Watching Videos Actively

I am taking a college class on flipping my classroom.  The idea is that I have students watch the videos the night before so I can spend more time working with students on the assigned work.  The thing is, most students I've worked with watch videos passively and don't know how to actively watch.

This is my fear when flipping my classroom but there are things I can do to turn students from passive to active viewers.  The good thing about videos is they help build background knowledge while providing another way of seeing the knowledge.  Videos can also enrich and clarify written text and deepen or solidify student learning.

There are several ways to accomplish this. The first is to use a three step process.  The first step is to provide questions to help students focus on the most important points.  Students write down their answers to the prompts or questions on paper or on a digital document.  Next, the class should rewatch the video together with the teacher taking time to stop the video to comment on things students need to be aware of while modeling appropriate behavior.  The final step is to debrief students to make sure they got the important information.

Other suggestions for using videos more actively is to give students a reason for watching the video, taking time to pause the video so students can write down answers to the questions or prompts, and turn on closed caption so students can read along with the narrator or presenter.

There are ways to increase student involvement to make them more active viewers.  Ask students to tweet their comments to each other with the appropriate hashtags or create a poll for students to answer with information from the video.  My favorite way is to use a video from Edpuzzle or use Edpuzzle to curate a video.

I prefer using a curated video because I can include comments on what to watch out for when doing the math, I can include a short answer question, or a multiple choice which students have to answer before they can move on.  I can also include directions for them to copy certain things into their notebooks.  Furthermore, I can check to see how long it took for them to complete the exercise so I know if they whizzed through it or really paid attention.  I can also see how many times students watched each section.

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

Warm-up

If there are 8 flowers per square foot, how many flowers will you find in 9 square yards?

Warm-up

If Water Lillies grow from 2 square feet to 25 square feet in 3 years.  How fast did it grow each month?

Splash!

Splash! is a mathematical software modeling app developed by Creative Learning Exchange to show system dynamics.  In other words, it allows people to model any simple system that increases or decreases.  

This app has versions for iOS and android.  Both versions are free.  It is fairly easy to use but since its for beginners it might be simplified.  

The person who lead the session used the rate of a bucket being filled with water at first and then added a second condition of water exiting.  This process used two different rates.  It was fairly simple to set up.

 The first thing one does is begins a new model by pushing a + button.  It has you name the model and the design page opens up.  Since I took the session at the Northwest Math conference, I had someone guiding me through the set up.

This group has prepared a really nice 43 page instruction booklet which explains how to use the app.  In addition, it shows how some of the different types of systems, this app can be used for.

The left side of the work area has the parts used to create the actual system.  Going from top to bottom, the first one is the container which represents the changing item such as cash, interest, CO2 levels, etc.  The next one is the pipe tool which notes the thing that causes the item in the container to change.  It's location determines if the change is positive or negative.

The circle is the auxiliary button which allows people to select a symbol  to use.  There are so many to choose from.  The arrow on the bottom is the connector which allows you to instruct the program on relating two things together. The buttons on the right provide the basic operations and the ability to add a graph.

I made a quick model for population with only the knowledge I had from the workshop. I can tell you it is not quite correct because I do not have the proper relationship between the population and birthrate.

One nice thing is that I can easily go back, change things, and make adjustments to the basic model until I get it right. There is an undo button when I get something wrong or I can delete things if needed.

Even without putting a graph into the model itself, it automatically makes graphs available.  

According to another presenter, when students set up a system in this type of modeling software, they only have to worry about how the pieces fit together to create the whole system.

Students do need to know rates for things like birth and death rates, or interest, or whatever but they do not need to really know the actual mathematical equations involved because the software provides it.

This app provides a visual of how the pieces interact with each other so they see the whole picture rather than struggling with the math.  As I'm exploring this app, I'm enjoying playing with it.  Creative Learning Exchange also provides lessons and quite a bit of support. I plan to continue playing with this app until I feel comfortable enough to use it in class with my students.

You might want to check it out by downloading the app and playing with it.  I think that students as young as 5th or 6th grade could run easy scenarios using this software.  Let me know what you think, I'd love to hear.

New Way To Teach Square Roots

One of the workshops at the math conference was on teaching students to find and simplify square roots.  It begins using concrete before moving to pictures to abstract.

It was awesome and I learned so much.  The activity uses small square of certain areas.  There are squares ranging from 2 cm squared to 10 cm squared.  These are not 2 x 2 but sqrt 2 by sqrt 2 so the area is 2 cm squared.  The same applies to each square.

The introduction starts with a square that has an area of 6 cm squared.  The diagram shows how each side is the sqrt of 6 cm.  The professor running the workshop, emphasized using the proper language every time including the unit.  He stated if there is no unit listed use units squared and the square root of 6 units because using the language of math properly helps.

After the introduction, students are given a square that is 12 cm squared.  They are expected to use smaller squares to cover the area exactly.  After checking things out, they'll discover they can use four   squares with an area of 3 cm^2.  So one side is 2 sqrt 3 and that is the square root of 12 simplified.  This part of the exercise has every step written out along with questions.

The students repeat the exploration using a square with an area of 45 cm^2.  After a lot of trying different possibilities, they'll discover they need 9 squares of 5 cm^2 to cover the square.  If they count things, they'll find the simplified version is 3 sqrt 5.

As they work through the packet, they move from having to fill the whole square to find the answer, to only needing to do the edges, to understanding it. For each part a step is removed so people are doing one more step during the practice.  About half way through, they are expected to draw in lines so they are creating a picture of the squares rather than using them physically.  By the end, they can do square roots.

