# number reasoning

There is a common exam question that I have never known the name of, and as such I have never been able to find a resource to practise it in lessons. They are questions like:

The above was taken from question 1 of the June 2013 Edexcel Higher paper. The examiners report for this question stated:

Part (a) of this question was well answered with over two thirds of all candidates being awarded the mark for a correct answer. Part (b) was poorly done even by some of the best candidates. Commonly seen incorrect answers included 17.93. An estimate (300000 ÷ 2) could have helped candidates with this part of the question.

With the above in mind, I created the following resource to be use as starters:

# equivalent fractions

Having read a superb post about the Singapore Bar Model from William Emeny I thought I would share these diagrams for introducing equivalent fractions:

Students identify that $\frac{5}{12}$ of the diagram is shaded blue.

With each square now shown in two pieces, they can then see that $\frac{10}{24}$ is shaded and that this is equivalent to $\frac{5}{12}$.

Once they are happy with the second step then there isn’t much of a leap to showing that $\frac{20}{48} = \frac{10}{24} = \frac{5}{12}$.

Whilst these diagrams are given in a slightly different format to the bar model, the idea is similar.

## presentation

Here is a small presentation that may be useful.

# magic names

Here’s a starter inspired by a problem in the excellent Cabinet of Curiosities book by Ian Stewart.

The names of 10 students are displayed around the diagram. Start from ‘Mister Mort’ and move clockwise along one edge for each letter as a name is spelled out. You should finish on that person’s name.

## create your own

It’s unlikely that your name is also Mr Mort and that you happen to teach a Michelangelo, so you can create your own version here.

• follow the link to Overleaf
• replace the names at the top of the file with words of length 3 - 12 (I have had to use first names and last names in the past to make up the longer names)
• make sure the starting point has length 10
• the preview should automatically update
• download the pdf from the menu at the top

NOTE: The above file is shared on Overleaf and can be edited by anyone, so if the file has been edited and is not usable then there is a read-only version here. You will need to copy the code, create a new paper and paste it into the new document.

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