Bridging Through 10 (Game 3)
With two other games I presented on this blog, we have seen how to help children get familiarised with the partition of 5 and 10 (number bonds to 5 and 10) and partition any number between 5 and 10 into 5 plus another number (Game 1), and with finding halves of even numbers and “almost halves” of odd numbers (Game 2). These skills can be used to add two numbers smaller than 10 whose sum is greater than 10.
A first method consists in using the partition of a number into 5 + another number; for instance, 8 = 5 + 3, so we have 8 + 8 = 5 + 5 (= 10) + 3 + 3 (= 6) = 16; and 6 + 8 = (5 + 1) + (5 + 3) = 10 + 4 = 14.
One can also use known doubles or sums of “almost halves” close to the addition we want to perform. For instance, 6 + 8 is one more than 6 + 7, that is, the two “almost halves“ of 13 plus 1, since 8 is 7 + 1. We therefore find that 6 + 8 = 6 + 7 + 1 = 14.
Another method is bridging through 10. As you will see, it is very useful for this method to be able to find easily the distance to 10 of any number between 1 and 9 (see Game 1). There is a nice game to visualise and practice the method of bridging through 10. This game is very similar to the game used to understand place value, just that we use cuisenair rods instead of 1-cubes and 10-rods. It changes everything because here the child has to partition the number correctly when they will have to bridge through 10. The game is also interesting because it shows that the same strategy can be applied to any addition. In fact, the difficult bit in 24 + 8 and 24 + 38 is the same as in 4 + 8 in the end.
So, we use a 10 cm x 10 cm square. With children who are not comfortable with partitioning numbers and finding the number bonds to 10, it might be a good idea to start with cm-paper, keeping in mind that the objective it to move to blank paper as soon as possible. Children take turns to roll a 10-sided die. They fill their square progressively, taking the number shown on the die with cuisenair rods. The first turns are used to fill the first column (or raw), so for instance for a player who has rolled first 4 and then 3, they have a square as shown below.
Let’s imagine the player rolls 5 at the next turn. It is where the bridging-through-10 strategy will have to be implemented.
First step: work out what number needs to be added to the 7 to get a full column. It is the number that added to 7 makes 10, so it is 3.
Second step: partition 5 (shown on the die) as 3 + 2.
Third step: take a 3-rod cuisenair to complete the column and place a 2-rod cuisenair in the second column.
They have found that 7 + 5 = 12.
If a 9 (or 8) is rolled, it might be a good opportunity (depending on the level of the players) to show that we can also add 10 (it’s a full column, so it can simply be added from the left, showing that the number of tens increases by 1 but the number of ones remains unchanged) and then remove 1 (or 2) since 10 is 1 (or 2) more than 9 (or 8).
The game goes on until one has completely filled their square.
Once this technique is well understood, we can also play with two 10-sided dice and a bank of coins as for Game 1 and Game 2. Players take turn to roll the dices, then they work out the sum of the two numbers shown on the dice and collect this amount in pence.
