Medium Term Planning Year 2 Theme 1: Using Place Value · PDF fileThe application and...

Using materials and a range of representations, pupils practise counting,

reading, writing and comparing numbers to at least 100 and solving a varie-

ty of related problems to develop fluency. They count in multiples of three

to support their later understanding of a third.

As they become more confident with numbers up to 100, pupils are intro-

duced to larger numbers to develop further their recognition of patterns

within the number system and represent them in different ways, including

spatial representations.

Pupils should partition numbers in different ways (for example, 23 = 20 + 3

and 23 = 10 + 13) to support subtraction. They become fluent and apply

their knowledge of numbers to reason with, discuss and solve problems

that emphasise the value of each digit in two-digit numbers. They begin to

understand zero as a place holder.

Medium Term Planning Year 2 Theme 1: Using Place Value and Number Facts to Solve Problems Approx 4 weeks

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KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson

The main focus of this theme is the reinforcement of place value, pattern and number facts up to at least 100; and their application in solving problems and real-life situations. Building on the reading and recording of numbers in Year 1, pupils will read and write numbers to 100, comparing numbers with up to 3 digits using inequality symbols (<>), understanding place value and estimating quantities for the first time. Pupils will explore numbers within a range of representations and situations, [objects, pictorial representations, number lines, tracks and hundred squares, measuring scales, coins and so on], to develop a deep and robust conceptual understanding which can be transferred to different contexts. For example, to further an understanding of numbers up to at least 100, pupils may be measuring, comparing and recording measurements in grammes, millilitres or metres and/or centimetres. In Mr Small’s house, the door frame was only half a metre high. Find some furniture which could fit through. The application and derivation of addition and subtraction facts will be integral throughout this theme. Continuing from Year 1, pupils will count in multiples of 2,5 and 10, using number patterns and place value to make connections and deductions. Money, the clock face and other measuring scales will be used to underpin this understanding: Khadija has 10p, 10p, 5p, 5p, 10p in her purse. How much does she have altogether? When counting in multiples, the language of scaling should be used: Khadija has 10p four times, which makes 40p.

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Number—Place Value

Recall and use addition and subtraction facts to 20 fluently

(and derive and use related facts up to 100.)

Count in steps of 2, 3, and 5 from 0, and in tens from any number,

forward and backward

Recognise the place value of each digit in a two-digit number (tens, ones)

Identify, represent and estimate numbers using different

representations, including the number line,

Compare and order numbers from 0 up to 100; use <, > and = signs

Read and write numbers to at least 100 in numerals and in words

Use place value and number facts to solve problems.

Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

Compare and order lengths, mass, volume/capacity and record the results using >, < and =

Find different combinations of coins that equal the same amounts of money

Number —Addition and Subtraction Measurement

Pupils practise addition and subtraction

to 20 to become increasingly fluent in

deriving facts such as using 3 + 7 = 10;

10 – 7 = 3 and 7 = 10 – 3 to calculate 30

+ 70 = 100; 100 – 70 = 30 and 70 = 100

– 30.

Pupils use standard units of measurement with

increasing accuracy, using their knowledge of the

number system. They use the appropriate lan-

guage and record using standard abbreviations.

N.C

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Repeated from Year One Pupils should be taught to:

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

given a number, identify one more and one less

identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

read and write numbers from 1 to 20 in numerals and words.

Pupils are introduced to the multiplica-

tion tables. They practise to become

fluent in the 2, 5 and 10 multiplication

tables and connect them to each oth-

er. They connect the 10 multiplication

table to place value, and the 5 multipli-

cation table to the divisions on the

clock face.

Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

Number—Multiplication and Division

© Wandsworth & Merton Local Authorities, 2014

Throughout Year 2, pupils will require daily practice of telling time to the nearest 5 minutes on an analogue clock, comparing and sequencing intervals of time and discussing the equivalence between minutes and hours, hours and days.

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Medium Term Planning Year 2 Theme 1: Using Place Value and Number Facts to Solve Problems Approximately 4 weeks

Khadija has 10p, 10p, 5p, 5p, 10p in her purse. How much does she have altogether? When counting in multiples, the language of scaling should be used: Khadija has 10p three times, which makes 30p.

If 70 + 4 = 74, what missing number would go in the box, below?

98 = + 8

EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims

KEY QUESTION ROOTS to be used and adapted in different contexts

If I know…….13 + 10= 23 and 13+11+ 24 then how could I work out……. 13 + 12?

Show me how you know that you are right with Dienes, numicon, a number line, a hundred square.

What is the same? What is different? (about odd and even Numicon pieces, about multiples of 5 and

multiples of 10.)

Show me……. (the number 98 with manipulatives, 100 ml in your jug, how many more I need…)

Odd one out. Karim has been counting like this: 3,6,9,11. Can you find his mistake and carry on the

pattern correctly?

What do you notice? 15 + 10 = 25, 15 + 11 = 26, 15 + 12 = 27.

15 + 20 = 35, 15 + 21 = 36, 15 + 22 = ?

Can you predict the answer to 15 + 30? 15 + 31? How?

What do you notice about the odd numbered Numicon tiles? Why?

How many

different number

sentences could

we write about

this set of coins?

Can some of the key thematic ideas be delivered as part of a mathemati-

cally-rich, creative topic?

Suggested ideas: The land of the Mr Men —what shape would Mr Greedy’s house be? How much taller is Mr Tall’s house than Mr Small’s? How much money does Mr Greedy spend at the shop? Focus on odd/ even house numbers, patterns on houses etc..

See Wandsworth LA Calculation Policy for more detail on

developing mental and written procedures!

There are ten candles in a pack.

If Abdi has 3 packs, how many

candles does he have?

If Salima has 4 boxes of

candles and 2 candles

extra, how many does

she have altogether?

How do you know?

There are 29 beads in this pot. I am putting one more bead in the pot. How many are in there now? How did you know? How can you check? Start with a different number of beads in the pot. Make a label to show how many beads there are. How many will there be if you take one out?

How many more does she need to make 50 candles?

Children explore the different constituent parts of a number. They use a number line (and hundred square) in combination with manipulatives such as dienes, place value counters, coins etc. to represent and repartition the number. They record their findings symbolically and apply this to problem-solving, i.e.

74 = + 4

Counting round a clock face provides an excellent opportunity to count in multiples of five or ten.

Pupils can count up and down a metre stick, to 100, in ones or tens. There are many

“real-life”, cross-curricular opportunities, such as growing plants, in which measuring

can be combined with counting, grouping and ordering numbers.

My bean is racing Kim’s bean.

Today Kim’s bean is taller. Hers

is 35 cm and mine is 28cm.

Non-routine problem.

With these three cards: How many 2 digit numbers can we make? How many 3 digit numbers can we make? What is the smallest/ largest number we can make?2 How do you know you are right? Can you order the numbers that you have made?

2 7 9


Medium Term Planning Year 2 Theme 2: Understanding Addition and Subtraction Approximately 3 weeks

National Curriculum

Aim

s: Fluency Reasoning Problem‐Solving


The main focus of this theme is the development of mental and written methods of addition and subtraction, and the underlying understanding. This will be acquired through consistent exploration with representations and concrete objects, such as numicon, dienes, place value counters and hundred squares; alongside modelling to support jottings, such as number lines, and formalised written algorithms. Pupils will add and subtract 2 digit numbers using practical, informal methods; whereas partitioning, counting strategies and number facts will be used to calculate with 1 digit numbers or multiples of 10. As in Year 1, measurement and real‐life problems will provide a context for solving problems throughout this theme. In some instances, a particular method will be taught and a context selected to support that: i.e. the bar model will be used as a representation for “difference” through the comparison of lengths and amounts of money. In other cases, a problem will be used as an opportunity for children to explore and compare different methods, and examine relationships: Amy needs 72p. If she already has 25p, how could we work out how much more she needs? Is there a different way that we can do this? How will we record what we have done? Children will see, for example, that subtraction can be done by counting on or counting back, either on a number line or as a formalised number sentence. To highlight the relationship between the two operations, and in preparation for work on inverses in Theme 3, addition and subtraction concepts will be taught simultaneously.

Repeated from Year 1, Number: Addition and Subtraction: • read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs

• represent and use number bonds and related subtraction facts within 20 • add and subtract one‐digit and two‐digit numbers to 20, including zero • solve one‐step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as

3 = – 9. From Year 2 Programme of Study: • count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward • recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

• interpret and construct simple pictograms, tally charts, block diagrams and simple tables • ask and answer questions about totalling and comparing categorical data.

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Addition and subtraction

Pupils extend their understanding of the language of addition and subtraction to include sum and difference.

Pupils practise addition and subtraction to 20 to become increas‐ingly fluent in deriving facts such as using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 – 3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30. They check their calculations, including by adding to check subtrac‐tion and adding numbers in a different order to check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commuta‐tivity and associativity of addition.

Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.

• choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the near‐est appropriate unit, using rulers, scales, thermometers and measuring vessels

• compare and order lengths, mass, volume/capacity and record the results using >, < and =

• recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

• find different combinations of coins that equal the same amounts of money

• solve simple problems in a practical context involving ad‐dition and subtraction of money of the same unit, includ‐ing giving change

solve problems with addition and subtraction: • using concrete objects and pictorial representations, in‐

cluding those involving numbers, quantities and measures • applying their increasing knowledge of mental and written

methods • recall and use addition and subtraction facts to 20 fluently,

and derive and use related facts up to 100 • add and subtract numbers using concrete objects, pictorial

representations, and mentally, including: ♦ a two‐digit number and ones ♦ a two‐digit number and tens ♦ two two‐digit numbers ♦ adding three one‐digit numbers

• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot .

