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Year 3/4 Mastery Overview
Spring
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Guidance
The White Rose Maths Hub has produced these long term plans
to support mixed year groups. The mixed year groups cover
Y1/2, Y3/4 and Y5/6. These overviews are designed to support
a mastery approach to teaching and learning and have been
designed to support the aims and objectives of the new National
Curriculum.
The overviews:
• have number at their heart. A large proportion of time is
spent reinforcing number to build competency.
• ensure teachers stay in the required key stage and
support the ideal of depth before breadth.
• provide plenty of time to build reasoning and problem
solving elements into the curriculum
This document fits in with the White Rose Maths Hub Year 1 –
6 Mastery documents. If you have not seen these documents
before you can register to access them for free by completing
the form on this link http://www.trinitytsa.co.uk/maths-hub/free-
learning-schemes-resources/
Once registered you will be provided with a Dropbox link to
access these documents; please be aware some school IT
systems block the use of Dropbox so you may need to access
this at home.
Mixed Year Overview
Since our Year 1 to Year 6 Schemes of Learning and overviews
have been released we have had lots of requests for something
similar for mixed year groups. This document provides the
yearly overview that schools have been requesting. We really
hope you find it useful and use it alongside your own planning.
We had a lot of people interested in working with us on this
project and this document is a summary of their work so far. We
would like to take this opportunity to thank everyone who has
contributed their thoughts to this final document.
These overviews will be accompanied by more detailed
schemes linking to fluency, reasoning and problem solving.
Termly assessments will be available to evaluate where the
children are with their learning.
If you have any feedback on any of the work that we are doing,
please do not hesitate to get in touch. It is with your help and
ideas that the Maths Hubs can make a difference.
The White Rose Maths Hub Team
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Mixed age planning
Using the document
The overviews provide guidance on the length of time that
should be dedicated to each mathematical concept and the
order in which we feel they should be delivered. Within the
overviews there is a breakdown of objectives for each
concept. This clearly highlights the age related expectations
for each year group and shows where objectives can be
taught together.
There are certain points where objectives are clearly separate.
In these cases, classes may need to be taught discretely or
incorporated through other subjects (see guidance below).
Certain objectives are repeated throughout the year to
encourage revisiting key concepts and applying them in
different contexts.
Lesson Plans
As a hub, we have collated a variety of lesson plans that show
how mixed year classes are taught in different ways. These
highlight how mixed year classes use additional support,
organise groups and structure their teaching time. All these
lesson structures have their own strengths and as a teacher it
is important to find a structure that works for your class.
Progression documents
We are aware that some teachers will teach mixed year
groups that may be arranged differently to our plans. We are
therefore working to create some progression documents that
help teachers to see how objectives link together from Year 1
to Year 6.
Linking of objectives
Within the overviews, the objectives are either in normal font
or in bold. The objectives that are in normal font are the lower
year group out of the two covered (Year 1, Year 3, Year 5).
The objectives in bold are the higher year group out of the two
covered (Year 2, Year 4, Year 6), Where objectives link they
are placed together. If objectives do not link they are separate
and therefore require discrete teaching within year groups.
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Mixed age planning
Teaching through topics
Most mathematical concepts lend themselves perfectly to
subjects outside of maths lessons. It is important that teachers
ensure these links are in place so children deepen their
understanding and apply maths across the curriculum.
Here are some examples:
Statistics- using graphs in Science, collecting data in
Computing, comparing statistics over time in History,
drawing graphs to collect weather data in Geography.
Roman Numerals- taught through the topic of Romans
within History
Geometry (shape and symmetry)- using shapes within
tessellations when looking at Islamic art (R.E), using
shapes within art (Kandinsky), symmetry within art
Measurement- reading scales (science, design
technology),
Co-ordinates- using co-ordinates with maps in
Geography.
Written methods of the four operations- finding the time
difference between years in History, adding or finding
the difference of populations in Geography, calculating
and changing recipes in food technology.
Direction- Programming in ICT
Objectives split across topics
Within different year groups, topics have been broken down
and split across different topics so children can apply key skills
in different ways.
Money is one of the topics that is split between other topics. It
is used within addition and subtraction and also fractions. In
Year 1 and 2 it is important that the coins are taught discretely
however the rest of the objectives can be tied in with other
number topics.
Other measurement topics are also covered when using the
four operations so the children can apply their skills.
In Year 5 and 6, ratio has been split across a variety of topics
including shape and fractions. It is important that these
objectives are covered within these other topics as ratio has
been removed as a discrete topic.
Times tables
Times tables have been placed within multiplication and
division however it is important these are covered over the
year to help children learn them.
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Everyone Can Succeed
As a Maths Hub we believe that all students can succeed
in mathematics. We don’t believe that there are individuals
who can do maths and those that can’t. A positive teacher
mindset and strong subject knowledge are key to student
success in mathematics.
Acknowledgements
The White Rose Maths Hub would like to thank the
following people for their contributions, and time in the
collation of this document:
Cat Beaumont
Matt Curtis
James Clegg
Becky Gascoigne
Sarah Gent
Sally Smith
Sarah Ward
More Information If you would like more information on ‘Teaching for Mastery’ you can contact the White Rose Maths Hub at [email protected] We are offering courses on:
Bar Modelling
Teaching for Mastery
Subject specialism intensive courses – become a Maths expert.
Our monthly newsletter also contains the latest initiatives we are involved with. We are looking to improve maths across our area and on a wider scale by working with other Maths Hubs across the country.
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
Year 3/4 Overview
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 Week 12
Au
tum
n
Place Value Addition and Subtraction Multiplication and Division
Sp
rin
g
Multiplication and Division Fractions and Decimals
Su
mm
er
Length and Perimeter
Time Shape
Volume and Capacity (Y3)
Co-ordinates
(Y4)
Statistics
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
Week 9
Week 10 Week 11 Week 12
Number: Multiplication and Division Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in context. Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects. Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objectives. Solve simple measure and money problems involving fractions and decimals to two decimal places Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods. Multiply two digit and three digit numbers by a one digit number using formal written layout. Find the area of rectilinear shapes by counting squares (link to multiplication)
Fractions and Decimals Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.
Compare and order unit fractions, and fractions with the same denominators. Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number. Count up and down in tenths.
Count up and down in hundredths. Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or
quantities by 10 Recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten. Recognise and show, using diagrams, equivalent fractions with small denominators.
Recognise and show, using diagrams, families of common equivalent fractions. Add and subtract fractions with the same denominator within one whole. Add and subtract fractions with the same denominator.
Solve problems that involve all of the above. Recognise and write decimal equivalents of any number of tenths or hundredths.
Recognise and write decimal equivalents to ¼, ½, ¾ Round decimals with one decimal place to the nearest whole number. Compare numbers with the same number of decimal places up to two decimal places. Solve simple measure and money problems involving fractions and decimals to two decimal places
Year Group Y3/4 Term Spring
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Mu
ltip
licat
ion
an
d D
ivis
ion
Solve problems involving multiplication
and division, using materials, arrays,
repeated addition, mental methods, and
multiplication and division facts, including
problems in context.
How many cupcakes are there altogether?
Kate arranges her flowers so there are 4 in a vase. How many flowers does she arrange?
Fill in the missing boxes
Colour in the multiples of 4 What’s the same? What’s different?
What’s the same? What’s different?
Sasha needs 40 points to buy a football. Blue counters are worth 3 points and green counters are worth 4 points. In a game she wins
Does she have enough? Explain why.
At the fair, how many buckets did each person knock down?
Here is a blue strip of paper. An orange strip of paper is four times as long. The strips are joined end to end. How long is the blue strip? How long is the orange strip?
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum Statement All students
Fluency Reasoning Problem Solving
Mu
ltip
licat
ion
an
d D
ivis
ion
Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.
Harry buys 6 chocolate bars, one chocolate bar costs 54p. How much does Harry spend? a) Write a number sentence to
represent the problem. b) Solve the problem.
Dan is using a number machine. Every number he puts in is multiplied by the same number. He puts 4 numbers in and the numbers that come out are 21, 49, 84 and 140. What could the machine be multiplying by?
Laura is making a sequence using shapes. She uses 3 circles, 4 pentagons and 5 rectangles. If she uses the same pattern to make a longer sequence, how many pentagons will she use in a sequence with 72 shapes altogether?
Miss Smith estimates;
399 x 60 = 240000 Is this a good estimate? Explain why.
In a box there are red and yellow cubes. For every 5 red cubes there are 3 yellow cubes.
Hannah says; Do you agree? Convince me.
An ice cream sundae is made from one scoop of ice cream, one topping and one sauce. How many different ice cream sundaes can be created from 5 different flavours of ice cream, 3 different toppings and 4 different sauces?
Jenny needs to buy 20 cupcakes for a party. A shop has two offers on cupcakes. Which offer is better? How much money will Jenny spend altogether?
