Problem solving

Problem-solving Investigations - Year 6

Problem-solving investigations provide a fun, stimulating context in which children can develop and exercise their ability to reason mathematically and think creatively. They provide extra skills practice and also provide a real challenge if the skill itself is proving undemanding for some children.

These problems  are designed to help children identify patterns, explore lines of thinking and investigate properties of numbers, shapes and measures. They can be used alongside the Hamilton plan for the week or independently. The teacher instructions for the whole term are collated in the Overview. Ruth's Advice gives some background and tips for using these investigations with your pupils.

Please note, we do not provide Investigations for Year 6 Summer Term in order to make space for SATs.

Supporting documents for set
  • Week
  • Title
  • Download
+ Details
Giant domino addition

Children follow a logic to convert arrangements of dominoes to numbers, and then perform a giant addition. They then create their own domino additions and explore addition patterns. 

+ Details
Crack the code

Children use logical thinking and number bonds to solve a mathematical puzzle involving multiplying by 10 and 100 and adding decimal numbers.

+ Details

Children subtract 5-digit numbers and look for patterns in the digital roots. 

+ Details
Ellipse in a circle

Children draw a circle and then use straight lines and angles to construct an ellipse within it.

+ Details
Magic multiplication squares

Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square.

+ Details
The eights have it

Children multiply numbers starting with 9 by 9 and add single-digit numbers in a decreasing sequence. They identify and describe the patterns and start to explain them.

+ Details
Awesome answers

Using a magic square to generate 3-digit numbers, children create divisions with dividends containing specified fractions.

+ Details
Dicey differences

Children use two dice with decimal numbers to find largest and smallest possible differences, and use mathematical reasoning to calculate the probability of getting close to a specified target.

+ Details
Weights in a line

Children use systematic working to calculate the number of possibilities of making weights, and then look for patterns utilising line graphs.

+ Details
Domino fractions

Children use dominoes to create fractions. They explore sums of fractions using equivalent fractions and related denominators.

+ Details
Stunning squares

Children explore patterns in the squares of numbers with reversed digits to find pairs of ‘stunning squares’.