Number, Place value & rounding Measurement

Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of three to support their later understanding of a third.

As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.

Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two‐digit numbers. They begin to understand zero as a place holder.

Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appro‐priate language and record using standard abbreviations.

Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’.

Pupils become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.

N.C.

• count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

• recognise the place value of each digit in a two‐digit num‐ber (tens, ones)

• identify, represent and estimate numbers using different representations, including the number line

• compare and order numbers from 0 up to 100; use <, > and = signs

• read and write numbers to at least 100 in numerals and in words

• use place value and number facts to solve problems.


Throughout Year 2, pupils will require daily practice of telling time to the nearest 5 minutes, comparing and sequencing intervals of time and discussing the equivalence between minutes and hours, hours and days.

The dog eats 95g of dog biscuits for his breakfast. A puppy eats 37g less than this. How much does the puppy eat?

Medium Term Planning Year 2 Theme 2: Understanding Addition and Subtraction Approximately 3 weeks

National Curriculum

Aim



KEY QUESTION ROOTS to be used and adapted in different contexts If I know……. then how could I work out…….? If I know that 3 + 7 makes 10, then how could I work out 13 + 17? 14 + 17? 40—13? Show me how you know that you are right. What is the same? What is different? … about counting across the hundred square in steps of 2 and 3. Why? What do you notice? about the pattern that is made if I keep subtracting ten from 105? Show me……. how you could find the difference between 25 and 77, how you can make 87p, how many more I need to make 30, 10 less than 63 using your hundred square Missing number/ function machine type questions: The “number cruncher” robot ate a 12, but spat out 20. Then he ate 40 and spat out 48. What do you think the robot could be doing to the numbers? What is our secret rule? Possibilities… Mary has two coins in her pocket. What amounts could she have? If the answer is…. 20, what is the question? I’m thinking of a number… I’ve subtracted 25 and the answer is 30. What number was I thinking of? Explain how you know. Another and Another… Show me a pair of numbers that total 30 and another pair, and another.

Can some of the key thematic ideas be delivered as part of a mathematically‐rich, creative topic? Suggested ideas: Our pet shop Pupils solve real life problems involving animals. For example, they could calculate with money to buy items for the pets. They could use measurement to solve problems regarding the housing and feeding of the pets.

See Wandsworth LA Calculation Policy for more detail on developing mental and written procedures!

Pupils “walk” around a hundred square to add/ subtract multiples of ones or tens. A playground hundred square provides a perfect setting for pupils to physically experiment with the effects of walking up/ down to add and subtract tens, or left/ right to add and subtract ones.

I notice if I walk down the hun‐dred square, I add ten each time

I started at 15. I took 6 steps down. I reached 75. I know that 15+ 60 =75

43 > 35

Using only 4 of these coins at a time, which different amounts can you make? What is the largest? What is the smallest? How do you know?


Compare different dog lead lengths. Measure and check. How much longer is the orange lead?

Each cat food box is 25cm long. How much space would be needed on the shelf for 2 boxes? How many boxes will fit onto a shelf which is 100cm long?

Non Routine Problem ‐ Alesha bought a monster using only silver coins. It cost her 45p. There are 9 different ways to pay 45p exactly using only silver coins. Find as many different ways that you can. What if the monster cost 50p. How many different ways are there to

pay now?

Pupils will explore addition and subtrac‐tion using different representations and contexts, including: a number line (and hundred square) dienes, place value counters, numicon and coins etc.. This will help them to understand the place value and symbolism involved in the cal‐culation; and to reinforce the importance of repartitioning. These concepts can then be applied to problem‐solving.

27 + = 30

The rat is 43cm long. The hamster is 35cm long. Which is longer? How do you know? What is the difference between the two lengths?

Exploring number partitioning with cuisenaire rods is an excellent way to understand and recognise commutativity and to generalise about number relationships.

I know that 7+3=10. So 27+3=30. To check this, I can partition 27 into 20 and 7. 20+7+3=20+10=30

Medium Term Planning Year 2 Theme 3 : Reasoning about Addition and Subtraction Approximately 2 weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths

• • • Count insteps of 2,3,5,and 0 and in tens from any number, forward and back • Recognise the place value of each digit in a two –digit number (tens, ones) • Read and write numbers to at least 100 in numerals and words • Use <, >, and =signs to compare numbers • Represent and use number bonds and related subtraction facts to 20, derive and

use related facts up to 100 • Recall and use multiplication and division facts for the 2,5 and 10 multiplication

tables, including recognising odd and even numbers • Choose and use appropriate standards units to estimate and measure length/

height in any direction (m/cm); mass (kg/g); temperature; capacity (litres/ml) to the nearest appropriate unit

• Tell the time to the hour and half past the hour • Identify known 2D and 3D shapes and begin to state their properties

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Measurement

• Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value • Find different combinations of coins that equal the same

amounts of money • Solve simple problems in a practical context involving addition

and subtraction of money of the same unit, including giving change.

• Interpret and construct simple pictograms, tally charts, block diagrams and simple tables

• Ask and answer simple questions by counting the num‐ber of objects in each category and sorting the catego‐ries by quantity

• Ask and answer questions about totaling and compar‐ing categorical data.

Pupils extend their understanding of the language of addition and subtraction to include sum and difference. Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 – 3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30. They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition. Recording addition and subtraction in columns supports place value and pre‐pares for formal written methods with larger numbers.

Addition and Subtraction Statistics

Pupils become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.

Pupils record, interpret, collate, organise and compare information (for example, using many‐to‐one correspon‐dence in pictograms with simple ratios 2, 5, 10).

N.C.

• Solve problems with addition and subtraction: ‐using concrete objects and pictorial representations, including those involving numbers, quantities and measures . ‐applying their increasing knowledge of mental and written methods.

• Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot.

• Recognise and use the inverse relationship between addition and sub‐traction and use this to check calculations and solve missing number problems.

• Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100.

• Add and subtract numbers using concrete objects, pictorial representa‐tions, and mentally, including:

‐ a two‐digit number and ones ‐ a two‐digit number and tens ‐ two two‐digit numbers


The main focus of this theme is the development of mental and written methods for addition and subtraction, to solve a variety of problems. Children will reason mathematically throughout the theme as they prove, justify, explain and present their thinking and calculations: Are these number sentences true or false? 98 – 18 = 70,46 + 77 = 123? Give your reasons. Pupils will further develop their reasoning skills and their understanding from theme 2, by investigating, and then demonstrating, their understanding of commutativity. If 13 +7=7 +13, then does 13‐7 = 7 –13. Why? Throughout this theme, pupils will be supported by a range of representations and through the recognition and application of the inverse relationship between addition and subtraction. The use of the bar model will be extended from Theme 2, with it now providing a visual representation of inverse, as well as “difference”. Pupils will be required to use their knowledge of inverse to check their calculations and to solve missing number problems. (e.g. 45 + __ = 71) Pupils will keep a written record of their work with manipulatives, either with jottings or formal written methods. They will be developing fluency with extended, written methods of addition and subtraction. They will transfer their skills into a range of money and statistics related contexts. Lily had 46p. Mahnoor had 33p more. How much money did Mahnoor have? How will you check that you are correct? Tom buys a chocolate bar for 45p and a packet of crisp for 40p. He pays using a £1 coin. What coins could he get in his change? Try to find all the possible answers. How do you know you have got them all? Within the context of statistics, pupils will construct a variety of simple graphs (pictograms, tally charts, block diagrams and tables) They could survey the class, e.g., If you were given £1 pocket money, what would you spend it on? and will interpret data from their own and others’ graphs.: How many more?, How many fewer?, What is the difference between…? What was the total of…..? are all question openers that require pupils to not only interpret data but to also apply their addition and subtraction skills.

Throughout Year 2, pupils will require daily practice of telling time to the nearest 5 minutes , comparing and sequencing intervals of time and discussing the equivalence between minutes and hours, hours and days.

Non routine problem: Based on Connect Three: Money by BEAM. Game for 2 children. Place one paper clip on the loop . Each player takes turns to move it 1 or 2 spaces around the loop and say the amount that it lands on. The player then places one of his/her colour counters on that amount on the grid. Keep playing until the counters have run out, then each player choose 3 connected counters to total. Highest score wins.

27p

National Curriculum

Aim


Medium Term Planning Year 2 Theme 3: Reasoning about Addition and Subtraction Approximately 2 weeks

Can some of the key thematic ideas be delivered as part of a mathematically‐rich, creative topic? Suggested ideas: Jack and the Beanstalk • What would a giant eat for breakfast? Pupils could design a shopping list for the giant’s breakfast or be given

a shopping list to work from (perhaps in the form of a table). How much money does he spend on food? If he has £1 to spend, what could he buy? How much change will he get? What coins could he use to pay for his shopping? Prove to me you have totalled your shopping list correctly. The giant spent between 50p and 60p. What two items did he buy? The giant spent £1 altogether. He bought a loaf of bread for 86p. What other item did he buy?

• Pupils could survey the class asking—If you were Jack what would you spend your golden coins on? They could construct graphs to show their data; and reason about the information shown, i.e. write their own statements or questions about their graphs.

• Jack decides to throw a party to celebrate defeating the giant. He invites four of his friends. Plan and budget for the party.


