Issuu

Stretch and Challenge 5 A problem-solving, cross-curricular programme for children working above end-of-year expectations

Peter Clarke

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Contents Quick reference guide to Stretch and Challenge 5

Introduction

The features of Stretch and Challenge

A possible Stretch and Challenge teaching and learning sequence

Links to the Year 5 Mathematics National Curriculum Programme of Study and Attainment Targets

Cross-curricular links to the National Curriculum Programme of Study

Resources used in Stretch and Challenge 5

The Issues

Teacherâ€™s notes

Resource sheets Record of completion

209

My notes

211

Pupil self assessment booklet

213

Other Resource sheets

215

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Quick reference guide to Stretch and Challenge 5 Domain(s)

Topic

Issue number

Teacher’s notes page number

Number: – Number and place value

Number

101

Number

104

Negative numbers

107

Number:

Addition

110

– Addition and subtraction

Subtraction

113

Number:

Multiplication

116

– Multiplication and division

Division

119

Number:

Mixed operations

122

– Addition and subtraction

Mixed operations

125

Mixed operations

128

Mixed operations

131

Number:

Fractions

135

– Fractions (including decimals and percentages)

Fractions

138

Decimals

141

Percentages

144

Percentages

147

Fractions, decimals and percentages

150

Length

153

Mass

156

Volume and capacity

160

Time

163

Temperature

166

Area

169

Area and perimeter

172

Measurement

175

Geometry:

2-D shapes

178

– Properties of shapes

3-D shapes

181

Movement and angle

184

Geometry:

Reflections

187

– Position and direction

Translations

190

Geometry:

Reflective and rotational symmetry

193

– Properties of shapes

Geometry

196

Geometry

199

Statistics

202

Statistics

205

– Multiplication and division

Measurement

– Position and direction Statistics

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Introduction

Introduction The National Curriculum emphasises the importance of all children mastering the programme of study taught each year and discourages the acceleration of children into content from subsequent years. The National Curriculum states: ‘The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.’ 1 However, the National Curriculum also goes on to say that: ‘Within each key stage, schools [therefore] have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage, if appropriate.‘ 2 Stretch and Challenge aims to provide support in meeting the needs of those children who are exceeding age-related expectations by providing a range of problem-solving and cross-curricular activities designed to enrich and deepen children’s mathematical knowledge, skills and understanding. The series provides opportunities for children to reason mathematically and to solve increasingly complex problems, doing so with fluency, as described in the aims of the National Curriculum: ‘The National Curriculum for mathematics aims to ensure that all pupils: • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.’ 3 Stretch and Challenge has been designed to provide: • a flexible ‘dip-in’ resource that can easily be adapted to meet the needs of individual children, and different classroom and school organisational arrangements • enrichment activities that require children to use and apply their mathematical knowledge, skills and understanding to reason mathematically and to solve increasingly complex problems • mathematical activities linked to the entire primary curriculum, thereby ensuring a range of cross-curricular contexts • an easy-to-use bank of activities to save teachers time in thinking up new enrichment activities • an interesting, unique and consistent approach to presenting enrichment activities to children. The Stretch and Challenge series consists of six packs, also available digitally on Collins Connect, one for each year group from Year 1 to Year 6.

1 Mathematics programmes of study: key stages 1 and 2 National Curriculum in England, September 2013, page 3 2 Mathematics programmes of study: key stages 1 and 2 National Curriculum in England, September 2013, page 4 3 Mathematics programmes of study: key stages 1 and 2 National Curriculum in England, September 2013, page 3

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Introduction Printed resources Containing: • Pupil activity booklets (Issues)

Stretch an d Ch al

len ge

• Teacher’s notes • Resource sheets Enriching at Assessment mathematical the heart and understanding from the start

Online resources at connect.collins.co.uk

PETE R CLARK E SERIE S EDITO R

Containing printable: • Pupil activity booklets (Issues) • Teacher’s notes • Resource sheets It is envisaged that the activities in Stretch and Challenge will be used by either individuals or pairs of children. However, given the flexible nature of the resource, if appropriate, children can work in groups. The activities are intended to be used: • as additional work to be done once children have finished other set work • by those children who grasp concepts rapidly and need to be challenged through rich and sophisticated problems • as in-depth work that is to be undertaken over a prolonged period of time, such as during the course of several lessons, a week or a particular unit of work • as a resource for promoting mathematical reasoning and problem solving and developing independent thinking and learning • as a springboard for further investigations into mathematics based on the children’s suggestions.

