Writing solutions to worded mathematical problems
In mathematics, students need to develop the ability to communicate their solutions and provide appropriate reasoning to support their working. Scaffolding use of appropriate terminology and notation will support students to be able to communicate their mathematical thinking independently, as will explicitly teaching how to write written solutions and extended worked problems.
Extension idea
High-ability students may have extensive prior knowledge. Pre-test to determine what curriculum can be compacted. This involves removing instruction related to the steps of the process where students already have mastery.
Understanding this strategy
Written solutions to worded problems in mathematics will contain some or all of the following features:
Formulate the problem mathematically
- Summary of important information given in a problem
- Definition of any variables
- Statement of relevant formulae, equations or functions that will be used in the solution of the problem
- List any assumptions
- Explain the reason for choosing a particular problem-solving strategy.
Sample strategies
Sample strategies teachers can use to support this component of writing and mathematical thinking:
Extension ideas
High-ability students could be:
- asked to create a word problem from a mathematical equation.
- asked to propose two different strategies to solve an open ended problem and explain which of these strategies would be most efficient.
- provided with a more complex word problem than their peers.
Reasoning and calculations
Reasoning for steps of working, linked to key information given in the problem
- Results of solving equations and performing calculations
- Supporting graphs, tables or diagrams
- Interpretation of graphs, tables or diagrams
- Evidence to support answer.
Sample strategies
Sample strategies teachers can use to support this component of writing and mathematical thinking:
Extension ideas
High-ability students could be:
- provided with data in a variety of forms to support them with their calculations.
- asked to transform data into more useable formats to support them with their calculations.
Reasoning and calculations
- Statement of a final answer, linked to the context of the problem
- Check to see that answer is reasonable.
Sample strategies
Sample strategies teachers can use to support this component of writing and mathematical thinking:
Extension idea
High-ability students could be paired together to review each other's answers and/or their justification of their solutions.