New Years Math

  I decided to check out the topic of New Years Math and actually found something.

The first website I found some great information on time zones, how many times the New Years is celebrated and when is it celebrated in Space.  Space is not a place I'd thought about before but there is the international space station so that would be applicable.

The second site is the Mathematicians New Year Resolutions from Math with bad drawings.  This is filled with humor concerning mathematics.  I loved the one about cleaning up my clutter which I would love to have as a poster in my classroom.

Then there is the Mathnasium site with a lovely new years card with the year done mathematically.  It does involve some higher level math but its still fun to see math used in a slightly different situation.  This is a tutoring site but the math is still there.

Of course you can check out the problem at this site on saving money for the next new year's with three different variations of the same problem. This particular site has tons of mathematically based tasks for k to 8 but the tasks come with possible answers, 

I am going to try to have my students keep track of how much they spend at the store each day, week, and month.  They buy tons of soda, chips, snacks and other goodies without keeping track of it.  I'd like them to discover they spend enough money for a trip to Los Angeles, Hawaii, or possibly even Europe in the space of 9 months.  This is my classroom resolution for 2016, help them see how much money they spend on soda etc.  

Carpentry

  As you know, I am always looking for ways to include real life math in my classroom.  Usually, I manage a project in Geometry but not in my other classes.  So I checked out sites for learning the math involved in carpentry.

My school used to offer carpentry but when the teacher retired, they didn't bother replacing him.  That is unfortunate.  So I needed to check and see where I could find information so I might create a unit for my pre-algebra class and maybe even my algebra class.

One of the first sites I found offers some great carpentry math. This looks at the slope or pitch of roofs.  The author relates rise and run to the pitch, to trigonometry and to the Pythagorean theorem.  This is so cool because the relationships are shown and it changes the math from being taught in a void to showing them good applications.  In addition, the entry includes quite a few formulas associated with roofing and writes many of them so they are related to previous formulas. 

The Carpentry Pro-Framer site has some really great information on the math carpenters use.   The author talks about easy ways to add or subtract measurements, figuring out how long joists should be, squaring various parts of a building,  or  locating windows or doors.

It is important to provide some practice problems so students are able to apply the math.  I found this online pdf filled with carpentry problems. I find the word problems the most exciting because you are more likely going to encounter a word type problem in the industry rather than just a list of numbers ready to go.  The word problems also require students to interpret drawings.

I found a site with a 4.5 min video where a carpenter explains how math is used.   The video could easily be used to introduce the topic and covers measurement, fractions, decimals and percents.  The way the pdf is structured, problems could easily be integrated into regular assignments so you don't have to take extra time to incorporate it.

Weather Math

  This morning while watching the news concerning flight delays due to weather, I wondered if there were any mathematical activities based on weather?  After a quick search I found somethings.

The Young Meteorologist site has some very nice math activities.   They have a weather graphing activity geared for 4th graders with a curriculum tie-in but it could easily be adjusted for older students.  Furthermore, it comes with a complete lesson plan that includes a chance for students to gather local information using various tools.  This is a nice science tie-in so it becomes a cross curricular activity.

Furthermore, there is an activity on Hurricane Math, PBS Weather math (grades 5 to 12), a weather calculator, and the weather data learning center for grades 3 to 5.  There are two other links that are out of date but I found a couple of other sites with the same type of materials.

UCAR out of Bolder CO has a nice web page of flood math.  They also have a nice site designed to create mathematical connections using science and patterns to explore weather.

Scholastic offers an online math game called Math Hunt  which is designed to teach students about meteorology while going through clues to solve mathematical problems.  The problems cover addition, subtraction, charts and graphs, conversions, decimals and percentages, multiplication and division, ratios and proportions. 

The EDN network has a nice in-depth article on the ways math is being used in weather called the math of meteorology.  It goes into nice detail about the variables used in weather, vectors, reading charts, etc.  This is a great article for upper level and honors students because it includes information on partial derivatives. 

In addition, there is a lovely power point presentation on how math is used in meteorology.  It is a more general presentation than the one through EDN but it does a wonderful job of explaining how various types of math such a geometry are used within meteorology.

This is the perfect topic to present as a combined unit with both the science and math departments.  Too often we teach our topics as isolated entities rather than actually working with other departments to create real cross curriculum units.  Imagine!  Meteorology is taught in Science, the math department provides the math, the English department can provide written reports while the media department could create daily weather reports as part of the school wide news.

Star Wars Math

  With the release of the newest Star Wars Movie recently, I decided to check into what math is available using it.

First off, I heard that Star Wars has grossed over 1 billion dollars in just a few days time.  You could have students take the average cost of a ticket and figure out approximately how many have seen the movie so far.

Second, I found the Mathematical Shed that has some Star Wars Math.  It has some things for elementary but it was the inforgraphic on the cost of building the Millennium Falcon most interesting.  Students could easily research the size so they can calculate cost per square foot.  In additon, they will have to convert the cost from British pounds to American dollars. 