If I have more than 10
red cubes, I will
definitely have more
than 10 yellow cubes. 5 cupcakes
for 40p
4 cupcakes
for 30p
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Mu
ltip
licat
ion
an
d D
ivis
ion
Solve problems including missing number problems involving multiplication and division, positive integer scaling problems and correspondence problems in which n objects are connected to m objectives.
Fill in the boxes:
5 x = 15
X 4 = 32
48 6 = 8
Jemima has a toy car measuring 8cm. Aisha has a toy train that is 8 times as long as the car. How long is the train?
Kainat is making buns. For every 40g of flour she needs 1 egg. If she uses 5 eggs, how many grams of flour does she use? If she uses 400g of flour, how many eggs doe she need?
Tami is planting bulbs. She has 76 bulbs altogether. How many complete rows of eight can she plant?
12 buns are shared between 3 boys. 16 buns are shared between 4 girls. Who gets more buns, boys or girls? Explain your answer.
For every 3 boys in class there are 2 girls. Which of the combinations of boys and girls could be correct? 18 boys and 12 girls 15 boys and 10 girls 21 boys and 9 girls 12 boys and 8 girls
Show your thinking using a picture.
Each tary can fit 8 gingerbread men on. I make two trays. Two people are correct, who do you agree with? Explain why.
Simone: Frazer: Aliyha: Jem:
Use the numbers 1 - 8 to fill the circles below:
Lottie is counting the number of legs
in her house. People and cats live in Lottie’s house. People have 2 legs; cats have 4 legs. If there are 26 legs altogether, how many cats and people might there be?
William has 3 t-shirts and 4 pairs of trousers, how many different outfits can he make?
How many different combinations of numbers can you find that would fit in the empty boxes?
5 x = 10 x
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Mu
ltip
licat
ion
an
d D
ivis
ion
Solve simple measure and money problems involving fractions and decimals to two decimal places.
A box of chocolates costs £1.25 Hannah and Thomas want to buy 4 boxes of chocolates. If Hannah pays £2.45, how much must Thomas pay?
Emma has five pounds. She spends a quarter of her money. How much does she have left?
In the sale I bought some clothes for half price. Jumper £14 Scarf £7 Hat £2.50 T-shirt £6.50
o How much would the clothes have been full price?
o How much did I spend altogether?
o How much did I save?
A class is planning a trip to a theme park.
How many tickets could they buy for £100. How many different ways can you find to do this?
Hazel buys a teddy bear for £6.00, a board game for £4.00, a cd for £5.50 and a box of chocolates for £2.50 She has some discount vouchers. She can either get £10.00 off or half price on her items. Which voucher would save her more? Explain your thinking.
Yasmin is choosing a new mobile phone. One phone costs £5.50 per month. The other costs £65.50 for a year. Which is the better deal over a year?
Kim bought a chocolate bar and a drink. The cost of them both together is in one of the boxes below.
Using these five clues can you work out which price in the boxes is correct?
1. You need more than three coins to make this amount.
2. There would be change when using the most valuable coin to buy them.
3. The chocolate bar cost more than 50p
4. You could pay without using any copper coins
5. The chocolate bar cost exactly half the amount of the drink.
£1.85 75p £1.56
£1.74 £2.25 £1.00
£1.80 80p £2.10
£1.44 £3.06 £1.50
£1.20 £1.25 £1.60
£1.45 90p £1.27
Theme park prices
Adult = £8
Child = £4
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Mu
ltip
licat
ion
an
d D
ivis
ion
Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods.
Use place value counters to multiply a two digit number and one digit number together. 4 x 23
Make 23 in each row using the place value counters. Add up each column, starting with the ones to find out your answer. 3 × 5 =
Complete this statement and use this to solve the multiplication below: 3 × 50 = 30 × 5 = 5 × 3 =
Solve:
I have 16 sweets in each bag and I have 4 bags. How many sweets do I have altogether?
Always, sometimes, never A two-digit number multiplied by a one-digit number makes a two-digit answer.
Fill in the missing boxes.
10 5 40
There are 24 sweets in each layer. Who do you agree with and why?
Chloe: Rhys:
Using the digit cards in the multiplication below how close can you get to 100?
Use the digits 0, 1, 2, 3, 4, 5, and 8. Combine to make one 2 digit number and multiply by another digit. What is the largest number can you make? What is the smallest number you can make?
The answer is 62. How many ways can you get the answer?
= x
2 3 4
× =
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum Statement All students
Fluency Reasoning Problem Solving
Mu
ltip
licat
ion
an
d D
ivis
ion
Multiply two digit and three digit numbers by a one digit number using formal written
layout.
