Counting Milk

We use addition throughout our daily lives, so it can be a great idea to start a conversation about addition when carrying out an everyday activity. In this case, a child in the nursery began counting the milk cartons on the counter, as shown in the picture below.

A practitioner then asked the child if there were enough milk cartons for all the children. This required the child to walk around the nursery and count all the children. When the number of children was larger than the number of milk cartons, she concluded that there were not enough cartons.

Accompanied by the practitioner, she went to the fridge to get more cartons of milk, but had to determine how many extra cartons were required. Whilst trying to work out the difference in the number of children and the number of cartons of milk can involve a subtraction sum, there is another way to find the correct number of milk cartons.

If you can remember the original number of milk cartons, you can then count on from this number until the total number of milk cartons is equal to the total number of children. Suppose there are \(20\) children in the nursery and there were \(15\) milk cartons already. Instead of saying the difference between \(20\) and \(15\) is \(5\), and so we need \(5\) extra cartons. We could say we start with \(15\) cartons and \(20\) children, if we add a carton, we will have \(16\) cartons and \(20\) children. We can carry on this sequence until we reach the carton that will be \(20\) in the sequence. Here, the need for carrying out a subtraction sum was eliminated, and the child could carry out the task simply by counting on. Reframing subtraction tasks can then change how accessible a task is. This was the method that this child found easier to use.

Fact families are a set of equations that describe the same fact but are shown in different ways, for example \(7+3=10\), \(10-7=3\) and \(10-3=7\) are all rearrangements of the same equation. In the case of the milk, if the number of children was \(20\), the number of original cartons was \(15\), then we could think of the unknown number of cartons as \(x\). This gives the equations: \begin{equation} 20 - 15 = x, \end{equation} \begin{equation} 15 + x = 20. \end{equation} The first equation corresponds to working out the number of extra milk cartons required. The second equation illustrates counting on from \(15\) to \(20\).