In addition, there is a presentation on the cost of building the Death Star which includes the staffing requirements.  Think about the fact that once its built, they have to pay people to run it. Even if its the military, they still get paid.  Then students could figure out the cost of supplies based on current food costs, etc. 

Toward the bottom are other activities for students.  One is a game called Race to the Death Star which comes in a downloadable, editable form and has eight problems students can work their way through.  Most of the problems are based on the original Star Wars Movies but some of the problems are nice.

There is also a game using characters from the Star Wars movies which requires players to convert between scientific notation and standard numbers.  In addition, there is a pod racing game, a coordinate grid exercise and a bunch of Legos activities. 

Another site, Manghammath, offers several Star Wars activities in a 39 page downloadable activity packet.  The packet provides a lovely review for a Pre-Algebra or Algebra class so they can review classifying numbers, decimals, etc.

I even found free classroom posters based on Star Wars to use in school. The first rule under the 8 Mathematical Practices of the Jedi Masters is "I can solve problems without giving up."  The thing I work so hard with my students on.  If they perceive the problem as too hard, they give up without trying.   I think I"ll download these posters and hang them in my room. 

Check these out if you want something a bit different in your classroom.

"When Will I Ever Use This?"

You know, the question that all students ask at some time but whose answer is not really known by most teachers other than the "You'll need it, trust me!" So I went looking for sites on how math is used in Forensics simply because I like the topic.

So with  all the crime shows like NCIS, Criminal Minds, and other analyst shows on television, students may actually be wondering what it takes to become a crime analyst.  So during my search I came across We Use Math.

This web site lists a large number of careers so students can see what type of education is needed and the minimal required mathematics courses for doing well within the career.  I started with a Forensic Analyst since I enjoy forensics.  According to the site,  you need College Algebra, Trigonometry, Geometry, Calculus 1 & 2, and Statistics to go into this field.  Furthermore, it gave examples of how math is used within the field and provided numerous links to further explore this field or any other field. 

Next I checked out the math required to become a physician.  It requires most of those courses plus a couple more recommended courses but they also say it depends on the requirements of the medical school.  On the other hand, a carographer requires the same as forensic analysts with the added courses of elementary statistics and spatial statistics.

I love that each entry includes how the math is used within the career and provides links so students can do further researching. As for the rest of the site, the staff has included some really nice materials such as a blog that talks about things like crime rates, and the mathematics theory that can be used to predict the wrinkles are formed on a curved surface such as raisins or finger prints.

They even include a teacher resource section with all sorts of goodies.  Free resources, posters, and even Math Puzzles and Games.  This is a site I will send my students so they can explore careers and read up on what it takes to succeed in Math.  This site reinforces two things I stress.  First you have to do the math to get better at it, kind of like practicing your basketball till you get good at it.  Second, it is alright to make mistakes because you learn from your mistakes.

The other place I found is the Forensics Outreach site where the author took time to give several specific examples of how math is used during a forensics analysis.  I didn't realize that trig is used to help determine where the killer.  They use distances, angles and basically triangulate the killers location.

Another mathematical skill is calculating proportions so as to figure out the height, weight, etc from a bone segment found without the rest of the body.  That is soooo cool.  I learned a couple things while writing this.

So the next time a student asks "When will I ever use this?"  send them to either of these sites.

Note:  Due to no internet where I am staying, I won't publish again till Monday.

Merry Christmas To All

I Love Math

  I Love Math is a website with some really nice materials to use in the classroom.  It has not been updated in a while but the activities are still there as relevant as when posted.

The materials are divided according to class they can be used in such as Pre-Algebra, Algebra, or even Calculus, games and puzzles or classroom forms.  I've used many of the materials in my class.

I love exploring this site each year.  I found a lovely exploration for systems of inequalities activity which could be used to introduce the topic, to review, or even for scaffolding.  I plan to use it when I get back after the holidays to help students activate the knowledge they learned just before the Christmas holidays.  The activity has them find points on a graph and then classify the location as within the solution set for the first line, second line, both lines or neither line. 

I've used the classifying triangles activity in my Geometry class before.  It has students use protractors to measure angles and sides before requiring them to classify the triangles by sides and angles.  I like this exercise because it makes the students aware that triangles can be classified by both sides and angles.  You can have a right isosceles triangle!

I just found an activity I want to use to review the Pythagorean Theorem when school starts again January 4th.  The activity has several word problems students can work using the Pythagorean Theorem and the answers are included but not in order.  Its all set so I could easily set up a search and rescue activity or I could have students work the problems in groups.

There are some really nice review games sprinkled through the sections.  In addition, there is a section of forms which have some lovely forms I use in my classroom.  I like to keep a hard copy of attendance and I found one I like in the math forms.  I've also found a parent communications log and a form I adjusted for the daily warm-ups and practice standardized test questions. 

Give it a look to see if there is anything you might use in class.  Why start from scratch when you can modify?