KEY QUESTION ROOTS to be used and adapted in different contexts If you know this: 87 = 100 – 13 what other facts do you know? Show me how you know that you are right. I’m thinking of a number. I’ve subtracted 70 and the answer is 30. What number was I thinking of? Explain how you know. What is the same? What is different? (23 +10=33; 10+23=33) What do you notice? Show me….. (48—9 on your number line, using cubes, 100 square) Find all the possibilities: How many ways can you show me that 79 subtract 13 is 66. How many different ways could the giant spend £2 on breakfast items. The answer is 35. What is the question? Add / Subtract another and another and another. What do you notice about the answers? Continue the pattern: 90 = 100 – 10, 80 = 100 – 20 Can you make up a similar pattern starting with the num‐bers 74, 26 and 100? Odd one out: Which one is the odd one out: 50, 24 + 26, 50—24 ? Why?



Be sure pupils do not develop the misconception that a larger number cannot be taken away from a smaller one. Pro‐vide examples of number lines that go beyond zero.

13 12

25

True or False

26 + 4 = 30

4 + 26= 30

26—4 = 30

4—26 = 30

Give your

reasons!

12 13

25

Pupils need to understand and show that

subtraction is not commutative.

Handful of Coins

Using a container of 2p coins, pupils close their eyes and take out a handful. They record how many coins they have taken out. Pupils repeat this a number of times and then record their data in a graph.

Which handful contained the most coins? Which handful contained the highest value of coins? How much money did you take in your first and second handfuls? How would your graph change if you took two less coins in the first and third handfuls? How much money would you have had in each handful if they were 10p coins instead of 2p coins?

I have more than 2 coins in my purse. The coin with the

highest value is not 50p. The total of the coins is more than

40p. Two of my coins have the same value. What coins do I

have?

Create a pictogram to show the amount of money saved in a piggy bank. Pupils could write their own questions about their data.


Pupils need to explore the inverse

relationship between addition and subtraction.

Find the sum of 12 and 15. What do you think you will have left if you now take away 15? Prove you are correct.

12p 15p

15p ?p

27p

27p Inversion

loops Bar model

Commutative Law of Addition Give the children two different colours of counters and a simple addition calculation to explore. The children represent each number in the calculation using the col‐oured counters. Ask them to add one of the coloured counters to the other and then vice versa. What do they notice? The total is the same! This could then be repeated with bead strings and base 10 apparatus. This idea could also be demon‐strated using the bar model or number lines.

Missing Symbols Write the missing symbols (+,‐,=) in these

number sentences.

80___ 20 ___100, 100__ 20__30, 87 ___ 13___ 100

Medium Term Planning Year 2 Theme 4: Solving Problems Using Geometry And Measurement Approx 2 weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum Aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson

The main focus of this theme is to develop children’s geometrical and measurement knowledge and fluency in the context of solving problems. Learning, during this theme, will be based around Christmas. Following on from their work in Year One, children will identify and sort a range of 2d/3d shapes in different orientations. Which 2d and 3d shapes can you find hanging on our Christmas Tree? How would you sort them? Children will develop their ability to confidently describe the properties of shapes ensuring correct vocabulary is used (sides, line of symmetry, edges, vertices, faces). Choose a present from Santa’s sack and describe its shape to a partner. How many presents in Santa’s sack have 4 or more vertices? Children will work with patterns of shapes and will explore position and direction concepts in practical contexts. Using the vocabulary clockwise, anti‐clockwise, quarter, half and three‐quarter turn, direct your friend to the secret Christmas present hidden in our classroom. Through practical exploration children will deepen their knowledge of measures. Order the Christmas presents from lightest to heaviest. Find me another elf half as high as this one. Opportunities to consolidate earlier addition and subtraction work should be exploited during this theme. Jasmine buys 1 candy cane and I choco‐late Santa. She pays using a £1 coin. How much change will she get?

• Count in steps of 2, 3 and 5 from 0, and in tens from any number, forward and back‐ward.

• Recognise the place value of each digit in a two digit number. • Compare and order numbers from 0 up to 100; use <,>and = signs. • Recall and use addition and subtraction facts to 20 fluently, and derive and use

related facts up to 100. • Recognise and use the inverse relationship between addition and subtraction and

use this to check calculations and solve missing number problems. • Recognise and know the value of different denominations of coins and notes. • Recognise and use language relating to dates, including days of the week, weeks,

months and years. • Interpret and construct simple pictograms, tally charts, block diagrams and simple

tables. • Ask and answer questions about totalling and comparing categorical data.

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Geometry—Properties of Shapes

• Identify and describe the properties of 2d shapes, including the number of sides and line symmetry in a vertical line.

• Identify and describe the properties of 3d shapes, including the number of edges, vertices and faces.

• Identify 2d shapes on the surface of 3d shapes.

• Compare and sort common 2d and 3d shapes and everyday objects.

Pupils handle and name a wide variety of common 2‐D and 3‐D shapes including: quadrilaterals & polygons, and cuboids, prisms and cones, and identify the proper‐ties of each shape. Pupils identify, compare and sort shapes on the basis of their proper‐ties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils read & write names for shapes that are appropri‐ate for their word reading & spelling. Pupils draw lines and shapes using a straight edge.

• Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers & measuring vessels.

• Compare and order lengths, mass, volume/capacity & record the results using >, < and = .

• Recognise and use symbols for pounds (£) and pence (p); com‐bine amounts to make a particular value.

• Find different combinations of coins that equal the same amounts of money.

• solve simple problems in a practical context involving addition & subtraction of money of the same unit, including giving change.

Measurement

Pupils use standard units of measurement with increasing accu‐racy, using their knowledge of the number system. They use the appropriate language & record using standard abbreviations. Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’. Pupils become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.

N.C.

Geometry—Position and Direction


• Order and arrange combina‐tions of mathematical objects in patterns and sequences.

• Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three‐quarter turns (clockwise and anti‐clockwise).

Pupils should work with patterns of shapes, including those in different orientations. Pupils use the concept and language of angles to describe ‘turn’ by applying rotations, includ‐ing in practical contexts (for exam‐ple, pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles).

Addition and Subtraction

• Solve problems with addition and subtraction: • Using concrete objects and pictorial representations, including those involving numbers, quantities and measures.

• Applying their increasing knowledge of mental and written methods.

Pupils extend their understanding of the language of addition and subtraction to include sum and difference. Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.

National Curriculum

Aim


Medium Term Planning Year 2 Theme 4: Solving Problems Using Geometry and Measurement Approx 2 weeks


KEY QUESTION ROOTS to be used and adapted in different contexts Odd one out …. Santa has sorted his presents according to their shape. Which presents are the odd ones out in this sack? How do you know? If I know that…. one reindeer weighs 15 kilograms, how much will two reindeers weigh? Show me…. two Christmas trees you have drawn whose length differ by 4cm. Another and Another…. Look at the pattern my baubles are making. What will my next bauble look like? And the next? And the next? What is the same? What is different? …. about the shape of these two Christmas decorations. True or False… this candy cane is half the size of this one, this Santa sack is twice as wide as that Santa sack. Is it possible…. Feel the presents in this sack. Is it possible that one of the presents is cube shaped? How do you know its not a football? Visualise…. two Christmas trees. One tree is half the size of the other tree. What could the lengths of both trees be? Always, Sometimes, Never true… The largest present under the tree will be the heaviest.

Can some of the key thematic ideas be delivered as part of a mathematically‐rich, creative topic? Suggested ideas: Christmas ‐ Making Gingerbread people and/or houses Children can apply their measurement skills by making gingerbread people or houses. They could be given a sweet‐spending budget. Each sweet has a cost and students plan which sweet decorations they will use, total their cost and calculate their change. Children can create designs for their houses using different 2d shapes. Using play dough, children can create a gingerbread man twice as wide or half the size as a partner’s gingerbread man. Children can measure the height of the gingerbread house and make gingerbread people who will fit inside the house. Children can work in groups to decorate gingerbread men creating repeating patterns with their decorations.

See Wandsworth LA Calculation Policy for more de‐

tail on developing mental and written procedures!

Children mix and match winter hats and scarves on the snowman and find all the different ways that they can be combined. How many different outfit combinations can they find? Increase the challenge by adding more hats and scarves.

What colour will the 6th candy cane in the sequence be? What colour will the 20th candy cane be? True or False—The 31st candy cane will be blue. How do you know?

Design a pattern and make your own Christmas wrapping paper.

Nahid is shopping at the Christmas Fair with these coins in her purse. Which things could she give ex‐actly the right amount for?

vertices.

Draw this Christmas angel after a quarter turn, half turn, three‐quarter turn.

Children design their own 2d shape wreaths or Christmas decorations. They can draw their own shapes or add shapes according to given cri‐teria. Your wreath must have at least 5 shapes with 4 straight sides and 3 shapes with line symmetry.

Use pattern blocks to design Christmas trees. Use two or three colours to make a symmetrical picture.


Set up a post office role play area and have the children weigh different Christmas presents that need to be posted. Children can calculate how much it will cost to send packages. For example, under 1kg—50p. 1kg –2kg ‐£1. They can calculate the cost for customers and work out change.

Choose a shape and describe it to your partner. If I draw 1 more cone, how many cones will there be? Colour the shapes with no vertices

Measure the height of each Christ‐mas present and then order them from shortest to tallest. Use candy canes to measure items in the

classroom. Measure your candy cane with a ruler and convert the candy cane measure‐ments into centimetres. How many candy canes will be needed to make a metre?

