Without using a calculator or paper can you think which of these two expressions has the largest value?
23 x 25
Put your left hand up if you think 23 x 25 is the largest.
Put your right hand up if you think 242 is the largest.
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:
This starter has scored a mean of 3.1 out of 5 based on 274 votes.
242 is the largest.
Here is a method for working out the answer to the first pair of values you see when this page is loaded; Which is the largest: 23 × 25 or 242?
You could imagine a 23 by 25 rectangle overlapping a 24 by 24 square with one common corner.
Let the area of the common, overlapping region be A then the area of the rectangle is A + 23 and the area of the square is A + 24. It is then quite clear that the area of the square is greater so the answer is 242.
Another strategy would be to realise that the results of the two calculations are quite close so think only of the final digit.
A third strategy (for those with more algebra) might be to consider the general case when the first expression is (n − 1)(n + 1) and the second expression is n2
The first expression can be simplified to n2 − 1, clearly smaller than the second expression.
There is a printable worksheet to go with this activity.
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.
Texas Instruments Nspire Calculator
This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.
For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...
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.
Click the images above to see all the details of these items and to buy them online.
Teacher, do your students have
access to computers?
Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a related student activity.