Area of Irregular Shapes

The other day, one of the teachers showed me a worksheet designed to have his students calculate area for an irregular shape and asked what the best way to teach students how to find area for this type of shape.

He teaches math to 5th and 6th graders and wants to make sure they are prepared when they get into high school.  I know from past experience that most students have trouble visualizing splitting the shape into two regular shapes.

I told him to copy the shapes onto graph paper so students can cut the shape into two regular pieces. There are at least three way students could cut this into smaller pieces.

1. Cut the top 2 x 3 area off so students are left with a 5 x 2 area.
2.  Cut the right 2 x 3 area off so students are left with a 2 x 5 area.
3.  Cut both the top 2x3 area and the right 2 x 3 area which leaves a 3 x 3 area.

No matter which way the student divides the shape, the area is the same. This is a good discovery because my students too often focus on "the correct way" to calculate area.

The second step would be to have students take the units and draw in the lines themselves to calculate the area by mathematically using a worksheet where they fill in the values as a guided practice.  This is the step to introduce the idea of subtracting distances to find the measurements of the smaller shapes.

The third step is having students calculate the shapes without drawing in the lines. By this point, students have developed the ability to see the smaller shapes. This process helps students develop the ability to picture the divisions possible in the irregular shape. 

Unfortunately, we assume that by the time students reach high school they know how to do this.  We forget that many students get teachers who are still into assigning worksheet after worksheet and do not differentiate or scaffold instruction.  So students are often missing pieces in their foundational knowledge.

Multiplying Binomials

When I teach students to multiply binomials, I teach the standard FOIL method because that is the method taught in every text book that I've ever used.  I teach three other methods to my students so they have a choice.  Not everyone finds the FOIL easy to do, especially if you end up multiplying a trinomial by a binomial.

The first alternative method I teach is what I call the distributive method.  You split the first term into two parts as seen in the example to the left.  Then the second term is left whole and put next to the split first terms.  Carry out the distributive property.  Combine the two like terms and you have the answer.

The cool thing about this particular method is that the reverse is the grouping process for factoring so there is a connection between this method and factoring trinomials.

The second alternative method is what I call the regular multiplication method.  I open by asking how you multiply 27 x 32. After they guide me through the process to the answer, I show them how to multiply the binomials using the same format.  I draw the dotted lines in so they see how it works and I tell them to include the plus or minus so the correct signs allow the correct answer.

Many of my students find this method so easy to do because it follows the same procedure they use for integers and for them it is comfortable to make the transference.

I just recently learned how to apply the lattice method of multiplication to multiplying binomials.  The only reason I include the lattice method is because the 5/6 th grade teacher favors using this method of multiplication in his classroom.  So now I'm getting students who know this method and showing them the lattice method can be extended to binomials makes it easier for them.

I admit, I had to learn the lattice method because its not one I'd encountered before but if its what my students already know, I decided to apply it to binomials.  It really does work.  If you've never seen it before the carry part is in the same square but in a different diagonal.

If anyone is interested, I could create a short video showing you how to do the lattice method of multiplication or as it is applied to binomials, let me know and I'll do it.

The students find having four choices a bit difficult because they are so used to being told to do it "This Way!" but they like finding the method that works best for them. 

Math Playground

Math playground is a website filled with nice interactive games.  They offer games for elementary and both middle school and high school which is great because even high school students enjoy playing video games.

First off, this site offers so many different activities, lessons and games to integrate into lesson plans.  I really didn't know what this site offered until I looked more deeply.


Math Playground offers quite a few videos for a variety of topics from  the basics of order of operations and divisibility rules to surface area and volume of 3D shapes.  The nice thing about videos is simply being able to assign each student a video to help reinforce their areas of weakness.  I like showing several videos on one topic spread out over several days.  My students love to watch videos.

In addition, this site offers some nice activities for Geometry, Pre-Algebra, Ratios and Percentages, Fractions and Decimals, all topics that are taught in middle school and in high school.  I have students in Pre-Algebra who have difficulty working with fractions and decimals.  Any chance I can give them to obtain additional scaffolding is worth it.

When I clicked on Pre-Algebra, I was taken to a page which listed all the games, activities, videos and word problem activities Math Playground offers.  I checked out the variable game where the student is an otter who swims in a race.  The idea is that the otter gains speed with every correct answer for a problem such as 3 x ? = 24.  There are 4 choices and you select the correct number to make the statement true.  It goes rather fast so the student has to really know their times tables or they will get frustrated.

The next activity I tried was the one dealing with linear equations.  The idea is to select the line from the choices which goes through several zogs (aliens) to be rescued.  If you are correct, you go to the next problem.  This activity starts out with x = or y = a constant.  I've found those are the two lines that students have trouble identifying and graphing the most.  Each level requires the students to do something different but are focused on a particular aspect of graphing linear equations.

