Find the length and width of a rectangle if its perimeter is 26cm and area is 40cm2.

What are the dimensions of a rectangle whose perimeter is 62cm and area is 210cm2.

Find the dimensions of a rectangle whose perimeter is 39cm and area is 72.5cm2.

Find the dimensions of all the rectangles whose perimeters in cm are twice the value of their areas in cm2.

## A Mathematics Lesson Starter Of The Day

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• Transum,
•
• The first three problems are in increasing order of difficulty. The first can probably be guessed, the second needs more of a strategy as the numbers are larger and the third involves a fraction so probably requires the application of a more generalised method. Refreshing the page generates three different rectangles to further consolidate any techniques learned in the first round. The fourth problem is only for Nobel prize candidates!
• Simon Fletcher, Bolton UK
•
• 52 cm rectangle perimeter 105 area. Is this correct? I've checked and can't find a solution.
• Transum,
•
• Hello Simon, so you are looking for two numbers (the height and the width) that add up to half the perimeter, 26cm, and multiply together to give an area of 105cm2.
We can write two simultaneous equations showing this information:
h + w = 26
hw = 105
We can combine the information in these two equations and eliminate one of the unknowns:
From the first equation we see that h = 26 – w
Substituting this into the second equation gives (26 – w)w = 105
Expanding the brackets gives 26w - w2=105
Rearranging gives w2 - 26w + 105 = 0
This is a quadratic equation which can be solved by factorising
(w – 5)(w – 21) = 0
So w could be 5cm in which case h would be 21cm or, w could be 21cm in which case h would be 5cm.
• Audrey Macmillan, @audproctor77
•
• Clarifying area/perimeter confusion using a Transum Starter. Great #mathschat on squares and rows.

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## Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

## Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=April3

Here are URLs which will take them to related student activities.

Transum.org/go/?to=Oblongs

Transum.org/go/?to=AreaBuilder

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