Pumpkin Teeth

Objective:  To assist students with number sense.

Materials:  Pumpkin Templates, counters or small blocks, growth mindset

The story:

Pumpkins have been cut with different amounts of teeth, sometimes equal on the top and bottom but usually a different amount of teeth on the top and bottom.

Grade 1 - 2: Print of pages 1 and 2 of Pumpkin Template

1. Provide students each with 4 blocks (or counters) and have them put them inside the large pumpkin mouth (page 1 of template).  Ask students to stand up and walk around and do a gallery walk of different ways to arrange 5 teeth into the pumpkin.
2. Draw 5 pumpkins on the board and ask students if they can determine all the ways to arrange 4 teeth. (5 different ways; 0 teeth on top, 1 on top, 2 on top, 3 on top or all 4 teeth on top) 
3. Have students flip over their sheet (page 2 of template), and give students 1 more block (a total of 5 blocks each), and ask them to show all the different ways to arrange 5 blocks.
4. Complete a gallery walk again.
5. Ask if we, as a class, figured out all the ways to arrange 5 teeth?

Grade 3 - 5: Print off pages 2 and 3 of Pumpkin Template

Might want to use part of the previous ideas and then…. Give students the second page template, and a handful of blocks...

1. Using page 2, Ask students how many different ways are there to arrange:
1. 1 tooth? (2 ways) 
2. 2 teeth? (3 ways)
3. 5 teeth? (6 ways)
4. 10 teeth?
5. What if there were 50 teeth?
6. Is there a pattern?
2. Using page 3, provide students each with 5 blocks (or counters) and have them put them inside either of the pumpkins, all in one pumpkin, or some in one and some in other..  Ask students to stand up and walk around and do a gallery walk of different ways to arrange 5 teeth into the 2 pumpkins.
3. Using page 2, Ask students if they can determine how many different ways to arrange:
1. 5 teeth in 2 pumpkins?
2. 6 teeth in 2 pumpkins?
3. 7 teeth in 2 pumpkins?
4. What about 50 teeth in 2 pumpkins?
5. Is there a pattern?

Grades 6+: Print off pages 2 and 3 of Pumpkin Template:

Might want to use part of the previous ideas and then…

1. How many ways can you arrange 5 teeth in 3 pumpkins?
2. How many ways can you arrange 7 teeth in 4 pumpkins?
3. Is there a pattern?
4. How many ways can you arrange n teeth in m pumpkins?

Halloween Math

As we approach Halloween here are some "Scary" problems your students might find interesting:

Elementary:  

3 different monsters were out for halloween.  Together they had 12 feet.  If each monster has a different number of feet, how many feet does each monster have?

Extensions:

• What could be the smallest total number of feet?
• If each monster has 2 more eyes than feet, what would be the total number of eyes?  Is there a total number of eyes that you cannot make?

Middle School:  

Zorbit's released some amazing pattern chats around Halloween.  Here are some of them: (For more halloween activities check out Zorbit's activities here)

Extension:

• Could you rearrange the pictures above to make it easier to see the pattern?  
• Can you make a pattern that doesn't increase at a constant rate?  How would you describe your pattern?

High school:

World War Z and Mathematics

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

For all resources click here.

Wacky Quadrilaterals

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:

Extension:

Simply show this animation and ask "What is this visually proving?"



A possible video to show is here:

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?"

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