Students should understand and use direct proportion and simple ratios in…

The idea

Genetic crosses predict the proportions of offspring genotypes and phenotypes. When outcomes are equally likely, the expected numbers can be expressed as a simple ratio, such as 1:1 for female to male offspring in a sex cross. Direct proportion means that as the number of offspring increases, the expected number of each type increases in the same proportion. For example, in a 1:1 cross, 4 offspring are expected to include 2 females and 2 males, 40 offspring are expected to include 20 females and 20 males, and 100 offspring are expected to include 50 of each. To use this, identify the ratio from the cross, add the parts to find the total number of parts, then divide the total number of offspring by that total and multiply by each part.

What earns the marks

• Identify the expected ratio of offspring types from the completed genetic cross.
• Add the parts of the ratio to find the total number of parts.
• Divide the total number of offspring by the total number of parts to find the value of one part.
• Multiply the value of one part by each number in the ratio to predict expected numbers.
• Recognise that expected numbers are proportions, so actual results may differ due to chance, especially with small sample sizes.
• Use direct proportion to scale predictions from a small expected sample to a larger one.

Common mistakes and how to put them right

• Adding the ratio parts incorrectly, for example treating 1:1 as three parts.

  Put it right: The total is found by adding all parts, so 1:1 gives two parts.

• Dividing by one part of the ratio instead of the total number of parts.

  Put it right: Divide by the sum of the ratio.

• Expecting observed offspring numbers to match predictions exactly.

  Put it right: Chance variation means real results can differ from expected proportions.

Exam tips

• Write the ratio clearly before doing any calculation so the parts are easy to identify.
• Show each step of the calculation, including the total number of parts and the value of one part.
• Use words such as expected or on average when stating predicted numbers, because actual results may vary.