Use counters to solve 126 x 4 Draw 4 rows and make 126 in each of them.
Add up the columns and exchange counters where needed to find the answer.
Sahil has 45 packets of sweets. Each packet has 6 sweets in it. How many sweets does he have altogether?
Penny says a two digit number multiplied by a one digit number will always give a two digit answer. Is she correct? Justify your answer.
Find the mistake that has been made in the calculation below. Explain and correct it.
47
X 8 3256
What digit goes in the missing box? Convince me. 3 x 4 = 140
What could the numbers in the multiplication be? Every digit is different.
Miss Wood orders some new whiteboard pens for Year 3 and 4. There are 160 children in Year 3 and 4. If she orders 6 boxes of 27 pens, will she have enough? Show your calculation.
In one month, Charlie read 814 pages in his
books. His mum read 4 times as much as Charlie which was 184 pages more than Charlie’s dad. How many pages did they read altogether? Use a bar model to help.
3
x
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum Statement All students
Fluency Reasoning Problem Solving
Are
a- M
ult
iplic
atio
n a
nd
Div
isio
n
Find the area of rectilinear shapes by counting squares.
Find the area of these shapes:
A rectangle measures 5 squares long by 3 squares wide. What is the area of the shape?
Max is building a patio made of 24 square slabs. What could the patio look like? Design it on squared paper. Max is using 6 coloured square slabs in his design. None of them are touching each other. Where could they be in the designs you have made?
A shape has the area of 17cm2. Could the shape be a rectangle? Explain your answer.
A rectangle measures 5 squares by 3 squares. Amy says;
Do you agree? Explain your thinking.
The area of any rectangle has an even number of squares. Do you agree? Prove it.
A fourteen sided shape has an area of eight squares. Draw the shape on squared paper.
How many shapes can you draw that have an area of 8 square centimetres?
Here is the floor plan of a lounge and a dining room. Each square represents 1m2
Sam is a carpet fitter. He charges £3 per metre squared. How much will it cost to have the whole area of the lounge and dining room carpeted?
The area must be 8
squares.
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All Students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.
Write the fractions shaded in the shapes below.
Find ½ of 16. Find ¼ of 16.
Find 1
8 of 16.
Shade in 2
8 of each of the diagrams
below.
Susie ate ¼ of a cake, Dinah ate ½ of what was left. Amarah ate the rest of the cake. Draw a diagram to show how much each of the girls ate.
True or False?
This shape is split into two equal halves
Explain your reasoning.
Only one person is wrong. Explain who. Tim: I’ve eaten one piece. That means
I have eaten 1
8.
Sally: I’ve eaten 2 slices which means
I have eaten 1
2
Jem: I have eaten 3 slices which means
I have eaten more than 1
4
Can you shade this diagram in
different ways to show 1
2 ,
1
3,
1
6 and
1
9
How many ways can you share this chocolate bar into equal pieces? What fraction would each person get? What is the maximum number of people you could share it with? The minimum number?
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctions
Compare and order unit fractions, and fractions with the same denominators.
Order from smallest to largest
3
9,
1
9,
8
9,
5
9,
9
9
Use <, > or = to complete the statements below
4
9
2
9
1
7
1
5
2+2
8
3+1
8
Which is greater? 1 ninth or 1 tenth
Gifty thinks 1
8 is greater than
1
4 because 8
is greater than 4. Do you agree? Convince me.
Rob thinks 1
4 is always the same but his
teacher has asked him to find a quarter of both these amounts.
a)
b)
Explain to Rob why it is not the same and create a rule with a partner.
Using equal sized strips of paper ask children to fold them into different amounts (e.g. quarters, sixths etc) and shade one part and write the fraction on each of them. Ask them to order them and explain to each other what they can see. Create a rule as a class: the bigger the denominator, the smaller the fraction.
Using equal sized strips of paper ask children to fold them into equal parts and shade one part. With another piece of paper do the same amount of equal parts but shade 2 of them and so on. Ask them to order them and explain to each other what they can see. Create a rule as a class: when the denominator is the same, the bigger the numerator, the bigger the fraction.
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All Students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.
Complete the fractions to describe the set of objects.
Write the fraction of each set of objects that is shaded.
Match the fraction with the correct image
This is 2
5 of a set of marbles. How many
would be in the whole set?
What could the numerator be? Explain why it can’t be 7.
What could the denominator be? Explain what it can’t be.
Kayleigh has 12 chocolates.
On Friday, she ate 1
4 of her chocolates
and gave one to her mum.
On Saturday, she ate 1
2 her chocolates,
and gave one to her brother.