The downside of this website is simply that when you type in the URL, you end up at the games page of games that seem to work on the iPad.  I could not find the videos or anything else.  Math Playground does offer a few individual game apps for the iPad, some of which are really good.  So this is a site for computers more than iPads.

Why Do We Always Teach It This Way

I wondered why we always teach students to distribute first when teaching them to solve a problem like the one to the left.  I know we teach it that way even for a problem like 2(10  + 3).  We have the students go through the same process of 2 *10 + 2*3 = 20 + 6 = 26.

My students often wonder why they have to carry out the process with integers.  I know it's used to help them learn the process but for most of us, its easier to multiply 2 * 13 rather than break things up.

I read an article that sounded like a cool way to solve the same type of problem.  Since there is only one variable, the other methods states one should divide first as long as the answer is divisible by the number in front of the parenthesis.

It saves a step and is much easier.  The article said one should use the distributive property if you have more than the one variable and will need to combine like terms.

I'd love some feedback from readers on this.   Do we have to teach students to always distribute or is it possible to teach them to learn to differentiate two different cases so they only distribute under certain circumstances?

Christmas Math

Its that time of the year when kids become distracted by the upcoming holidays.  The last couple of days before holidays can be difficult so why not take advantage of the season with Christmas math designed for older students.

I found a lovely website with all sorts of math problems including some fun holiday math.  Yummy Math actually has a whole bunch of interesting math but more about that later.

The first activity listed has to do with the most efficient way to wrap packages.  As a set up, the activity includes an article on this topic with an accompanying video. The activity focuses on using surface area and they Pythagorean Theorem.

Yummy Math is a paid site that allows people to access parts of the site for free but if you want the solutions you must join.  For this activity, I was able to access the worksheet but not the extensions.  However, the accompanying worksheet is great because it includes the URL for a video to be watched prior to doing the worksheet and all the instructions are set out step by step.

The second activity deals with estimating the number of 12 packs of soda that were used to create a Santa display.  One part of this activity helps students hone their number sense by looking at a picture and making guesses.  Then the class discusses which guesses are too large or too small.  I don't often have enough activities of this type to help develop number sense.  This activity comes with two additional pictures of Christmas items made of 12 packs of soda so students can practice this skill.

The final activity lists three popular movies and students are asked to decide which of the three movies made the most money.  This activity helps students learn to analyze real data.  Students are required to round, compare and create graphs.

Now for the rest of the site.  Yummy Math has problems for grades K to 12.  The high school material is divided into five different strands and each strand is further subdivided by type.  I clicked on Geometry, HSG and came up with 35 different results.  The first activity in this strand is based on the rescue of the Chilean Miners and students are required to run a variety of volume, surface area, and lateral surface area calculations all related to the rescue.

The calculations are based on the volume of the living area, the amount of ore in the escape tunnel, the lateral surface area of one of the shaft linings, and the chamber's depth under the surface of the earth.  Just think, math based on a real life event.  The same math, the rescuers would  have had to use!  I could even coordinate this activity with the social studies class so they can show the movie while my class does the accompanying activities!

Yesterday, I wrote that in addition to providing the what, we need to provide the why for learning math.  We have to give a reason and we have to make it relevant.  This does the job.  This activity gives students a good reason why it is important to know how to find volume, surface area, and lateral surface area.

I've got YummyMath bookmarked so I can find it again.  These activities do not have that contrived feel that others have.  Give the site a check and enjoy exploring it.  Right now, the home page has a ton of Christmas activities to share with your math classes.

Interesting Information on Brain Research

  I came across a very interesting article on brain research and presenting material to students.  The article, by Curtis Chandler,  suggests 3 brain based strategies to help increase student learning.    I liked that each strategy was clearly presented and suggestions made to implement the strategy.

The first strategy or principal has to do with timing.  The author states that timing is everything.  Apparently we learn best either at the beginning or the end but not well in between.  He also claims that it is best to present the correct information at first rather than having students brainstorm ideas so they remember it properly.

The second strategy or principal is to make it relevant.  We have to be able to verbalize both the what the concept is and why its important.  In other words, students have to have a reason to learn it.  We need to provide real life connections so they know why they are learning it.  Math cannot be taught in a vacuum.

The third strategy simply deals with when to teach topics. If they are interrelated, can the topics be taught at separate times.  If not, can they be taught in such a way as to help students learn to differentiate between the topics.  Otherwise, they can confuse the topics and have trouble doing both topics. 

I have two books I've been trying to read but haven't finished them on teaching math and the brain.  The first is How the Brain Learns Mathematics by David A. Sousa and the other is Learning to Love Math: Teaching Strategies That Change Student Attitudes and Get Results by Judy Willis.  Honestly, I keep misplacing the books and my time tends to be more limited than I like.  So I've decided or rather made a resolution to work on reading a few pages a day and synthesizing one or two main ideas until I finish both books.  Yeah!

By the way, both books have some wonderful ideas and materials.  Check them out.

The San Francisco Exploratorium.

