Percentage Increases & Decreases in One Step

Mark-ups in the one-step method are more efficient than the two-step method but are more difficult to understand. One significant obstacle to understanding is a common  view that percentages over 100 are impossible. Yet one-step mark-ups require such  percentages.

Using Materials

Problem: “The farmer begins the season with some cows. After they have had their calves the number of cows the farmer owns has increased by 50%.” Students cut a paper strip to represent 100%, and another strip to represent 50%. Discuss why the strips together represent 150% of the original number of cows.

Problem: “The population of a town drops by 6%. Cut a strip to show why the town’s new population is 94% of the old population.”

Using Number Properties

Problem: “The painter estimates the cost of painting Dale’s house will be $4,123 plus GST at 12.5%. Dale wants to know what he will have to pay altogether. He claims he can work out the answer by going 1.125 x 4 123. Is Dale correct? Explain.”
(Answer: Dale is correct. 100% + 12.5% = 112.5 % = 1.125.)

“What is the answer rounded sensibly?”
(Answer: 1.125 x 4 123 = 4 638.375 ≈ $4,638 to the nearest dollar.)

Examples: Worksheet (Material Master 8–21).

Understanding Number Properties:

The Minister of Finance increases the rate of GST to 20%. Make up a problem for the cost of building a house when GST is added and solve the problem.