- Saturday 14 March 2020
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Mathematics can often prove to be a challenging subject to engage students with. This is unsurprising: in the classroom, maths practice often involves dull repetition and rarely requires further exploration. However, as any mathematician will tell you, mathematics is about much more than learning times tables.
Thankfully, Pi Day has arrived: the perfect time to celebrate and teach students how interesting, clever and entertaining mathematics can be. Today’s blog is dedicated to mathematical activities, tricks and quirks that might spark a fresh interest in the magic of numbers.
Note that most of these activities require an understanding of subtraction, addition, multiplication and division, and so are appropriate for older students.
Warm-up: What can maths do?
If students aren’t interested in maths, they likely don’t understand that it gives you the power to perform magic tricks and see through closed hands. Of course, that’s not true, but a good Pi Day lesson can imply otherwise through fun teacher demonstrations, like those below.
Pick a card!
For this activity you will require an ordinary deck of cards.
Ask a volunteer to pick any card. They may reveal it to the class but not to you. Next, ask them to:
- double the card’s face value (where ace = 1, jack = 11, queen = 12 and king = 13)
- add 4
- multiply by 5
- add the suit value (club = 1, diamond = 2, heart = 3, spade = 4)
Ask the student for the number they came up with. Mentally subtract 20 from their result. The tens and hundreds digits of the resulting number will give you the card’s face value and the ones digit the suit value. For example, 74 implies a seven of spades. Complete your trick with a classic ‘is this your card’ reveal.
Which hand?
For this activity you will require a five-cent and a ten-cent coin.
Select a volunteer and ask them to hold one coin in each hand behind their back. You will be guessing which coin is in which hand. Ask your volunteer to:
- multiply what’s in their right hand by 2
- multiply what’s in their left hand by 3
- add the two answers together and tell you the result
If the answer is odd, the five cent is in the left hand. If it’s even, it’s in their right hand.
Maths is truly magical!
For this activity you will require a deck of cards.
Ask a volunteer to cut the deck roughly in half and to count the number of cards in the cut’s top half. Take the split deck back and do the following:
- Add the digits of the counted number of cards together.
- Count this number of cards up from the bottom of the top half. Show the class your last card: this is your ‘card of truth’.
- Put the deck back together.
- Spell out the following phrase, dealing one card for each letter: ‘Maths is truly magical’.
At ‘L’, you should find your ‘card of truth’: maths must be magical after all!
Explore this!
Once you’ve shown off some teacher tricks, invite students to explore the following maths mysteries themselves.
Dice stacking
This activity requires each student or pair to have three dice. Provide them with the following instructions:
- Stack the dice in any order on top of each other.
- Find the total of the five hidden numbers.
- Subtract the number shown on the top face from 21.
- What do you find? Try it again and see if you can discover a pattern.
Spell and count
Ask students to pick absolutely any number and do the following:
- Write the number out in words.
- Count the letters.
- Write this number of letters in words.
- Count the letters ...
- And so on!
- What eventually happens?
Reaching fifteen
Ask the students to pick any number.
- Multiply the number by 3.
- Add 45 to your answer.
- Multiply that answer by 2.
- Divide that answer by 6.
- Subtract your original number from this answer.
- What is your final number?
- Try it again with a different number!
Thirty-seven
- Ask students to pick a 3-digit number with repeated digits (111, 222, 333 etc.).
- Add the 3 digits.
- Divide the original number by the 3-digit sum.
- What do you find? Does this always happen?
Brain challenges
Even though they are difficult, out-of-the-box maths problems can be far more interesting than ordinary equations. This is even more true when students can work together to solve the problem. Consider giving your class some of the following challenges.
Making 4 L
Imagine you have a 5-L cup and a 3-L cup. Using these two cups and no other containers, how can you measure 4 L of something? (Because this is a difficult problem to manage without visuals, it may be help to actually bring in cups to represent 5 L and 3 L, along with a supply of water or sand.)
Solution:
- Fill the 5-L cup. Pour from this into the 3-L cup.
- Throw out what’s in the 3-L cup.
- Pour the remaining 2-L from the 5-L cup into the 3-L cup.
- Fill the 5-L cup again.
- The 3-L cup has 2 L inside it. Fill the remaining 1 L with water from the 5-L cup.
- Your 5-L cup now has 4 L inside it.
Posting problems
I want to post a recorder that is 19 cm long. However, the only postage box available has a width of 12cm and a length of 16cm. How do I post it?
Solution: Place the stick diagonally!
Eight eights
Using only addition, how can you use eight eights to get to the number 1000?
Solution: 888 + 88 + 8 + 8 + 8 = 1000
Jack’s beanstalk
Jack decided to grow a mighty beanstalk to reach the clouds. The special seed he planted grew a stalk that doubled in height each day. It took 10 days for the beanstalk to reach the clouds. How many did it take to reach halfway?
Solution: Nine days. If the height doubled each day, it would have been halfway up the day before.
Pi recital
Many students are likely not familiar with the concept of Pi yet. While there’s no need to go too deep, it could be a fun conclusion to the lesson to introduce the number. (Note that some understanding of decimals is required to comprehend Pi at a basic level.)
While most explanations of Pi cover definitions like ‘circumference’ and ‘radius’, it’s sufficient for students to know the following:
Pi is a special number that is related to circles.
In fact, we can find the size of any circle’s perimeter just by knowing Pi and how wide the circle is.
Provide students with some string and an image of a circle. Ask them to measure how long the circle’s outside is, using the string and a ruler. They should find it quite difficult! However, measuring the circle’s width is relatively easy and only requires a ruler.
We write Pi as π, which looks like a letter rather than a number.
Technically, Pi should be written 3.14159265358979323846264 ... and so on. It’s a number that never ends.
People find this infinite nature of Pi so cool that there’s a world record for Pi recitation. Pi reciting contests are also held across the world.
It might be fun to hold a class Pi contest, to see who can learn the most digits of Pi. It’s also a possible introduction to teaching personal methods of recall, such as songs and mnemonics.
Kickstart that mathematical affection!
No matter what activities you do, the importance of Pi Day is sharing a positive, excited approach towards mathematics. That’s the best way to kindle student curiosity. Who knows? There may be a future mathematician in your classroom!
Many of these fun tricks and ideas come from the ever-popular mathematician Dr Paul Swan, who has written several mathematics resource books for R.I.C. Publications in the past. Search ‘Paul Swan’ in our store to see what’s on offer.
Enjoyed this post? View our full range of maths education resources, and explore the maths section of our blog.