the level of their calculation skills.

If a student has  good reading comprehension, they are able to acquire new knowledge much easier because they are able to relate the new with what they already know.  In addition, they can complete word problems and tasks with less effort.  So if they struggle with reading comprehension, they tend to struggle with tasks and word problems that require mathematical reasoning.

There is also research to indicate that older students who struggle with solving word problems, or written tasks, it is often a lack of reading skills that is at the root of the problem.  One researcher found that by working on reading comprehension skills with high schoolers, their math scores improved by almost 15 percent. This makes sense because high school students are taking more and more tests that require them to justify their answers, comprehend situations and contexts so without good reading comprehension skills, they may not understand the test questions.

For younger students, there is something called "Moved by Reading" to help them develop better understanding of mathematical word problems.  This two step process begins with concrete to more of an abstract application.  In the first step students read the word problem and then play with toys or objects to recreate the situation of the word problem.  This method helps them create a lot of information in their minds so they understand the problem better.  The second step, is to ask them to create images in their mind of the problem.  One effect of this method is to improve reading comprehension and it also increased student understanding of math problems within context while learning to extract the necessary information.

So it might be worth talking to the reading teacher to get some ideas for incorporating certain reading comprehension strategies into the classroom to help students improve their test results.  Let me know what you think, I'd love to hear.  I'll be back with some strategies one can incorporate into the classroom.

Making Math More Visual

 On Saturday morning, I got up bright and early (before seven) to attend a webinar on taking problems from the textbook and adjusting them to make them more interesting.  In other words, how to spark curiosity so students want to do math.

The basic idea is to remove as much actual written information as possible and replace it with visuals.  This way students are given the chance to hypothesis, test, revise, and estimate until they arrive at their final answer.

You might start by showing three squares on the screen and ask students what do they think comes next.  After they have a chance to speculate, show the next one which shows six squares in two rows. Ask them to make suggestions about what is next.  Do this for two more times, then ask them to provide a possible mathematical rule.

Now, I know that many of us have trouble figuring out how to represent something visually.  I am too literal so if the problem was about gallons of milk, I'd use gallons rather than thinking of squares and rectangles to represent the same system.  Thus there is a website that can help us get started.  It is called Math is Visual.

The site has videos designed to be used by the teacher a step at time.  It sets up the situation, includes pause prompts at the appropriate point, and includes information for the teacher to help use these effectively.  The instructions walk the teacher through the video step by step with associated screen shots so you know what is happening.

I counted at least 40 videos on a variety of topics including solving one and two step equations, probability, area, mean, operations on integers, and so many other topics.  It is just a matter of looking through them to decide if these activities work best for a lesson or to reinforce certain skills, or perhaps to allow practice to hypothesizing, testing, etc.

This site was created by the Make Math Moments guys who gave the webinar I attended early Saturday morning.  I love having access to these because as teachers we are told to use multiple representations and we don't always know how to create them for certain concepts.  This helps.  I have students whose basic skills are way below grade level so I can use some of these to help strengthen skills like applying the four operations to negative numbers.

Check the site out and let me know what you think.  I am glad I was directed to the site because I can use them today.  Have a great day.

Warm-up

In 2013, walnut growers received $1.85 per pound and now they get $0.81 per pound.  What was the percent of decrease in prices. 

Warm-up

In 2014 pistachio growers received $3.54 per pound but now they get $1.80. What is the percent discount?

Student Response Systems

As teachers, we love organizing activities that involve all the students.  We love it when we can get them all interested in something they see as fun but we know is providing us with information and helping them learn.  One of these things we use are student response systems.

The system I use the most in class is Kahoot.  I am always able to find one on the topic I'm teaching and I use it frequently because students love it.  They are always trying to be number one.

Another system that I've used at conferences but never in my class is Plickers.  Plickers is a student response system that uses cards that have A, B, C, D on them.  The students are given a multiple choice question or true/false question and they hold up the appropriate letter.  The teacher uses their own device with the Plickers app on it to scan all the cards and record answers.  It provides a nice quick assessment and the teacher can download the cards for free and make their own or they can buy them already done.  Best of all, it's free.

