Think back over your maths this year. When a whole class picks a favourite sport, one sport always gets chosen more than the rest. In maths that most-chosen one has a special name — the mode. If you drew a bar chart of favourite sports, how would you spot the mode straight away?

Here is a favourite-sports chart to read together. Read the tallest bar, then the shortest. Then we will work out how many more chose the top sport than the bottom one, and finally which sport is the mode. Watch how we trace each bar across to the scale rather than guessing by height.

Now we hunt for missing numbers on the balance. A letter can stand for the missing number just like a box does — so b means the same thing as □. We will work through □ + 5 = 11, then b − 4 = 6, then □ + 8 = 14. Look carefully at the take-away one: on b − 4 = 6 the letter is the amount we start with, before we take any away. So the start must be bigger than the 6 we are left with. Predict how much bigger, then slide the beam to check. Watch the beam: it only hangs level when both sides weigh the same.

Now three fresh puzzles on the board. Each one is a small step harder. First we find a missing number: □ + 6 = 15. Next comes a take-away one with a letter: b − 3 = 9. Last comes a fact family. A fact family is the same three numbers making one add sentence and one take-away sentence. If we know that 6 + 7 = 13, then the same three numbers also make 13 − 6 = □. Work out what belongs in the box from the add sentence, predict the value, then level the beam to check each time.