Square and triangular numbers

The Maths Habit

Everyone in this room shakes hands with everyone else. How many handshakes is that?

435 for a class of 30

Square number
The number of dots in a square pattern.
Triangular number
The number of dots in a triangle pattern.

Pattern 1

Pattern 2

Pattern 3

Pattern 4

Pattern 1

Pattern 2

Pattern 3

Pattern 4

Draw the next pattern. How many dots?

Pattern 1

Pattern 2

Pattern 3

Pattern 4

Draw the next pattern. How many dots?

Pattern 1

Pattern 2

Pattern 3

Pattern 4

Find the next two square numbers. Write each jump in its bubble.

Pattern 7
Count the dots in each L shape.
L shapes1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
16+925+1136+1349+1564+1781
The jump grows by2each time.

Find the next two triangular numbers. Write each jump in its bubble.

Pattern 8
Count the dots in each row.
Rows1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
15+621+728+836+945+1055
The jump grows by1each time.

Find the next two square numbers. Write each jump in its bubble.

Pattern 7
Count the dots in each L shape.
L shapes1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
16+925+1136+1349+1564+1781
The jump grows by2each time.

Find the next two square numbers. Write each jump in its bubble.

Pattern 10
Count the dots in each L shape.
L shapes1 + 3 + 5 + … + 19 = 100
49+1564+1781+19100+21121+23144
The jump grows by2each time.

Find the next two square numbers. Write each jump in its bubble.

Pattern 7
Count the dots in each L shape.
L shapes1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
16+925+1136+1349+1564+1781
The jump grows by2each time.

Find the next two triangular numbers. Write each jump in its bubble.

Pattern 7
Count the dots in each row.
Rows1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
10+515+621+728+836+945
The jump grows by1each time.

Find the next two square numbers. Write each jump in its bubble.

Pattern 7
Count the dots in each L shape.
L shapes1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
16+925+1136+1349+1564+1781
The jump grows by2each time.

Find the next two square numbers. Write each jump in its bubble.

Pattern 8
Count the dots in each L shape.
L shapes1 + 3 + 5 + … + 15 = 64
25+1136+1349+1564+1781+19100
The jump grows by2each time.

Find the next two square numbers. Write each jump in its bubble.

Pattern 7
Count the dots in each L shape.
L shapes1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
16+925+1136+1349+1564+1781
The jump grows by2each time.

Find the next two triangular numbers. Write each jump in its bubble.

Pattern 10
Count the dots in each row.
Rows1 + 2 + 3 + … + 10 = 55
28+836+945+1055+1166+1278
The jump grows by1each time.

Square and triangular numbers worksheet, page 1

Square and triangular numbers worksheet, page 2

Answer sheet

  1. Add two triangular numbers that are next to each other, such as 6 + 10. Try some more pairs. What do you notice?

    Always a square number

  2. One number between 2 and 50 is both a square number and a triangular number. Which is it?

    36

Five people all shake hands with each other. How many handshakes? What kind of number is it?

10, a triangular number

  1. What is the 9th square number?

    81

  2. Write down the triangular numbers in this list: 12, 21, 25, 28

    21 and 28

  3. Ravi says 24 is a square number because 12 × 2 = 24. Is Ravi right? Explain how you know.

    No: 24 is not a whole number squared
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