Exponential Error

A Mathematics Lesson
Starter Of The Day

23 = 8

32 = 9

24 = 16

42 = 16

43 = 64

103 = 1000

102 = 100

101 = 10

100 = 1

10-1 = 0.1

Can you spot the mitsake?

Starter of The Day Transum Mathematics Topics


Topics: Starter | Indices | Logarithms

  • Transum,
  •  
  • At the time of writing this is a new starter idea. It is intended for pupils who can confidently understand the facts in the left column but may need to consider some of the unfamiliar facts in the lower part of the right column leading to discussion or research (on a calculator maybe). Of course this starter would also be suitable for older pupils who already know about indices less than one. What was the reaction when you revealed the answer?
  • Josh Hand, King's Worcester
  •  
  • Excellent - well done. The more of these the better.
  • Dana Issam, UAE
  •  
  • I think the error is in the 2^4, all of the other sums are related to the rules of indices.
  • Peter Wright, St Joseph's College
  •  
  • Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
    Thanks for such a great resource!
  • Alice, Wisconsin
  •  
  • I can't spot any mistakes. What is the answer, please.

    [Transum: The answer Alice is lower down this page but you must be logged in as a teacher to see it.]
  • Ryder Craig, Linwood Avenue School, Christchurch
  •  
  • If you want the answer I guess you have to read the question carefully.
  • Veena, India
  • Thursday, June 19, 2025
  • The right side column has decreasing powers while left side it is not ... also bases are different...should the question be reframed?

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.
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Previous Day | This starter is for 1 August | Next Day

 

Answers

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Online Maths Shop
Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

Transum.org/go/?Start=August1

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to the Indices Pairs game.

Transum.org/go/?to=indices

Student Activity

 

Maths Trivia

The digits of the number are the same as the digits of the power of ten in these cases:

1.3712885742 = 100.13712885742
237.5812087593 = 102.375812087593
3550.2601815865 = 103.5502601815865

Can you find any other interesting facts about indices?

You can find more mathematical trivia at Transum.org/go/?to=Trivia

 

 

There are many more resources on this website designed to support a deep understanding of indices. These range from an introduction to square numbers for Primary school pupils to rationalising the denominators of surds for more advanced students. The best way to find what suits your students is to visit the Indices topic page or use Transum’s search facility. If you can’t find what you're looking for, feel free to get in touch.

Indices
Activity
A self marking exercise on indices (powers or exponents) including evaluating expressions and solving equations.

Indices Pairs
Activity
The traditional pairs or pelmanism game adapted to test knowledge of indices.

Standard Form
Activity
Test your understanding of standard form (scientific notation) with this self-marking quiz.

Standard Order
Activity
Arrange the numbers given in standard form with the smallest at the top and the largest at the bottom.

Estimate Powers and Roots
Activity
Estimate the powers and roots of the given positive numbers.

Power Play
Activity
Exercises on powers and roots and simplifying index expressions involving numbers of the same base.

Indices True False
Activity
Arrange the given statements involving indices to show whether they are true or false.

Power Shift
Activity
Arrange the given numbers as bases and indices in the three-term sum to make the target total.

Standard Form Algebra
Activity
Deeply test your understanding of standard form (scientific notation) by involving a little algebra.

Dr Tim's Indices Challenge
Activity
Dr Tim Honeywill has come up with these challenges to test your understanding of indices and algebra.

Logarithms
Activity
Self-marking exercises on evaluating logarithms and using them to solve equations.

 

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