These activities come from my friend, Beth. She's a math whiz. Funny story: In college, when she couldn't sleep, she'd count in cubes. Not sheep. In CUBES. She's taken exponents and made them kid (and mom!) friendly. Have fun!
Square numbers are one of my favorite things. The thing that makes them fun for me is a little too hard for our kids, but they can still have fun finding square numbers and eating them (if you choose something fun like marshmallows or Froot Loops to play with). I’ll use tiles in my example.
One tile technically shows the smallest square number, but it is not interesting.
Give your child 4 tiles. Have her make a square with them.
How many tiles go across the bottom? (2) How many tiles tall is the square? (2)
Let’s make the square bigger. Let’s make it be three across and three tall. To be a square, the number across and the number tall have to be the same. Fill in the new rows to make a full square. How many tiles did it take to make this new square? (9)
Let’s make one more square. How many will go across the bottom this time? (4) And how many tall will it be? (4) How many tiles does it take to make the whole square? (16)
If your child is good at math and you want to challenge him, ask him to find the pattern of how many you add on each time to get the next square number. To get from 1 to 2, you add 1. To get from 2 to 4, you add 2. To get from 4 to 9, you add 5. To get from 9 to 16, you add 7. So the numbers you are adding on are these: 1, 3, 5, 7, 9, … You add on consecutive odd integers. Call them “skip numbers” or “every other number” if your child doesn’t know about odd numbers yet. The reason lies in the tiles: every time you make a bigger square, you add on an equal row and column as what you just had, plus ONE CORNER TILE to complete the square.
Triangular numbers are ones that can form a triangle when you arrange that many objects. The smallest triangular number is 3.
The next triangular number is 6.
Next up is 10.
As you can see, you add one row each time with one more object than the previous row had. Give your child Cheerios, marshmallows, pennies, Legos, whatever is age-appropriate and you have on hand. Have your child make a triangle with 3 of them. Show your child that you get a bigger triangle when you add a new row with 3 more in it. Ask your child to find what the next bigger triangle will be (one new row with 4) and how many total are in this new triangle (10). Have your child do this two more times to get the next two triangular numbers (15 and 21). Your child can simply count them each time, or if the child is older encourage adding (1+2+3+4+5+…). Perhaps with adding your child can calculate the next bigger triangular number without using manipulatives.