Problem Solving with Place Value

Understanding place value provides the essential foundation for so many aspects of mathematics.  From multiplying and dividing by powers of ten, understanding the equivalence between fractions, decimals and percentages to learning how to write and calculate with numbers in standard form. 

The videos below show how I use the place value table to teach these topics conceptually.

Problem Solving with Place Value

I designed this problem-solving lesson to deepen students’ understanding of place value so they can connect it to other aspects of mathematics including listing permutations, odd and even numbers and money.  By linking to these topics, the questions are challenging, yet remain accessible to students in key stage 3 as well as those studying the foundation GCSE course.

The lesson consists of six problem-solving questions all centred around place value.  In addition to the teacher’s presentation there is an accompanying worksheet for the students so they can work through the problems at their own place. 

Here is a sample of three of the questions.

Linking place value to arithmetic

Problem Solving with Place Value

In this question students link their understanding of place value to writing numbers in figures from words.  Next, they use column subtraction to find the difference between two numbers.

Linking place value to permutations

Problem Solving with Place Value

In this question students are asked to arrange the four single digit cards to make the numbers between 230 and 430.

Students link their understanding of place value to listing permutations.

Linking place value to odd and even numbers

Problem Solving with Place Value

To work out the smallest, even number students need to find two three-digit numbers with the smallest difference. 

To calculate the biggest, odd number they need to find two numbers with the greatest difference.

Both questions can be completed through a method of trial and improvement.  More able students would use:

  • odd + odd = even
  • odd + even =odd
  • even + odd = odd
  • even + even = even.

Teach this lesson


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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.


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