Another possibility is Go Formative. This has a free version that allows teachers to create quizzes and lessons, or access pre- made ones.  If you want to make your own, you can upload a pdf, google doc or other document, add places for students to answer, edit questions, and you are set.  This program also provides immediate feedback which is important and relies on class codes to join an activity.

Another one I have used in class is Quizizz.  This is a bit different than Kahoot because once the game starts, the students are given each question individually and each person gets the questions in a different order.  At the end, they can see how they did with their final scores.  Some of my students like it but others do not.  I've used it for my Academic Decathlon students and they liked it.  They can also go back over the questions to see what the correct answer is.  I use it primarily as an in class activity but it can be assigned for homework since they can do it and the final scores are compared.

All of these student response work well in the classroom.  They provide immediate feedback to the students so they know how they did and what they need to work on.  In addition, the gamification of learning makes it more interesting for the students.  They are willing to do these activities so they are learning.

If you want more activities then you have now, check out these cites and give them a try.  Let me know what you think, I'd love to hear.  Have a great day

10 Ideas To Improve Reviewing Material.

It is important to review material on a regular basis so students are able to retain the material but there are only so many ways to review.  I use a few ways but I've had to extend my list so I'm sharing them with you in case you need new ideas.

1.  Create task cards with problems and a QR code on them.  The idea is that students work out the problem and check their answer using the QR code to see if they are correct.

2.  Create a set of cards with problems on them.  Place a QR code on each card but the answer contained is not the one for that card.  Students have to scan the codes until they find their answer.  They then do the problem associated with that card and repeat until they've worked their way through all the problems.  Yes, this is scavenger hunt that uses QR codes.

3. Give students white boards or iPads with drawing apps.  Place a problem on the board and have students work the problem out.  When everyone is done, you ask them to show their answers to you by raising them above their heads.  I've done this but had students signal me when they got an answer.  I'd either draw a smiley face or a frown to indicate if the answer was correct or incorrect.

4.  Create a set of cards that pairs of students can use to quiz each other.  This is one way to engage students in pairs.

5.  Tape cards with questions under a few seats before class starts. Then during class call out "hot seat" letting students know they should check to see if there is a question under their chair.  They are expected to answer the question but they can also ask for help from other students.

6.  Quiz, Quiz, Trade - is an activity where every student in class is given a card with a task or problem on it.  Students divide into groups of two.  The first student poses the problem to the second student who answers it.  The first student indicates if the answer is correct or incorrect.  If it is incorrect, the first student explains how to do it and the answer.  Then the second student poses their problem or task and the first student tries to do it.  If the answer is correct, great, if not the second student explains how to do it and provides the answer.  When they are done, they head off to find a new partner and repeat the process.

7.  Have students create their own problems for a group test.  Each student contributes one problem with the answer worked out.  The teacher takes all the problems to make a practice test for all the students.

8.  Create pairs problems where each partner has a different set of problems but the problems have the same answer so if they don't agree on the answer it means one or both are wrong yet if they agree on the answer, it means they are both correct.  I've found when students disagree over the answer, they check each other's work and discuss things.

9.  Around the world with math.  Have all but one student sit in their chairs.  The last student stands behind one of the chairs of the sitting students.  The teacher asks the question and the idea is for the two to work the problem to see who can get the correct answer first.  If the standing student gets the correct answer, they move to the next student but if they are incorrect, they have to sit down and the sitting student will stand and move to the next chair.  Repeat until all the students have had at least one chance to answer a question.  If the class if small enough, you might go through the class twice or more.

10.  Set up stations around the room.  Each station is designed to help students work on specific skill. In math, most tests cover a whole chapter of skills so each station will focus on one or two sections of the chapter in preparation for taking a test.

Encouraging Mathematical Discussions

Encouraging mathematical discussions among students can be very difficult for many reasons.   First there is mathematical vocabulary.  Many words mean one thing in general conversation while it means a totally different thing in math.  One such word might be product.  In the general population, it means something made to sell at a business while in math it means the result of a multiplication problem.

