The idea in brief. When the pieces are identical, a length you cannot measure can be written two ways, and the two ways must agree; so name one piece's breadth 1 unit, count the figure in units, and let the two readings fix what a unit is. Write one length two ways, name the breadth as 1 unit, and read a width only from what the figure shows when one rectangle is turned on its side. In the lesson. You have split figures into rectangles to find their area. Today, we will use identical rectangles to find a missing length. Identical rectangles have equal lengths and equal breadths. Find a side you can measure two ways.
Lesson video, with the working
Identical pieces
5 min 08 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Question 1 of 8 · Basic · free to tryA large rectangle is made from 3 identical small rectangles. 2 horizontal…A large rectangle is made from 3…
A large rectangle is made from 3 identical small rectangles. 2 horizontal rectangles are stacked with their short sides against one upright rectangle. The stack exactly matches the height of each upright rectangle. Each small rectangle is 10 cm long. Find the length of the large rectangle.
The length of a small rectangle equals 2 breadths.
Breadth = 10 ÷ 2 = 5 cm
Large rectangle length = 10 + 5 = 15 cm
The length of the large rectangle is 15 cm.
Answer: 15 cm
For parents
How do you solve identical rectangles questions in P3?
In these questions several equal rectangles are fitted together and only one measurement is given.
What your child learns here
In these questions several equal rectangles are fitted together and only one measurement is given. This page applies the Primary 3 outcomes on the area and perimeter of a rectangle to that kind of puzzle, using units to link the sides.
Identical rectangles all share the same length and the same breadth.
A side that cannot be measured directly can be written in units of a side that can.
Once one unit is found, every side, the area and the perimeter follow from it.
When pieces are joined, the joins inside the figure are not part of its perimeter.
Does the answer make sense?
When the question asks for an area, your child's answer must be one small piece's area times the number of pieces, since identical pieces leave no gaps. When it asks for the perimeter of the joined figure, it must be less than all the pieces' perimeters added, because inside joins do not count.
How to practise these questions
The Basic questions practise using the equal sides of identical pieces to find a missing length. The Intermediate questions add arrangements where pieces sit in different directions, so a long side matches several short sides. The Challenge questions ask for the area or perimeter of the whole after the piece sizes are worked out. If an identical pieces question is stuck, watch its solution film and return to it later from Revision.
Questions parents ask
What does 1 unit mean in an area question? It is a name for a length we do not know yet, such as the breadth of one rectangle. Writing other sides as so many units lets the child compare them before any number is found.
Is this the same units idea as in bar model questions? Yes, it is the same way of thinking. A length is written as so many equal units, a total is matched to a number, and one unit is found by dividing.
Why does the perimeter change when the pieces move? When pieces touch, the edges along the join are hidden inside the figure. A different arrangement hides different edges, so the outside edge changes length while the total area stays the same.
