B7.1.4 · Strand 1, sub-strand 4

Ratios and Proportion

Comparing quantities with ratios and rates, and solving proportion problems.

1. Lesson 1 · B7.1.4.1.1 · about 45 min

   Ratios and the Language of Ratio

   Masons, cooks, farmers and market women compare quantities all the time: one headpan of cement to three of sand, two cups of water for every cup of rice. A ratio is the mathematician's way of making such comparisons exact. In this lesson you will write ratios, simplify them and describe them in clear words like "twice as many" and "for every".

2. Lesson 2 · B7.1.4.1.2 · about 45 min

   Unit Rates and Rate Language

   "GH₵9 a litre", "60 kilometres per hour", "GH₵20 per kilo": rates are everywhere in Ghanaian life, from the fuel station to the trotro to the meat seller at Salaga Market. In this lesson you will turn a ratio into a unit rate (the amount for ONE unit) and use it to work out costs, distances and best buys quickly and correctly.

3. Lesson 3 · B7.1.4.1.3 · about 50 min

   Tables of Equivalent Ratios and Sharing in a Ratio

   When Auntie Esi cooks jollof for a party of 50 instead of a family of 10, she does not guess: she scales up every ingredient in the same ratio. In this lesson you will build tables of equivalent ratios, link them to equivalent fractions, and use them to share money and materials fairly in a given ratio.

4. Lesson 4 · B7.1.4.1.4 · about 50 min

   Proportional Reasoning: Missing Values and Graphs

   Map readers, forex bureau attendants and shopkeepers all use proportional reasoning: if 1 cm on a map stands for 5 km, then 7 cm stands for 35 km. In this lesson you will find missing values in tables of equivalent ratios, test whether a table is proportional, and plot the pairs on a graph to see the straight line through the origin that every proportional relationship makes.

5. Lesson 5 · B7.1.4.1.5 · about 50 min

   Percent as a Rate per 100

   "40% off!", "6% interest", "35% commission": percentages are on shop windows in Osu, on bank posters and on every salesman's payslip. A percent is simply a rate per 100. In this lesson you will find a percent of any quantity and use it to work out commissions, discounts, sale prices, interest and even the original price before a discount.