Medium Term Planning Year 2 Theme 5: Solving problems involving multiplication and division Approximately 4 weeks

Approximately weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims

The main focus of this theme is to introduce pupils to multiplication tables, and then use them to solve both

multiplication and division problems. Children will already have experience of doubling and halving (&

quartering in fractional contexts), and counting in different steps. They will now take this a step further by

representing multiplication tables as patterns, both practically and visually. Children will explore patterns

found in repeated addition 4 x 3 = 3 + 3 + 3 + 3 …. 3, 6, 9, 12 … and record by highlighting multiples on a

number line, in a hundred square: can you describe the pattern? and on a clock face: is 43 a multiple of 5? How

do you know? They count forwards and backwards to answer multiplication and division questions, and use

counters and other objects in arrays to support the commutative aspect of multiplication 3 x 4 = 4 x 3 . This will

reinforce a clear understanding of the equals sign e.g. as a balance, either side has the same value as or ‘the

same value, but different appearance’, leading on to solving missing number (empty box) puzzles.

Multiplication and division facts (and doubling/halving) will be explored alongside each other 2 x 5 = 10, 10 ÷ 5

= 2 , ½ of 10 = 5, ⅕ of 10 = 2 as ‘fact families’. Children develop mental strategies to work out unknown facts,

for example, 8 x 4 = 8 x 2 x 2. Finding fractions of a quantity is explicitly related to division ¼ of 40 = 40 ÷ 4

though practical exploration building on fractions work in Year One (to be continued in theme 6). Regular

opportunities to practise and learn multiplication and division facts support their use to solve word problems

and problems involving fractions: I know 1/2 of 8 is 4 because I can double 4 to get 8.

SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson

STATU

TORY

NON‐STA

TUTO

RY

Number ‐ Multiplication and Division

Pupils use a variety of language to describe multiplication and division.

Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multi‐

plication tables and connect them to each other. They connect the 10 multiplication table to place value,

and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication

tables and recall multiplication facts, including using related division facts to perform written and mental

calculations.

Pupils work with a range of materials and contexts in which multiplication and division relate to grouping

and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate

these to fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and

inverse relations to develop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4).

• Recall and use multiplication and division facts for the 2, 5 and 10 multiplication, including recognising odd

and even numbers.

• Calculate mathematical statements for multiplication and division within the multiplication tables and write

them using the multiplication (×), division (÷) and equals (=) signs.

• Show that multiplication of two numbers can be done in any order (commutative) and division of one num‐

ber by another cannot.

• Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental

methods, and multiplication and division facts, including problems in contexts.

Number ‐ Fractions

Pupils connect unit fractions

to equal sharing and group‐

ing, to numbers when they

can be calculated, and to

measures, finding fractions

of lengths, quantities, sets of

objects or shapes. They meet

2/4 and 3/4 as the first ex‐

amples of non‐unit fractions.

Using materials and a range of representations, pupils

practise counting, reading, writing and comparing num‐

bers to at least 100 and solving a variety of related prob‐

lems to develop fluency. They count in multiples of three

to support their later understanding of a third.

As they become more confident with numbers up to

100, pupils are introduced to larger numbers to develop

further their recognition of patterns within the number

system and represent them in different ways, including

spatial representations

N.C.

• Recognise, find, name and

write fractions, 1/3, 1/4,

2/4 and 3/4 and 3/4 of a

length, shape, set of

objects or quantity (unit

fractions only in theme 5).

• Write simple fractions for

example, 1/2 of 6 = 3


• Tell and write the time to five minutes, including quarter to/past the hour and draw hands on a clock face to show these times

• Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

• Ask and answer simple questions about totalling categorical data by count‐ing the number of objects

• Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts to 100

• Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

• Describe position, direction and movement, including whole, half, quarter and three‐quarter turns (from Year 1)

• Find different combinations of coins that equal the same amounts of money

• Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

• Identify, represent and estimate numbers using different representations, including the number line

Number ‐ Place value


National Curriculum

Aim


Medium Term Planning Year 2 Theme 5: Solving Problems involving multiplication & division Approximately 4 weeks



True or false? When you count up in tens starting at 5 there will always be 5 ones. How do you know?

Making links with fact families: 6 x 4 = 24, what else do I know? (4 x 6, 24 ÷ 6, 24 ÷ 4, 1/4 of 24, 1/6 of 24)

Missing numbers 10 = 5 x What number could be written in the box?

Prove It: Which four number sentences link these numbers? 3, 5, 15?

Use the inverse to check if the following calculations are correct: 12 ÷ 3 = 4, 3 x 5 = 14

What do you notice? ¼ of 4 = 1, ¼ of 8 = 2, ¼ of 12 = 3 Continue the pattern. What do you notice? Show that 8 x 4 = 4 x 8

Can some of the key thematic ideas be delivered as part of a mathe‐

matically‐rich, creative topic? Suggested ideas: Jurassic Park

Dinosaur travel in herds of 8. How many dinosaurs are there in 4 herds?

Iguanodon have three toes on each of its four feet. How many toes does

an Iguanodon have in total?

Fossils are packed in boxes, 6 rows with five in each row. How many in

one box? Two boxes?

Triceratops means ‘three‐horned face’. How many

triceratops are in the herd if you can count 21 horns?

Dinosaur footprint investigations (see below)

A dinosaur eats ¼ of 20 ferns. How many ferns does he get?

A velociraptor is about 2m long. If 10 velociraptors marched nose to tail

how long would the line be?

Jurassic Park tickets cost £5. How many friends can you take for £40?

See Wandsworth LA Calculation Policy for more detail on developing

mental and written procedures!

Models for multiplication:

We have 15 counters each. I have

5 groups of 3 counters, ‘3 five

times’. You have 3 groups of 5

counters.

I know a row ⅓ is of the

counters because it is one

row out of 3 rows

Non routine investigation: Jurassic Park has Coelophysis (which move

on 2 legs), Diplodocus (4 legs) and Triceratops (4 legs). The park keeper

counts 48 legs. How many of each dinosaurs could there be? What if

there were 28 legs?

www.kangaroomaths.com

Arrange 10 counters into an array (e.g. 2 x 5) and then turn the array 90°

to reveal its commutative partner (e.g. 5 x 2). Explain that 2 x 5 has the

same value as 5 x 2, both with a total of 10. Children can explore the

multiplication sentences made with 20 counters (2x10, 10x2, 4x5, 5x4).

Draw out the division facts: 20 = 4 x 5 so 20 ÷ 4 = 5 etc


⅓ of 9 = 9 ÷ 3 = 3

What fact families can you find using this array? How can you prove it?

(This diagram demonstrates each row as a fifth of the whole )

Medium Term Planning Year 2 Theme 6: Fractions of shapes, lengths, sets of quantities Approximately 3 weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily

The main focus of this theme is to recognise, name and write the unit fractions ⅓ and ¼ and to introduce non‐unit fractions 2/4 and ¾. Through practical exploration children will continue to develop the concept of fractions being equal parts of a whole. They will explore the different ways paper rectangles can be halved and quartered by folding and cutting and learn to recognise and name the equal parts created; including counting more than 1 part to find 2/4 and ¾. This will also help children to see equivalence between halves and quarters. Building on work in Year 1, chil‐dren should be taught to recognise the name of the fraction family (denominator) first, by considering how many parts, in total, comprise one whole; and the symbolic recording of the fraction alongside this. In this way, pupils will begin to explore thirds as a family divided into 3 equal parts, find ⅓ practically and count in 3s on a number line. How many parts has this ribbon been divided into? How could we write the fraction of it that I am holding now? Pupils should recognise the link between multiplication and division, i.e. counting in 3s, sharing between 3 and finding 1/3. What fraction is left? How do you know? How do we write this? Throughout this theme, as in Year One, pupils will explore fractions of shapes, quantities, lengths and sets of objects (e.g., there are 4 of us, and 12 counters. We are going to share these counters equally. How many will we each have? Can we think of a number sentence, e.g. 3 + 3 + 3 + 3, so a quarter of 12 is 3.) Still using pictorial models alongside, children will count in halves and quarters on a num‐ber line starting from different numbers. Let’s count in half centimetres up to 10cm. Look at how the 2x table is con‐nected to halves and doubles and explore how to find a quarter by halving and halving again, moving on to finding 3/4 by finding 3 parts. Find a quarter of this rectangle by halving and halving again. Now do the same to the number 8.

• recall and use addition and subtraction facts to 20 fluently, and derive

and use related facts up to 100

• add and subtract numbers using concrete objects, pictorial representa‐

tions, and mentally, including: a two‐digit number and ones and a two‐

digit number and tens

• Continue to count in multiples of 2,5 and 10 and begin to count in mul‐

tiples of 3

• tell the time to five minutes, including quarter past/to the hour

• know the number of minutes in an hour and the number of hours in a

day

• identify and describe the properties of 2‐D shapes, including the num‐

ber of sides and line symmetry in a vertical line

STATU

TORY

NON‐STA

TUTO

RY

Fractions

Pupils use fractions as ‘fractions of’ discrete and continu‐ous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal shar‐ing and grouping, to numbers when they can be calcu‐lated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet 2/4 and 3/4 as the first example s of non‐unit fractions. Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the num‐ber line (for example, 1 1/4 , 1

2/4 (or 1 1/2 ), 1

3/4 , 2). This reinforces the concept of fractions as numbers and that they can add up to more than one.