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Introduction

The features of Stretch and Challenge Pupil activity booklets (Issues) • Each of the 36 Issues in Stretch and Challenge 5 consists of a four-page A5 pupil activity booklet (to be printed double sided onto one sheet of A4 paper). • The 36 Issues cover the different domains and attainment targets of the Mathematics National Curriculum Programme of Study (see pages 11–20). • The Issues have been designed to resemble a newspaper, with each of the Issues consisting of between five and eight different activities, all related to the same mathematical topic. • It is important to note that children are not expected to complete all the activities in an Issue nor work their way through an Issue from beginning to end. For many children not all of the activities offered in an Issue will be appropriate. When choosing which activities a child is to complete, teachers should ensure that the activities do not accelerate the child into mathematical content they may not be familiar with, or are unable to reason more deeply in order to develop a conceptual understanding. Rather, activities should be chosen on the basis that they engage the child in reasoning and the development of mathematical thinking, as well as enriching and deepening the child’s mathematical knowledge, skills and understanding. • The terms ‘Issue’ and ‘Volume’ have been used rather than ‘Unit’ and ‘Year group’ because they are in keeping with the newspaper theme. Types of activities • Each of the 36 Issues in Stretch and Challenge 5 are designed to deepen children’s mathematical knowledge, skills and understandings, and enhance their use and application of mathematics. There are four different types of ‘using and applying’ activities in the series: What’s the Problem?

The Puzzler

Looking for Patterns

Let’s Investigate

• Alongside developing children’s problem-solving skills, the series also provides activities with cross-curricular links to other subjects in the primary curriculum. The following shows the Stretch and Challenge features and its corresponding primary curriculum subject. Curriculum subject

Stretch and Challenge feature

English

The Language of Maths

Science

Focus on Science

Computing

Technology Today

Geography

Around the World

History

In the Past Famous Mathematicians

Art and design / Music

The Arts Roundup

Design and Technology

Construct

Physical Education

Sports Update

• As well as the features mentioned above, other regular features in Stretch and Challenge include: Money Matters

At Home (home–school link activities).

• A chart showing the link between the Issues, the Stretch and Challenge features and crosscurricular links can be found on pages 21 and 22. • Inquisitive ant is a recurring feature of the series. In each Issue there is an ant holding a mathematical word or symbol. Children locate the ant and write about the meaning of the word or symbol.

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Introduction Teacher’s notes Each of the 36 Issues includes a set of teacher’s notes, including answers. Issue 2 - Number

Issue 2

Prerequisites for learning Lists the prerequisites for learning that children need to have acquired prior to this Issue.

Mathematics topic

Number

Issue number

Resources

Prerequisites for learning

Resources

• Read Roman numerals to 1000 (M) and recognise years written in Roman numerals • Identify prime numbers • Understand square numbers, cube numbers and other powers • Explore number sequences, patterns and relationships • Use simple expressions and formulae in words and symbols

pencil and paper Resource sheet 2: My notes (optional) Resource sheet 3: Pupil self assessment booklet (optional) calculator computer with Internet access

To aid preparation, the resources needed for the Issue are listed. Teaching support

Teaching support Page 1

Provides teaching points for each of the activities in the Issue. These may be helpful when introducing the Issue to the children, or when children experience difficulty whilst working on a particular activity.

In the Past • Ask the children to write some calculations using Braille. In order to do this they will need to know the following:

Lists the associated knowledge and skills that contribute to understanding the Issue topic.

Page 2 Looking for Patterns • The order of the relative frequencies of letters in the English language is generally agreed upon to be as follows: e, t, a, o, i, n, s, h, r, d, l, c, m, w, f, g, y, p, b, v, k, j, x, q and z. • If necessary, tell the children that E followed by T are the two letters that appear most often in English language text. • Children use Morse code to send a message to a friend.

Simplifications

Almost all of the activities in Stretch and Challenge can be undertaken either individually or in pairs (or sometimes in small groups).

What’s the Problem? • The largest Roman numeral you can write using each symbol once only is quite simple: it is the seven Roman numerals written in descending order.

Where appropriate, offers suggestions for supporting children who may be experiencing difficulties understanding the main mathematical ideas.

Let’s Investigate • Children will probably need access to the Internet to ﬁnd out the meaning of a bar (overline) above a Roman numeral. If this is not possible tell the children the Hindu-Arabic equivalent of V (i.e. 5000) and X (10 000). Can they identify a pattern in order to correctly write the Hindu-Arabic equivalent for the three other Roman numerals? • Children write other numbers in Roman numerals using a bar (overline) above the numeral and give them to a friend to write the equivalent Hindu-Arabic numeral.

Where an activity is particularly suitable for pairs to work on, this is denoted by .

Extensions Where appropriate, offers suggestions for extending children’s understanding if you feel they are developing a good understanding of the main mathematical ideas.

When children are likely to need access to a computer, this is denoted by .

101

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AfL • What patterns / relationships do you notice? What conclusions can you draw? • Can you give me a rule to describe this? • Can you predict what the next number / the answer will be? What did you base your prediction on?

When children are likely to need access to a computer with Internet access, this is denoted by .

Assessment for Learning Each Issue includes a list of questions specifically designed to assist in assessing pupils’ understanding of the Issue topic. Issue 2 - Number

Answers

Page 4 Let’s Investigate The prime numbers to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Page 1

These are provided where appropriate.

There are eight twin primes to 100: 3 & 5; 5 & 7, 11 & 13; 17 & 19; 29 & 31; 41 & 43; 59 & 61; 71 & 73.

