Explanations

Number – Addition and subtraction (Jump strategy on an empty number line – Stage 1, Mathematics K–6 Syllabus (PDF, 201 pages, 960 KB – refer page 47).

The teacher models the jump strategy to students as follows:

Step 1
The teacher poses the problem 46 + 35 and writes the problem on the board.

Step 2
The teacher says, ‘I am going to solve this problem by using a jump strategy.
When I use the jump strategy (teacher points to visual chart):

• I use an empty number line.
• I break up (partition) the number to be added into tens and ones.’

Step 3
The teacher says, ‘First I draw an empty number line’. The teacher draws an empty number line on the board.

Step 4
The teacher says, ‘The first number is 46. I write 46 below and at the beginning of the number line.’

Step 5
The teacher says, ‘35 is the two-digit number to be added to 46. I break the number to be added into tens and ones. 35 is made up of 3 tens and 5 ones.’

Step 6
The teacher says, ‘To 46 (points to 46) I am going to add 3 tens and 5 ones’.

Step 7
The teacher says, ‘On the number line I make 3 jumps of ten. Each time I jump, I record the jump on the number line. Counting on from 46 by 10, I get 56, 66, 76.’ The teacher models recording each jump on the number line (see below).

Step 8
The teacher says, ‘Next I count on the 5 ones by making 5 jumps of one. Each time I jump I record the jump on the number line. Counting on from 76 by ones, I get 77, 78, 79, 80, 81.’ The teacher models recording each jump on the number line (see below).

Note: At steps 7 and 8, the teacher could discuss using the jump strategy with a different number of jumps.

Step 9
The teacher says, ‘The answer to our problem is 81, that is 46 + 35 = 81’.

Step 10
The teacher reiterates the steps followed to solve the problem. The teacher says, ‘To solve the problem 46 + 35, I wrote 46 on an empty number line. I then broke up (partitioned) 35 into 3 tens and 5 ones. I made 3 jumps of ten (teacher points to the number line) and 5 jumps of one (teacher points to the number line). Each time I jumped I recorded the result (teacher points to these). The answer to the problem 46 + 35 is 81.’

Step 11
The teacher models using the jump strategy to check the answer and to add the numbers in the reverse order (ie 35 + 46).

Number – Addition and subtraction (Adding two or more numbers with trading – Stage 2, Mathematics K–6 Syllabus (PDF, 201 pages, 960 KB – refer page 49).

Step 1
The teacher poses the problem 136 + 156 and writes the problem on the board for solution using a formal written algorithm. The teacher says, ‘It is important when using the algorithm that we keep the ones, the tens and the hundreds under each other in the correct columns. This is because we are adding the ones to the ones, the tens to the tens and the hundreds to the hundreds’.

Step 2
The teacher says, ‘When I am adding using the algorithm I always start with the ones’.

Step 3
The teacher adds the ones by saying and pointing to the relevant parts,
‘6 + 6 = 12. 12 is made up of 1 ten and 2 ones, which means I will have to trade. I have to trade if the total when I add the column is ten or greater’.

Step 4
The teacher says, ‘I write the 2 ones underneath in the ones column and the ten from the 12 is traded to the tens column. I write it above and to the left of the 3 in the tens column’.

Step 5
The teacher says, ‘I now add all the numbers in the tens column’.
The teacher adds the tens by saying and pointing to the relevant parts, ‘1 ten + 3 tens + 5 tens = 9 tens’.

Step 6
The teacher says, ‘I got 9 tens. Because this is less than 10 tens (that is 100), I do not have to trade’.

Step 7
The teacher says, ‘I write the nine underneath in the tens column, remembering that another name for 9 tens is 90’.

Step 8
The teacher says, ‘I now add the numbers in the hundreds column’. The teacher adds the numbers in the hundreds column by saying and pointing to the relevant parts, ‘1 hundred + 1 hundred = 2 hundreds’.

Step 9
The teacher says, ‘I write 2 underneath in the hundreds column. Another name for 2 hundreds is 200’.

Step 10
The teacher says, ‘I know from using the algorithm that 136 + 156 = 292. Does our answer make sense? We can check our answer in a number of ways. We could:

• estimate what the answer is by rounding up and adding the two numbers together, and check to see if our estimate is close to our written answer
• check our answer by going over the steps we have followed orally or mentally to make sure we have added and traded correctly
• use the split method or the jump method on an empty number line to check if we have the correct answer
• use a calculator to check our answer’.