This is a level 3 activity from the Figure It Out series.
A PDF of the student activity is included.
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Deductive reasoning involves using a logical and systematic approach to solve problems. In this activity, students need to find a simple way to write down the result of each function. This should enable them to identify whether the functions they have used are effective in achieving the correct orientation or have resulted in a loop that simply returns the cups to a previous iteration.
The students may find it helpful to use materials in their investigation, for example, cups or double-sided counters.
Recording trials is an important part of problem solving. In this exercise, a written or pictorial record will help the students to discover if their instructions are effective in finding the correct orientation or creating a loop that leads to an earlier iteration. Ask the students to decide how to represent the orientation of the cups so that they can keep a running record.
Discuss with the students the two types of commands available: changing orientation by turning cups over (A) and swapping positions (B, C, and D). Extend the activity by asking the students to investigate which sequences are needed to swap cup positions, for example, swapping the cups in:
3rd and 4th place (Answer: D→C→D)
1st and 2nd place (Answer: C→B→C)
1st and 3rd place (Answer: D→C→B→D→C→D→C)
2nd and 5th place (Answer: it’s impossible)
Ask: What patterns can you see? Which cup never changes position?
Discuss with the students whether the results of this investigation would be useful when reorienting another arrangement of cups, for example, 
. Ask Why or why not?
Challenge the students to generalise their findings by asking them what advice they can give to Uncle Arun so that he isn’t limited to trial and improvement. For example:
- Cup 5 always stays put.
- To invert a cup in positions 2, 3, and 4, you need to move it to position 1.
Invite the students to add a fifth command, for example, E: Turn the third cup over. The students can explore which new command is the most useful. This type of thinking is similar to that involved in designing computer software. Encourage the students to demonstrate the effectiveness of their new command.
Recording information in systematic, concise, and coherent ways develops the key competency using language, symbols, and texts.
Technology-related student activities
- Examine a product and identify its systems. A bike, for example, could have steering, propulsion, warning, and protective systems.
Sometimes, the systems may not be easily identified or understood, for example, the black box. You could ask your students to identify products that have black box systems (for example, computers and cameras). - Examine Rube Goldberg or Heath Robinson drawings of humorous systems. Have students design their own. See www.wired.com/gadgetlab/2010/03/rube-goldberg-video-gallery
- Examine everyday products or designs and suggest modifications to improve safety. For example, how could an electric kettle be made safer?
Exploring the technology-related context
Developing a technology can take a lot of time and effort. If a particular design has a number of systems within it, it can be difficult to ensure that each functions appropriately. For example, a car has steering, braking, and electrical systems, and it may take a lot of trialling to produce a fully functioning prototype. Car designers must also comply with safety requirements and include systems to protect drivers and passengers in the event of crashes or system failures.
Answers to activity
1. a. The moves so far are:
b. A→B→A. (A again, to reverse it back to 
, then B to get it to 
, then A to get 
)
c. Answers will vary. For example, you can do it in 4 steps if you use D→C→B→A. (Komal and Uncle Arun used 7 steps on their first attempt.)
2. Answers will vary. The fastest way (3 steps) is: