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Geometry - Number and shape patterns

Grade 3Cambridge (IGCSE)

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Identifying the 'Core' in Repeating Patterns: The core is the shortest part of the pattern that repeats. For example, in the sequence Circle, Square, Circle, Square, the core is (Circle, Square).

A repeating pattern of a blue circle and a red square.

📐Formulae

Next Term=Previous Term+Rule\text{Next Term} = \text{Previous Term} + \text{Rule}

Total Sides=Number of Shapes×Sides per Shape\text{Total Sides} = \text{Number of Shapes} \times \text{Sides per Shape}

💡Examples

Problem 1:

Look at the growing pattern of squares below. Term 1 has 11 square, Term 2 has 33 squares, and Term 3 has 55 squares. How many squares will be in Term 55?

A sequence of square blocks showing 1, 3, and 5 squares respectively.

Solution:

  1. Identify the number of squares in each term: 1,3,5,…1, 3, 5, \dots
  2. Find the rule: 3−1=23 - 1 = 2 and 5−3=25 - 3 = 2. The rule is to add 22 to the previous number.
  3. Continue the pattern: Term 4: 5+2=75 + 2 = 7 Term 5: 7+2=97 + 2 = 9

There will be 99 squares in Term 55.

Explanation:

This is an arithmetic growing pattern where we add 22 at each step.

Problem 2:

An arrow pattern is rotating. If Term 1 points Up and Term 2 points Right, what direction will Term 4 point?

Three arrows showing a clockwise rotation: Up, Right, then Down.

Solution:

  1. Identify the rotation: From Up to Right is a quarter turn (90∘90^\circ) clockwise.
  2. Apply the rule to find the sequence:
  • Term 1: Up
  • Term 2: Right (90∘90^\circ turn)
  • Term 3: Down (90∘90^\circ turn from Right)
  • Term 4: Left (90∘90^\circ turn from Down)

Term 4 will point Left.

Explanation:

The pattern follows a consistent rotation of a quarter turn clockwise for every new term.