In addition, students can use these same squares to learn more about the Pythagorean theorem.  Students take the squares and work on putting them together so they form the edges a right angle triangle.  For instance, if the two smaller squares have sides of area 4 and 4, the larger square is 8, it shows they have a right triangle.  As they play with the area squares, they might notice that the total of the two smaller squares is less than the larger square and it forms an obtuse triangle.  If the total of the two smaller squares is bigger than the larger square, they have an acute triangle.

So cool.  Students see how the Pythagorean theorem is saying when you add the areas of the sides together, you end up with the area of the hypothenuse but that is not shown as often. This led me to wonder if I could use the length of the sides to show the triangle inequality theorem which says that the length of two sides added together must always be longer than the third side to have a triangle.

I really loved this activity and can hardly wait to use it in my classroom.  I'd love to hear what you think about it.  I got the information from a Professor who teaches in North Carolina.  If you want his information, leave a note and I'll be happy to share.  Have a great day.

It Takes That Much?

 I just finished an article on Cochineal.  Its a but that lives and dies on a cactus plant in Mexico. This insect is what was used to produce red dies back in the 17th and 18th centuries in Europe. I read of an incident where the Earl of Essex captured a Spanish Galleon containing 27 tons of this dye.

It takes 70,000 insects to make one pound and another 2000 to make a ton.  So it took 70,000 x 2000 x 27 or 3,780,000,000 bugs for that shipment.

So I wondered about natural dyes in general and what it took to get a pound or how to calculate the amount needed and talk about math and its uses.  It is definitely used here.  According to one site, the amount of dye material (plants, etc) for natural dying is based on the amount of fabric you  wish to dye.  It is referred to as WOF or weight of fabric.

For instance if you want to dye some fabric a medium red using madder, it has a 50% WOF so if you want to dye one pound of cotton, you would need half a pound or 8 oz of madder.  On the other hand if you wanted to use Cochineal (an insect that provides a red dye, you'd use 6 percent Cochineal to one pound of fabric or about one ounce of dye.

According to another site, it is recommended one use equal amounts of plant material as fabric so if you want to dye one pound of fabric, you'd use one pound of plants. The plants are chopped up and  heated in water for a couple of hours.  I saw a suggestion of equal parts of plants and water to get a good dye.

In addition, there are mordants used in dyeing. Mordants help prepare the cloth for dyeing and the final color depends on the mordant.  Some examples are:

1. Aluminum Sulfate or Alum is 12 percent of the weight of the fabric or 2 ounces per pound of fabric.

2. Cream of Tarter about 6 percent of the weight of the fabric or about 1 ounce per pound of fabric.

3.  Iron via old rusty nails is set at 1/2 ounce of iron to 500 grams of fiber.

There are other mordants but many of them are rather toxic and most are 1 ounce per pound of fabric.

There are also fixatives which help set the dye.

1.  Salt is set at one part to 16 parts water.

2. Vinegar is used at one part per four parts of water.  I use this if I think something I just bought might need this treatment.

3. Baking soda requires  1/2 cup per gallon of water.

So dyeing using natural plants, etc use a lot of math.  As you can see, there are ratios and percentages involved.  This is real life math because any dyer who uses natural plants, etc have to use this math.  Let me know what you think, I'd love to hear.  Have a great day.

Easy, Quick, Math Games

One of the sessions I attended at NWMC focused on easy games designed to help students work on basic skills while encouraging higher level thinking skills. Most of these games do not require much more than paper and pencil for the students. The teacher doesn't need anything more than numbers, dice, or markers.


1. "24". is a game where the teacher provides four random numbers between 1 and 9.  The students have to use addition, subtraction, multiplication, division, exponents, and grouping.  The idea is students need to use all four numbers with the appropriate operations to make 24. This game can be done as speed  competitions if you want.  It provides immediate feedback, while creating mathematical dialog.  At the end of the year, hold a tournament with brackets and everything.

2. "Bowling".  Students write the numbers 1 to 10 in a vertical column.  Provide 3 single digit numbers between 0 and 9.  This is the first roll.  Students are to use these numbers to find as many numbers on the list mathematically.
You get a 1, 5, 7
1 = 7 - (5 + 1)
2 = 7 -5 * 1
3 = (7-5) + 1
4 = 5 - 1^7
5 = 5 * 1 ^ 7
6 = 5 + 1^7
7 = 7 * 1^5
8 = 7 + 1^5
9 =
10 =
Once you've done all the numbers you can, you'll roll again and have students use these numbers until they can't find any more.

3. "Hit, Almost, Miss.  You choose a three digit number.  Students make a guess on the digits giving three at a time.  You'll write H for you got the right number, A is Almost in that the number is there but not in that place, and M is for miss or you didn't get close to the number.  It is best to write the H, A, M in a triangle so students don't know exactly which digit it is.

4.  Throw away.  You have students make 6 spaces so you have three in one row and three in the next row to look like this.   ___. ____.  _____
                                    ____. ____  _____
                                   ___________________

You give a target number such as 981.  So you roll one number and call it out.  Students decide if they want to keep the number or throw it out.  If they keep it, they have to write it in a space, they cannot wait.  Then roll another number and repeat.  Eventually, you will roll the dice 9 times and students use 6 numbers while throwing out three.  Numbers can be repeated and students may add or subtract the three digit numbers to get the final one.

Here are four games you can use to spice up your classroom, give students a chance to practice skills and promote higher level thinking and mathematical discourse.  Let me know what you think, I'd love to hear.  Have a great day.