• Identify and describe the properties of 2‐D shapes, including the number of sides and lines of symmetry in a vertical line

• Recognise, find, name and write fractions, 1/3, 1/4, 2/4 and 3/4 and 3/4 of a length, shape, set of objects or quantity

• Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.

Multiplication and Division Geometry : Properties of shapes

Pupils use a variety of language to describe multiplication and division.

Pupils are introduced to the multiplication tables. They practise to become fluent in the

2, 5 and 10 multiplication tables and connect them to each other. They connect the 10

multiplication table to place value, and the 5 multiplication table to the divisions on the

clock face. They begin to use other multiplication tables and recall multiplication facts,

including using related division facts to perform written & mental calculations.

Pupils work with a range of materials and contexts in which multiplication & division relate to grouping and sharing discrete & continuous quantities, to arrays and to re‐peated addition. They begin to relate these to fractions and measures (for example, 40÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (e.g., 4 × 5 = 20 and 20 ÷ 5 = 4).

Pupils handle and name a wide variety of common 2‐D

and 3‐D shapes including: quadrilaterals and polygons,

and cuboids, prisms and cones, and identify the proper‐

ties of each shape (for example, number of sides, num‐

ber of faces). Pupils identify, compare and sort shapes

on the basis of their properties and use vocabulary

precisely, such as sides, edges, vertices and faces.

Pupils read and write names for shapes that are appro‐

priate for their word reading and spelling.

Pupils draw lines & shapes using a straight edge.

N.C

• Recall and use multiplication and division facts for the 2, 5 and 10 multiplication ta‐

bles, including recognising odd and even numbers

• Calculate mathematical statements for multiplication and division within the multiplica‐

tion tables and write them using the multiplication (×), division (÷) and equals (=)

signs

• Solve problems involving multiplication and division, using materials, arrays, re‐peated addition, mental methods, and multiplication and division facts, including problems in contexts.


Throughout Year 2, pupils will require daily practice of telling time to the nearest 5 minutes on an analogue clock, comparing and sequencing intervals of time and discussing the equivalence between minutes and hours, hours and days.

National Curriculum

Aim


Medium Term Planning Year 2 Theme 6: Fractions of shapes, lengths, sets of quantities Approximately 3 weeks



What is the same/different about 1/2 and 1/3?

Show me how to work out how I can share 12 apples between four children.

True or false? 1/2 of 12 is bigger than 1/3 of 9.

True or false? There are 3 numbers between 0 and 30 that are multiples of 2, 5 and 10.

The answer is half, what is the question?

1 1/4, 1 2/4, 1

3/4, 2 …… If I keep adding on a quarter, will 3½ be in my sequence. How do you know?

What are your top tips for working out fractions of amounts?

What the same/different between the two times table, and halves and doubles?

3 x 4 is the same as 4 x 3. Prove it. Is this the same for other numbers? Does it work with division?

If I know 1/3 of 6 is 2, then how could I work out 2/3 of 6?

Can some of the key thematic ideas be delivered as part of amathematically‐rich,

creative topic?

Suggested ideas: Create a fraction museum. Children to create own representations of

fractions using cubes, buttons, pencils, collage, lego, counting equipment. Children to

create a half, a third etc and label their fractions. Children from other year groups to

visit and record fractions and answer questions. Some unlabelled fractions can be

‘mystery fractions’. Can they decide what fraction the model represents? Could lead

into equivalent fractions. Link to literacy—posters, labels, tickets etc.



Pupils have pieces of paper, can you

fold the paper into 4 equal parts? How

many different ways can you do it?

How do we know that they are equal?

Can they be placed over each other

exactly? Looking at quarters of differ‐

ent shapes. How have you divided

your shape into quarters?

Non‐Routine problem: How many different triangles can

you draw, with 1 dot inside? What are its properties?

How about 2 dots? 3 Dots?

Create different visual

representations of

fractions by folding and

cutting.

How could you represent

thirds on this wall? What

do you notice?

Can you continue the sequences?

What if the number line started at 5?

Mina has thirty‐two stickers. She gives half to her brother. How many stickers does she give him?

Anna has 50 pencils. She puts 5 pencils in each party bag.

How many bags does she put pencils in?

What other shapes

can show these

fractions?

Are these all half?

How could you check

they are half? Which

are not half? How do

you know?

From a selection

of shapes, pupils

sort the shapes

that show 1/2

and those that

do not.

How many ways can you shade

1/4 of this shape? How do you

know it is a quarter? Shade 2/4.

What do you notice?

Find a

quarter of 8

8cm 7cm 5cm 5 1/2 8 1/2

Count up in halves and quarters in the context of length.

4 1/2 4cm 3cm 3 1/4 4 3/4 3 3/4

Pick a multiple of 3. Draw a

snake with that number of body parts.

Make 1/3 of the body red.

Can you draw other snakes

with a different number of

parts with half their body

filled in? A quarter of their

body?

Pupils find a quarter of a quantity by halving and halving again.

They can show this by halving and halving a shape to find a

quarter, then relate this to finding a quarter of a number.

C

C

C

Medium Term Planning Year 2 Theme 7: Understanding and Reasoning about Time Approximately 3 weeks

National Curriculum

Aim



The main focus of this theme is to develop children’s conceptual understanding of time and its application in solving problems and real life situations. Building on time work in Year 1, children will work with a range of clocks , watches and pictorial representations to become proficient at telling and writing the time to five minutes, including quarter past/to the hour. They will be able to draw the hands on a clock face to show these times. Children should be presented with opportunities to problem solve around time‐telling and to compare and sequence time. These clocks show when Tim and Fateha’s lunch breaks start and end. Which child has the longer lunch break? Put these clocks in order from the earliest to latest time. What is the same and what is different about the times on these clocks ( half past twelve and six o’clock or nine fifteen and a quarter to three)? The application and derivation of time facts is vital to this theme alongside opportunities to reason about time. The time is 3:15pm. Kate says that in sixty minutes she will be at her football game which starts at 4:15pm. Is Kate right? Explain why. Learning will be reinforced by rehearsing aspects of time on other occasions during the school day. Show me the time the lesson started on this clock. Now show me the time the lesson finished. How long did that lesson take? Children may also benefit from a daily routine of counting in 5 minutes, quarter hour or half hour intervals using a counting stick (extended to 12 divisions) or around a clock face. In preparation for Year 3, in the latter part of this theme, children could be introduced to simple time interval calculations, using the inverse relationship between addition and subtraction. Cinderella begins cleaning the ugly sisters’ shoes at five minutes past one. She finishes at half past one. How long did this take? How could we work this out using a clock face? A number line? What was the time ten minutes be‐fore she began cleaning the shoes? Show this time on your clock face.

•Develop quick recall of 2,5,10 multiplication and division tables.

•Find 3/4, 1/4, 1/2 and 1/3 of a shape, length, set or quantity.

• Recognise and use symbols for pounds (£) and pence (p); combine

amounts to make a particular value.

• Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts to 100

•Identify and describe the properties of 2d and 3d shapes

• Recognise the place value of each digit in a two digit number.

•Read and write numbers to at least 100 in words.

•Use <,> and = signs to compare numbers.

•identify and describe the properties of 2‐D shapes, including the number

of sides and line symmetry in a vertical line

STATU

TORY

NON‐STA

TUTO

RY

Measurement

• Compare and sequence intervals of time

• Tell and write the time to five minutes,

including quarter past/to the hour and

draw the hands on a clock face to show

these times.

• Know the number of minutes in an hour

and the number of hours in a day.

Pupils use standard units of measurement with increasing accuracy, using their knowl‐edge of the number system. They use the appropriate language and record using stan‐dard abbreviations.

They become fluent in telling the time on analogue clocks and recording it.

• Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward.

• Identify, represent and estimate numbers using different representations, including the number line.

Using materials and a range of representations, pupils

practise counting, reading, writing and comparing num‐

bers to at least 100 and solving a variety of related prob‐

lems to develop fluency. As they become more confident

with numbers … pupils … develop further their recognition

of patterns within the number system and represent them

in different ways, including spatial representations.

N.C

• Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures and by applying their increasing knowledge of mental and written methods.

• Recognise and use the inverse relationship between addition and sub‐traction and use this to check calculations and solve missing number problems.

Pupils extend their understanding of the language of addition and

subtraction to include sum and difference.

Addition and Subtraction


Place Value


Non Routine Problem ‐

Order, Order! Order these activities from the shortest to longest period of time. Convince me your order is right. Time: • Taken to travel to school. • For mustard and cress to grow from seeds.

• Taken to eat a biscuit. • Between your 6th and 7th birthdays. • Taken for frogspawn to grow into a frog.

• Taken to walk across the playground. • Taken for the moon to orbit the earth.

National Curriculum

Aim


Medium Term Planning Year 2 Theme 7: Understanding and Reasoning about Time Approximately 3 weeks


KEY QUESTION ROOTS to be used and adapted in different contexts Show me the time school starts. Now show me the time 5, 10, 15 minutes before/after this time. True or False… There are 60 minutes in a hour. There are 30 minutes in ½ hour. There are 15 minutes in ¼ hour. There are 24 hours in a day. How do you know? True or False… It takes Max 15 minutes to walk to school. Millie says it takes her longer as it takes her ½ hour. Is she correct? Why? If I know ..there are 60 minutes in a hour then how could I work out… how many minutes are in 2 hours? What is the same? What is different? about these clock faces. What different answers could we have (all possibilities) You have 1 hour to fill your time at the weekend. You must do at least 4 activities in this time. What could you do and for how long? Undoing Marcia finished her bike ride at 4:30p.m. She rode for 30 minutes. What time did she start her bike ride? Make an estimate Approximately how long does your favourite show last? Your swimming lesson take? Your journey to school?

