Maths

Place value and column calculation

Build, read and partition three-digit numbers, then practise column addition and subtraction with exchanging. The pages include worked examples, missing-number tasks and a two-step library-books problem. Pupils can explain each exchange with place-value language. Check the examples first.

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Count hundreds, tens and ones in each picture. The number boxes are left for pupils.

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Page 1

NAME
CLASS
DATE
LEARNING GOAL
I can use hundreds, tens and ones to
build, split and add three-digit numbers.
SUCCESS CRITERIA
I can say what each digit in a three-digit number is worth.
I can partition a number into hundreds, tens and ones.
I can add and subtract in columns, exchanging when I
need to.
1
Build it on the mat
2 marks
Draw 243 with flats, rods and cubes in the right columns. Then write each digit in its box.
H
Hundreds
a flat is worth 100
DIGIT
T
Tens
a rod is worth 10
DIGIT
O
Ones
a cube is worth 1
DIGIT
2
What number is shown?
3 marks
Count the flats, rods and cubes. Watch out: one picture has no tens, so you need a zero.
a
Number: 
b
Number: 
c
Number: 
MATHS WORDS
digit
value
hundreds
tens
ones
zero
partition
exchange
Zero holds the place. In 207 the 0 tells us there are no tens. Without it, 207 would turn into 27.
Place value and column calculation · Build and read
MATHEMATICS
AGES 7 TO 9
PLACE VALUE
PLACE VALUE AND COLUMN
CALCULATION
Build, read and split numbers, then add and subtract in columns.
Page 1 of 3

Page 2

3
Partition it
3 marks
Split each number into hundreds, tens and ones. The first one is done for you.
e.g.
356 = 300 + 
50
 + 
6
a
472 = 
 + 
 + 
b
608 = 
 + 
 + 
c
 = 500 + 20 + 9
4
Worked example: column addition with an exchange
H
T
O
2
4
7
+
1
3
5
3
8
2
1
247 + 135 = 382
1. Line up the digits. One digit in each square, ones under ones.
2. Start with the ones. 7 + 5 = 12, which is 1 ten and 2 ones. Write 2.
3. Exchange the ten. Write a small 1 under the line in the tens column.
4. Add the tens, then the hundreds. 4 + 3 + 1 = 8 tens. 2 + 1 = 3 hundreds.
5
Column addition
4 marks
Start with the ones. Made 10 or more? Exchange: write the 1 under the line.
6
Spot the mistake
2 marks
A pupil worked out 268 + 157 and got 325. Explain the mistake, then do it correctly.
The mistake is in the 
 column because ...
Place value and column calculation · Column addition
PLACE VALUE
COLUMN ADDITION
SPLIT AND ADD IN COLUMNS
H
T
O
3
1
4
+
2
5
2
a
H
T
O
2
3
9
+
1
4
7
b
H
T
O
1
6
5
+
2
7
3
c
H
T
O
4
5
6
+
2
7
8
d
H
T
O
2
6
8
+
1
5
7
3
2
5
1
PUPIL'S ANSWER
H
T
O
2
6
8
+
1
5
7
YOUR ANSWER
Page 2 of 3

Page 3

7
Column subtraction
3 marks
Not enough to take away? Exchange from the next column: cross out its digit, write one less above it.
8
Library books
2 marks
a The school library has 264 books. A delivery brings
158 more. How many books does the library have now?
Answer: 
 books
b Then pupils borrow 135 books. How many are left on
the shelves?
Answer: 
 books
9
Missing digits
2 marks
Write the missing digit in each dashed square. Start with
the ones.
In b, I knew there was an exchange because ...
GO FURTHER
Make the largest and smallest numbers with
these cards. Find the difference.
3 5 8
 − 
 = 
CHECK YOURSELF
I put one digit in each square.
I started with the ones every time.
I checked 8a: my answer − 158 = 264.
Not yet
Getting there
Got it
Place value and column calculation · Subtract and solve
PLACE VALUE
COLUMN SUBTRACTION
SUBTRACT AND SOLVE
H
T
O
4
3
5
2
−
1
2
7
2
2
5
2 − 7? Exchange a ten: 12 − 7 = 5. Then
4 − 2 and 3 − 1.
e.g.
1
H
T
O
4
8
6
−
2
5
3
a
H
T
O
5
4
1
−
2
1
6
b
H
T
O
6
2
3
−
3
8
1
c
H
T
O
SIGN: + OR −
a
H
T
O
SIGN: + OR −
b
H
T
O
4
6
+
2
5
7
1
3
a
H
T
O
5
4
−
2
5
3
1
8
b
Page 3 of 3

The pupil task

What pupils will do

Read the place-value learning goal and model 243 with hundreds, tens and ones. Check that pupils understand why zero holds a place in a number such as 207.

Learning objective

Represent three-digit numbers in hundreds, tens and ones, partition them and calculate addition or subtraction in columns, exchanging when required.

When to use it

Use this after pupils have worked with hundreds, tens and ones and are ready to exchange between columns. Start with the place-value mat and zero placeholder, then move to the worked addition and subtraction examples before pupils try the independent questions.

What’s included

A place value mat links number reading and partitioning with column calculations. Worked addition, subtraction, missing digit and error analysis tasks help pupils connect the written method with a library books problem and further challenge.

A teaching sequence

Represent three-digit numbers in hundreds, tens and ones, partition them and calculate addition or subtraction in columns, exchanging when required.

Count hundreds, tens and ones in each picture. The number boxes are left for pupils.

Read the complete material

Build hundreds, tens and ones

Complete the place-value mat and identify numbers represented by flats, rods and cubes. Explain the value of each digit.

How does a zero show that one place has no units of that value?

Partition and exchange

Partition three-digit numbers into hundreds, tens and ones, then read the worked addition example and follow each exchange step.

Why does 12 ones become one ten and two ones?

Explain the calculation error

Try a column addition and explain the error in the supplied incorrect sum before completing the subtraction example and questions.

Where should the exchanged ten or hundred be recorded?

Check with the inverse

Use the library-books context, missing-digit problems and largest/smallest number challenge; finish by checking an answer with the inverse operation where possible.

Does subtracting the delivery from the new book total recover 264?

Before you teach

Look for the thinking behind an answer, choose the support your class needs and leave room for an independent response.

What to look for

Look for digits aligned in the correct columns and an exchange recorded when a total reaches ten or more. Ask, “What does this exchanged ten represent?” If a zero is omitted or digits are misaligned, return to the place-value mat and rebuild the number.

Give a little support

Use base-ten blocks or draw flats, rods and cubes before writing a column calculation. Begin with an example that does not require exchange, then model one exchange slowly and link it to the value of the digit.

Take the idea further

Ask pupils to create a three-digit addition or subtraction that requires an exchange and write a check using the inverse operation. Compare two ways to represent the same number, including one with a zero in the tens place.

Things to keep in mind

Worked examples model methods but do not provide full answers. Check calculations before using the sheet as a marked assessment. Link exchanges to place value, particularly when regrouping between columns, and verify any written answer key separately.

Keep the idea. Make it yours.

Bring your topic, learning goal and class context to PLAI™, then review what you create.

Make one for my class

Ideas to try with your class

Sample teaching perspectives on what to try, what to adapt and what to watch for.

📖

Book and Biscuit

The three-page activity builds three-digit numbers with hundreds, tens and ones, partitions them, then practises column addition and subtraction with exchanging. The learning goal and success criteria spell out the value of each digit and the operations expected.

🧽

Board Eraser

The progression links concrete representation to partitioning and written calculation. The opening example, 243, gives pupils a specific number to represent before moving into the column methods.

✏️

Spare Pencil

Keep the hundreds, tens and ones columns labelled while pupils draw or use base-ten materials, and ask them to name each digit's value. Return to the representation when an exchange step is difficult to explain.

😐

Calm Table

The page covers selected three-digit calculations and does not establish fluency across all numbers or strategies. Check every exchange against the represented quantity rather than relying only on the written column layout.