  Since the San Francisco Exploratorium deals with science, I wondered if they had any math activities for students.  Sure enough, they do and they are science based so students can see a link between the two topics.

I checked out activity to make an inclinometer or an instrument to calculate height of a rocket or building.  It takes few supplies to create one and the exercise includes lesson on using it once its finished. The last page of the activity includes a grid so students can draw a scale model of the building or rocket.  It is simple and really impressive.

In addition, there is an activity to build a rocket out of paper and other easily obtained materials. It also has instructions for building the rocket launcher and using the inclinometer to find how high the rocket launched.  So this exercise provides a practical application for a tool the students made.

Furthermore, there is another exercise that has the students building a stride meter based on the length of their own stride, a meter stick,  a centimeter stick and dice.  I like this unit because the science department is always borrowing my meter sticks and I do not get them back.  Now I can share this with the science department so she can have the students create their own for the class.

These activities are from The Math Explorer.  The Exploratorium has some nice hands on math activities designed to explore other mathematical concepts.

At one point, you have to teach about radioactive decay if you teach a higher level math.  The activity has you using pennies to help create the understanding of how radioactive decay.  It is easy to have students do the exploratory activity prior to teaching it in class so they have a much better foundational understanding.

Another activity shows the use of vectors with moving objects.  I really like seeing some activities for up level maths.  I plan to implement several of these activities in Algebra II and Pre-Calculus.

I think I'm Finally Getting It!

Over the past few weeks, my teaching style is changing.  In stead of introducing and teaching a single topic for a few days, then moving on.  I am giving a short introduction to something I'll be teaching in a couple of days, adding more information and practice to the main topic and reminding them of materials we just got done doing.

Right now, in Geometry we are studying the Pythagorean Theorem in preparation for learning the basic trigonometric ratios.  I found a worksheet that also included an exercise on having students determine the type of triangle using the Pythagorean Theorem.

So today, I showed them how to use the results of the Pythagorean Theorem to determine if the Triangle is Obtuse, Right, or Acute.  In addition, I slid in the Triangle Inequality Theorem so they learned how to tell if the lengths would make a triangle. 

It actually made more sense to the students when I put these all together rather than teaching them separately.  I felt like the students actually understood the material better this way.  I plan to continue doing things this way.

I've also found that I teach the original lesson and have them do the math the long way, then let them use the calculator to finish it so they can focus on the lesson and not getting messed up on the calculations. 

Mathpapa app

 I love checking out the math apps section of the iTunes store on a regular basis because new apps are hitting the market on a regular basis.  I've found lots of calculators and equation solvers for various levels of math but none I was really interested in.

  The other day I was looking through various apps and came across Math Papa.  Mathpapa is specifically designed for solving algebraic equations but it is quite different from most calculators and equation solvers that I've found.  Most calculators just give the answer. Even my favorite one, My Script Calculator, provides the answer if you put the problem in so it can but it does not explain how to get the answer.

Mathpapa is different from most calculators in that it explains step by step how to answer the problem.  I really like that because it reinforces the process with the students.  If they get stuck, they see what they have to do next rather than finding the answer without knowing the process. 

I put in 2x + 3 = 23 to test the app.  I've typed out the answer so you can read it better.

Solve
Let's solve your equation step-by-step.
2x + 3 = 23
Step 1: Subtract 3 from both sides.
2x  + 3 - 3 = 23 -3
 2x = 20
Step 2: Divide both sides by 2
2x/2 = 20/2
x = 10
Answer x = 10.

I tried a few different types of problems to see if they work.
1.  Equations with variables on the same side.
2. Equations with a square root such as sqrt(2x+6) = 8
3. Factoring quadratics such as x^2 + 4x + 4.  It does not factor quadratics with complex roots.
4.  Factors perfect cubes such as x^3 -1
 5.  It solves systems of equations such as 4x + 3y = 2 and 4x + 3y = 12. In addition, it allows students to choose to see the graph.
6.  It will change a two variable inequality into slope intercept form and provide the graph to accompany it.
7.  It even provides a graphic solution for systems of inequalities.
8.  I tried a circle and it provides the x = sqrt answer but does not graph it.

There is a pro version for $1.99 but honestly, the free version does just about everything I need it to do and I want to put this on my classroom set over the holidays.  I don't mind students using this type of calculator because of the explanations involved.

Look What I Found.

  Today I did a quick search for math website and found this really cool site.  It is filled with tons of interactive math games.  Interactive Sites for Education has a lists of interactive websites for a variety of topics.

I selected Geometry to check out first.  I tried a new one for learning reflection and it just didn't seem to work on my computer so I can't report on that game.  I'll try it on my iPad if my internet is up and working later on.

So I went to a different interactive game for teaching symmetry.  This one had two characters who spoke during the game.  It simply looked a the basics of simple symmetry which is a good introduction for students who are below grade level.

I tried a rotational symmetry exercise that turned out to be much harder than I first though because you have to create the pattern in the other three quadrants so as the axis turns, the pattern matches up.  I tried several times before I got it right.  It is nicely challanging.

