Word Problems

"My pupils can work out the calculation but cannot apply it in context when given word problems..." is the exasperated lament of many educators when teaching maths at all school 

ages. Over the years, I have tried a variety of ways to help pupils to solve word problems but for the majority of pupils, using SPOT has resulted  in the most success so far.

Underlining and key words did not work for me: some pupils underlined everything, rendering the text even harder to decipher and key words can be misleading.

I therefore decided to note the most frustrating scenarios when working on this type of maths problem solving.

  • Pupils get to the end of a problem and in their relief, forget to revisit the question and by doing this often do not answer the actual question, despite having completed lots of correct calculations.

  • Numbers appear to be picked randomly from the text and inserted into calculations which do not fit with the given scenario.

  • Although they are capable of carrying out the necessary calculations, pupils struggle to make sense of what the question is asking them to do.

  • Solutions are written down without any regard for the fact that they are nonsensical, such as declaring that the price for five oranges is £375! 

So to tackle these, SPOT was introduced.

Sentence

Picture

Operations

Test

Sentence  

A sentence is written at the start, after reading the question, that includes underlined spaces for pupils to fill in the answers at the end. This makes them look carefully at what the question requires at the start and ensures they revisit the question at the end. 

Picture    

This is some sort of visual image such as a sketch, a diagram, a bar model or even annotations on an illustration that has been provided which helps pupils to make sense of the problem. This step could actually include resources such as blocks or counters or even pupils acting out how to work the answer out for the first few numbers and then applying this to the larger numbers.

Operations   

Once pupils have an understanding of what is required, they need to create some calculations and this reminds them to think carefully about the operations needed as well as how many are needed.

Test     

This involves testing the answer for sense and checking against any estimates. It could also include working backwards , such as adding to check a subtraction calculation. 

Example 

A school teacher is working out how many writing pens should be ordered for his class for the school year.

On average, a ten year old writes 7 words per line and fills 24 lines per page.

An average word uses 6cm of ink.

For one page of writing, how many words are written and how many centimetres of ink is used? 

The pupil would then go back and fill in the answers in the initial sentence. If, at that point, the answer was still in centimetres, they would be more likely to notice and change it to metres. They would also be reminded that there were two parts to the answer.

The pupil would then go back and fill in the answers in the initial sentence. If, at that point, the answer was still in centimetres, they would be more likely to notice and change it to metres. They would also be reminded that there were two parts to the answer.

Some pupils could benefit from seven blocks on top of a ruler to represent one line and then repeat this for two and three lines so that they could see how the total is achieved by multiplying the number of words by the number of lines - in effect, they would have the start of an array of blocks. 

Of course, lots of pupils would have further lines showing their calculations, since they would not be completing these in their head but this just illustrates how the SPOT process works.

See Free Resources for a PowerPoint download of this that can be used in the classroom.

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© 2018 by Mathsmoves