The prompt was devised by Pal Rayit during a year 10 (grade 9) lesson on multipliers linked to percentage increase and decrease. Pal describes how she started the lesson with 60 x 1.2 on the board:
"I just wrote it down on the spur of the moment after visiting the inquiry maths website. Even though I hadn't thought about the numbers, the pupils automatically linked 0.2 to 20%. When I questioned them about what 1 stood for, they immediately came up with 100%. So what percentage is 1.2? 'It's 120%, miss!' I was gobsmacked. What really impressed me most was the eagerness of the pupils in trying to explain."
One student then noticed that 60 x 1.2 equals 60 + 12. As a prompt, the equation has the potential to initiate different inquiry pathways:
- Search for examples of a similar type and graph the results (see below).
- Consider two decimal places, for example 50 x 1.25 = 50 + 12.5.
- Explore what happens when the decimal number is less than one (90 x 0.9 = 90 - 9) or greater than two (16.67 x 2.5 = 16.67 + 25).
- Explore what happens when the decimal number approaches one.
- Find more examples through deductive reasoning, rather than through pattern spotting or exploration.
- Change the operations in the prompt, for example 72 ÷ 1.2 = 72 - 12.
- Replace the decimals by fractions, for example 72 ÷ 6/5 = 72 x 5/6.
Pal concludes the report on her lesson by saying: "I couldn't believe how easy it was to teach the topic. The prompt automatically led to the multiplier being used. I intend to use the inquiry maths website a lot more. Keep up the good work! You have introduced a new way of teaching which is actually working and more useful then a whole exercise on a topic."
Pal Rayit is a teacher of mathematics at St Joseph's Catholic High School Slough, Berkshire (UK). You can follow her on twitter @triggermaths.