Here is a bar chart of the shoe sizes in a 4th Class. Look at it for a moment. Which shoe size is worn by the most pupils? And how far apart are the smallest and the biggest sizes on the chart?
Take two or three hands-up answers, not open call-outs. Do not name the words mode or range yet — let pupils describe "the biggest bar" and "how spread out it is" in their own words first.
Four charts on the board, each one already built. On the first, the tallest bar is the fruit chosen by the most pupils, so that value is the mode. On the pets chart, the largest is 8 and the smallest is 2, so we take 8 − 2 = 6: the range is one number you get by subtracting. Then watch for a chart where two bars reach exactly the same top height, and one where a single very tall bar stretches the spread right out.
Say verbatim: the mode is what happens most, the range is how spread out it is.
Here is a chart of library books borrowed each day that we can explore. The daily totals are:
First, find the mode. Which value comes up more than once? Now the range. What is the smallest total, and what is the largest? Say the subtraction aloud, then check.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud. Draw the answers out of the class rather than reading them off the board: the value 8 comes up twice, so 8 is the mode; the smallest total is 5 and the largest is 11, so the range is 11 − 5 = 6.
Watch for the mode-versus-range mix-up: the mode is a value that repeats, the range is largest take smallest. Hold out for pupils naming both parts before you accept the range. Revoice a strong answer: so eight is the mode because it turns up more than once, and the range is six because eleven take five is six.
In your maths copy, look at this small set of numbers and write down the mode, then work out the range. Copy the numbers out in a row first:
Write "mode = ___" and then "range = largest − smallest = ___", showing your subtraction underneath.
Walk the room glancing for the subtraction being written out (9 − 2), not just the answer — this is whole-class copybook practice, not marking. The mode here is 4 because it appears three times.
Today we work through four data sets, each a little trickier. For each one we find the mode and the range, and we say the subtraction aloud before we check.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The fourth set is the one that lands the big idea: one outlier stretches the range far wider than the other sets even though most of the data is unchanged. Ask the class to predict which set will have the biggest range before the last reveal.
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