Year 4 Teaching Sequence 12 - Assess and review (five days)
Some key themes from this term:
 Place value of four-digit numbers, ordering and locating them on a landmarked line (1000s labelled) and locate
numbers to 1000 on an ENL
 Find 1, 10, 100 or 1000 more/less than four-digit numbers
 Begin to use expanded vertical addition to add pairs of three-digit numbers
 Derive quickly pairs of two-digit numbers with a total of 100, e.g. 72 +
= 100 and use o find differences between
two- and three-digit numbers, e.g. 137 – 72
 Multiply and divide two-digit numbers by single digits (partitioning and ‘chunking’)
Use this week to give further practice on the above areas according to your day-to-day assessment of chn’s progress so
far. The aim is to try to secure these areas before moving on during the following term, so select from, adapt and add to
the activities below accordingly. It is sometimes difficult to ascertain the level of different chn’s understanding, and so
these Teaching Sequences are intended to provide a chance for you to explore more deeply the ways in which different chn
approach and solve mathematical problems in different contexts within each of the topics covered this term.
Also see oral and mental starter banks 1, 2, 5, 6 and 10.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS12 – Aut – 5days
Objectives:
 Locate 3- and 4-digit numbers landmarked lines (1000s labelled)
 Understand what each digit represents in a 3- or 4-digit number
 Find 1, 10, 100, 1000 more/less than four-digit numbers
 Begin to use expanded vertical addition to add pairs of three-digit numbers (not crossing 10s, 100s or 1000), and then those
where the ones digits total more than 10
 Derive quickly pairs of two-digit numbers with a total of 100, e.g. 72 +
= 100.
 Use complements to 100 to find differences between two- and three-digit numbers, e.g. 137 – 72.
 Begin to multiply two-digit numbers by single digit numbers, using well-known multiplication facts and place value, e.g. 24 × 3
 Divide two-digit numbers by one-digit numbers, using chunking on an empty number line, e.g. 42 ÷ 3
Whole class
Launch the ITP 20 cards. Choose random
cards, four cards, minimum 0 and maximum
9, and then ‘go’. Drag the four cards to the
top using the arrows, and click to reveal.
Ask chn to use these four digits to make the
largest and smallest four-digit numbers they
can and to write them on their whiteboards.
Group activities
Group of 4-5 chn
Ask chn to divide their whiteboards into
eight, and to write a four-digit number in
each space.
Ring any numbers that are less than 2000.
Ring any number greater than 8000.
Ring any numbers between 3000 and 4000.
Ring any even numbers.
Ring any multiples of 5.
Continue asking chn to ring numbers until
one child had ringed all numbers.
Ask chn to choose eight new numbers and
repeat.
Easier: Have a 0-10 000 available to help.
Paired/indiv practice
Resources
Give chn each a 1000 to 2000 line
(see resources) and between them
a spinner board and paper clip
(see resources) or use a blank
dice and write +1, -1,+10, -10, +100
and -100 on the six sides. Chn
both start on 1500, spin a paper
clip around their pencil (or roll
the dice) and draw a hop or jump
accordingly, e.g. if the paper clip
lands on +10, then draw a jump
from 1500 to 1510, labelling both
the jump and where they land.
The first one to jump beyond
1100 or 1900 wins.
Easier: Chn use a landmarked
1000-2000 line (see resources).
Harder: Chn use a 1500 to 2500
line (see resources) and start on
 ITP 20 cards
 a large 0-10
000 landmarked
line (1000s
labelled)
 1000 to 2000
lines (see
resources)
 spinner board
(see resources)
 landmarked
1000-2000 lines
(see resources)
 a 1500 to 2500
line (see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS12 – Aut – 5days
Display a 0-10 000 landmarked line (1000s
labelled), and ask chn to mark these on the
line, using their knowledge of ordering
three-digit numbers to help. Drag the cards
around to make other four-digit numbers
and ask chn to place these on the line.
Repeat using new sets of four cards.
Write the following additions on the board:
267 + 221, 312 + 123, 224 + 203, 334 + 161.