I also checked out the Algebra section.  I tried the model algebra game where you learn to solve one and two step equations.  I tried one of the one step problems and it uses a scale so the equation is set up with the x and the constants.  Then using the opposite values you find the answer.  It is really easy to use.

I tried the Locating the Alien activity which has students finding the aliens and reporting their position by coordinates (x,y).  This is  a fun activity and I enjoyed it.  I can see using in my Pre-Algebra class to practice coordinates.  I can also see it being used as scaffolding in my Algebra I class. 

I don't know if they will work as well on the iPads but it does work on the computer.  I'll check it out and report back.

Wow

  Today went very well and I think I found a balance for calculators in one class.  Tuesday,  I introduced/reviewed the Pythagorean Theorem in geometry. 

I had the students work some basic problems by hand.  I started by doing a few problems on the board that they copied down.  Next step was to have them try some themselves but after a couple minutes I worked it on the board in case they got stuck.  It worked quite well.

Today, I had them work more problems using a calculator so they could concentrate on when to add or subtract.  I gave them the if there is a hypotenuse length, they subtract to find the missing side and if they only have side lengths, they add to find the missing hypotenuse.  It was great because they spent a lot of time on learning when to add vs subtract and they didn't have to worry about their math.

At the end of the class period, a few students bemoaned the fact that class was over already.  That was so great.  In addition, the worksheet they used today included problems on using the theorem to determine if the triangle is acute, right or obtuse. 

Monday, we will stray to another worksheet long enough to learn to use the theorem to decide the type of triangle.  I will let them use the calculators again because it seems to take some stress off and allows them a chance to learn the material. 

From here, the students will be learning trig ratios and they need the Pythagorean Theorem for those.  I think I'll also look for some real life examples so they know there is a use for this material.

Badges

I have been reading about using badges to help motivate students, show achievement, and help students learn better.  I admit, I've been curious as to how I could use them in a math classroom for something other than discipline.  Its easy to figure out how to apply badges to behavior but not to learning the math itself. 

So I did a search and came up with some nice information.  Trever Reh has a lovely article on his blog from 2013 that has ideas for badges that could easily be used in the classroom.  He has examples and suggestions including one for those who come up with a creative way to explain their work.  He includes pictures and shares where his ideas came from.

I also found a lovely question on making your own badges.  There is a lovely blog entry by Billy Meinke on making your own badges.  I've included this because most of the information I found came from various websites who offer people the chance to earn badges as they work their way through the material.

So now we come to the question of how do you decide what to award badges for?  This article is great because it discusses criteria for awarding badges to effectively increase student motivation and provides information on where to create the badges and how to award them.  It has the specifics I need to get started.

Faculty Focus has an article with additional things to think about before you actually implement badges.  It focuses on bringing the badges into the classroom rather than using them.  It gives questions one can think about.  In addition, Inside Higher Education has an article with recommended places to create your digital badges.

I love the internet because I can find information on so many different educational topics including creating digital badges.

I Started One!!!!!!

Today is Wednesday.  My classes are only 40 minutes instead of the usual 55 minutes.  So on short days like this, I assign math tasks. I decided it was the perfect time to start a 3 act math task.  I chose Dandy Candies.  It was fun.

The first time I showed the short 1 min clip, I had the students just watch it.  I asked a couple questions and I replayed the video so students could find the answers to my questions.  The final time I showed the video, I stopped it so my students could record the information for each arrangement. 

I actually had all the students paying attention to the video and sharing the answers with each other.  There was even some discussion on the number of units used to create the rectangular prisms.  I asked the students to find the two arrangements that had not been shown as a choice.  This took most of the rest of the class period.

The class went extremely fast with no behavior issues or students trying to sleep.  Just before the ending of class, they wrote down the question.  When we revisit this activity to finish it, I am going to review calculating surface area so they can answer the questions in Act two.  Due to the way my students learn, I had to explore a couple of the questions earlier during the video so they would have something to focus on. 

I look forward to finishing this up next week.  I"ll give you an update then.

Math Central

Math Central is a lovely website maintained by the University of Regina for both students and teachers.  The site offers a resource room, a data base of answers to questions, information on mathematicians, math beyond school, problem of the month and several other sections such as links and outreach activities which are oriented for Canada.

The resource room has a variety of materials for elementary, middle school and high school.  Since I teach high school, I checked out some of the high school topics.  If you look at all the high school strands, there are 102 activities to choose from.  Some topics are a bit esoteric for what is normally taught but they can be used to show students things outside the normal material covered.

The quandaries and queries section holds answers to questions asked by people.  The topics are arranged in alphabetical order  and each topic might have more than one question and answer associated with it. 

The math beyond school has two pages worth of how math is used in real life for grades 10 to 12.   The real life examples are available for grades K to 12.  While the examples do not include the actual mathematics, they do give a good summary of the math.  For instance, the article on airlines provides information on all the different ways airlines use linear programming to help schedule pilots, sell seats, and keep costs as low as possible.

