Year 6 Teaching Sequence 9 - Assess and review (five days)
Some
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key themes from this term:
Order numbers with one, two or three decimal places, and place them on a number line
Understand and use equivalence between decimals, fractions and percentages to find fractions of quantities
Add/subtract any pair of four-digit numbers (including amounts of money) mentally, using jottings or a written
method, approximating first
Multiply and divide two-digit numbers by single-digits mentally
Multiply two-digit numbers by two-digit numbers, multiply four-digit numbers by single-digit numbers and multiply and
divide three-digit numbers by single-digit numbers using a written method, approximating first
Choose calculation methods, including using a calculator
Use this week to give further practice on the above areas according to your day-to-day assessment of the children’s
progress so far. The aim is to try and secure these areas before moving on during the following term to select from, adapt
and add to the activities below accordingly. It is sometimes difficult to ascertain the level of different children’s
understanding, and so these Teaching Sequences are intended to provide a chance for you to explore more deeply the ways
in which different children approach and solve mathematical problems in different contexts within each of the topics
covered this term.
Also see oral and mental starter banks 1-4 and 6.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9– Aut – 5days
Objectives:
 Understand what each digit represents in a number with up to two decimal places
 Begin to recognise and use numbers with three decimal places
 Recognise equivalence between fractions e.g. between 1/16s, 1/8s, 1/4s and 1/2s; 1/100s, 1/10s and 1/2s
 Multiply two-digit numbers by single-digit numbers by partitioning, e.g. 47 × 6 = (40 × 6) + (7 × 6)
 Divide two-digit numbers by single-digit numbers, including those leaving a remainder
 Give an answer to a division as a mixed number, e.g. 39 ÷ 4 = 9¾
 Approximate first before calculating
 Revise using the grid method to multiply three-digit numbers by single-digit numbers and to multiply two-digit numbers by
two-digit numbers
 Use the grid method to multiply four-digit numbers by single-digit numbers
 Using chunking on the ENL to divide three-digit numbers by single-digit numbers, including those leaving a remainder
 Revise adding two numbers with the same number of decimal places using vertical addition, including amounts of money, e.g.
£35.75 + £26.78
 Revise subtracting four digit numbers by counting up, e.g. 5431 – 2789
 Choose mental, written or calculator methods to work out addition and subtraction calculations
Whole class
Group activities
Paired/indiv practice
Resources
Give chn a set of digit cards, and ask them to
take out 3, 4, 5 and 6 and put the rest aside.
What is the biggest number that you can make
using three or more of these digits, between 3
and 4? (3.65) Write the number on your
whiteboards. And the smallest? (3.45) Work
with your partner to make three numbers
between. Show chn a line from 3 to 4 with
tenths marked (see resources). Invite chn up
to the board to place their numbers, using the
tenths to help.
What’s the smallest number with three
Group of 4-5 children
Ask chn to divide their whiteboards
into twelve parts (a four-by-three grid)
and to write a number with two decimal
places between 1 and 2 in each part.
Ring any numbers that:
 are between 1.2 and 1.3;
 round to 1.5 to the nearest tenth;
 are between 1.7 and 2;
 has four digits;
 are nearer to 1 than 2;
 are nearer to 1.4 and than 1.5 etc.
Ask chn to use three of the digits
4, 5, 6 and 7, to make as many
numbers with two decimal places
between 5 and 6 as they can.
They draw a number line from 5
to 6 and place them on it.
They use all four digits to make
two numbers with three decimal
places and place them on the same
line.
Easier: Chn use place the numbers
on a line with tenths marked (see
 Digit cards
 3-4 number line
with tenths
marked
 5-6 number line
with tenths
marked (see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9– Aut – 5days
decimals places between 3 and 4 that we can
make using these four digits? And the largest?
Work together to place these on the line.
Show chn a line from 0-1, marked in tenths
(see resources). Where would we mark 50% of
the way across this line? How do you know?
Mark on 50% below the line and ½ above the
line. Where would mark 25% of the way across
this line? How did you work it out? Draw out
the equivalent fraction of ¼, and mark both on
the line. Where would we mark 0.1 on this line?
How do you know? What fraction is equivalent
to 0.1? And percentage? Mark 0.1 and 1/10
above the line and 10% below the line. If you
were asked to find 80% of a quantity, how
would you work it out? Discuss this with your
partner. Take feedback. Draw out for example
knowing that 80% is equivalent to 8/10, finding
1/10 and multiplying by 8. Mark 8/10 and 80%
on the line. If you were asked to multiply a
quantity by 0.3, how would you do this? Talk to
your partner. Take feedback. Draw out for
example knowing that 0.3 is equivalent to 3/10,
finding 1/10 and multiplying by 3. Mark 3/10
and 0.3 on the line.
So we can use our knowledge of equivalent
The first child to ring all twelve
numbers wins.
Repeat.