Which of these do you think will have totals
nearer to 400 and which do you think will be
nearer to 500? Why? Discuss this with your
maths partner.
Write the following additions on the board,
and ask chn to agree in pairs an estimate for
each to the nearest 100:
624 + 113, 624 + 172, 412 + 401, 575 + 113.
Record the following additions on the board
and explain that one is correct and two are
wrong:
432 + 215 = 746, 523 + 124 = 647, 678 + 121
= 739.
Discuss with your partner which ones you
think are wrong and why. Use estimating to
help. Draw out how the answer to 432 + 215
is going to be nearer to 600 than 700, and
can’t be more than 700 as 32 + 15 is not
more than 100. Discuss how the answer to
689 + 121 is going to be closer to 800 than
700 and so 739 is too small an answer.
2000.
Group of 4-5 chn
Challenge chn to work in pairs to come up
with a three-digit addition where the total
is between 500 and 600. They can only use
digits 0, 1, 2, 3, 4 and 5. Take feedback.
Ask chn to sort them into two sets, those
with an answer nearer to 500 and those
with an answer nearer to 600. Ask chn to
work out the answer to check.
Repeat this time asking each pair of chn to
come up with two additions between 300
and 400, one nearer 300 and one nearer
400. Check the answers as a group.
Easier: Use place value cards to help.
Harder: Totals between 450 and 550, then
between 350 and 450.
Ask chn to use the digits cards, 0,
1, 2, 3, 4 and 5 (once only) to
make the biggest three-digit plus
three-digit addition and the
smallest that they can. They then
make at least five additions with
totals in between, and put them in
order.
Easier: Use place value cards 500,
400, 300, 200, 100, 50, 40, 30,
20, 10, 5, 4, 3, 2, and 1.
Harder: Chn make the smallest
and biggest totals, and then find
all the possible totals using 510 as
the first number (there are six).
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 100s, 10s and 1s
place value
cards
Y4 Maths TS12 – Aut – 5days
Write 132 – 68 on the board and ask chn to
discuss how they might find the answer.
Draw out J10 (take away 60, then 8),
overjumping (take away 70, then add 2) and
T100 (find a difference between 68 and 132,
passing through 100). Ask chn to vote for
the strategy they would find easiest in this
case.
Draw an ENL jotting to show the jump from
68 to 100, and then from 100 to 132. Discuss
adding 2 to make 70 and then 30 to make
100, saying that some chn might do both
stages in their heads, or some might draw to
hops to help them keep track. Agree that
the answer is 64. What do you think is the
difference between 69 and 133? Discuss it
with your maths partner. Draw out that the
answer is the same, and the difference has
been moved along the number line by 1.
Challenge chn to think of another pair of
numbers with a difference of 64. Take
feedback and draw ENL jottings to confirm.
Group of 4-5 chn
Display the following table of a
supermarket’s prices:
Item
Value
price
Deluxe
price
Four-pack
of tinned
tomatoes
99p
£1.65
Rice
69p
£1.25
Pack of
tomatoes
89p
£1.75
(on the
vine)
Six-pack
of crisps
85p
£1.49
Orange
juice
77p
£1.69
(freshly
squeeze
d)
Tomato
sauce
68p
£1.35
Difference
in price
Challenge chn to find pairs of
numbers between 40 and 160 with
a difference of 64. They should
draw jottings to show this.
Easier: Chn use a 50 to 150
landmarked line (see resources)
to help find the difference
between 89 and 105, and then try
to find other pairs of numbers
with the same difference.
 50-150
landmarked
lines (see
resources)
Explain that the cheaper prices are ‘value’
no frills items, and the more expensive are
higher quality versions.
Ask chn to estimate which pair of items
have the greatest difference in price, and
the smallest. Chn to find out.
If all the value prices went up by 5p and all
the deluxe prices went up by 5p, what would
happen? What if the value process went up
by 5p, and the deluxe prices by 10p?
Easier: Work out the differences together,
supporting chn in how to draw an ENL.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS12 – Aut – 5days
Write the following digits on the board: 3, 4
and 5.
