Multiplication 7
‘Ladder layout’ 3-/4- digit decimal
numbers by single digit numbers
Objectives

Use the grid method to multiply three-digit numbers by single-digit
numbers

Use the extended standard algorithm (‘ladder’ layout) to multiply
three-digit numbers by single-digit numbers

Use the extended standard algorithm (‘ladder’ layout) to multiply
four-digit numbers by single-digit numbers

Use rounding and mental strategies to make approximations

Choose a mental or written method to multiply three-digit
numbers by single-digit numbers
For this unit you will need:
small sticky notes
Watch out for pupils who:

make frequent place value errors when using the ‘ladder’ layout
(extend standard algorithm), they may need to return to using the
grid method;

make frequent errors when adding up the partial products in the
grid method; they may be more accurate using the ‘ladder’ layout;

having made a mistake, do not notice that their answer seems
unreasonably large/small. Encourage them to make estimates
using rounding and mental methods.
HSNP © Hamilton 2014
Keeping up Term 3
Multiplication 7
Session 1
Objectives: Use the grid method to multiply three-digit numbers by singledigit numbers; Use the extended standard algorithm (‘ladder’ layout) to
multiply three-digit numbers by single-digit numbers; Choose a mental or
written method to multiply three-digit numbers by single-digit numbers
Teacher input with whole class
 Draw a grid on the board and ask pupils to help you to fill it for 864 × 6
to multiply a number on the top row by 6 and write the answer in the
appropriate place. Ask the rest of the class to check the products
(particularly the place value for each) and then find the total of the
three products.
×
800
60
4
6
4800
360
24
5184
 Show pupils how we can use the ‘ladder’ layout to record the same
multiplication. Point out that that this can make the addition of the
products easier:
864
× 6
4800
360
24
5184
Paired pupil work
 Pupils make up their own 3-digit by 1-digit multiplications. One pupil in
each pair uses the grid method to find the answer, and the other the
‘ladder’ layout. They then check their answers, including the three
products. They swap roles for the next one and so on.
Teacher input with whole class
 Write 420 × 2, 123 × 3 and 442 × 5 and ask pupils to discuss in pairs if
they need to use a written method for these. Take feedback, drawing
out mental strategies, but using the same partitioning technique as we
use with the written methods. Also remind pupils how they can halve
one number and double the other to work out 442 × 5 as 221 x 10.
HSNP © Hamilton 2014
Keeping up Term 3
Multiplication 7
Session 2
Objectives: Use the extended standard algorithm (‘ladder’ layout) to
multiply three-digit numbers by single-digit numbers; Use rounding and
mental strategies to make approximations
Teacher input with whole class
 Write the following on the board and ask pupils to work out the
hidden digits:
□□□
× 7
1400
350
28
1778
 Take feedback and agree the multiplication as 254 × 7.
Paired pupil work
 Pupils choose their own three-digit numbers to multiply by 6. Then use
the ladder method to work out the answer without their partner
seeing, then cover the top number with a mini sticky note. They each
try and guess the three-digit number in each other's multiplications.
 Repeat this time choosing numbers to multiply by 7, and then by 8.
Teacher input with whole class
 Write the following multiplications on the board: 8 × 235, 528 × 6, 5 ×
874, 783 × 4, 8 × 329.
 Remind pupils how they can round three-digit numbers to the nearest
100 and then multiply to find an approximate answer.
 Ask each pupil to choose one of the multiplications to work out exactly.
Ask one pupil to tell the class the answer. If others have this exact
answer they keep quiet. Others use rounding to guess which
multiplication they worked out.
 Who worked out a different multiplication? They tell the class the
answer and they try and guess which one it was.
 Repeat twice more.
HSNP © Hamilton 2014
Keeping up Term 3
Multiplication 7
Session 3
Objective: Use the extended standard algorithm (‘ladder’ layout) to
multiply three-and four-digit numbers by single-digit numbers
Teacher input with whole class
 Draw a grid on the board and ask different pupils to fill in different
parts to work out 5678 by 6. Ask the rest of the class to check the
products (particularly the place value for each) and then find the total
of the four products.
 Show pupils how we can use the ‘ladder’ layout to record the same
multiplication.
5678
× 6
30000
3600
420
48
34068
 Ask pupils to find the digital root (3). They then use the ‘ladder’ layout
to work out 8765 × 6 and find the digital root (3 again).
 They multiply 5678 and 8765 by 5 to see if the same occurs. (Both
products have the digital root 4.)
Pupil work
 Give these calculations to six pupils, who each work out one of them.
123 × 4, 234 × 5, 345 × 6, 456 x 7, 567 x 8, 678 × 9.
 They compare answers, then add the digits of each answer to find the
digital root. They discuss what they notice.
 Next they work out 1234 × 5, 2345 × 6, 3456 × 7, 4567 x 8, 5678 x 9
6789 × 10 and discuss what they notice about the digital roots.
Teacher input with whole class
 Pupils feedback what they found. (Multiplying the three-digit numbers
give a pattern of digital roots of 6 and 9. Multiplying the four-digit
numbers gives a pattern of digital roots with 3, 5, 9).
HSNP © Hamilton 2014
Keeping Up Term 3