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are and tri gular nu

These staircases show another way of making triangular numbers .

• •

1
You can fit the 1st and 2nd 3 6 10
1 +3=4
triangular numbers together
• 4 = 2 2
to make the 2nd square number.

This is one way to write
about the result .
. -.... ~- ------
IT] • Try to fit these together to make square numbers.

a the 3rd and 4th triangular numbers
b the 5th and 6th triangular numbers.
• Choose materials to help you, if you want.
• Write about your results.
[3J Show diagrams for two other square numbers less than 100

made from two triangular numbers.

[2J Complete this table to show square number totals up to 100.

Position 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
Triangular numbers 1 3 6 10 15

Square numbers 1 4 9

~ What are the positions of the two triangular numbers which together make:

a the 19th square number b the 28th square number?

2
CHALLENGE 2 -1 = 3
2
3 -3 =
• Copy and continue this pattern for 10 rows.
2
• Explain what you notice about the results. 4 -6 =

I STEPS 5:14 1 I •