On Sunday, she ate 1
3 of her
chocolates. How many did she have left? What fraction of her starting number is this?
There are 3 whole pizzas and 6 children. How many different ways can the pizzas be split so the children get the same amount?
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number.
Emily buys a box of 24 chocolates.
She eats 𝟏
𝟒 of the chocolates and her
Mum eats 𝟏
𝟑 .
How many chocolates are left?
George and Grace have ordered lemonade. Grace has a small lemonade which is 250ml. George has a large lemonade which
is 𝟒
𝟏𝟎 more than a small.
How many millilitres does George have?
If George only drinks half of his lemonade and Grace drinks three quarters of her lemonade, who drinks the most? Show your working.
The school kitchen needs to buy potatoes for lunch. A large bag has 200 potatoes and a
medium bag has 𝟑
𝟓 of a large bag.
The school cook says Is she correct? Explain your reasoning.
True or False
To find 𝟑
𝟖 of a number, divide by 3 and
multiply by 8. Convince me.
These three squares are 𝟏
𝟒 of a whole
shape. How many different shapes can you draw that could be the complete shape?
Work out the answer to each question to make it through the maze.
4
7 of
56
24
2
9 of
81
1
3 of
75 18
32 16 25
3
5 of
35
6
8 of
32
4
6 of
30
20 24
21 18 20
2
7 of
42
2
3 of
27
Finish 12 16
S
I need 150 potatoes so I will
have to buy a large bag
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All Students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Count up and down in tenths.
Shade the diagram to continue the pattern.
Finish the sequences: 1
10 ,
2
10 ,
3
10 , ___, ____, ___
Whole, nine tenths, eight tenths ….
Complete the sequences:
Circle and explain the mistakes in the sequences below. 1
10 ,
2
10 ,
4
10 ,
5
10,
6
10
The cake is split into 10 equal pieces.
One person is correct. Explain who:
Simon: I will have 2
10 so I will have the
least amount
Katy: I can’t have 1
2 because there won’t
be enough pieces left.
Tariq: I will have 3
10, which is more than
Simon.
True or false? Explain why. Tulisa says that 10p is one tenth of £1. Owen says that 20p is two tenths of £2.
On a number line o to 1, label:
0.7, 3
10,
1
10, 0.9,
10
10
Order the diagrams and describe how you have ordered them.
How many ways can you represent one tenth? You don’t always have to use 10 equal pieces…
Shade the 100 square in, to show different amount of tenths. How many ways can you do this?
1
10
2
10
4
10
5
10
3
10
7
10
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All Students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10.
Here is a number line from 0 - 1. Can you fill in the missing fractions on the number line?
0 5
10 1
Draw and shade shapes to show the
following fractions.
1
10
6
10
8
10
Find a tenth of: 60 50 40 30 What do you notice?
What do you notice in the number sentences below?
1
10 of 20 = 2
2
10 of 20 = 4
3
10 of 20 = 6
Can you continue the pattern up to 10
10 ?
Three pizzas are shared equally between ten children. If each pizza is cut into 10 pieces, how many pieces will each child get? Prove it using a picture or diagram.
Lara has 30 cherries.
On Monday she gives 1
10 of the cherries to
her mum and then eats 7.
On Tuesday she eats 2
10 of the cherries and
gives 6 to her mum.
On Wednesday she eats 5
10 of the cherries.
How many cherries does she have left?
Build a tower, using 30 cubes. You can only make it by combining tenths e.g. I could make it with 21 red cubes (seven tenths of 30), 3 blue cubes (one tenth of 30) and 6 yellow cubes (two tenths of 30). How many combinations can you come up with?
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
Count up from 0 on the number line to find the value of the missing amounts.
Continue the sequences: 2.45, 2.46, 2.47, ___, ___, ____ 𝟐𝟓
𝟏𝟎𝟎,
𝟐𝟔
𝟏𝟎𝟎,
𝟐𝟕
𝟏𝟎𝟎, ___, ____, ____
4.32, 4.31, 4.30, ___, ___, ___
If this block is worth 1 whole Work out the value of:
Convince me that 4.27 is halfway between 4.22 and 4.32
Write down a fraction that could go in each section of the number line.
Jasper says Do you agree? Explain your answer; use a place value grid to help.
Fill in the gaps to find the missing numbers.
If the arrow is pointing to 4.56, what could the start and end numbers be? Can you find more than one option?
True or false? Explain why. Create your own part whole models.
