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Year 6

Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram

I can explain how any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram.

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Year 6

Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram

I can explain how any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram.

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Lesson details

Key learning points

  1. The area of a parallelogram is equal to the area of the rectangle created by rearranging the parts.
  2. A parallelogram can be decomposed into a rectangle and 2 identical triangles.
  3. Rearranging the parts of a parallelogram helps to calculate the area.

Keywords

  • Parallelogram - A parallelogram is a quadrilateral with two pairs of parallel and equal sides.

Common misconception

Pupils who have learned about parallelograms often have a fixed idea of what they look like and do not realise that squares and other kinds of rectangles are also parallelograms.

The lesson defines parallelograms, giving three criteria, including parallel sides and equal pairs of opposite angles. Reinforce with pupils that these match the set criteria.


To help you plan your year 6 maths lesson on: Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram, download all teaching resources for free and adapt to suit your pupils' needs...

It is useful for children to practically create parallelograms in the lesson. Number rods are suggested as a manipulative for this but equal-length pieces of straw or matchsticks could work as an alternative.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Which of these statements is true of a rectangle?
Correct answer: It has four sides.
All four sides are different lengths.
Correct answer: Opposite sides are the same length.
Q2.
Which of these statements is true of a square?
Correct answer: It has four sides.
All four sides are different lengths.
Correct answer: Opposite sides are the same length.
Correct answer: It is a kind of rectangle.
Q3.
A parallelogram has sides.
Correct Answer: four, 4
Q4.
Which of the shapes is a parallelogram?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q5.
Which of the statements is true of all parallelograms?
All of the interior angles are always different to each other.
All of the interior angles are always the same as each other.
Correct answer: Pairs of opposite angles are equal.
Q6.
Which of these statements describe shapes a and b?
An image in a quiz
Correct answer: They have the same area.
They have a different area.
They are the same polygon.
Correct answer: They are different polygons.

Exit quiz

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6 Questions

Q1.
The number rods have been used to make a parallelogram. Which of the statements is true?
An image in a quiz
Correct answer: The same shape can be turned into a rectangular paralleogram.
The shape cannot be turned into a rectangular parallelogram.
The shape is already a rectangular parallelogram.
Q2.
A shape has been made from number rods. Which of the statements is true?
An image in a quiz
The shape is not a rectangular parallelogram.
Correct answer: The shape is a rectangular parallelogram.
Correct answer: It might have been a non-rectangular parallelogram which has been repositioned.
Q3.
The triangles have been cut off the ends of a parallelogram and repositioned. Which of the statements is true?
An image in a quiz
A rectangular parallelogram has been formed.
A new non-rectangular parallelogram has been formed.
Correct answer: It is no longer a parallelogram.
Q4.
The parallelogram is cut along the marked line. Complete. The parallelogram has been decomposed into a triangle and a .
An image in a quiz
Correct Answer: trapezium
Q5.
Which of these statements are true? A parallelogram….
Correct answer: can be turned into a rectangle by cutting two triangles off and repositioning.
Correct answer: can be turned into a rectangle by moving one of the triangles to the other side.
cannot be turned into a rectangle, unless it is already one.
Q6.
Which of these statements is true?
Correct answer: A parallelogram and a rectangular parallelogram can have the same area.
A parallelogram and a rectangular parallelogram cannot have the same area.
Adding a triangle to a parallelogram can give it the same area as a rectangle.