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## 'All in a Jumble' printed from http://nrich.maths.org/

### Why do this problem?

The problem presents many different quantities and units. It involves thinking about large and small numbers and 'back of an envelope' estimations and unit conversions. It offers an ideal opportunity for class discussion and convincing arguments.

### Possible approach

In preparation for a lesson in a computer room, show the small interactivity to the class, and ask for volunteers to move items and explain their reasons. Set homework to research different units and bring their notes to the computer lesson. Showing students a few different sets of 15 items, could suggest some unfamiliar units to look up.

Ask students to work in pairs, so they must discuss and convince each other (e.g. like when couples play "Who Wants to be a Millionaire"). They could settle which items are a "final answer" and drag these to the top of the list. They could choose one item to "ask the audience" - and have a short plenary where these questions are asked and answered by other students in the class.

For most of the lesson, allow students to work at the task, using exercise book/whiteboard to control/motivate - eg students could write the scores they get each time they check. The whiteboard could be a leader board, with "100% and number of tries" recorded to motivate others. With some classes, it may be appropriate to encourage students to write out their estimating processes and unit conversions, in their exercise books. Students could also record useful numerical facts.

### Key questions

Which of the units could be used here?
Which of the items are easiest/hardest?
What do you know that is relevant here?

### Possible extension

Challenge students to get "100% in 3 tries" twice in a row!

### Possible support

Print a few copies of some of the 15 question tables (see note at end of the problem). Ask students to identify all the items on one sheet which measure length, say. They could delete all other items and all inappropriate units. In small groups, ask students to estimate the different lengths in any units of their choice, and convert these estimates to other sensible units. Based on this working, ask them to match up item, number and unit for all the lengths.