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Mixed up Mixture

Can you fill in the mixed up numbers in this dilution calculation?

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Dilution Series Calculator

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

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Investigating the Dilution Series

Which dilutions can you make using only 10ml pipettes?

Conversion Sorter

Stage: 4 Challenge Level: Challenge Level:1

Why do this problem?

This problem allows practice of conversions in a context which might be more difficult than that usually available to the students, made accessible by the card sorting process.

Possible approach

This problem works well as a group or individual activity. Suggest the students try to work out which cards could appear at each step, even if they are initially unsure of the entire calculation. There are various ways that they can do this: either directly by working out the conversion or by logically eliminating cards which do not directly follow from the previous one. At each stage, encourage clear explanation of reasoning.

Once the calculation is completed, read through it together and be sure that it make sense.

Key questions

  • Are there any cards which definitely do not follow directly from the first card?
  • What physical quantities is the question referring to? Are you unsure as to the meaning of any of the symbols?

Possible extension

You might naturally try Mixed up Mixture next.

Possible support

Can the students find the solution by trial and error (by noting the direction of the ball, they could quickly work out the final ordering)? Then, they can try to understand the final calculation.