Many of the mathematical equations using symbols such as a * b can be read as "a times b", "the product of a and b" or "multiply a and b" so there is more than one way to read it.  In addition, when translating from the symbols to verbal or vis-versa there are rules to it's context and students have to aware of it.

Sometimes one of the hardest things is to get students to talk to each other rather than only asking the teacher for help.  One way to work around this is to have students ask for help from three different students before they ask the teacher for help.  One has to take time to help students learn to ask for help because I've heard them ask like this "Did you do 12 yet? No? OK" and repeat the question rather than asking "Could you look at this problem and suggest a way I could start it?"  One other way to handle this is to assign "expert" students that other students can ask before they ask you.

Next, have students work independently before having them work in small groups because they need time to assemble their thoughts and figure out what they know or don't know.  Once they've had time to do this, they can work with other to compare and contrast their approaches and answers.  During the process, they are conducting a mathematical discussion.

Teachers can use questions to help promote mathematical discussions in class.  I know I often get stuck looking for new ways to ask questions but I found this list that helps.  It is a list of 100 questions designed to help encourage discussion among students.  Some of the questions are designed to help their perseverance, while others help students connect mathematics to their application or conjure, invent, or solve problems.  Check it out if you need help with your questioning.

Help students understand that they learn when they make mistakes.  Too many students want to get the "right" answer the first time, not understanding that every time they make a mistake and correct it, they are developing a deeper understanding.  If students do not like the grade on their work, they are allowed to go back and make corrections but they are also required to explain why they made the mistake.  This process helps them learn the material so much better.

Teach students to work collaboratively using think-pair-share or numbered heads.  Numbered heads is great for groups of three or four because each person in every is assigned a number between one and three or one and four.  The teacher calls out a number and the student with that number is expected to provide a response so it is necessary for everyone in the group to understand.  This encourages students to talk so everyone in the group has the same level of understanding so they are all prepared to answer the question when called upon.

Run some quick assessments so the teacher knows the level of understanding.  Quick assessments can include thumbs up/ thumbs down, choose a corner, use a random name generator to get a name to call on, or red/yellow/blue cups to have students show how well they think they understand the material.

It is important to encourage mathematical discussions because students need to be able to express themselves.  I've noticed that students who have low scores in reading and writing often struggle in math because they lack the vocabulary to understand what is being asked.  This is one reason to encourage vocabulary development.

Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If a crayon is 3.94 inches long, how many crayons make a mile?

Warm-up

If each crayon weighs 3 grams, how many do you need to make 1/2 a kilo?

Developing a Deeper Conceptual Understanding.

Unfortunately, many of us are required to teach using either a set textbook or we have to use the textbook and all the associated materials.  As teachers we are expected to make sure students understand the concepts and the material being taught.

Fortunately, there are ways to make the material easier to understand for students.  Right now in Geometry, I'm teaching rotations.  When a figure is rotated 90, 180, 270 degrees, it is fairly easy to teach because the x and y either change position, change sign or both but when trying to teach them to rotate a figure say 120 degrees it becomes a bit harder.  I tried teaching it using the materials provided by the district but it didn't go well, so I've begun using specific videos.  These videos are much better at showing how to do things visually so student actually understand the process better.

The first thing is to have an opener that helps students get in the mood.  This is the place you might have students write down the learning objective with the criteria so they know when they have learned it.  The opener is also a great place to throw in a quick review such as kahoot or maybe a hook to get their attention.  I've found activities such as "Which one doesn't belong" or Esti-mysteries are perfect as warm-ups.

When introducing the topic, use multiple representations such as mathematical symbols, a drawing, a photo, manipulatives, or number lines.  The more representations a teacher can use, the better the chance a student has of understanding the concept.  I've used area modeling to show distributive property, regular multiplication, and binomial multiplication.

In addition if it is possible to do a problem more than one way, show students multiple ways to do it.  Teachers should also take time to encourage students to develop their own way to solve the problem.  When students develop a correct method of solving a problem, have them share it with the class. The more ways a student knows to do a problem and the more strategies they know, the deeper the conceptual understanding they develop.

If it is possible, show how the math would be used in a real life situation, another subject, or how the concept developed over time.  This helps students see the connections and develop a deeper understanding.  This can sometimes be the hardest step of using it.  I'm currently teaching linear equations in Algebra I and I bring in pictures of mountains along with topographic maps so students can practice calculating slope or grade.

Encourage students to discuss the material and provide a written explanation of  it.  When students can discuss it and write about it, they have a better understanding of the material.  Some of the suggested ways to encourage discourse is "think-pair-share", small group discussions, planning a video, create a drawing,

It is important to finish the class properly rather than just dismissing it.  There are three things that can be accomplished in the final five to seven minutes of class.  First, one can carry out a small assessment in the form of an exit ticket, thumbs up, down, or in-between, choose a corner of the room, or other activity.  Second, review the objective and the success criteria so students are reminded of both.  Third, preview homework or material for the next day with a brief sentence or two.

These steps are designed to help students develop a deeper conceptual understanding of the material.  Let me know what you think, I'd love to hear.  Have a great day.

Where To Go To Find Real Life Applications of Math.

 It is always nice to have a list of places to go to find real life math applications.  I don't always like the problems you find in the textbook because the problems seem almost contrived but if I can find problems with a real feel, I use them if at all possible.

This site has a list of links teachers can use to find real life applications for grades K - up to high school.  Since I work with high school students, I paid more attention to the activities for middle school and above.

One suggestion from math-kitecture is to create a floor plan of the class room using architectural methods to create it.  This activity requires estimation, measuring skills, proportions, and ratios to create a floor plan to scale before they utilize a CAD program to make the computer based one.  Teachers have sent in lessons plans that use the site create a dream bedroom or other things.

In addition, they offer lots of links to other activities such as skyscrapers, scale drawings, and area in home decorating.  The site also has students finding geometric shapes in regular buildings and structures.

On the other hand, this site focuses on uses of math within the construction industry,  It offers a variety of activities for different age groups.  For instance, the construction tool box contains 14 different sections from the introduction to a lesson dealing with acoustical ceiling lesson, to soil excavation to resources for teachers.

If you need to sneak some financial math in, check out this treasury site with several different lessons combined into one unit called "Money Math: lessons for life".  Some of the concepts covered in this unit include percents, data analysis, measurement, averages, reasoning, spreadsheet, and problem solving.  The first unit is on the secrets to becoming a millionaire, the second is on wallpapering a room,  the third is on money and taxes, while the fourth is on spreadsheets.  The lessons are set up with step by step directions so the teacher knows what questions to ask, what to have the students do and everything else that is needed.

There are also two links provided the send you to places to get ideas for mathematically based projects.  One is Math Motivation that offers 20 different projects  such as playing the stock market for gain or loss, or figuring out when professional athletes burnouts and so many more.  The other site, has possible projects like creating plans to do something to improve things in their community or see how things could change in the Olympics if the races are done differently.  The lessons have everything you need to run these projects.

This site is a portal to lesson plans created by teachers and university personnel in Pennsylvania.  They have a search engine to help you find lessons on specific topics.  I did a general search for middle school and high school level plans and came up with quite a few.  There were two lesson plans on the lottery.  One dealt with the chances of winning while the other and the cost.

I looked at the lesson on chances to see what it included.  It includes the standards, overview, materials, context, mathematical ideas, exploration, discussion, and extensions.  Everything a teacher needs to teach a lesson. There are also lots of illustrations to support the material.  There is also a student handout to accompany the lesson but you have to be a member of the community to access it but it doesn't cost anything to join.

If you are looking for some real life applications of math, check these out.  I know I plan to do some of these on those short weeks when you need something a bit different.  Let me know what you think, I'd love to hear.  have a good day.

Cool Site For All Sorts of Math Things.

 The other day I came across a website Mathsbot.com. It has virtual manipulatives that work on an iPad rather than only on the computer but it is easier to use on the computer due to the curser.  This site also offers so many other things that I think I just added it to my list of decent resources.  

As far as ease of use, I didn't find any directions on how to use the manipulatives but I did learn to use them after playing with each one for a few minutes.  This means with just a bit of experimentation, you figure out how to use it.