We’re going to use these to make a two-digit
numbers to multiply by a single digit, e.g. 34
× 5. Revise how to work this out, modelling
the jottings on the board. What
multiplication might have an answer bigger
than this? To make the biggest answer
possible, where do you think we should put
the 5? And the 4? Try 54 × 3 and 53 × 4.
Even though both 3 and 4 are in the units,
the answers are vey different, why? Draw
out that in the second example we are
working out four 50s, instead of three 50s,
and so the answer is much bigger.
Ask chn to work in pairs to agree what
multiplication might give the smallest
answer.
Group of 4-5 chn
Display the following ‘ready reckoner’ with
‘coffee splats’ made from pieces of paper
to cover parts of the table:
Item and
price
2 items
3 items
4 items
Peach, 42p
Melon
slice, 32p
Banana,
41p
Apple, 35p
84p
64p
£1.26
96p
£1.68
£1.28
82p
£1.23
£1.64
70p
£1.05
£1.40
Pot of
grapes,
45p
Pot of
cherries,
54p
90p
£1.35
£1.80
£1.08
£1.62
£2.16
Challenge chn to make as may
different two-digit by single digit
multiplication as they can using
the digits 2, 3 and 4 (there are
six).
Harder: Ask chn to first predict
what the multiplication with the
biggest answer might be, and the
smallest.
 Activity sheet
of table of
prices and costs
of multiples of
these (see
resources)
Sally is selling fruit at the school fair. She
has made herself a table of the prices of 2,
3 and 4 of each to save her having to work
it out when people buy more than one
piece/pot of fruit. But she’s spilled coffee
all over it! Let’s help her to work out the
missing numbers. How much do apples cost?
How do you know? How can we work out the
price of two peaches? And 4? Discuss how
you can multiply 42p by 4, or double the
price for two peaches. Discuss each in turn,
and complete the table.
Easier: Cover fewer prices, mainly prices of
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS12 – Aut – 5days
What are ten 4s? And three 4s? What is 40
add 12? So how many 4s are in 52? How
could we draw this on an empty number line?
10 lots of 4
0
two items, and just one of four, e.g. apples.
Harder: Also cover some prices of three
items.
Group of 4-5 chn
Draw a jotting as follows:
3 lots of 4
40
52
What multiplication and division sentences
can we write?
What are ten 5s? And two 5s? What are
twelve 5s? So how many 5s in 60? Sketch a
drawing on your whiteboard to show this.
What multiplication and division sentences
can we write?
Write 61 ÷ 5 on the board. What do you
think the answer to this might be? Discuss
how there will be a remainder. What
numbers between 50 and 70 wouldn’t leave a
remainder when divided by 5? How do you
know? If there is no remainder, then we say
the number is divisible by 5.
Is 52 divisible by 4? Yes, we saw that
before. Is 52 divisible by 3? We could draw
a jotting to find out. Ask chn to sketch a
jotting to find out if it is divisible by 3.
Is 54 divisible by 4? How could we find out?
Ask chn to sketch a jotting to find out if
there is a remainder.
0
50
65
The answer is 13.
The person who worked this out hasn’t
labelled the hops and jumps, or written
down the division they were working out.
What division do you think it was? What
clues do we have?
How could we check our answer? What are
ten 5s? And three 5s? And 50 and 15?
What multiplication can we write?
Draw similar sketches for 56 ÷ 4, 48 ÷ 4, 48
÷ 3 and 57 ÷ 3.
Harder: Sketch 75 ÷ 5, 68 ÷ 4, 72 ÷ 4, 54 ÷
3 and 63 ÷ 3 (as two jumps of ten lots of 3,
and one lots of 3).
Ask chn to work in pairs to find
out which numbers are divisible
by (i.e. leave no remainders) 3 or
4, both or neither:
42, 45, 48, 50, 52, 54, 56 and 60
They should draw jottings in their
books to help, and draw a table of
their results.
Easier: Provide a table onto which
chn can record their results (see
resources).
Harder: Find all the numbers
between 40 and 60 which are
divisible by 3 or 4, or both.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheet
of table (see
resources)
Y4 Maths TS12 – Aut – 5days