Can some of the key thematic ideas be delivered as part of a

mathematically‐rich, creative topic? Suggested ideas: Cinderella Use the story of Cinderella to explore time. Pupils create a time line of

Cinderella’s day. They draw pictures of the different activities she did and

draw the time on clocks to show when she started and finished each activ‐

ity. They calculate the time Cinderella took to complete different chores.

These two clocks show the time Cinderella started cooking dinner and the

time she finished. How long did it take her to cook dinner for the ugly sis‐

ters? Which chore took Cinderella the most/least amount of time? Pupils

plan the ball. They are given a list of what needs to happen before mid‐

night and plan how much time should be spent on each activity. They

draw on clocks the start and finish time for each activity. Pupils consider

how princesses, princes, wicked stepmothers or ugly step sisters spend

their time. They show this information on a time line or a chart, drawing

clocks to show when they start and finish each activity.



Minute Game (A game for 2 players)

You need:

• 2 counters or small cubes • 5 prizes • dice showing 5 mins/10mins/15 mins (adapt an ordinary dice) First of all put your counters on 12. When it’s your turn roll the dice and say the number of minutes. Move your counter clockwise that many minutes. (Remember, from one number to the next is 5 minutes). The rest of the game each time you land on, or pass, 12 you win a prize. The first person to collect 3 prizes wins the game.

In preparation for Year 3, children should use number lines to aid their calculations when solving time problems

NRICH— What is the time? Activity Can you put the times on these clocks in order?

Children need to work with a range of clock faces and should be provided with opportuni‐ties to label clock faces in dif‐

ferent ways.

Give the chidren a clock and set the time cards face

down in a pile. One child takes a time card and sets

the clock to that time. The other child checks it, if

correct, the card is kept, if not it is replaced in the

pile . The children change roles.

Children subtract and add time to design a schedule of events for a Carnival. They need to read the clues care‐fully. Children could be given clocks that show the time for each clue and the task could be to match the clock to the clue. 1. The show starts at 2pm. 2. At 4pm tea and cakes are sold. 3. 45mins before the cleaners finish, the gate is closed. 4. 15mins after tea and cakes, prizes are announced. 5. The cleaners finish at 6pm. 6. An hour after the show starts, the circus begins. 7. 30mins after the show starts the fun fair opens. 8. 15mins after the circus starts, the band pa‐

rades through the town

Use the Telling the Time ITP. This ITP can be used to show analogue time, digital time or synchronised analogue and digital clocks. The program allows you to add or subtract a selected time interval.

Playing the NRICH Stage 1 Stop the Clock game is a fun way to get children adding and subtracting time and also gets them problem solving and reasoning. (See the NRICH website)

Make a display using as many different clocks and watches as

possible.


Draw four things you did today. Make the

clock show the time you did each thing.

The students found a baby bird on the playground. After lots of research , they discovered that they should feed it once every 15 min‐utes. The first feeding was at 9:15 a.m. Show the time of the first 5 feedings. On a number line and on the clock faces.

Medium Term Planning Year 2 Theme 8: Solving Geometrical Problems Approx 3 weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum Aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson The main focus of this theme is for children to extend and deepen their prior understanding of 2d and 3d shapes and apply this understanding to solve geometrical problems. Pupils will need to build on their earlier experiences of geometry with specific teaching of symmetry and shape vocabulary: Describe this shape to your partner without telling them its name. In order to develop their fluency in identifying and describing the properties of 2d and 3d shapes, children should be provided with regular opportunities to explore shapes using a range of real life, concrete objects and pictorial representations. Model making activities using equipment such as plasticine, straws, construction kits or geoboards will enable children to deepen and consolidate their knowledge of shapes. I used one square and 4 equal sized triangles to make my 3d shape. What’s my shape? Show me a shape on your geoboard that has a line of symmetry. Interpreting and constructing a range of diagrams (Venn, Carroll and tree—not in the NC, but very relevant here), charts and tables will help children distinguish and reason about the properties of shape. What headings could we use for this venn diagram? Construct a chart to show how many of each shape we found outside. Children will sort and compare shapes, including different varieties of the same shape and shapes in different orientations. Show me what my triangle will look like after a three quarter turn clockwise. Problem solving tasks should be designed to exploit previous knowledge learnt in other themes, such as patterns and sequences, measure and number. Draw the next 5 shapes in this pattern. Arrange your set of solids in order of height/weight. Can you find other ways of ordering them? Through their explorations of shapes, pupils will further embed the concepts of mental calculation: I have some shapes in my bag. Altogether there are 18 vertices. What shapes could I have in my bag?

• Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

• Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables.

• Recognise, find, name and write fractions halve, thirds, quarters, two‐quarters and three quarters of a length, shape, set of objects or quantity.

• Find different combinations of coins that equal the same amounts of money. • Tell and write the time to five minutes, including quarter past/to the hour and draw

the hands on a clock face to show these times. • Interpret and construct simple graphs, tables and charts, e.g.—Weekly Weather

Chart. • Recognise appropriate units of measure to use when measuring a range of every‐

day objects. • To understand that addition and multiplication can be done in any order

(commutative) and that subtraction and division cannot.

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Geometry—Properties of Shapes

• Identify and describe the properties of 2d shapes, including the number of sides and line symmetry in a vertical line.

• Identify and describe the properties of 3d shapes, including the number of edges, vertices and faces.

• Identify 2d shapes on the surface of 3d shapes.

• Compare and sort common 2d and 3d shapes and everyday objects.

Pupils handle and name a wide variety of common 2‐D and 3‐D shapes including: quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape. Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils read and write names for shapes that are appropriate for their word reading and spelling. Pupils draw lines and shapes using a straight edge.

• Choose and use appropriate standard units to estimate and measure length to the nearest appropriate unit, using rulers.

• Solve simple problems in a practical context involving addition and subtraction of money of the same unit including giving change.

Measurement

Pupils use standard units of measurement

with increasing accuracy, using their

knowledge of the number system. They use

the appropriate language and record using

standard abbreviations.

Comparing measures includes simple

multiples such as ‘half as high’; ‘twice as wide’.

N.C

• Interpret and construct simple picto‐grams, tally charts, block diagrams and simple tables.

• Ask and answer simple questions by counting the number of objects in each category and sorting the catego‐ries by quantity.

Pupils record, interpret, collate, organise and compare information.

Geometry—Position and Direction


Statistics

• Order and arrange combinations of mathematical objects in patterns and sequences.

• Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three‐quarter turns (clockwise and anti‐clockwise).

Pupils should work with patterns of shapes, including those in different orientations. Pupils use the concept and language of angles to describe ‘turn’ by applying rotations, including in practical contexts (for example, pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles).

National Curriculum

Aim


Medium Term Planning Year 2 Theme 8: Solving Geometrical Problems Approx 3 weeks


KEY QUESTION ROOTS to be used and adapted in different contexts Odd one out …. Show children a selection of shapes. Which one is the odd one out? Why? Challenge pupils to find as many different reasons for each shape as possible. If I know that…. One cube has 6 square faces. How could I work out … how many squares I will need to build 2 cubes? 3 cubes? Show me…. Something in the room that is a cylinder, sphere, triangular shape. Looking at a selection of shapes in differ‐ent orientations and sizes, can you show me the squares? Looking at a selection of regular and irregular shapes, can you show me the pentagons? Another and Another…. If I’m making my pattern by alternating shapes with rectangular faces and shapes with circular faces. What could the next shape in my pattern be? And the next? And the next? What is the same? What is different? …. about these two triangles, a square and a rectangle, prisms and pyramids. Possibilities….I have 3 shapes in this bag. All of my shapes have 5 or more sides. What shapes could be in my bag? True or False… A square has 4 lines of symmetry. Show me how you know you are correct. Is it possible…. Feel the shape in my bag. Is it possible that it is a ….? How do you know the shape isn't a ….? Visualise…. Imagine a cube. Four faces are yellow. The rest are blue. How many faces are blue? Picture a triangular prism. Dip it in paint. Make a print of each face. What shapes are you printing? In your head picture a rectangle that is twice as long as it is wide. What could its measurements be? Always, Sometimes, Never true… When you fold a square in half you will always get a rectangle.


mathematically‐rich, creative topic? Suggested ideas: The Shape Store Children set up a Shape Store in the class‐room. Customers come to buy a shape but they have forgotten its name. They have to describe the shape to the shopkeeper. Children arrange shapes in pat‐terns to display in the front window of the store. Can the customers guess the pattern rule? Customers order 3d shapes that need to be sent in the post. The store sends the shapes “flat packed”. “Flatten” the shapes using polydron ( or a similar modelling material) ,identify or draw the nets that will make the ordered 3d shapes. The cost of 2d shapes is determined by how many sides the shape has. 50p for each side. How much would a pentagon, octagon and hexagon cost? Look at the pricelist. I have £5 to spend. What shapes can I buy? All shapes that roll are being sold at half price. What’s their new cost? Design a castle made out of 3d shapes. How many of each shape do you need? What’s the cost of buying these shapes? Design advertisements for shapes sold at the store.

See Wandsworth LA Calculation Policy for more

detail on developing mental and written proce‐


Can you figure out what each shape is worth?

