Jump & split strategies for addition
Theory
The jump strategy and the split strategy are two Year 3 maths ways to add. The jump strategy moves along a number line, while the split strategy uses partitioning to break numbers into hundreds, tens and ones. This page shows both strategies for two- and three-digit addition, including jumps past a hundred and regrouping. Curriculum: VC2M3N04 / AC9M3N03.
The jump strategy and the split strategy are two ways to add. Both break the numbers into easy parts, add the parts, and then put them back together. They always give the same total.
In the jump strategy you keep the first number whole and split only the second number into tens and ones. Then you jump along a number line, jumping the tens first and the ones next. For \(47 + 35\), start at \(47\), jump \(+30\) to \(77\), then \(+5\) to \(82\).
In the split strategy you partition both numbers by place value into hundreds, tens and ones. Add the matching parts, then combine. For \(53 + 24\): \(50 + 20 = 70\) and \(3 + 4 = 7\), so \(70 + 7 = 77\). When the ones make more than \(9\), you regroup the extra ten.
Three-digit numbers split the same way: \(452 = 400 + 50 + 2\). A jump can also be a hundred, such as \(+100\), and a jump can cross a hundred on the number line, as in \(196 + 40 = 236\).
How to add with the jump strategy
- Start with the first number. Mark it on a number line and leave it whole.
- Jump the tens. Split the second number into tens and ones, then jump forward by the tens.
- Jump the ones. From there, jump forward by the ones. The number you land on is the total.
How to add with the split strategy
- Partition both numbers. Break each number into hundreds, tens and ones.
- Add the matching parts. Add hundreds with hundreds, tens with tens, and ones with ones.
- Combine and regroup. Add the parts back together, carrying an extra ten or hundred if a part is too big.
| \(\text{Tens: }50 + 20\) | \(=\) | \(70\) |
| \(\text{Ones: }3 + 4\) | \(=\) | \(7\) |
| \(70 + 7\) | \(=\) | \(77\) |
So \(53 + 24 = 77\).
| \(\text{Tens: }60 + 20\) | \(=\) | \(80\) |
| \(\text{Ones: }8 + 7\) | \(=\) | \(15\) |
| \(80 + 15\) | \(=\) | \(95\) |
The \(15\) carries an extra ten, so \(68 + 27 = 95\).
| \(148 + 30\) | \(=\) | \(178\) |
| \(178 + 6\) | \(=\) | \(184\) |
So \(148 + 36 = 184\).
| \(\text{Hundreds: }100 + 100\) | \(=\) | \(200\) |
| \(\text{Tens: }50 + 20\) | \(=\) | \(70\) |
| \(\text{Ones: }6 + 8\) | \(=\) | \(14\) |
| \(200 + 70 + 14\) | \(=\) | \(284\) |
The stall sold \(284\) apples in all.
| \(196 + 40\) | \(=\) | \(236\) |
| \(236 + 7\) | \(=\) | \(243\) |
The first jump crosses \(200\). So \(196 + 47 = 243\).
| \(352 + 100\) | \(=\) | \(452\) |
| \(452 + 40\) | \(=\) | \(492\) |
| \(400 + 90 + 2\) | \(=\) | \(492\) |
Jump \(+100\), then \(+40\). The split strategy gives \((300 + 100) + (50 + 40) + (2 + 0) = 492\) too.
| \(\text{Hundreds: }300 + 200\) | \(=\) | \(500\) |
| \(\text{Tens: }60 + 40\) | \(=\) | \(100\) |
| \(\text{Ones: }5 + 8\) | \(=\) | \(13\) |
| \(500 + 100 + 13\) | \(=\) | \(613\) |
The tens make a whole hundred and the ones make \(13\), so \(365 + 248 = 613\).
(i) Where does the first jump land?
(ii) How big is the second jump?
| \(128 + 30\) | \(=\) | \(158\) |
| \(165 - 158\) | \(=\) | \(7\) |
(i) \(158\).
(ii) The second jump is \(+7\), and \(30 + 7 = 37\), the number being added.
Common pitfalls
Frequently asked questions
What is the jump strategy in maths?
The jump strategy adds by moving along a number line. Keep the first number whole, split the second number into tens and ones, then jump the tens first and the ones next. For \(47 + 35\) you start at \(47\), jump \(+30\) to \(77\), then \(+5\) to \(82\).
What is the split strategy for addition?
The split strategy breaks both numbers into hundreds, tens and ones, adds the matching parts, then combines them. For \(53 + 24\) you add \(50 + 20 = 70\) and \(3 + 4 = 7\), so the total is \(77\).
What is the difference between the jump and split strategy?
In the jump strategy you keep the first number whole and split only the second number, then jump along a number line. In the split strategy you break both numbers into place value parts and add the matching parts. Both give the same total.
How do you use a number line to add?
Mark the first number on the number line. Jump forward by the tens of the second number, then jump forward by the ones. The number you land on is the total.
Do the jump and split strategies give the same answer?
Yes. They break the numbers apart in different ways, but they add the same amounts, so they always reach the same total. Trying both is a good way to check your work.
What do you do when the ones add up to 10 or more?
Add the ones as usual, then regroup. For \(68 + 27\) the ones are \(8 + 7 = 15\). Combine \(80 + 15 = 95\), so the extra ten from the \(15\) is carried into the tens.