Tutorial

Solution Model

Some math questions can be defined as a single mathematical task, such as solving an equation. More complex questions are defined through multiple, interdependent tasks. For such problems, you define a solution model, which identifies the tasks and how these are scored.

Examples of math exercises that have a solution model are:

  • Complex mathematical procedures, such as finding the formula of the tangent to a graph.
  • Story problems, where a real-world problem is decomposed into multiple mathematical steps.

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Example: Story problem

Consider the following story problem.

Nicole buys a sweater for €63,50. The original price was €74,95.
What percentage was the discount? Round your answer to the nearest whole number.

You can define this exercise with a single task as follows:

However, a student will probably split his solution in parts:

  1. Calculate the price difference €74.95-€63.50
  2. Calculate the difference as a factor: \frac{difference}{€74.95}
  3. Convert the fraction into a percentage: factor \times 100%

You can define such a solution model in AlgebraKiT, so that these intermediate steps are correctly evaluated. 

  • Create an interaction of type algebra
  • Add a step using the green plus + symbol, next to the word ‘solution’. Click on the triangle to name this step ‘factor’.  Add another step and call it ‘difference’.
  • Give each step a description. The description defines ‘what’ this step means and is used by AlgebraKiT to generate hints and worked solutions.
    Give the steps the descriptions: “the price difference”, “the discount as a decimal number” and “the discount as a percentage”.
  • Set the mathematical task for each step.
    •  €74.95-€63.50
    • \frac{difference}{€74.95}
    • factor \times 100%
  • Set accuracy. Step ‘factor’ should be accurate to at least 3 decimal places. The solution step must be rounded to 0 decimal places. 

Run the exercise to see the result:

Interactive student exercise:

Worked solution:

Add feedback on incorrect input

Students often make the mistake to use the wrong price for calculating the percentage. You can add feedback for such input.

Multiple solution strategies

A student could also use a difference approach to solve this problem:

  1. Calculate the discounted price as a factor
  2. Convert this factor into a percentage
  3. Calculate the discount percentage

You can add steps 1 and 2 to the solution model in the same way as you did before. Step 3 defines the final answer, which was 15%. By adding an extra task to the step ‘solution’ with the definition based on the newly added steps, AlgebraKiT ‘knows’ there are two ways to calculate the solution. 

The solution step now consists of two tasks, to define there are two ways to get to the final answer

Note: each step, not only the solution step, can consist of multiple tasks. When putting multiple tasks next to each other, the outcomes of all tasks should be equal. As you define multiple strategies to get to the result of that step, and the result of a step should always be the same independent of the strategy chosen.

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