Wednesday, June 12, 2019

Monster Soup!

Monster Multiplication Game

Scenario:  We are cooking monsters today!!!  Some monsters have 1 eyes, others have 5 eyes, and there are even other crazy monsters.  We want to get as close to the number of eyes the recipe calls for as possible.

Do example of “1 eyed monsters” with students. Have one student up to the front to demonstrate with you.

Activity:  Roll two 10 sided dice.  Determine which roll you want, and that is the number of monsters you will add to the recipe.  Repeat 4 more times. (Total of 5 rolls of 2 dice, each time picking one of the 10-sided dice to represent the number of monsters you add to the pot)

Provide each student with a recording sheet and place them in the appropriate station to practice the fluency skill they need:

A possible progression could be: (Dr. Nicki Newton progression of multiplication)

  1. 1 eyed monsters - 30 eyes or 10 eyed monsters - 300 eyes or 5 eyed monsters - 150 eyes
  2. 2 eyed monsters - 60 eyes or 4 eyed monsters - 120 eyes  or 8 eyed monsters - 240 eye
  3. 3 eyed monsters - 90 eyes or 6 eyed monsters - 180 eyes or  9 eyed monsters - 270 eyes
  4. 7 eyed monsters - 210 eyes

Thursday, May 23, 2019

Wacky Quadrilaterals

Image result for quadrilateral

What happens when you make a quadrilateral (a four sided object) and connect the midpoints of each side?  What if you did this over and over again?

Here is an activity that investigates that!

Wacky Quadrilaterals

  1. Draw any quadrilateral that takes up most of the page.  Measure the interior angles and add them all together and record this.  Measure and record the perimeter
  2. Measure and determine the midpoint of each line.  Connect the midpoints and make a new quadrilateral.  (Iteration 1) Measure the interior angles of the new quadrilateral and perimeter.
  3. Repeat step 2, and fill in the chart with the sum of the new angles and perimeter.
  4. Estimate what the sum of the angles and perimeter will be the for 10th shape.  (Do not make the 10th shape, simply estimate based on the pattern).
  5. Color in your shape to make a creative design.

What do you notice?  Wonder? What would be the sum of the interior angles of iteration 10?  Perimeter?

Here is a recording sheet.

A possible example:


Simply show this animation and ask "What is this visually proving?"
Image result for quadrilateral

A possible video to show is here:

Friday, March 29, 2019

How often do I do math?

I have seen English teachers sit around and discuss the books they are currently reading, or Social Studies teachers debate current issues and the impact they may have on society.  I have seen CTS teachers talk to their students about the home projects they are working on;  whether it be a new woodworking project, an automotive problem they are trying to solve, or even how one is trying to code an arduino board to allow for more functionality within their home.  As I visit and meet more teachers, I am constantly hearing about teachers being 'students' of their own subject area outside the walls of their classroom.

This then caused me to reflect, which I will ask you to do as well, on the question "How often do I sit down and work on mathematical problems outside my own classroom?"

When I first asked this question, I sadly had to respond with "rarely or never".  At the time, I would ask my students to try multiple questions daily, learn new ideas, consolidate older information and ultimately be problem solvers around questions they have never seen before; sadly I modeled none of this outside the walls of my classroom.

Perseverance, resiliency, creativity, and critical thinking is what I expected of my students on a daily basis around mathematics, but until I embraced these practices in my own life I didn't actually know what if felt like to be stuck in a problem without knowing what to do.

"What do you do when you don't know what to do in a math problem?"  I asked this question to 800 Grade 4 - 12 students and the number one answer (by over 80% of the respondents) was "ask the teacher".   This was startling!!  I couldn't arm my students with authentic problem solving strategies until I actually put myself in their shoes.  Once I tried working on problems that caused me to stop and ask "what should I do now?", I was able to understand that global problem solving strategies was missing in my own math classes.

Originally, I would teach  "When working on a problem from unit X, try these strategies.  On unit Y, try these.." and so on.  The issue is that I wasn't teaching true problem solving but instead strategies specific to certain domains.  After trying math on my own time, and at my own level, I quickly learned that some of the best strategies include, but not limited to, are:
  • Visualize the problem; draw it out.
  • Guess and check; change guess slightly and see how it changes the result.
  • Approach it logically;  Use "if then" statements to simplify information.
  • Identify a pattern; change a number, a sign, or something critical and see how it changes the problem.
  • Work backwards; if we can hypothesize the result, what else would have to be true?
  • Solve an easier problem;  simplify the problem into one that is easier to work with and see if you can identify anything new.
My challenge for myself now, and I am extending it you as well, is to try a math problem once a week.  Ensure the problem isn't one that you can solve in seconds, or even minutes.  Try and find one that makes you reflect on "What do you do when you don't know what to do in a math problem?"

Friday, December 14, 2018

Triangle in a circle

Show this first animation and ask, what do you notice?  What do you wonder?

Then ask the following:  If the diameter of the circle is 8 cm.  What (or when) is the largest area?  What are the dimensions of this triangle? 

After students solve that pose, When is the area exactly half the largest?  What are the dimensions of that triangle?  What is the angle?

After some work time and playing around with the above problem, show them this animated version

Wednesday, December 5, 2018

Trig Ratios animated

Two different triangles are animated.  Show your class this animation and simply ask:
  • What do you notice?
  • What do you wonder?

After some conversations show them this one, with the side lengths being shown and ask again:

  • What do you notice?
  • What do you wonder?

Lastly, show them this image and ask them "How could we analyze this?"

  Some possible routes:

  • Prove the sides hold true for Pythagorean theorem
  • What angle(s) would be in the triangle?
  • How are these 2 triangles similar?  How are they different?

Wednesday, November 28, 2018

Area and perimeter of a triangle

Another way to possibly introduce, or reinforce, the area of a triangle and perimeter could be to show this gif:

Ask, "What do you notice?  What do you wonder?".  After some discussion pose, if not already asked, the following questions:

  • When is the area the least/greatest?
  • When is the perimeter the least/greatest?

After some discussion show this gif.