Take Sides

A Maths Starter Of The Day

Without using a calculator or paper can you think which of these two expressions has the largest value?

23 x 25

242

Right Hand Up Left Hand Up

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.

A Mathematics Lesson Starter Of The Day


Share

Topics: Starter | Mental Methods | Mixed

  • Transum,
  •  
  • This activity gives the teacher some instant feedback from the class. Who puts their hand up really quickly? Who is more hesitant waiting for other pupils to act first? Who’s facial expression shows the most focussed concentration? Who changes their mind when they see how the rest of the class are siding?

    Of course the most important part of this Starter will be the discussion generated.

    Don’t forget to click the ‘Next’ button above to get a new pair of expressions for your class to 'take sides'.

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 3.1 out of 5 based on 274 votes.


Previous Day | This starter is for 29 November | Next Day

 

Answers

242 is the largest.

Hand Up

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.

Overlapping
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.

Worksheet

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.

 

Puzzle Master Banner
Numbers and the Making of Us

Numbers and the Making of Us

I initially heard this book described on the Grammar Girl podcast and immediately went to find out more about it. I now have it on my Christmas present wish list and am looking forward to receiving a copy (hint!).

"Caleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists." more...

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=November29

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=digivide

Student Activity

 


Apple

©1997-2020 WWW.TRANSUM.ORG