This is a very flexible puzzle. It can be adapted

by making the grid bigger or smaller or

changing the totals.

Loop of String Children work in small groups. Give each group a length of string. What shape can you make if everyone holds a corner? Can you make a shape with all sides the same length? How many lines of symmetry does your shape have? Recordings of the findings can be made using drawings or sticking down the string on big sheets of paper and making a display for the classroom wall. See NRICH Website for Mrs Trimmer’s String and Stringy Quads. Both are activities based on this idea.

Using three lines divide this rectangle into four parts. Each part must contain a triangle, a rectangle, a pentagon, a hexagon, a cylinder and an oval. From NRICH

Skeleton Shapes are made with balls of modelling clay and straws. Children can experiment building their own shapes before completing the NRICH activity Skeleton Shapes found on the NRICH Website. Anna makes a cube using straws. First she joins four straws to make a square. Then she joins more straws to make a cube. Altogether, how many straws has she used?

How many different solid shapes can you make using

up to 6 polydron tiles?

James is making a polygon mobile from straws. He has 25 straws. He is making triangles and squares. How many of each can he make? Work out all the possibilities.

Here are some shadows of 3d shapes. What shapes can they be? See NRICH activity Shadow Play found on the NRICH Website.

Join the dots—all except one. Can you find different ways of doing this? What shapes do you make?

Choose a label in secret. Put all the shapes that belong with that label in the circle. Leave the other shapes outside the circle. Can you guess what label I chose?

Give children logic problems that require them to use their shape and position knowledge. There are three shapes in a row. What order are they in and what colour are they? Clues: The cube is in the middle. The pink shape is not on the right. The cone is on the left. The red shape is next to the pyramid. The cone is not blue.

Ask children questions about shapes in a grid: What shape is above the black square? What shape is 2 places to the right of the red circle? Draw a shape with more than 5 sides next to the blue pentagon. Children can create their own grids and questions to share with the class.

TES iboard has a Shape Sorting game the children can use to create their own tree and Carroll diagrams. Children can create their own Venn diagrams using shapes and hoops.

Measuring Children can have a selection of reular and irregular shapes and count the number of sides. Which of these are pentagons? Why?


Medium Term Planning Year 2 Theme 9: Reasoning About Sequences and Patterns Approx 3 weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson The main focus of this theme is to develop children’s reasoning through the exploration of sequences and patterns. It is expected that children will not only identify a sequence or pattern and continue it, but will also reason about it. Initially, children will discuss and observe a set of numbers or shapes, guided by probing questions, to analyse whether there is a sequence or pattern rule; before moving on to proving, justifying, explaining and presenting their thinking and calculations. For example: 46, 51, 56 ... What’s the same/different about this sequence? What calculation would I do to find the next number? Explain how you know. Children should experience sequences and patterns within our number system to help embed a deeper understanding of place value and number facts. Listing, and visualising numbers on a 100 square will help them with this. True or False ‐When you count up in tens starting at 5 there will always be 5 ones. Continue the pattern, 90=100‐10, 80=100‐20, 70=100‐30 Explain what is happening. Exploring patterns in the 2, 5 and 10 times tables will help children develop their multiplication and division fluency. Look at where I am placing my counters on the hundred square. What am I counting in? How can you tell from the pattern I make? What is happening to the ones digit? Pupils will also count in 3s from 0, pattern spotting and using multiple representations e.g. numicon, 100 square.Opportunities to build on prior learning are exploited in this theme as children are presented with a wide variety of sequences and patterns to explore. ¼of 4=1, ¼of 8=2, ¼ of 12=3. Continue the pattern. What do you notice? Name the 2d shapes that come next in this pattern and tell me about their properties. Number sequences and patterns can be made real by applying them to problem solving in familiar contexts, such as in nature or on a calendar. Kevin has just started karate lessons. He has a lesson every six days. His first lesson is on a Monday. On which day of the week will his fourth lesson fall?

• Tell and write the time to five minutes and draw hands on a clock face to show these times.

• Recall time facts—days of the week, months in the year, days in each month, hours in a day, minutes in an hour , days in a year etc.

• Develop quick recall of 2,5,10 multiplication and division tables. • Find 3/4, 1/4, 1/2 and 1/3 of a shape, length, set or quantity. • Identify and describe the properties of 2d and 3d shapes. • Recognise the place value of each digit in a two digit number (if appropriate extend

to three digits). • Read and write numbers to at least 100 in digits and words (if appropriate extend

to three digits). • Compare and order lengths, mass, volume/capacity and record the results using >,

< and =. • Find different combinations of coins that equal the same amounts of money.

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Place Value

• Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and back‐ward.

• Read and write numbers to at least 100 in numerals and in words.

• Use place value and number facts to solve problems.

• Identify, represent and estimate numbers using different representations, including the number line.

Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of three to support their later understanding of a third. As they become more confident with numbers up to 100, pupils are introduced to larger numbers to de‐velop further their recognition of patterns within the number system and represent them in different ways, including spatial representations. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two‐digit numbers.

• Order and arrange combinations of mathe‐matical objects in patterns and sequences.

• Use mathematical language to describe po‐sition, direction and movement, including movements in a straight line and distinguish‐ing between rotation as a turn and in terms of right angles for quarter, half and three quarter turns (clockwise and anti‐clockwise).

Geometry ‐ Position and direction

Pupils handle and name a wide variety of common 2‐D and 3‐D shapes including: quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils draw lines and shapes using a straight edge.

N.C.

• Solve problems with addition and subtraction: ‐using concrete objects and pictorial representations, including those involving numbers, quantities and measures.

‐applying their increasing knowledge of mental and written methods.

• Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

• Add and subtract numbers using concrete objects, pictorial representa‐tions and mentally, including: a two‐digit number and ones, a two‐digit number and tens , 2 two‐digit numbers

• Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

• Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.

Pupils extend their understanding of the language of addition and subtraction to include sum and difference. Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 – 3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30. Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. Pupils …...begin to relate (multiplication and division) to fractions and measures .

Number + ‐ x ÷


• Write simple fractions

for example,

1/2 of 6 = 3 and

recognise the equiva‐

lence of 1/2 and 2/4.

Fractions

Pupils should count in frac‐tions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line. This rein‐forces the concept of frac‐tions as numbers and that they can add up to more than one.

Someone has taken a number from the line then closed up the other numbers. Which of these numbers belongs on the line? How do you know? 15, 19, 16, 7, 18

National Curriculum

Aim


Medium Term Planning Year 2 Theme 9: Reasoning About Sequences and Patterns Approximately 3 weeks


KEY QUESTION ROOTS to be used and adapted in different contexts Prove it. 3, 6, 9, 12, 15,….. Will 23 be in this sequence? How do you know? Be the teacher! Spot the mistake and correct it…. 45, 40, 35, 25 5 ½, 6 ½, 7 ½ 8, 8 ½ True or False …… I start at 3 and count in tens. I will say 30. Odd one out. Which number is the odd one out? Why? …. 2, 4, 6, 7, 8, 10, 12 Continue the pattern. What do you notice…. 10, 20, 30, 40, 50, .., .., .. 5, 10, 20, 40, 80, ……. Find the family member. Which of these numbers, 5, 48, 57, could appear in my sequence,4, 8, 12, 16, 20, 24, 28, 32, 36, 40. How do you know? Show me …… the next 3 shapes in my pattern. 3, 8, 13, 18, 23, 28….What do you notice? Place blue counters on the multiples of 5 on your hundred square. Now place red counters on the numbers in this sequence: 3, 8, 13, 18 …. What is the same? What is different? And another…. And another. 53, 63, 73, 83,…. Show me the next number in my sequence. And the next. And the next. What do you notice? What’s the same? What’s different? Are they the same size? Is the blue a half? always a half?

Can some of the key thematic ideas be delivered as part of a mathemati‐

cally‐rich, creative topic?

Suggested ideas: Islamic Patterns

Examine and discuss a range of Islamic patterns.

What shapes can the children see? What are the properties of these shapes?

Give children a range of 2d shapes and ask them to fit them together so there

are no gaps. Which shapes could fit together? Which don’t? Draw a pattern

by fitting shapes together and drawing around them. Colour in using a

repeated pattern. Explain how you did this. Children could use an ICT

program to create different patterns based on hexagons, octagons and stars

by manipulating the basic shapes in different ways.



Non Routine Problem ‐ Calendar Conundrum Choose a rectangle of 4 numbers on your calendar. Add the diagonal numbers. What is the answer? What do you notice? Try it again using a different rectangle. What do you notice this time?

Children should be encouraged to draw number sequences on number lines or hundred squares. They can explore the concept of In‐verse by reversing the process and commutativ‐ity. Ask children to solve problems using the sequence. E.g.— On Monday two strawberries grew on Farmer Brown’s strawberry plant. Every day after that 3 more strawberries would grow. How many strawberries would he have after 6 days? In the next field Farmer Green grew 2 strawberries on the Monday and then 6 grew each day. How many days until he had 20 strawberries?

Martha notices some analogue clocks hanging in a row on

the classroom wall.

She thinks each clock shows a time 15 minutes later than the

clock before it. Is she correct? How do you know?

Use the numbers in the circle

to make a pattern.

How can you prove

your sequence is correct?

