### Square and triangular numbers | nzmaths

Add up odd numbers from 1 onwards and you get square numbers! 1 is a square It is good to know this, as it may help you solve things one day. Squares and. Give a general expression for the nth term of a patternDescribe the links between different Adding odd numbers seems to lead to square numbers. If we put n. Third, we explain how even and odd number combinations will always end in the previous square, one takes the difference of the two numbers that are next to .

Shuffle the 36 cards.

### Intro to even and odd numbers (video) | Khan Academy

Lay the 36 cards out in 6 rows of 6 cards each. Be sure to deal the top row from left to right. Then deal the second row beneath it from left to right.

And so on with each succeeding row laid out underneath the one before. Ask your friend to look at the cards and tell you which row the chosen card is in.

Remember what number the row is. Carefully pick the cards up in the same order you laid them down.

## Square and triangular numbers

So the first card on the left of the top row is on top of the stack, and the last card on the right of the bottom row is on the bottom of the stack. Now lay the cards down in 6 rows of 6 cards each, but this time spread the card one column at a time.

Instead of proceeding from one row to the next, proceed from one column to the next. Lay the first six cards in a column from top to bottom on the far left. Then lay out the next six cards in a second column of six cards just to the right of the first column of six cards. Continue doing this until you have 6 columns of 6 cards each which looks the same as 6 rows of 6 cards each -- because it is the same. Once again ask your friend which row contains the chosen card. When you friend tells you which row the card is in, you can say what the exact chosen card is.

If your friend said the card was in row 2 the first time, and in row 5 the second time, then the chosen card is the one in the second column of the fifth row. This is because the way you arrange the cards, what were rows the first time around become columns the second time around.

## Square number

Back to Top Lightning Calculator Here's a trick to wow them everytime! But seven pennies or twelve pennies cannot be arranged that way. Numbers of objects that can be arranged into a square array are called "square numbers. Square arrays must be "full" if we are to count the number as a "square number. The number 12 is not a square number. Children may enjoy exploring what numbers of pennies can be arranged into an open square like this.

They are not called "square numbers" but do follow an interesting pattern. Squares made of square tiles are also fun to make. Again, the number of square tiles that fit into a square array is a "square number. Connections with triangular numbers If you count the green triangles in each of these designs, the sequence of numbers you see is: If you count the white triangles that are in the "spaces" between the green ones, the sequence of numbers starts with 0 because the first design has no gaps and then continues: Remarkably, if you count all the tiny triangles in each design -- both the green and the white -- the numbers are square numbers!

This connection between square numbers and triangular numbers can be seen another way, too. Build a stair-step arrangement of Cuisenaire rods, say W, R, G.

Then build the very next stair-step: W, R, G, P. Each is "triangular" if we ignore the stepwise edge. Put the two consecutive triangles together, and they make a square: