Oblongs  - A Maths Starter Of The Day

Find the length and width of a rectangle if its perimeter is 16cm and area is 12cm2.

What are the dimensions of a rectangle whose perimeter is 40cm and area is 75cm2.

Find the dimensions of a rectangle whose perimeter is 27cm and area is 45.5cm2.

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


Share

Topics: Starter | Area | Geometry | Mensuration | Shape | Simultaneous Equations

  • 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.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 2.9 out of 5 based on 526 votes.


Previous Day | This starter is for 3 April | Next Day

 

Answers




3 and 3/2

4 and 4/3

5 and 5/4

6 and 6/5

7 and 7/6

8 and 8/7

9 and 9/8

10 and 10/9

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.


Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

 

Rubiks Cube Puzzle

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone.

Online Maths Shop

Laptops In Lessons

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).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=April3

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

Transum.org/go/?to=Oblongs

Student Activity

Transum.org/go/?to=AreaBuilder

Student Activity

 


Apple

©1997-2019 WWW.TRANSUM.ORG