Easier: Sketch a number line from 1 to
2 to help, and play with one place
decimals to begin with.
Harder: Encourage chn to include a few
numbers with three decimal places.
Group of 4-5 children
Fuel has gone up a lot over the past five
years. One report says that LPG gas has
gone up by 150% over the last 10 years.
How can this be possible? If it was £20
per bottle 10 years ago, and it had gone
up by 100%, how much would it be now?
So what do you think the current price
is? What if it had gone up by 200%? So
a price can be increased by more than
100%, but it’s not often that we hear
about this, as prices usually increase
that much over a longer period of time.
Can a price be decreased by more than
100%? Why not?
A chef has a recipe for chicken biryani
and rice for 10 people. He needs to
increase the quantities by 150%. How
many people will this feed?
Display the recipe for 10 people:
2 kg of boneless skinned chicken breast
4 medium onions
500ml plain yoghurt
resources).
Harder: Ask chn to use the digits
4, 5, 6 and 7, to make as many
numbers between 5 and 6 as they
can. They place them on a number
line (see resources).
Chn mark on a 0-1 line (marked in
tenths) as many equivalent
fractions, decimals and
percentages as they can. They
then use these equivalents to help
them find the quantities, writing
which equivalent they used to help
them (see resources).
Easier: Slightly easier activity
sheet with easier fractions,
percentages and amounts to work
with.
Harder: Slightly harder activity
sheet with harder fractions,
percentages and amounts to work
with.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 0-1 line,
marked in
tenths (see
resources)
 Activity sheets
(see resources)
Y6 Maths TS9– Aut – 5days
fractions, decimals and percentages to find
fractions and percentages of amounts, using
whichever equivalent is easiest to work with.
Write the digits 7, 8 and 9 on the board.
What two-digit by single-digit multiplication
could we make using these digits? Take one
suggestion and write it on the board. Can you
think of a multiplication with an answer
greater than this? Work in pairs to find the
multiplication with the greatest possible
answer that you can. Take feedback. Discuss
how 9 x 87 gives a greater answer than 8 x 97,
as in the first example both parts of the twodigit number are multiplied by 9, the biggest
possible number.
Point to the original multiplication. Can you
think of a multiplication with an answer smaller
than this? Work with a partner to find the
2 tsp (10ml) chilli powder
2 tsp (10ml) garam masala
2 tbsp (30ml) grated fresh ginger
2 tbsp (30ml) garlic paste
2 tsp (10ml) turmeric
8 tbsp (120ml) ghee (or butter)
4 cups basmati rice
2 litres water
4 tsp (20ml) finely chopped fresh
coriander
Ask chn to work as a group (giving
several ingredients to each pair) to
work out the quantities needed for 25
people.
Harder: Increase the quantities by
120%, for 22 people.
Group of 4-5 children
We’re going to write our 36 times table!
Record the first few facts in the way
that you normally record times tables:
1 times 36 is 36
2 times 36 is 72
3 times 36 is 108.
or:
36 × 1 = 36
36 × 2 = 72
36 × 3 = 108.
How can we work out 4 times 36? What
fact do we already have to help us? And
how can we work out 5 times 36?
Continue adding other multiples until
Challenge chn to come up with at
least five two-digit by single-digit
multiplications with answers
between 500 and 700, and then at
least five two-digit by single-digit
divisions with answers between 10
and 15.
Easier: Multiplications with
answers between 100 and 500.
Divisions with answers between 5
and 10.
Harder: Multiplications with
answers between 700 and 800.
Divisions with answers between 15
and 20.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9– Aut – 5days
multiplication with the smallest answer that
you can.
Repeat this time trying to find the two-digit
by single-digit divisions with the biggest and
smallest possible answers.
Write the digits 5, 6, 7, 8 and 9 on the board.
What do you think is the biggest four-digit by
single-digit multiplication we can make using
these five digits? Ask chn to work in pairs for
a while and then write 8765 × 9 and 9765 × 8
on the board. Which of these do you think will
have the bigger answer, or do you think they
will both give the same answer? Ask chn to
work out the answer to each and discuss why
one gives a bigger answer than the other. Take
feedback and draw out that in the first part
each of the four-digit numbers is being
multiplied by 9, whereas in the second each
part is only multiplied by 8, so the first gives a
bigger answer. Use these five digits to make
the smallest four-digit by single-digit
multiplication that you can. Ask chn to work in
pairs and then take feedback.
Now use four of these digits to make a threedigit by single-digit division with the biggest
answer that you can. After chn have been
working for a while ask them what they have
you have the 36 times table up to 10
times 36.
What division facts can we now write?
Ask chn to write these at the side.
How many 36s are in 396? What can we
use to help? How many 36s are in 720?
1800?
Easier: Write the 24 times tables.
Harder: Write the 76 times table.