0 0.25 0.5 0.75 1 1.5
A B C D E
0.15 0.35
0.17
0.22
If I multiply ten by ten I get one
hundred so if I multiply tenths by
ten I get hundredths
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctions
Recognise and show, using diagrams, equivalent fractions with small denominators.
Complete the statements:
1
2 =
6
1
2 =
4 =
8
Draw diagrams to show fractions that are equivalent to
1
2,
1
3,
2
5
Match the diagram to the equivalent fraction.
What’s the same? What’s different?
1
4 ,
2
8 ,
3
12
Here is a diagram that has some sections shaded.
Ailish says, “I am thinking of an equivalent fraction to this where the numerator is 5.” Is this possible? Explain why.
Explain how this diagram shows both 2
3
and 4
6
Can you work out the missing values?
1
2 =
4 − 2
2 × 2
3
4 =
5+1
3+5
Can you create your own for a friend to complete?
Play pairs. Create a set of cards that have different diagrams and fractions on. Children turn 2 over in their go. If they are equal fractions then they keep the pair. If not, they turn them back over and it is the other players turn. The player who has the most pairs at the end wins.
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Recognise and show, using diagrams, families of common equivalent fractions.
Fold the strips of paper into halves, quarters and eighths. Shade in one half and find the equivalent fractions for quarters and eighths.
Stick the bar models in your book and draw a number line for each. Colour in the equivalent fractions.
Complete the statements:
𝟐
𝟓 =
𝟏𝟎
𝟒 =
𝟐
A pizza is cut into 8 slices. Zara says, Is she correct? Convince me by using a diagram.
Look at the three pictures. What’s the same and what’s different?
Two paper strips are ripped. Which paper strip was originally the longest? Explain your answer.
Harry says, “ 𝟑
𝟒 is always the same as
𝟔
𝟖
” Jenny says, “ 𝟑
𝟒 is equivalent to
𝟔
𝟖 but
isn’t always the same amount.” Use diagrams to show and prove your answer.
Use the digit cards to fill in the boxes below.
Print the square below several times on a sheet. Children investigate the
different ways they can show 𝟏
𝟐,
𝟏
𝟒,
𝟏
𝟑,
𝟏
𝟔
1
5
1
5
1 1 2 3
5 5 6
= =
If I take half of the pizza, and my
brother takes 4 slices, we will
both have the same amount
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All Students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Add and subtract fractions with the same denominator within one whole.
Complete the statements:
1
5 +
3
5 =
6
8 -
3
8 =
2
10 +
3
10 +
4
10 =
Write these statements using
numbers: 1 sixth + 3 sixths = Sixths 5 eighths - 3 eighths = Eighths
Find the sum of: 2
12 ,
4
12 and
5
12
Explain why only the numerator changes in this calculation
2
5 +
9
5 =
Rick is stuck on the calculation
11
6 -
3
6 =
His friend, Susie, draws him the following model to help.
Susie says, “Now take 3
6 away”.
Rick is confused because he thinks the
diagram shows11
12.
Explain the diagram to Rick and work out the answer.
Use some of the cards below to make a fraction sentence. Can you make more than 1?
How many fraction addition and subtractions can you make from this model?
Do your additions and subtractions always have to be 1 part add 1 part or subtract only 1 part? Can there be more than 2 parts?
7 - 3 4
+ 7 = 1
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Add and subtract fractions with the same denominator.
Calculate:
Use diagrams and bar modelling to solve the problems below.
𝟑
𝟖 +
𝟐
𝟖 =
𝟓
𝟔 +
𝟑
𝟔 =
𝟕
𝟖 -
𝟐
𝟖 =
𝟓
𝟕 -
𝟐
𝟕 =
Sarah eats 𝟑
𝟖 of a bunch of grapes;
Tom eats 𝟐
𝟖 of a bunch of grapes.
What fraction of the grapes have they eaten altogether?
Fill in the box:
𝟓
𝟖 + =
𝟕
𝟖
𝟓
𝟔 - =
𝟏
𝟔
Explain what fraction calculation the diagram is showing. Can you make your own?
True or False
𝟓
𝟏𝟐 +
𝟑
𝟏𝟐 =
𝟖
𝟏𝟐
𝟓
𝟏𝟐 +
𝟑
𝟏𝟐 =
𝟖
𝟐𝟒
𝟓
𝟏𝟐 +
𝟑
𝟏𝟐 =
𝟒
𝟔
Explain your reasoning.
Describe the pattern:
𝟕
𝟏𝟎 -
𝟏
𝟏𝟎 =
𝟔
𝟏𝟎
𝟔
𝟏𝟎 -
𝟏
𝟏𝟎 =
𝟓
𝟏𝟎
Can you continue the pattern?
