This is a difficult Starter so there is a prize of a watch if you can complete it.

For each pair of numbers multiply the sum by the difference then divide the answer by 5 without using a calculator.

 3, 2 8, 7 14, 12 18, 14 22, 18 24, 16 14.5, 14 10.5, 10.5

## Sorry

At least one of your answers is wrong.

Congratulations, all of the answers are correct.

You have won a watch. You can watch this sheep for as long as you want!

## A Mathematics Lesson Starter Of The Day

A Starter which is similar to this one but slightly harder is Multiply, Add, Subtract and Divide.

Share

Topics: Starter | Mental Methods

• 7 Mandelbrot, Admiral Lord Nelson School
•
• When calculating difference the order is usually taken as important so some of the answers should be negative. Or are we mistaken?
• Laura, Minnesota
•
• I think this is a good way to get your students to do mental math, however if I were to use this with students who knew about negative numbers it wouldn't work. With the order the numbers are set up in 4 of the answers should have actually been the negatives of what the 'correct' answer on the site gives.
• Transum,
•
• Thanks so much for your comments. I think we have an ambiguous situation here. Should the difference between two numbers always be positive? This topic was discussed on the Math Forum - Ask Dr. Math. In support of this idea is the following:
In any real situation I can think of, if you were to ask someone for the difference between, say, 3 and 5, the answer would be 2 not -2! We tend to think of differences as positive numbers, and thus the proper rendition of that expression algebraically would be |3-5| (or |5-3|). This is the same idea as the "distance" between two numbers on the number line, which is always positive.
In textbooks, as you've observed, it seems common in 'word problems' to make a different convention, that 'the difference between a and b' means a - b.

The full discussion can be seen here.

Perhaps we'll wait for a few more comments on this page and then adapt this starter to conform with the opinions of the majority. In the meantime you'll see that all the pairs of numbers above have the largest first to take out the ambiguity.

Thanks once again for your feedback 7 Mandelbrot and Laura.
• Don, Loughborough
•
• I disagree with Mandlebrot and Laura. I think difference means the positive difference and not a rigid formula of the first number take away the second - in this regard it's disappointing that you've changed the starter (it looks as though you have). If you have students provide you with a negative answer then perhaps it will lead to an interesting discussion about word problems and the wording of questions, which they'll learn more from than just a correct answer.
• Y. Bonter, Cardinal Newman School
•
• Isnt the definition of the difference the highest number take away the lowest number.
• 11S Coln House,
•
• We enjoyed the challenge and thank you for giving us a free lesson!!!!!
But we thought the prize was misleading.
• Benjamin, Sydney
•
• Argh, I checked my answers and it said they were wrong so I pressed the back button and it took me back to the home menu of starter of the day (the calendar). I pressed forward and it took me back to the page saying my answers were wrong! In other words it deleted my answers! It took me so long! Please get rid of this bug!
[Transum: Sorry about that Benjamin, you must have accidentally pressed the back button twice. As a result of your feedback the page has been rewritten so that the use of the back button is not required.]
• Benjamin, Sydney
•
• Ok, thanks! Anyway, I finished it and the prize was very funny!
• Samuel, Hornsby
•
• Wow what a funny prize hope you have more prizes like this again!
• Jackie, South Australia
•
• Please could we have the answers? Every way we have written this it comes up as wrong. Thank you.

[Transum: Sorry Jackie. The answers are only available to teachers when they are signed in.]

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.

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 2.7 out of 5 based on 54 votes.

Previous Day | This starter is for 27 October | Next Day

 1 3 10.4 25.6 32 64 2.85 0

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.

Dividing by five is a great deal to ask,

But an easier method will help you.

Dividing by ten is a much easier task,

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?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).

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

Transum.org/go/?Start=October27

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

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

For Students:

For All: