Getting Ready for School Math: Number Skills Before First Grade
Hiroki Obara · Developer
When a child is about to start school, many parents begin to wonder whether they should be doing some math at home first. School starts at different ages in different countries, and what children are expected to know on day one varies too. Still, the question is the same everywhere: what is worth doing with numbers before school, and in what order?
There is a view that a child does not need to be able to calculate before starting school. What can help instead is plenty of experience counting things and getting a feel for amounts, through play and everyday life. This post sets out what to do and in what order.
What early-years guidelines say
Here are three examples of what official guidelines expect before or at the start of school.
In Japan, where children start first grade at six, the national Course of Study for Kindergarten (2017) lists, among the qualities to develop by the end of early childhood, “interest in and a sense of quantities, shapes, signs and letters,” built up “through play and daily life.” First grade itself starts with counting and seeing numbers in groups of ten.
In England, children in the Reception year are assessed against an Early Learning Goal for Number. It asks for a deep understanding of numbers to 10, including how each number is made up, recognising amounts up to 5 without counting, and recalling number bonds up to 5 and some to 10.
In the United States, the Common Core kindergarten standards include counting to 100 by ones and tens and fluently adding and subtracting within 5.
The details differ, but all three put counting and a sense of small numbers first, not written calculation.
1. Counting
The first step is counting. Being able to recite “one, two, three” is not the same as being able to count things.
To count objects, a child has to match one number to one object, and understand that the last number said is how many there are in total. In a 1990 study by psychologist Karen Wynn, children could recite numbers well before they could hand over exactly three things when asked for three.
At home, you can keep counting with a pointing finger: handing out snacks, climbing stairs, setting out plates. When you finish, ask “How many altogether?” That links the last number to the whole amount.
2. Seeing amounts
Once counting is comfortable, add experiences where the amount is clear without counting.
Up to about three, people can see how many at a glance. Arranged like the dots on a die, five and six become easy to see too. Games with cards and dice, and simple board games, are good for building this sense.
The other part is comparing. “Which has more?” “How many more to make them the same?” These questions treat numbers as amounts, and they are also the doorway to subtraction.
3. Making ten
If you want to go one step further before school, get friendly with the number ten. There are ten fingers on two hands. If a child can answer “How many more does 7 need to make 10?” with their fingers, it helps a great deal later with addition that crosses ten.
This is the start of the making ten strategy, which I wrote about in How to Teach the Making Ten Strategy. Before school, though, there is no need to practise it on paper. Fingers, or ten counters, are plenty.
4. Reading and writing numerals
Reading and writing numerals can come last. A numeral is a name for an amount. If a child learns the shape “7” without a sense of the amount, they still do not know how many it is.
There are endless chances to read numbers in daily life: calendars, clocks, lifts, bus numbers. Writing can wait until the child can hold a pencil and draw lines. I put an order for writing digits in How to Teach Kids to Write Numbers.
What not to overdo
There are also things that need not be overdone before school.
Piles of worksheets. If a child enjoys them on their own, there is no need to stop. But when a parent sets a daily quota, it can become the start of disliking math.
Stopping finger counting. Counting on fingers is a natural way to check an amount with your eyes. It is fine in the first year of school. Children stop needing them in time.
Rushing ahead. Even if a child learns multiplication tables before school, first grade still starts with counting. Knowing it all already can make lessons dull.
Keep it out of “study time”
One way of thinking is not to turn number preparation into study time. Handing out snacks, playing a board game, counting the days on a calendar until school starts. Through moments like these, numbers slowly become familiar.
What MathCal can do
MathCal is a math practice app where children handwrite answers on the screen, and I make it. Grade settings run from grade 1 to grade 6, and the App Store lists ages 6 to 8. For a child who has not started school yet, it can wait until they can write numerals.
Today’s Drill, Today’s Challenge and Today’s Lesson on the home screen are free every day. If no birthday is set, Today’s Drill is chosen from the Basic Calculation Drill and the Fill-in-the-Blank Drill, and Today’s Lesson from Addition Beads and Subtraction Beads. The bead lessons bring a Montessori material onto the screen, so a child can move beads and see the amount.
Choosing drills and lessons from the full lists, and using settings such as addition only, No Carrying or Borrowing, or Enable Dots on Number, which shows a dot for each unit, requires a one-time purchase. There are no ads, and no data is collected.
In my interview, I said of the bead lessons that, being a digital app, they cannot fully reproduce the feel and the 3D texture of the real thing, and that this is where the real material is needed. The heart of number preparation is counting real things by hand, snacks or counters. The app can come after that, as practice in linking numerals to amounts.
