Worksheet: Shape Patterns

In this worksheet, we will practice using tables to investigate shape patterns, find the rule a pattern follows, and predict future shapes in the pattern.

Q1:

What will the 16th shape in this pattern be?

  • A
  • B
  • C
  • D
  • E

Q2:

William is going to make a repeating pattern with this repeating part.

What are the first 9 shapes in this pattern?

  • A
  • B
  • C
  • D

He notices that the 3rd, 6th, and 9th shapes are all squares. He guesses that the 12th and the 15th shapes will be squares because they are multiples of 3, and there are 3 shapes in the repeated part.

Is his guess correct?

  • Ano
  • Byes

What will the 31st shape be?

  • A
  • B
  • C

Q3:

If the given pattern is extended to have 11 polygons, how many of them will be green?

Q4:

Predict how many hexagons will be present if the given pattern is extended to have a total of 38 polygons.

Q5:

Benjamin is making patterns using his baby brother’s shape tiles. He placed 1 rectangular tile followed by 2 triangular tiles and then 1 square tile in a line. He repeated this until 8 tiles were placed. How many square tiles did Benjamin use?

Q6:

How many triangles will be there when the pattern is extended to have 32 polygons?

Q7:

Olivia is making patterns of shapes using matchsticks.

She records the number of matchsticks and the number of squares for each shape in the table.

Number of MatchsticksNumber of Squares
Shape 141
Shape 2103
Shape 3165

Select the rule for making the next shape.

  • AAdd 8 matchsticks to make 2 more squares.
  • BAdd 8 matchsticks to make 4 more squares.
  • CAdd 2 matchsticks to make 8 more squares.
  • DAdd 6 matchsticks to make 4 more squares.
  • EAdd 6 matchsticks to make 2 more squares.

Q8:

How many polygons will be there when the pattern is extended to have 5 pentagons?

Q9:

Daniel is making patterns of shapes using matchsticks.

How many matchsticks does he add each time?

How many matchsticks will be in Shape 5?

Q10:

If this pattern repeats, what will shape number 26 be?

  • A
  • B
  • C
  • D

Q11:

By considering a sequence for the number of chords in each of the circles shown, find the number of chords that would be in the 5th shape.

Q12:

Look at this pattern and choose the correct words to complete the rule.

Rule: To get the next shape we squares.

  • Aadd 8
  • Badd 4
  • Cadd 2
  • Dadd 1
  • Eadd 6

Q13:

In the given figure, each side of each polygon is 3 inches. If the pattern is extended, how many polygons should there be to have a total perimeter of 105 inches?

Q14:

Natalie is making patterns of dots that look like squares.

She notices that the rule for the number of dots to use is add two more dots than you added before.

How many dots will be in Square 6?

Q15:

The figure shows a sequence of shapes. Write down a sequence for the number of line segments each shape contains.

  • A4,6,8,10
  • B1,2,3,4
  • C4,8,12,16

Q16:

Daniel is making patterns of dots that look like triangles.

The rule for the number of dots to use is add one more dot than you added before.

How many dots will be in the next triangle?

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