Math Project Ideas

This is an assortment of math project ideas and puzzles.  I'd love to hear of any different math brain teasers that aren't represented here.   Another good place to look for math games for kids is math ixl.

A yellow banner that says Mathematics, and has red stars under it in a line.

Math Project Idea #1 - Red & Black

Equipment:

You will need approximately one deck of cards for each student.  On the plus side, mixing all the cards together is no problem.  In fact, I started keeping my ruined decks of cards in a box as complete decks are not necessary.  Just throw away the bent cards and keep the rest.

Play:

There are several variations depending on the level of your students.  

Set aside the Jacks, Queens and Kings.  Aces count 1.  Red cards are negative and Black cards are positive. Groups of 2 to 4 students are good for this.

Addition/Subtraction - Each player plays a random card stating the value.  A six of hearts would be "negative six" the next player plays a 4 of spades and would say "negative two", because the negative six and his positive 4 make a negative two. The next player plays a 3 of diamonds for a "negative five".

Multiplication/Division - Add the Royal cards (Jack, Queen, and King).  Play the Addition/Subtraction game except when a black Royal is played you multiply, when a red Royal is played you divide.

Say the first card played is a Queen of Spades play another card.  This means the next card played is a multiple.  We're at zero now so when I play a six of clubs, I say "zero" (0 times six).  The next card is a nine of spades, that player says "nine".  Next card Queen of Hearts so play another card, it's an eight of spades and nine divided by 8 gives us a total of 9/8ths or we'd accept 1 and 1/8th. The next card is a six of diamonds for a total of 9/8 minus 6 or "negative 4 and 7/8", I'd accept -39/8.

You get the idea.  You can see that Multiplication/Division will slow things down a bit.  Realistically, you could let the students use a calculator and call out decimals for this one.

Math Project Idea #2 - How high is the building

Not too original here, a lot of you may have learned this one in scouts.

Equipment:

A yard stick (or a meter stick)

A tape measure

About 3' of rope (or 1 meter - I'm not picky)

A building

A sunny day

The Project::

Say there's this building and you want to figure it's height.  The problem is that no one will let you actually climb a ladder or something and measure it.  Heck, your tape measure probably isn't that long anyway.

You have to do this fairly quickly and accurately or you will get mixed results.  Find level, flat, ground and stand your yardstick perpendicular to it.  Now measure the shadow.

Meanwhile, have someone take the tape measure and measure the shadow of the building (again you want to end up measuring a line that is perpendicular to the building).

Let the building's height be h.  The building's shadow is bs, and the yardstick's shadow is ys.  We'll measure everything in inches so the yardstick will be 36

so -  h/bs = 36/ys  If I multiply both sides by bs I get   h=36(bs)/ys - plug in the measurements and h is the height of the building.

Why does this work?

The sun is about 149,597,870,700 meters or 92,955,807 miles from the earth.  Of course the distance varies, but my point is that it is a long way off.  Sunlight travels all the way from the sun to the earth, hitting the earth with nearly parallel beams of light.  So, by the mathematical laws concerning parallel lines the heights divided by the shadows should be proportional.

Math Project Idea #3 - the Facade 

If you did math project idea #2 you now know how tall the building is.  If you want to make a scale model of the front of the building - you've come to the right place.  If this is a brick building I recommend this site in England that lets you print out scale model bricks for free!  It's called Paperbrick

Cardboard or heavy construction paper

Something to cover it with that looks like the building

Digital Camera (or smart phone)

Printer

Make a scale model of the front of your building.  Take a photograph of a window from a measured distance from the window.  Measure the window and the picture of the window.  How far off from the scale of the building facade are they.  Change the distance from the window to correctly make them proportionate.  If you half the distance, you double the size of the picture of the window.  If you double the distance, you double the size.

Once you have the correct scale, have your friends stand in the window.  Take the picture and print it off on photographic paper - so it shines like glass.


Math Project Idea #4 - 180 Degree Triangle

This one is pretty easy.  

Step 1)  Cut a triangle from a piece of paper.  Discuss the fact that all three angles will add up to 180 degrees for any triangle.

Step 2)  Discuss the fact that a straight line measures 180 degrees.

Step 3)  Tear the triangles into three pieces.

Step 4)  Re-Assemble the pieces so that all three points or angles of the original triangle are touching each other, arranged so they form a straight line.

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, Math Project Ideas