Find three ways to complete each calculation.
𝟏𝟐
𝟗
𝟖
𝟗
How many ways can you complete the calculation?
𝟐
𝟕 +
𝟕 =
𝟕
𝟕 -
𝟕
How many ways can you complete the calculation?
- =
+ =
+ -
= 9
7
+ =
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All Students
Fluency Reasoning Problem Solving
Fra
ctio
ns
Solve problems that involve all of the above.
Use different concrete objects and
pictorial representations to make 3
6
Phil baked a chocolate and banana
loaf. He ate 3
6 of it. Rich ate
2
6 of it.
What amount of loaf was left?
Fill in the missing boxes
1
5 +
2
5 +
2
5 =
4
7 -
7 =
5
7 -
5
7
1
4 +
2
3 + +
1
3 = 2
Raja has a number card. He says, “Three eighths of my number is 20.” Is he correct? Explain why.
Kate has a number card. She says, “Three quarters of my number is 18.” Her friend, Sally, says, “Six eighths of the same number is also 18.” What is the number on the card? Who is correct? Sally or Kate.
Three pandas shared 1 bamboo stick. They split it into equal parts and each had an odd number of parts. What are the possible fraction amounts that each panda had? Can you use a strategy or a method?
How many different ways can you complete the number sentences?
5
6
1
8
40
? + =
- =
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
De
cim
als
Recognise and write decimal equivalents of any number of tenths or hundredths.
Complete the table:
Fraction Decimal 𝟔
𝟏𝟎
0.2
𝟑𝟕
𝟏𝟎𝟎
0.68
Match the fraction to the correct decimal.
What fraction has been made in the
ten frame? What decimal has been made?
Give the children 2 ones in place value counters.
Explain that we are going to try and divide them by 10. Show we need to exchange our 2 ones for 20 tenths. Now when we share between 10 groups we
have 0.2. This proves that 𝟐
𝟏𝟎 = 0.2.
Can the children use this to prove
that 𝟓
𝟏𝟎 = 0.5
Helen, Adam and Sam are talking about which fractions are equivalent to 0.4. Who is correct? Justify your answer.
Use the five digit cards to complete the statement below.
Fill in the missing numbers below so the fractions and decimals are equivalent in each row of the table. One has been done for you.
Fraction Decimal
𝟑𝟓
𝟏𝟎𝟎
0.35
_𝟒
𝟏𝟎𝟎
0.2_
𝟏𝟎
_. 4
𝟓𝟎
6. _
6
10
6
100
53
100
6.1
0.6
0.06
5.3
0.53 Adam: ‘
4
10 i s equivalent to 0.4’
Helen: ‘40
100 i s equivalent to 0.4’
Sam: 1
4 i s equivalent to 0.4’
0 0 1 6 6
= .
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
De
cim
als
Recognise and write decimal equivalents to 𝟏
𝟒,
𝟏
𝟐,
𝟑
𝟒
Fill in the table:
Match the fraction to the correct decimal.
Write the fraction that matches to each decimal.
o 0.25 = o 0.5 = o 0.75 =
Using place value counters, show that 1 divided into 2 equal parts is 0.5 Can you show that 1 divided into 4 equal parts is the same as 0.25? Write an explanation for a friend.
Harry has written the decimal equivalents to a half and a quarter. Can you explain to him what he has done wrong? What could you use to show him?
Harry: 𝟏
𝟐 = 1.2
𝟏
𝟒 = 1.4
Use the number cards 0 - 5 below to complete the number sentence.
Which number did you have left over?
Complete the number sentence below using the number cards 0 – 5:
Which number did you have left over? Was it the same number as before?
Which extra number would you need to make a number sentence that used your left over number?
1
4
1
2
3
4
0.34
0.3
0.4
0.5
0.75
0.25
= .
. =
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
De
cim
als
Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths.
Complete the table below:
Starting number
÷ 10 ÷ 100
34 57
60 7
Divide by 10
Complete the calculations
o 42 ÷ 10 = o 42 ÷ 100 = o 9 ÷ 10 = o 9 ÷ 100 =
What do you notice?
I divide a number by 100 and the answer is 0.5. What number did I start with? Prove how you know
True or False A two digit number divided by 10 always gives an answer with one decimal place. Prove it.
Jessie and Tammy are dividing
numbers by 10 and 100. They start with the same 1 digit number.
What number did they start with? Prove it.
Katya has multiplied a number by 100. Her answer is between 40 and 45. What number could she have multiplied? How many possibilities can you find?