Group of 4-5 children
Write the following grid multiplication
on the flipchart in advance:
× 5000
300 30
5
3
15,000
900
90
15
16,002
Cover 5000, 300, 30, 5 and 3 with Postit™ notes. On the following pages do
the same for 4 x 2435 and 4 x 3576.
Show this to the chn. Ask them to
discuss in pairs what numbers might be
hidden and why. What two numbers
might be multiplied together to make
15,000? Remember that one of them is
a multiple of 1000 and the other a
single-digit. Agree that the numbers
could be 5000 and 3 or 3000 and 5.
What numbers might have been
multiplied together to make 900? List
possibilities, 900 × 1, 100 × 9, and 300 ×
3. So what must the single-digit on the
left be? And the multiple of 1000? And
100? So what are the other missing
Ask chn to work in fours to roll a
dice to generate five digits. They
then work in pairs to use the
digits to make the biggest fourdigit number by single-digit
number multiplication, two-digit
by two-digit multiplication and the
biggest three-digit number by
single-digit division that they can
using four of the digits. They
compare their results with the
other pair. Repeat.
Easier: Generate four-digits to
make three-digit number
multiplied/divided by single-digit
number calculations, finding the
biggest multiplication that they
can and the smallest division.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Prepared
flipchart as
opposite and
Post-it™ notes
 Dice
Y6 Maths TS9– Aut – 5days
found about the divisor (the number they are
dividing by). Do you want it to be as big as
possible or as small as possible? If you split a
number in small groups will you have more or
fewer groups than if you split the same
number into larger groups? Ask chn to
continue working on the problem. Take
feedback, focusing on how chn decide where to
place each digit.
numbers? Remove the Post-its™ to
check. Ask chn to work on the next two
examples in pairs.
In advance draw the following division
on the flipchart:
459 ÷ 6 = 76 r 3, covering 459 and 6
and the labels of jumps on the ENL with
Post-it™ notes.
r3
0
Ask chn to make the biggest and smallest
four-digit plus four-digit total they can using
the digits 2, 3, 4, 5, 6, 7, 8 and 9 (18,395 and
6047). Is it possible to make a total under
6000? Why not? Work in pairs to try and
make a four-digit plus four-digit addition with
a total as close to 12,000 as you can. (It’s
possible to make 11,996!) Take feedback and
ask chn to share how they decided where to
420
456 459
Ask chn to discuss in pairs what the
division might be. We can work out the
first number quite easily by looking at
the line. If the answer is 76 r 3, what
might the labels to the two jumps be?
Repeat with 419 ÷ 9 and 678 ÷ 8.
Easier: Multiplications: 2 x 2335, 3 x
2335, and 4 x 3554. Divisions: 279 ÷ 6,
200 ÷ 9 and 197 ÷ 8.
Group of 4-5 children
Write the following calculations on the
flipchart:
32,498 + 67,987
5421 × 20
569 ÷ 7
482 × 1.5
7.6 × 4.7
42 ÷ 0.7
Chn roll a 0-9 dice four times to
make a four-digit number, and
repeat to make a second. They
record a subtraction, largest
number first and an addition.
Repeat until they have three
additions and three subtractions
using four-digit numbers. Ask chn
to look at their calculations and
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 0-9 dice
Y6 Maths TS9– Aut – 5days
put each digit. Discuss the thousands digits
and how if they are trying to make totals close
to 12,000 for example, it might be that using 6
and 5, 7 and 4, 8 and 3 or 9 and 2 in the
thousands place might give an answer close to
12,000 because the three-digit parts of the
numbers may have a total close to 1000, taking
the total over or close to 12,000.
Challenge chn to use the same digits to create
a four-digit subtract four-digit answer as as
small as they can.
3456
- 2987
3 [2990]
10 [3000]
456
469
After they have been working in pairs for a
while, discuss how they are deciding where to
place the each digit. What can you say about
the thousands digits? If we want the smallest
difference that we can, what can you say
about the three-digit part of the larger
number? And the three-digit part of the
smaller number?
Repeat, this time trying to find the greatest
difference that they can.
21,000 – 18,997
You can use a calculator to work out the
answers to only three of these
calculations. Which would you choose
and why?
Ask chn to work in pairs to answer each
calculation, using a calculator for only
the three they have chosen, estimating
the answer to each calculation first.
Challenge them to come up with four
calculations (+, -, × and ÷) with more
digits that they are used to calculating
with, but easy enough not to use a
calculator.
Easier: Write the following calculations
on the flipchart:
32,498 + 67,987
5421 × 10
427 ÷ 7
482 × 20
7.6 × 4.7
42 ÷ 0.7
20,000 – 19,997
predict which will give the biggest
answer and the smallest answer,
and then to write them in order.
They use whichever methods they
feel most comfortable with to
find the answers.
Easier: Chn only predict the
largest and smallest answers.
Harder: Chn also write a
subtraction with a smaller answer
than any of their calculations and
an addition with an answer
greater than any of their
calculations.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS9– Aut – 5days