I played with the algebra tiles manipulative.  I was thinking (x + 2)(x+ 3) when I created the problem but it could easily be a simple multiplication problem such as 12 x 13.  For the original problem I get x^2 +2x + 3x + 6 or x^2 + 5x + 6.  For the other I get 100 + 20 + 30 + 6 or 156 as an answer.  I believe this is now referred to as an area model.  

I love using this type of model when teaching binomial multiplication because it helps student visual the process and it show why you end up with certain terms.

I also played with the equation solver which is a way to visually show how things work.  I laid out my original equation as you can see.  What I discovered is that this defaults to the inequality sign so you have to click the set equal button to get it to be right.

To use it you would place the opposite value on the "number you want to move to the other side" and you have to place the same value on the other side which reinforces the idea of doing the same thing to both side.

In addition to manipulatives, there are pages of formulas and information on interior and exterior angles, trig ratios, angle names, basic angle rules, fractions, decimals, percentages, numbers and words, and polygon names.  these can be printed out for students to use if they need them.

There is a section on puzzles with several different types. The puzzle to the right is an example of a simultaneous grid.  Each shape has a value.  It appears the green rhombus is worth one  while the blue triangle is three.  That means the yellow circle is worth zero.

To discover if this is true, one just clicks on the square to see if the choices are correct.  I cans see placing one of these in front of class as a warm up because it requires some critical thought.

Another puzzle is the four operation puzzle where students place the digits 1 to 9 in the appropriate blanks to make the totals correct.  The puzzle allows one to click on the blanks to see if the selection is correct.  Again this makes a nice warm-up.

There is a section designed to generate questions from differentiated questions to test questions to worksheets, to topic ladders and loop cards.  I like the loop cards because they are set up so the answer to the problem on one card appears on the next card with a new equation.  This could be used in two ways.  First the cards could be printed out and hung around the room so students can follow the path working out the problem, then searching for an answer while writing on a master sheet.  The other way it can be used is to pass them out to students and having them say the problem.  Another student then says "I have the answer" and gives it before reading out the next problem. Continue around the room until it goes back to the first person. The loop cards allow you to change the number of cards produced. The nice thing is these generators produce more than one set for each one and offers a variety of possibilities.

This is followed by a starters and drill section a variety of activities from number squares and number of the day to Do It now and matching pairs.  These are nice because it is possible to get a whole new set every day and they are easy to use as warm-ups.

The last section is tools with a variety of things from the missing grids to function machines, to frequency tables.  Some can be used to learn things such as which are prime numbers based on the Sieve of Eratosthenes to Pascals triangle, to so many other things.

Check it out to see if you are interested in any of the resources.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If each block has a volume of 27 millimeters cubed, what is the total volume for this group.  Explain your answer.

Warm-up

You just spelled your name using alphabet blocks.  What is the total number of vertices for all the blocks.

"Figure This!"

 I am always on the lookout for activities designed to encourage critical thinking or conversation.  Too many times, the activities I find are based on filling out a worksheet but I found a website with problems rather than just worksheets.

The site "Figure This" created by the National Council of Mathematics for families to use together.  It appears the site has not been updated since 2004 but the problems are still able to be accessed. Although the site is listed for grades 6 to 8, I believe the material could easily be used in high school.

The problems are listed in two ways on the website.  The first listing is the challenge index which lists all 80 problems with a small description of each.  The other listing is via the math index which classifies the same activities as either Algebra, Geometry, measurement, numbers, or statistics and probability.  Many problems are listed in more than one category.

One such problem is titled "Stamps".  It shows up under Algebra, Geometry, and Numbers.  According to the list under Algebra, this problem deals with linear equations, graphs of lines, and representing patterns.  This activity also covers coordinate geometry, solving problems with percentages, decimals, and fractions.

Every problem has a hint button with the problem, and the site has the full answer.  When I say full answer, it shows four different ways to solve this particular problem so it is not one with only one way to get to the solution.

