The place value inquiry is suitable for pupils aged between 10 and 12. The prompt is a number line with a microscopic view of a section of the line. The teacher can run the inquiry as open or structured depending on the experience of the class with inquiry learning and on the pupils' levels of initiative (see levels of inquiry).
The inquiry starts with students posing questions and speculating about the relationship between the two parts of the number line. Different pathways can emerge from the initial phase depending on the start number (positive or negative, whole number or decimal, tenths or hundredths, and so on) and on the intervals chosen. One point that often needs reinforcing is that the intervals on each line must be the same, but each interval on the blue line is a tenth of the interval on the black one. Pupils can decide to divide the blue line into more intervals, which might lead to the appearance of recurring decimals. This, in turn, can give rise to a discussion on degrees of accuracy (and rounding) and and on the advantage of fractions in this context.
In a structured inquiry, the teacher might pose questions and set tasks, perhaps after conducting a discussion around the meaning of the prompt. A planned lesson around place value (incorporating, for example, units, tenths and hundredths on the number lines) might be followed by tasks that involve filling in missing numbers when given two pieces of information about the black or blue line. The teacher might build up to posing challenging questions, such as: If the main number line started at 5 and finished at 19, what is the fourth number on the blue line? (An interesting discussion has arisen in a year 7 class about whether it is possible to complete the missing numbers when given one number on each of the lines). Once students have practised finding the interval on the black line by dividing the difference between the start and finish numbers by the number of intervals, then they could experiment with their own start and finish points.
Two tasks to support inquiry.
Promethean flipchart download
Smartboard notebook download