Maths Super-Strategy: Partitioning Power!

Hello Amazing Mathematicians! Today, we’re going to learn a really clever mental maths strategy called Partitioning. It sounds a bit like “party,” and it is fun because it’s all about breaking numbers down into smaller, friendlier pieces (like their tens and ones) to make adding and subtracting in your head much easier. It’s like having a superpower to take numbers apart and put them back together!

What is Partitioning and How Does It Work?

Partitioning means you split a number into its different parts. For example, the number 23 can be partitioned into 20 (two tens) and 3 (three ones). Once you’ve broken a number down, you can add or subtract those smaller parts one at a time, which is often much simpler!

Using Partitioning for Addition (e.g., 345 + 23)

Let’s look at 345 + 23.

• We keep the first number (345) whole.
• Now, let’s partition the second number, 23. We can break 23 into 20 (its tens) and 3 (its ones).
• Step 1: Add the tens part first. So, take 345 and add the 20.
  • 345 + 20 = 365. (Remember how we add multiples of 10? Only the tens digit changes here!)
• Step 2: Now, take that result (365) and add the ones part, which was 3.
  • 365 + 3 = 368. (Remember how we count on small numbers?)
• So, by partitioning 23 into 20 and 3, we found that 345 + 23 = 368!

Using Partitioning for Subtraction (e.g., 78 − 25)

Let’s try 78 − 25.

• Keep the first number (78) whole.
• Partition the number we’re subtracting, 25. This can be broken into 20 and 5.
• Step 1: Subtract the tens part first. So, take 78 and subtract 20.
  • 78 − 20 = 58.
• Step 2: Now, take that result (58) and subtract the ones part, which was 5.
  • 58 − 5 = 53.
• So, by partitioning 25 into 20 and 5, we found that 78 − 25 = 53!

Sometimes you might even partition both numbers, especially if they are both 2-digit numbers! (e.g., 42 + 35 could be 40+2 + 30+5, then add the tens 40+30=70, add the ones 2+5=7, then 70+7=77). Partitioning is flexible!

Practice Your Partitioning Power! (18 Questions)

Ready to try breaking numbers apart to solve problems? Here are 18 questions. For each one, think about how you can partition one of the numbers (usually the smaller one, or the one being added/subtracted) to make the calculation easier in your head.

(Your web app with the 18 questions will go here. The questions should lend themselves well to partitioning strategies.)

Why is Partitioning Such a Smart Strategy?

• Makes Big Problems Smaller: It turns one tricky sum into a few easier mini-sums.
• Builds Place Value Skills: You get really good at seeing the tens and ones (and hundreds!) inside numbers.
• It’s Flexible: You can often partition numbers in different ways to suit the problem or what you find easiest.
• Reduces Mental Overload: It’s easier to hold smaller steps in your head than one big calculation.

Tips for Grown-Ups: Helping with Partitioning

Partitioning is a key mental maths strategy that involves breaking numbers into (usually) their place value components (e.g., hundreds, tens, ones) to simplify calculations. It supports a deeper understanding of number structure.

• Visualise with Place Value Tools: Using base-ten blocks or place value arrow cards can help children physically see and manipulate the partitioned parts of numbers.
• Start with 2-Digit Numbers: Introduce partitioning with 2-digit + 2-digit or 2-digit − 2-digit numbers before moving to 3-digit numbers.
• Model Different Ways to Partition: Show that while partitioning into tens and ones is common (e.g., 23 = 20 + 3), sometimes other partitions can be useful (e.g., for 78 − 25, one might do 78 − 10 − 10 − 5).
• Encourage Verbalising: Ask children to explain their partitioning steps. “First I added the tens, then I added the ones.”
• Link to Known Facts: Partitioning often reveals simpler calculations that rely on known number bonds or adding/subtracting multiples of 10/100.