Use the number cards below to fill in the missing digits.
0 ÷10 = .4 x 10 = 3 8 ÷100 = 1 6
5. 2 x 100 = 7
9 7 3 2 1
8 4 9 6 5
6
10 10 1
My number has 0 ones
and 4 tenths
My number has 0 ones, 0
tenths and 4 hundredths
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
De
cim
als
Round decimals with one decimal place to the nearest whole number.
Round the following numbers to the nearest whole number:
3.2 = 4.7 = 25.5 =
Write all the decimals with one decimal place that round to 32 to the nearest whole number.
Sort the numbers below into the table rounding each of them to the nearest whole number.
Rounds to 23
Rounds to 24
Which decimals below round to 4 when rounded to the nearest whole number?
4.2, 3.8, 4.5, 3.5, 4.7
Explain your reasoning.
Two numbers with one decimal place both round to 23 The numbers add up to 46 What could the two numbers be? Explain your thinking.
Roll two dice. Using the numbers make two numbers with one decimal place. Round the numbers to the nearest whole number. How many combinations of the two dice can you find that would round to the same whole number?
Using the digit cards below, how many numbers can you make with one decimal place that would round to 45. You can only use each card once per number. Can you make more or less numbers that round to 46? If you were given this number card:
How many numbers could you make that round to 47?
23.1
23.5
23.9
23.2
23.4
22.8
24.4
24.3
22.5
4 4 5 6 3
7
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
De
cim
als
Compare numbers with the same number of decimal places up to two decimal places.
Fill in < and > in the boxes below: 3.56 3.62 7.21 7.12 3.45 3.42
Order the decimals below from smallest to largest.
Laura has £3.45, Hamid has £4.35. Who has the most money?
Serena says
Is she correct? Explain your thinking.
The numbers below are ordered from smallest to largest. Circle the mistake.
4.52, 4.63, 4.62, 4.65, 4.68 Can you replace the mistake with a number that would fit in the sequence?
Put a digit in each box to order the decimals in ascending order.
2 4 2 6
5 3
3 0 3 9
How many different numbers with 2 decimal places can you make using the grid below and four counters? One has been done for you.
10s 1s 0.1s 0.01s
Can you order your numbers in descending order?
Three children have numbers with two decimal places. They each give a clue to their number. Can you work out which clue matches to which child?
Billie Shakat Nita
3.15 4.14 3.13
3.51 3.48
3.52 3.57
3.42 3.43
My number has a one in the
tenths column.
My number has the same
amount of ones and hundredths.
My number is the largest
number.
When I am comparing numbers with
2 decimal places, the number with
the largest number of hundredths is
the largest number
© Trinity Academy Halifax 2016 [email protected]
Year 3/4
Term by Term Objectives
National Curriculum
Statement
All students
Fluency Reasoning Problem Solving
Fra
ctio
ns a
nd
De
cim
als
- M
on
ey
Solve simple measure and money problems involving fractions and decimals to two decimal places.
A box of chocolates costs £1.25 Hannah and Thomas want to buy 4 boxes of chocolates. If Hannah pays £2.45, how much must Thomas pay?
Emma has five pounds. She spends a quarter of her money. How much does she have left?
In the sale I bought some clothes for half price. Jumper £14 Scarf £7 Hat £2.50 T-shirt £6.50
o How much would the clothes have been full price?
o How much did I spend altogether?
o How much did I save?
A class is planning a trip to a theme park.
How many tickets could they buy for £100. How many different ways can you find to do this?
Hazel buys a teddy bear for £6.00, a
board game for £4.00, a cd for £5.50 and a box of chocolates for £2.50 She has some discount vouchers. She can either get £10.00 off or half price on her items. Which voucher would save her more? Explain your thinking.
Yasmin is choosing a new mobile phone. One phone costs £5.50 per month. The other costs £65.50 for a year. Which is the better deal over a year?
Kim bought a chocolate bar and a drink. The cost of them both together is in one of the boxes below.
£1.85 75p £1.56
£1.74 £2.25 £1.00
£1.80 80p £2.10
£1.44 £3.06 £1.50
£1.20 £1.25 £1.60
£1.45 90p £1.27
Using these five clues can you work out which price in the boxes is correct?
7. You need more than three coins to make this amount.
8. There would be change when using the most valuable coin to buy them.
9. The chocolate bar cost more than 50p
10. You could pay without using any copper coins
11. The chocolate bar cost exactly half the amount of the drink.
Theme park prices
Adult = £8
Child = £4