In case you are interested, the stamps problem states that you've found an old roll of 15 cent stamps before asking how many 33 cent stamps must you mix with the 15 cent stamps to find exactly $1.77 so you can mail a package.  The hint suggests students use as many 33 cent stamps with the difference made up of 15 cent stamps but the hint does not show unless the student clicks on the word.

The site also allows the challenges to be printed off complete with answers and hints should you want to use several different ones at math stations or they can be read from online.  It is possible to print the challenges off, separate the problems from the explanations and the answers so you could place the challenges at a station and the explanations in a different place.

The way these problems are designed, it is quite easy to have students explain their thinking process via video or flip grid once they've found solution.  If students get stuck while working on it, the teacher can ask students to share their thinking when they ask for help.  What did they try that got them to the point they got stuck.

The problems cover a variety of topics such as how long it takes the Arctic Tern to fly from the Arctic to the Antarctic and back again, or calculating BMI (Body Mass Index) to determine if someone is over weight, or life expectancy, or which windshield wiper cleans the most area.  So many of the challenges are based on real life.

Check it out to see if you can use it in your classroom.  Let me know what you think, I'd love to hear. Have a great day.

"Where Math Meets Art" at the Smithsonian.

The Smithsonian has works created by American Artist David Crockett Johnson. Although he was known for his  cartoons such as Barnaby, children books such as "Harold and The Purple Crayon" and book illustrations, he had time to create works based on mathematical theorems, mathematics, and mathematical physics.

He created over 100 pieces of art between 1965 and his death in 1975.  He is different from most artists creating art based on mathematics in that he connected geometric constructions to specific mathematicians.

He is reported to have told a friend in 1965 that he wanted to do a series of "romantic" tributes to the great geometric mathematicians beginning with Pythagoras.  He enjoyed doing Euclid, Archemedies, and so many others.

Furthermore, he based his early paintings on illustrations in the book "The World of Mathematics" published by James R. Newman in 1956.  But as time went on, Crockett began studying the mathematics in the book which caused him to begin creating his own constructions. Due to this study, Crockett published two papers on mathematics.  One dealt with estimating the value of pi geometrically, and the other focused on constructing a polygon with seven equal sides.

Crockett differed from most artists the time because he created small paintings on masonite rather than canvas.  He also used house paint he had mixed at the local hardware store but his painting was good enough to have showings at several galleries in New York City and Connecticut.  About 80 of the 100 paintings can be found at the National Museum of American History.

Although most of us are not in a position to head for the Smithsonian or the National Museum of American History, this site has interactive copies of these pictures. Each picture has the title of the math the artist used to create his painting, the drawing on sketch that inspired the drawing,  the name of the mathematician, and a description of the painting.

One painting celebrates the mobius strip while another creates a spiral based on the first 16 square roots based on Theodorus of Cyrene.  There is the great one on based on the proof of the Pythagorean theorem used by Euclid.  There is even one illustrating logarithms using both geometric and arithmetic progressions.

I really like that each piece has the piece itself,  the drawing it's based on and a wonderful description explaining the painting.  I can see using some of these paintings to show how artists might interpret the actual mathematics of the theorem.  I read somewhere that mathematicians use visuals more often than the actual equations and this is perfect for this.

There were hints in his work that he enjoyed mathematics before he began painting these works of art.  In his Barnaby cartoons, he had a character who spoke in complex algebraic equations.  Originally, the algebraic equations were nonsense but later on he took time to make sure his equations said something.  Mathematicians of the time loved it because they got the joke but his regular readers didn't. The mathematically based paintings made up the third phase of his artistic life.

He did not have a a degree in mathematics but he had a mind that could "see" it and he enjoyed working with it.  Let me know what you think, I'd love to hear.  Have a great day and I hope you share some of these paintings with your students.

Number Rock

 Number Rock is a site geared for grades K to 8. It has some short animated music videos one can use in the high school math class, especially for students who are lacking certain skills.

The site has some free videos while it does require money if you want to access all their videos.  On the other hand, they also have posted some on Youtube.  Unfortunately, some of the videos use images I don't like.

