Discovery Math Activities Round-Up

I saw a meme on Facebook that says: "Think you're bored? When Sir Isaac Newton invented calculus it was during the plague. Do you have any idea how bored you have to be to invent calculus?" Now the truth is Gottfried Wilhelm Leibniz, a German mathematician, published the same discoveries around the exact same time as Isaac Newton. Each mathematician claimed the other stole his ideas, but it is believed that both actually discovered the same thing separately around the same time. (For more about Isaac Newton click here and I share a little more about both men here.) 

But I digress onto a bit of mathematics history and am letting my geek side show. The meme got me thinking. During this Covid-19 pandemic I was thinking it would be great to share some discovery math activities so your kids can actually discover math during this "plague". I also will share some activities fellow Kid Blogger Network members shared with me. 

Now let's begin with some simple ones. The first one is working with our basic operations. You need a group of objects. Anything will work. Let's say a bag of marbles for example. Sit with the child and ask if they have 3 marbles (give them 3) and then get 2 more (give them 2 more) how many will they have? Use the marbles to do simple addition and subtraction problems. Then you can introduce multiplication. Ask what will happen if you get three marbles five times. Put the marbles in five rows of three. Have them try some more problems. (I know this works because my nephew did something similar when he thought my parents asked him for 3 times 5 and not 3 plus 5 when they were playing addition facts over the phone.) For division I am going to refer you to this post about a book called A Dozen Cousins and an activity I made up to go with it.

After you explore the groups of 12 you can pick another number and play with the marbles. 

Now I was a high school math teacher so most of my teaching skills are for the higher math topics. However with some simple teaching manipulatives you can teach other topics pretty easily. For example the activities I shared with these fraction discs.

Geometry lends itself to so much discovery. The truth is we usually learn Euclidean geometry and this is the geometry that Euclid discovered and proved back around 300 BC. A book I loved to use that uses a discovery approach is Discovering Geometry by Michael Serra. Now I used the addition that came out in 1993. There are newer ones now available on Amazon. Throughout the book there are investigations to discover the geometry. Some easy ones you can do is using a protractor and ruler. Draw two intersecting lines and measure the angles. You should see the opposite angles (officially called vertical angles) are equal.

Vertical Angles

Another easy one with angles would be to draw a pair of parallel lines and a transversal (line through both) and measure all the angles. See which are congruent. Try another drawing. Does it work the same?


You can also draw a triangle and cut it out. Tear the corners off and line the corners up. The three corners should fit together to be one line or 180 degrees.
You could also take a triangle and fold each of the vertices to one another to find the midpoint of each side and then join the midpoints and see the midsegments of the triangle. Look for characteristics of midsegments (parallel to opposite side and  half the length of the opposite side).

Cut outs rectangles, rhombuses and squares. Compare opposite sides, angles, etc. Then fold the diagonals and look for theories on them. 

Another great tool is a geoboard. There are so many investigations you can do with it. I shared some in this post. I love playing with area on geoboards. You can also explore area with them. Kids should be able to discover that the area of a triangle is half the area of a rectangle. If they know multiplication they should be able to discover the area formula for the rectangle by looking at them and counting the squares. You can also visualize the Pythagorean Theorem with the geoboard.

Now March 14th is official Pi Day for us math geeks (3/14 is like 3.14). I have shared several activities on various Pi Days over the years. The first I would like to share is to discover the value of pi. It is finding round objects and measuring the circumference and the diameter of each.

Another year I shared a way that Archimedes used to estimate pi. It involves some geometry and a bit of trigonometry (though I do offer a download without the trig) so it is for older kids. 

Another fun geometry investigation is discover the Euler's Formula. I shared about it here.
I could keep going with geometry investigations but want to share some other topics. In algebra you can use a graphing calculator or drawing graphs to discover how slope works as well how to move the graph. It is great to play with the y=x^2 family. It will help them see how to move the graph up and down as well as left and right. 

Learning about sine, cosine and tangent is relatively easy as well. You need to create some similar right triangles (similar means the corresponding angles will be congruent). Then compare the ratio of the sides. Do each leg over the hypotenuse (sine and cosine) and the legs over each other. Notice that the ratios are the same in the similar triangles. The ratios are the trig functions. 

Ok, that is enough from me. Now for some I received from some blogging friends. I would love to hear about any you have tried or if you try any of ours!

Activities from Other Blogs

1) From Little Bins for Little Hands: Geometric Shapes Activity
2) From Mama Smiles: Snack Counting and Grouping
3) From Megan Zeni: Patterns Outside & In Nature
4) From Mama Smiles: Fun Statistics for Kids
5) From JDaniel4's Mom: A Homemade Balance Scale (Ok, not completely discovery based but could be used for some discovery learning)
6) From Our Family Code: Fibonacci & Pi Suncatchers