In The language of mathematics in science (2016), Boohan notes that a key difference between calculations in mathematics and science is that in science the numbers we calculate with most often have a unit as well as a number. Students need to pay attention to the manipulation of not just the numbers but the units as well. Addition and subtraction of values can only be done if they are expressed in the same units. In these questions the units have been chosen to be the same.

Students may be tempted to use number lines of positive and negative numbers to combine the forces. When forces are in opposite directions it is simpler to take the smaller force from the larger and to consider the direction separately. This approach can help to clarify the idea that forces have both size and direction.

This response activity gives students the opportunity to consolidate their understanding of balanced and unbalanced forces by calculating and describing resultant forces.

This activity is very similar to one used in the key concept PFM1.3: Balanced and unbalanced forces. It gives students the opportunity to practise applying their understanding and to clarify their thinking through practising calculations. To support this, students could answer the question in pairs or small groups. Listening to individual groups as they work often highlights any difficulties they might have. These can often be overcome, through a whole class clarification or redirection part way through the activity.

Allowing only one student in each pair or small group to write down the answer on behalf of the group encourages discussion of both the science and of the presentation of the answer.

Differentiation

If some students are working with a teaching assistant, then a list of prompt questions for the TA could help to make this activity more purposeful.

1. 305 N forwards (right)
   
2. 25 N forwards (up and right)
   
3. 323 N forwards (right)
   
4. 27 N forwards (down and left)
   
5. 0 N no resultant force (not ‘no force’)
   
6. 25 N backwards (left)

Boohan, R. (2016) The language of mathematics in science, Association for Science Education, Hatfield, England.