They have one on inequalities geared for fourth grade but it uses the idea that the alligator eats the larger number.  If that is the only way students can remember how to use the inequality sign, I'll live with it but I'd prefer the student actually know what is going on.  I do have students in high school who have issues with the inequality signs, so this would be appropriate.

Some of the videos I see that I could use for my high schoolers include the one on inequalities, the rules of rounding, integer numbers, numerical expressions, comparing or ordering decimals, order of operations, area model multiplication, rounding numbers, square, prime, and composition numbers, multiplying or dividing decimals, triangles, and so many more topics.

Each video has a ton of support materials such as work sheets, games, quizzes, worksheets, lesson plan, drills, answer keys, and the ability to download the video but to access these you need to sign up for the service.  They do give a 30 day trial should you desire to check out all the materials It appears that you can access every video they've produced on Youtube but there are no support videos.

Although the videos are geared for younger grades, I see using some of the videos as a way of supplementing, reviewing, or differentiating material.  Since these are music videos, kids are likely to enjoy listening to them.  In addition, they provide a great review of things they should know but may have forgotten.

These videos are easily assigned to students to watch the night before so they have reviewed the material before you have to teach the lesson.  I watched the video on the coordinate plane and the chorus talked about counting left or right for the x-axis and up or down for the y axis which is something my students often forget.

I looked at another video on 3 dimensional shapes geared for 3rd to 5th graders but it is one I could easily use in my geometry class when we get to 3 dimensional shapes.  This one discussed various shapes such a pyramids built by the Egyptians and two other groups.  They talked about the square base and triangular sides that make up the pyramid.

Each video is quite short so it won't take a lot of time. Some videos are actual songs while others are raps.   I think I would create a viewing guide so students can fill out the guides as they watch the video but I would do this only after I let them watch the video through once.

This one resource I intend to add to my the ones I already use in my classes.  I often list videos for students to watch when they are traveling or sick so these would be good for reviewing how to do certain things.  Check out the videos, let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If a 1.5 ounce box of candy has 27 hearts in it, how much does each heart weigh?

Warm-up

According to this t-shirt, how many years did it take the Vikings to get to America, after they got to England?

Two Truths and a Lie variations.

Two truths and a lie is a great activity where three statements are made.  Of those three statements, one is a lie while the other two are truths and the person reading it must decide.  Often times the lies are not that easy to determine.  


If you look at the picture of the bell peppers, I could say:

1.  The peppers are arranged so there are four rows of four and one row of two.

2.  One - ninth of the green peppers have some red.

3. Two - ninths of the peppers are yellow.

Which one is the lie?  If you aren't sure it's the middle one because there are only 14 green peppers and two of them are red so the fraction should be one - seventh.  The one - ninth is based on counting all the peppers, not just the green peppers.

When using photos or diagrams, people have to think hard about how the written apply to the visual and determine if the interpretations are correct.  It can spark lots of discussion among students which helps increase their understanding and mathematical vocabulary.  In addition, the teacher can place a photo on the board or in google classroom so students can create their own two truths and a lie.  Once students have finished creating their two truths and a lie, place them up around the room and let students check out each one.  You could even have students work their way through each other's creations.

If you want to use an already created two truths and a lie as part of the unit, Desmos has four already made.  They deal with lines, parabolas, conic sections and exponentials.  The activities have a graph and ask the student to select the lie and justify their choice.  All four are set up so you can add one or the students can add their own.

Another possibility is to select a graph without any information on it, create two truths and a lie for it and then have the students determine the lie.

I might come up with something like this for this graph.

1.  The graphs shows a repeated pattern of a decrease, gentle increase followed by a sharp increase in the purchase of chocolate.

2.  The graph shows a car hitting the breaks, starting to speed up, stomping on the gas petal before slamming the breaks to stop, starting again and speeding up rapidly.


3.  A person is walking back from the store, they climb a hill for a bit, then begin to go down a slight hill before going down a steep hill rather quickly, then they start doing up a hill again, before starting down a hill and finally running down a hill.

You can also give each student the same picture so they can create their own.  I'm going to let you figure out which one is the lie.

Let me know what you think, I'd love to hear.  have a great day.

Happy New Year