Estimate and find percentages of whole number and decimal amounts.
Number Framework Stage 8
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 15%. Dale wants to know what he will have to pay altogether. He claims he can work out the answer by going 1.15 x 4 123. Is Dale correct? Explain.”
(Answer: Dale is correct. 100% + 15% = 115 % = 1.15.)
“What is the answer rounded sensibly?”
(Answer: 1.15 x 4 123 = 4 741.45 ≈ $4,740 to the nearest ten dollars.)
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.