The final section that is usable is the problem of the month.  Although these problems are no longer being produced, the old ones are available to use.

Maths Frame

  Maths Frame is a website from the UK that has some nice materials to use in the classroom.  This site offers quite a few games, some of which are free, that provide scaffolding for certain math skills.

I clicked on the resources tab first and checked out a huge list of possible games.  The first game I looked at is called Coordinates - reasoning about position and shapes.   You are given a choice of four levels. The first two levels limit coordinates to one plane while the second two levels use all four coordinates.  The second shape was a rectangle and I had to find the missing coordinate.

If you do not select the proper answer, it just disappears.  Only the correct coordinate will work.  Then I checked specific math topics such as comparing and ordering numbers.  There were two different free games I could have chosen.  One was comparing numbers on a number line while the other has the player estimating the position of the number on a number line.

Although many of the games are geared for younger children, there are some free games that could be used by middle school or high school students who need extra work on certain topics.  I found a perfect game for my pre-algebra class. They are starting the unit on decimals tomorrow and most of the students are well below grade level with their skills.

Its called Placing Calculations on a Number Line which has students work with either whole numbers or decimals.  They either add, subtract, multiply, or divide numbers and select the answer on a number line.  I checked out adding decimals and discovered students are given a choice of ten different possibilities to practice.  I don't know if it will work on my iPad but it does work on my Mac.  I'll know when I try it in my classroom.

Go check it out and see if it works for your students.

Math Guide

I checked out one of these top 10 or 20 lists and Math Guide was one of the sites listed.  Math Guide has lessons, interactive quizzes, and worksheet generators. 

I checked out the lesson in Pre-Algebra titled "Operations on Integers".  The lesson comes with a reading assignment that includes several videos and a quiz for each section.  This means they read a section, watch the video and then take the appropriate quiz.

 The quiz has a few questions that can be checked at the end. If an answer is wrong, the student is given the correct answer and another chance to take a different quiz.  Even if the results are 100 percent, another quiz is offered.  They can also go into the quizzes without reading the lesson or watching the videos so students can easily return again and again to practice.  The quiz is a simply written one which should work on the iPad without any trouble.

They cover pre-algebra, algebra, geometry, college algebra or advance algebra with vectors, trig, and conic sections.  The index lists all the subjects and each lesson has a guide so you know if there is a reading, video, quiz, or activity.  In addition, there are worksheet generators available for most topics.

Furthermore, there is a teacher section with additional materials to help round out the lessons.  In the teacher section there are  tutorials, worksheet generator, standardized test help, several general review games,  research and links.

This is a very nice site with everything you need to plan units or to use as differentiation so students get the scaffolding they need.  For me, I love they offer math baseball, football and jeopardy templates so teachers can design their own versions of these popular games.

The one link takes teachers to a website for integrating computer technology into the classroom.  Topics include common core math, standardized test prep, math resources, software and technology integration.  The technology integration looks at the topic in general, offers sites to find materials, and other information.

Dan Meyer's 3 Act Math Tasks and Assessments

I have been wanting to implement Dan Meyer's 3 Act Math Tasks because I've been very impressed with the ones I looked at but I've never figured out how to implement them.  I need to continue moving due to the amount of material I need to teach while trying to help students develop perseverance. 

Since I've switched from word problems to performance tasks, I do have a place I can slip these math tasks into the same slot I do performance tasks because they are another item to help build persistence.  I could easily spread this activity over two or three days.

I realized today that there is nothing in the rules that states I must give a test with all four parts in one class period. I should explain that I write the every test with four parts.  The first three sections have tests current materials while the final section covers previous material.  A student does not need to retake any part they pass.  This means if they pass parts 1, 2, and 4, they receive a 75 percent.

In addition, I have them select say four out of six problems.  I usually have one easy problem, one hard and the rest are medium level problems.  I find that some students do the bare minimum while others attempt all the problems so if they miss one, they have another chance to pass the section.

I’m playing with the idea of giving the test over four days, one part each day but only assign it after I do the warm-up and the day’s lesson with perhaps one or two guided practice problems.  I know many of my students suffer from big time test anxiety. 

Or I could set up the test in 4 sections on a web based test site or google docs so the students can take it on a digital device.  The test could be set up for answers only while they show the work on a scratch paper.  I think I'm going to administer my next test this way to see if my students do a better job and are less anxious during the test.

Figure This!

  The website Figure This:  Math challenges for Families is a part of the National Council of Teachers of Mathematics and is filled with lots of short performance tasks.  That's right, performance tasks but these differ from most others.

There are about 80 challenges (as the site calls them) that are classified according to Algebra, Geometry, Measurement, Number, or Statistics and Probability.  In addition, there is a short description giving you an idea what each challenge focuses on.

As for the challenges themselves, they are very short with illustrations and hints to help students work their way through the problem.   You do have the choice of selecting a specific problem or taking a random challenge.

