# Prompt 38: Simultaneous Equations (Elimination and Graphing)

Lesson 2: Starter

Questions:

1. In which order do you teach graphing, elimination and substitution? Does it matter which order they are taught in?
2. How do you introduce solving simultaneous equations? Which problem do you use? Is it devoid of context?
3. What prior learning needs to be re-capped or mastered before starting with any of these techniques? How do you ensure this is retrieved and fluid? i.e. adding and subtracting negative algebraic terms for elimination, gradients of straight lines for graphing, etc. Would you re-cap in starters? homework tasks? full lessons?
4. See the applet below. Would you have students explore solutions graphically as an independent/collaborative task, would you lead a discussion with this applet, or would you simply not use it?

Question:

1. Are any of these helpful facts for students to verify? In some case, can students prove them to be true?

# Prompt 36: Dividing Fractions

Questions:

1. If you choose to divide fractions using the standard technique of multiplying by the reciprocal, how could you use cell 2 and cell 4 as a learning experience? i.e. Would you provide these as something that higher attaining students can verify with more examples? When might it be easier to use cell 4 rather than multiplying by the reciprocal?
2. In regards to cell 2, would you ever consider teaching fractions by always finding a common denominator first when adding, subtracting, multiplying and dividing – then have students reflect on which operation they don’t need to do this for?

# Prompt 33: Creating and Solving Linear Equations in the Curriculum

This prompt is designed to get departments thinking about where in the curriculum students must create and solve linear equations. Can you think of any other concepts this connects to? Are you teaching creating linear equations explicitly? Do the department have a common approach to solving linear equations?

Further questions:

• For cell 3 and 5, are you explicitly teaching cross multiplication as a trick, or is it something students develop themselves? What the the issues with cross multiplication?

• Further topics: Direct/Inverse Proportion, Simple Interest, Similar Shapes, Angles in Parallel Lines

# Prompt 32: Approximating Pi

This is less of a pedagogy prompt, and more of a prompt to help us discuss and explore approximations of pi with the maths enrichment club at school around pi day. Hope it’s useful.

# Prompt 31: Distance-Time Graphs (Starter)

An object moves away from a point, X. Describe what it is doing in each section of the graphs below.

After a first lesson on Distance-Time Graphs, I gave this as an independent starter. After 30 seconds, I said, “There may be parts of the graph that you are struggling to describe – keep thinking and you will have the opportunity to discuss this with your partner in 2 minutes.

Would you do anything differently?

# Prompt 29: Angle Sum of a Triangle Proofs

Questions

1. When do you choose to prove this? Do you begin intuitively and then only prove when students have knowledge of angles in parallel lines? Could you use the proof in cell 1 immediately?
2. How do you choose to prove that the angles in a triangle sum to 180 degrees? One of the techniques above, all of them?
3. Could you utilise the idea of goal free problems so that students identify all angles they can in the 4 cases above and then you reveal that they have just proven that the angles in a triangle add to 180 degrees in 4 ways?

To have students complete a proof, I developed one that provides multiple avenues in the final step, so as to increase the chances of a proof from more students: