Square and triangular numbers

The Maths Habit

How many dots?

2 × 5 = 10

3 × 4 = 12

3 × 10 = 30

Which make a square? Which make a triangle?

ASquare

BNeither

CTriangle

DTriangle

A square: as many rows as dots in a row.A triangle: each row has 1 more dot.

Row: A line of dots that goes across.

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

rows×dots in a row=dots

Pattern1234Dots14916

1Draw the next pattern.One more row, and one more dot in each row.
2Count the dots.Rows × dots in a row.
3Fill in the table.The dots are the square numbers.

These are square patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

4×4=16

3Fill in the table.

Pattern234Dots4916

These are square patterns. How many dots are in pattern 6?

1Draw the next pattern.

Pattern 4

Pattern 5

Pattern 6

2Count the dots.

6×6=36

3Fill in the table.

Pattern456Dots162536

These are square patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

4×4=16

3Fill in the table.

Pattern234Dots4916

1

2

rows×dots in a row=dots

3Fill in the table.

These are square patterns. How many dots are in pattern 3?

1Draw the next pattern.

Pattern 1

Pattern 2

Pattern 3

2Count the dots.

3×3=9

3Fill in the table.

Pattern123Dots149

These are square patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

4×4=16

3Fill in the table.

Pattern234Dots4916

1

2

rows×dots in a row=dots

3Fill in the table.

These are square patterns. How many dots are in pattern 8?

1Draw the next pattern.

Pattern 6

Pattern 7

Pattern 8

2Count the dots.

8×8=64

3Fill in the table.

Pattern678Dots364964

These are square patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

4×4=16

3Fill in the table.

Pattern234Dots4916

1

2

rows×dots in a row=dots

3Fill in the table.

These are square patterns. How many dots are in pattern 5?

1Draw the next pattern.

Pattern 3

Pattern 4

Pattern 5

2Count the dots.

5×5=25

3Fill in the table.

Pattern345Dots91625

1

2

rows×dots in a row=dots

3Fill in the table.

1These are square patterns. How many dots are in pattern 7?

1

Pattern 5

Pattern 6

Pattern 7

2

7×7=49

3

Pattern567Dots253649

2How many dots are in square pattern 10?

1

Pattern 10

2

10×10=100

3

Pattern12…10Dots14…100

3This square pattern has 81 dots. Which pattern is it?

1

81 dots

2

9×9=81

3

Pattern12…9Dots14…81

Pattern 1

Pattern 2

Pattern 3

Pattern 4

last pattern+new row=dots

Pattern1234Dots13610

1Draw the next pattern.Add a new row at the bottom. It has 1 more dot.
2Count the dots.The last pattern + the new row.
3Fill in the table.The dots are the triangular numbers.

These are triangle patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

6+4=10

3Fill in the table.

Pattern234Dots3610

These are triangle patterns. How many dots are in pattern 6?

1Draw the next pattern.

Pattern 4

Pattern 5

Pattern 6

2Count the dots.

15+6=21

3Fill in the table.

Pattern456Dots101521

These are triangle patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

6+4=10

3Fill in the table.

Pattern234Dots3610

1

2

last pattern+new row=dots

3Fill in the table.

These are triangle patterns. How many dots are in pattern 3?

1Draw the next pattern.

Pattern 1

Pattern 2

Pattern 3

2Count the dots.

3+3=6

3Fill in the table.

Pattern123Dots136

These are triangle patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

6+4=10

3Fill in the table.

Pattern234Dots3610

1

2

last pattern+new row=dots

3Fill in the table.

These are triangle patterns. How many dots are in pattern 7?

1Draw the next pattern.

Pattern 5

Pattern 6

Pattern 7

2Count the dots.

21+7=28

3Fill in the table.

Pattern567Dots152128

These are triangle patterns. How many dots are in pattern 4?

1Draw the next pattern.

Pattern 2

Pattern 3

Pattern 4

2Count the dots.

6+4=10

3Fill in the table.

Pattern234Dots3610

1

2

last pattern+new row=dots

3Fill in the table.

These are triangle patterns. How many dots are in pattern 5?

1Draw the next pattern.

Pattern 3

Pattern 4

Pattern 5

2Count the dots.

10+5=15

3Fill in the table.

Pattern345Dots61015

1

2

last pattern+new row=dots

3Fill in the table.

1These are triangle patterns. How many dots are in pattern 9?

1

Pattern 7

Pattern 8

Pattern 9

2

36+9=45

3

Pattern789Dots283645

2Ali stacks cans in a triangle. How many cans does he need for 6 rows?

1

4 rows

5 rows

6 rows

2

15+6=21

3

Rows456Cans101521

3These are triangle patterns. How many dots are in pattern 5?

1

Pattern 2

Pattern 3

2

6+4=10

10+5=15

3

Pattern2345Dots361015

Is it right?
Thumbs up: right. Thumbs down: wrong.

Square pattern 3 has 6 dots.
Wrong: 3 × 3 = 9
16 is a square number.
Right: 4 × 4 = 16
10 is a triangular number.
Right: 6 + 4 = 10
12 is a square number.
Wrong: 3 × 3 = 9, 4 × 4 = 16
Triangle pattern 5 has 15 dots.
Right: 10 + 5 = 15

Square and triangular numbers worksheet, page 1

Square and triangular numbers worksheet, page 2

Answer sheet

Add two triangular numbers that are next to each other, such as 3 + 6. Try some more. What do you notice?
A square number
Which number between 2 and 50 is a square number and a triangular number?
36
Four friends meet. Each friend shakes hands with every other friend once. How many handshakes are there?
6

How many dots are in square pattern 5?
25
How many dots are in triangle pattern 6?
21
How many dots are in square pattern 7?
49

Exit tickets to print