Furthermore, there is a teacher corner where you can go to download the files in a pdf format.  In addition, the teacher corner has ideas for teachers, the standards these challenges met in the past. Although these problems may not meet current common core, the standards of performance will help build persistence.

I like that some of these challenge srelate to real life.  For instance, one found under rate of change (slope) that deals with salaries.  The problem uses information from the early 90's on women's vs men's salaries.  The question asks if woman's salaries are catching up to men's salaries as stated in the headline.  Once student figure the answer to this, a second part could be added with current figures to see if the rate has changed and if so by how much?  In addition, there is a note at the bottom of the exercise that tells you who uses this type of data.

I just found the "Did you know?" button which provides additional tidbits on the topic from the challenge.  I clicked on it and learned something about salaries but the information is dated but with a bit of research, the students can see how these pieces of information have changed.  In 1996, Germans had the highest per hour pay in manufacturing.  I'm wondering if Germany still pays the most or if another country has taken that honor.

I think it would be easy to add a small worksheet requiring students to go online to research who gets paid the most for manufacturing or which city has the highest salaries in the country. 

St. Louis Zoo

  Yesterday, my students went on a virtual field trip where they learned about the mathematics used by the zoo.  In addition, they saw some animals they'd never heard of.

For instance, the first animal they learned about was the Hellbender which is a salamander found in Missouri.  Its also known as the snot otter and a few other names.  Aside from learning about the animal, my students learned that hellbenders born in the wild only had a 5 to 10% survival rate while those born in captivity had a 75 to 90% survival rate.  It took the zoo 20 years to determine these figures.

Another animal, they got to check out was a Capybara which is the worlds largest rodent.  It can grow up to 150lbs.  The pharmaceutical math they learned in this section required them to figure  out the dosage for an 85 pound animal. It was great  because the medication was a ratio using kilograms so students had to convert from pounds to kilograms and then use a ratio to finish calculating the dosage. Since the medicine came in 7.5 mg or 15 mg, the students had to figure out how many of which tablet they were going to use.  In addition, they had to calculate the liquid dose.

The last examples was great. The students saw the data in table form for four baby hedgehogs and they saw the same data shown in several lines on one graph.  They learned that the lines indicated the animals were all healthy and gaining weight regularly.  In addition, the female hedgehogs gained less weight than the males.  It was great because she had a live hedgehog to show the kids.  It turns out the creature is nocturnal and has developed a great sense of smell to compensate for the lack of vision.

I've got another virtual field trip scheduled for next week so the students can learn more about probability.

Fun Math

Fun Math is a math website by Cynthia Lanius from Rice University.  It has some very interesting  real life units.

For instance she has one called the Mathematics of Cartography or the math of maps.  She starts with what is a map, the history of map making and offers several math problems involving the use of maps from rate/time/distance to systems of equations.  She includes teacher lesson plans.

Another two activities use small mathematical tricks to use with calendars.  They are cool because Cynthia even provides the math to show why the tricks work.  I think its great because these tricks apply to any month you choose.

Another activity has to do with graphing stress as a rate of change.  The activity asks questions which help the  students interpret the graph.  I like that.   Too often, students do not get a chance to practice reading and understanding graphs.  Furthermore, there are three other graphs for students to practice these skills.  At the end, she shows the answers to the questions on the first graph.

Finally, she has a lovely fraction activity using pattern blocks both real and on-line.  Its cool because she is asking students to look for relationships among the various pattern blocks.  Although many students have fractions down pretty well, they are often weak in seeing relationships that exist between the math and reality.  This is a good way to help students develop the understanding.

Give it a look to see what materials can be used in your classroom to help create a better understanding of the materials.  Its a fun site.

Previewing

I received training several years ago on a way to teach so students retain the material better.  One thing they said was that you needed to preview the information with the students so they start to build a foundation.

To me, that meant I would introduce it the day before I taught it but honestly, it really didn't word.  This week, I've got students finishing off a project while preparing for a test, so I'm spending about 5 min. talking about the next unit.

I'm spending the week, just giving a little bit of information.  Its almost like a movie trailer that wets your appetite, but doesn't tell everything.  Yeah, the preview in math is that small glimpse into the future so students start building connections and memory.

I remember the instructors stating that for a student to learn, they need to be exposed to it multiple times over a 21 day period.  This means it starts with a teaser to start their brains into learning it, then increase the amount they get during the actual instruction time, and to include a bit of a review of the material.  The review can be just a bit, like a short review you gave your friend of the latest movie or that quick chat you have with a friend to compare views.

You briefly mention the topic and how it relates to the current topic so the students need to pull up the information to help the brain move the information from short term to long term memory.  Sometimes I feel like I'm kind of slow at learning to apply things I've learned but often that is because it takes me a while to figure out how to integrate the learning into my style of teaching.

It also helps if I can see the material applied in a real situation with someone explaining what part is this or that.  Ohhh well, better late than never.