6 9

15 12

3 18 0

Counting Stick A counting stick is a useful and flexible tool for counting in steps and seeing pat‐terns. Children can count forwards and backwards in different step sizes and form different starting points. Number cards can be attached to aid fluency or missing number questions can be asked to promote reasoning: If this is 20 and we are counting in 2’s, what number is this? Where will 26 be? Point to the centre of the stick and ask questions such as If this is 30, what are the numbers either side. What are the numbers at the beginning and the end of the stick? What else could they be? Children can specify any value for the numbers so long as they can justify their answers.

Explore the domino pattern activities on the NRICH website. Next Domino, Domino Sequences and Dom‐ino Number Patterns.

Which comes next in each

pattern of dominoes?

How do you know?

Write some number sequences with 8 in them. Explain your number sequences to a partner. Can you show your sequence on a number line and make up a story that goes with it?

Let children explore the environment around them for examples of patterns and sequences. They can photograph what they find and later explain to the class the patterns and sequences they discovered. You may even want to mention the Fibonacci sequence!

Hopscotch (Taken from National Strategies, Finding rules and Describing Patterns) What number patterns can you see? What is happening to the numbers in: the single squares, left hand double squares, right hand double squares? Can you say what the rule is? Can you continue the different sequences? Can you predict what the tenth number will be in the right hand double square sequence? Why is this easy to predict?

https://www.ncetm.org.uk/resources/40533 This video on reinforcing Tables Facts in KS1 models pupils using visual and numerical pat‐terns in times tables.


Reference 1/4 turns and language

of position and turn in relation to

the clock face and time.

Medium Term Planning Year 2 Theme 10: Asking And Answering Questions About Data Approx 4 weeks

National Curriculum

Aim


KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum Aims SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson The main focus of this theme is to develop children’s mathematical skills to interpret and construct a range of simple graphs (pictograms, tally charts, block diagrams and simple tables) and to ask and answer questions about the data presented in graphs. Children will be involved in a range of activities that encompass all areas of the data handling cycle and which make links to other areas of the curriculum and their everyday lives. For example, presenting children with a hypothesis to investigate, such as Boys in Year 2 eat more fruits and vegetables than girls in Year 2 requires them to collect, record, represent and analyse real data in a meaningful way. Children should be taught how to collect and represent data efficiently and opportunities to use ICT should be exploited (see back page). Children will be encouraged to make links between number lines and scales on graphs. Multiplication and division facts for the 2, 5 and 10 times tables will be applied when reading and constructing simple graphs. In Raheem’s graph, 1 orange represents 10 people. To represent 30 people he said he needs to draw 3 oranges. Is he correct? Show me how you know. How many groups of 5 do I have in my tally chart? The exploration of graphs will also enable children to reason about data. True or False—The bar chart tells me twice as many people like strawberry than lime. Throughout the theme, children will be presented with statistical data activities which require them to apply their measurement skills. How many jumps can you do in a minute? How many hops? Can we tabulate? They will also use addition and subtraction to solve problems. I sorted my 2p, 5p, 10p coins into this graph. Altogether how much money do I have?

• Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and back‐ward.

• Recognise the place value of each digit in a two‐digit number (tens, ones). • Compare and order numbers from 0 up to 100; use <, > and = signs. • Recall and use addition and subtraction facts to 20 fluently, and derive and use related

facts up to 100. • Recognise and use the inverse relationship between addition and subtraction and use

this to check calculations and solve missing number problems. • Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables,

including recognising odd and even numbers. • Recognise, find, name and write fractions , , and of a length, shape, set of objects or

quantity 1/3, 1,4, 2/4 and 1/2. • Write simple fractions for example 1/2 of 6 =3 and recognise the equivalence of 2/4 is a

1/2. • Identify and describe the properties of 2d and 3d shapes. • To understand that addition and multiplication can be done in any order (commutative)

and that subtraction and division cannot. Daily routines to include—Telling the time, counting in different steps and number bonds.

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Statistics

• Interpret and construct simple pictograms, tally charts, block diagrams and simple tables.

• Ask and answer simple questions by count‐ing the number of objects in each cate‐gory and sorting the categories by quanti‐ties.

• Ask and answer questions about totalling and comparing categorical data.

Pupils record, interpret, collate, organise and compare information (for example, using many to one correspondence in pictograms with simple ratios 2, 5, 10).

N.C.

• Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.

• Solve problems involving multiplication and division, using material, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

• Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures and applying their increasing knowledge of mental and written methods.

Pupils use a variety of language to describe multiplication and divi‐

sion. Pupils work with a range of materials and contexts in which mul‐

tiplication and division relate to grouping and sharing discrete and

continuous quantities, to arrays and to repeated addition. They begin

to relate these to fractions and measures (for example, 40 ÷ 2 = 20, 20

is a half of 40). They use commutativity and inverse relations to de‐

velop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4).

Addition, subtraction, multiplication and division


Measurement

• Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels.

• Compare and order lengths, mass, volume/capacity . • Recognise and use symbols for pounds (£) and pence (p); com‐bine amounts to make a particular value.

• Solve simple problems in a practical context involving addition and subtraction of money of the same unit.

Pupils use standard units of measurement with increasing

accuracy, using their knowledge of the number system. They use

the appropriate language and record using standard abbrevia‐

tions. Comparing measures includes simple multiples such as

‘half as high’; ‘twice as wide’.

Pupils become fluent in counting and recognising coins. They

read and say amounts of money confidently and use the symbols

£ and p accurately, recording pounds and pence separately.

National Curriculum

Aim


Medium Term Planning Year 2 Theme 10: Asking and Answering Questions About Data Approx 4 weew‐

weweeweeks EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims

KEY QUESTION ROOTS to be used and adapted in different contexts What is the same? What is different?.... Pictogram, Bar Chart (with given topic/data) Do, then explain …. Draw the correct number of tally marks in the chart to represent your data. Explain your thinking. Tell me the story….. What does the information in this graph tell us about how children travel to school? True or False ‐ ….. More people travel to school by car than walk. Make up your own true or False statement about the pictogram. Possibilities...Twice as many children like chocolate than strawberry. Draw the bars on the chart to represent how many children like strawberry and how many like chocolate. If I know….. That 1 image in the pictogram represents 5 people, then how can I work out.. How many people like foot‐ball? Show me …. How to draw the bars on this chart to represent my data. Odd One Out… Which bar has been drawn incorrectly? How do you know? Is it possible …. If each image represents 2 people. Is it possible to represent 9 people on this pictogram? How? Prove it…. Three fewer people like bananas than apples.


mathematically‐rich, creative topic? Suggested ideas: Visiting the Seaside

Children can work in groups to design a visit to the seaside. They collect data from a variety of people about their favourite things to do at the seaside, what they like to eat there, how much they would want to spend on a day out to the seaside, how far they would be prepared to travel, etc. Children can produce a variety of graphs for the data they have col‐lected. They can then use this information to design a visit to the seaside. They can design a timetable for the day and produce brochures advertis‐ing their day out. Children can work in groups to make different flavoured ice cream to sell at the seaside. Children in another class can taste their ice cream and vote for their favourite. Children can produce graphs to show the results.

See Wandsworth LA Calculation Policy for more

detail on developing mental and written proce‐


Noah watched the animals going into the ark. He was counting and by noon he got to 12, but he was only counting the legs of the ani‐mals. How many creatures did he see? Can find other answers? Tell someone how you found these answers out.

Try out the NRICH Activity, Ladybird Count. http//nrich.maths.org/2341

Using ICT Data Loggers—There are a variety of different types available that enable children to collect accurate data efficiently. How can we find the quietest place in the school? Use sound level meters to record sound levels in different places at the same time of day? How can we turn these into bar graphs? What do they tell us? Data Handling ITP and Create a Graph Web‐sites—Useful website that enable teachers and children to create their own graphs. Create an interactive whiteboard file— Create a file containing the children’s names or photo‐graphs. Children can drag and drop the their name/photo into the correct place on a table, pictogram, or block graph during registration to create data that shows how many children are having sandwiches, school dinner, etc.

Create pictograms quickly in groups or as a class. Initially create pictograms using real data, for example ask children to take off one shoe and organise them into rows of shoes with laces, buckles, Velcro strap, etc. Children can then draw their shoe on sticky notes and take it in turns to place it in the correct place on a large paper picto‐gram. This will quickly generate a set of class data and provide opportunities for questions to be asked.

Ensure that children experience exam‐ples of block graphs and pictograms where the information is represented horizontally, as well as examples where they are represented vertically.

Work with 5 friends. Each choose 6 books from the bookshelf and care‐fully measure each one. Record the height of the books in a chart using the headings(<15cm, 15‐19cm, 20‐24cm, 25‐29cm, >30cm). Convert the information in the chart into a block graph.

Children work in groups. You will need a dice marked 1 –10. Each child rolls the dice to find out how much money they have won. Each one wins the number of 5p coins shown on the dice. Children can play several rounds before totalling their winnings. Construct a graph to show how much money each child in the group won.

Give children database cards about animals (maybe children can research and create their own cards). Cards can include informa‐tion about the animals weight, height , number of young, aver‐age lifespan, etc. Children can sort the information into differ‐ent types of tables and graphs. For example, Construct a table to sort your animals into those Taller than 1 metre/Shorter than 1 metre.

How many more years does an African elephant live compared to a baboon?

How many fewer years does the cheetah live compared to the zebra?

What is the difference between a

giant panda and baboon’s life span?

Create human graphs with children. It is a great way to help children learn about the scales on a graph and what they represent.

Interpret pictograms where multi‐ples of 2, 5 and 10 are used.


Medium Term Planning Year 2 Theme 1: Using Place Value · PDF fileThe application and...

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