A special clock for American Independence Day. It only uses the digit 4.
Can you design a special clock for a different day of the year using a different digit?
Topics: Starter  Arithmetic  Investigations  Problem Solving
This evening, I was at a parentsâ€™ evening @NDHSSheffield and this clock was on the wall in one of the maths rooms! #CoolMaths pic.twitter.com/05mSlRVBLF
— Mrs Grant (@MrsGrant_BATL) March 9, 2018
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Previous Day  This starter is for 4 July  Next Day
There are of course many ways pupils might respond to this challenge but here is an example of a solution
$$1=\left(\frac{9}{9}\right)^9$$
$$2=\left(\frac{9+9}{9}\right)$$
$$3=\sqrt{9}+99$$
$$4=\sqrt{9}+\frac{9}{9}$$
$$5=\sqrt{9}!\frac{9}{9}$$
$$6=\sqrt{9}\times\sqrt{9}\sqrt{9}$$
$$7=\sqrt{9}!+\frac{9}{9}$$
$$8=9\frac{9}{9}$$
$$9=9+99$$
$$10=9+\frac{9}{9}$$
$$11=99\div9$$
$$12=9+\frac{9}{\sqrt{9}}$$
This type of challenge has been around for a long time. The first known reference is in a book called "The Schoolmasters Assistant: Being a Compendium of Arithmetic, Both Practical and Theoretical". It was written in 1762 by Thomas Dilworth, an English cleric. Here is the wording as it appeared in the book:
$$33+\frac33 = 34$$
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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=July4 However it would be better to assign one of the student interactive activities below. 

Here is the URL which will take them to a related student activity.
Here is the link to the pairs game based on AmericanEnglish and BritishEnglish mathematical words.
Transum.org/go/?to=MathvsMaths
Here is a visual aid for teachers to use when teaching alalogue time.
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