Four's Independence

$$\frac{44}{44}$$
$$\frac{4\times4}{4+4}$$
$$\frac{4\times4-4}{4}$$
$$4+4\times(4-4)$$
$$\frac{4}{4}+\sqrt4+\sqrt4$$
$$\frac{4}{4}\times4+\sqrt4$$
$$\frac{44}{4}-4$$
$$4+4+4-4$$
$$4+4+\frac{4}{4}$$
$$\frac{44-4}{4}$$
$$\frac{44}{\sqrt4+\sqrt4}$$
$$\frac{44+4}{4}$$

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?

A Mathematics Lesson Starter Of The Day

Starter of The Day Transum Mathematics Topics


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Topics: Starter | Arithmetic | Investigations | Problem Solving

  • Transum,
  •  
  • An alternative way of using this Starter is to have it on the screen when the pupils are coming into the room then, after everyone has had chance to see it, turn off the projector and ask the class to reproduce it as best they can. Each number of the clock is replaced by four fours. Happy Independence day to all in the USA.
  • Chistopher Boyle, St James's
  •  
  • The clock got the four sign incorrect! It could have been 4 x (4/4).

    [Transum: Thanks for your comment Christopher, but if you use the correct order of operations (BIDMAS) the multiplication should be done before the addition. The four is in fact correct. Your suggestion only includes 3 fours. Keep looking for errors though as feedback is very much appreciated]
  • Mrs Grant, Twitter
  •  

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Answers

There are of course many ways pupils might respond to this challenge but here is an example of a solution

$$1=\left(\frac{9}{9}\right)^9$$

$$2=\left(\frac{9+9}{9}\right)$$

$$3=\sqrt{9}+9-9$$

$$4=\sqrt{9}+\frac{9}{9}$$

$$5=\sqrt{9}!-\frac{9}{9}$$

$$6=\sqrt{9}\times\sqrt{9}-\sqrt{9}$$

$$7=\sqrt{9}!+\frac{9}{9}$$

$$8=9-\frac{9}{9}$$

$$9=9+9-9$$

$$10=9+\frac{9}{9}$$

$$11=99\div9$$

$$12=9+\frac{9}{\sqrt{9}}$$

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:

Dilworth Challenge Dilworth Portrait

$$33+\frac33 = 34$$

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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=July4

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

Transum.org/go/?to=onedigit

Student Activity

Here is the link to the pairs game based on American-English and British-English mathematical words.

Transum.org/go/?to=MathvsMaths

Student Activity

Here is a visual aid for teachers to use when teaching alalogue time.

Transum.org/go/?to=clock

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