In the Past Braille message reads: ‘I can read Braille’. Messages and numbers will vary. Page 2

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Looking for Patterns Answers will vary. In general however, the greater the frequency 102 a letter is used in the English alphabet, the simpler the code for that letter. For example, the two letters that appear most often in English language text are E and T, and these have the simplest Morse identiﬁers: E (•) and T (—). Although not all of the vowels have the simplest of Morse identiﬁers, A, E and I each only have one or two symbols, i.e. A (• —); E (•); I (• •). What’s the Problem? I, V, X, L, C, D, and M MDCLXVI (1666) MCDXLIV (1444)

3 + 5 = 8; 5 + 7 = 12; 11 + 13 = 24; 17 + 19 = 36; 29 + 31 = 60; 41 + 43 = 84; 59 + 61 = 120; 71 + 73 = 144. With the exception of the ﬁrst twin primes (3 + 5 = 8), the sums of all the other twin primes are divisible by 12. 3 × 5 = 15; 5 × 7 = 35, 11 × 13 = 143; 17 × 19 = 323; 16/06/16 29 × 31 = 899; 41 × 43 = 1763; 59 × 61 = 3599; 71 × 73 = 5183. The product of each twin prime is one less than the square of the number that lies between the two numbers of the twin prime, i.e. 3 × 5 = 15 42 = 16 16 – 1 = 15 Let’s Investigate 3 For 3 =

V X XXV XLVI LXXXIII 5 10 25 46 83 A conventional Roman numeral with a bar (overline) above the numeral is multiplied by 1000. X 10 000

XXV 25 000

Let’s Investigate

V 5000

11:14 AM

XLVI 46 000

LXXXIII 83 000

Page 3 Looking for Patterns The next number in the sequence is the sum of the previous two numbers: 2, 5 , 7 , 12, 19 , 31, 50 , 81, 131 1 , 6, 7 , 13, 20 , 33 , 53, 86 , 139

7 6

For 4 = 4 For 5 = 5 For 6 = 6 For 7 =

7 9

1 3 For 8 =

8 4

1 2 For 9 = 9 For 10 = 0

3, 9 , 12, 21 , 33, 54 , 87, 141 , 228

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Introduction Class/Teacher:

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Stretch and Challenge 5 Record of completion

Resource sheet 1

THE

Maths

S&CCNPM Volume 5 Volume 1

TheHerald Maths Herald

Names

Name:

Date: Date:

Name:

Date of starting issue:

Number

Negative numbers

Addition

– Multiplication and division

Number: – Addition and subtraction

Multiplication

Mixed operations

Fractions

Decimals

Percentages

Fractions, decimals and percentages

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Resource sheet 2

Number: – Fractions (including decimals and percentages)

Subtraction

Division

– Multiplication and division

Number:

Number Number

My notes

Stretch and Challenge Issue

Number: – Number and place value

Topic

Number: – Addition and subtraction

Domain(s)

Date of finishing issue:

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Record of completion

To assist in keeping a record of which Issues children have completed. Once a child has completed an Issue you could either put a tick or write the date in the corresponding box.

THE

Maths

Name:

The pupil activity booklets have been designed to resemble a newspaper. This means that quite often there is insufficient space in the booklets for children to show their working and answers. You may decide to simply provide children with pencil and paper to record their work or an exercise book that they use as their ‘Stretch and Challenge Journal’. Alternatively, you could provide them with a copy of the A5 booklet: ‘My notes’ (to be printed doubled sided onto one sheet of A4 paper). This can then be kept, together with the child’s copy of the Issue and, if appropriate, their ‘Pupil self assessment booklet.’

S&CCNPM Volume 5 Volume 1

TheHerald Maths Herald

Date of starting issue:

My notes

Name:

Date: Date:

Date of finishing issue:

What have you learned?

Whichever method you choose for the children to record their working and answers, i.e. on sheets of paper, using a ‘My notes’ booklet, in an exercise book, or any other method, children need to be clear and systematic in their recording. What did you use to help you?

Resource sheet 11

Coordinates grids (0 to ±4) Resource sheet 3

1 –4 –3 –2 –1 0 –1

1 1

–2

Pupil self assessment booklet Each Resource Pack in the Stretch and Challenge series includes an age-appropriate pupil self assessment A5 booklet (to be printed double sided onto one sheet of A4 paper).

The booklet is designed to provide children with an opportunity to undertake some form of self assessment once they have completed the Issue. After the children have completed the booklet, discuss with them what they have written. This can then be kept, together with the child’s copy of the Issue and their working out and answers, including, if appropriate, ‘My notes’.

–3

–4

–2 –3

–4

1 1

–4 –3 –2 –1 0 –1 –2

–3

–4

Busy Ant Maths Stretch and Challenge 5

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–4 –3 –2 –1 0 –1

–3

–2

1 1

–2

–4 –3 –2 –1 0 –1

1 –4 –3 –2 –1 0 –1

–2

This booklet is a generic sheet that can be used for any, or all, of the 36 Issues in the Resource Pack.

–4 –3 –2 –1 0 –1

Other Resource sheets

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For some of the activities, children are required to use a specific Resource sheet. These are included both in the back of this Resource Pack and the online resources.

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Issue 21 - Volume and capacity

Issue 21

Volume and capacity Prerequisites for learning

Resources

• Read, choose, use and record standard metric units to estimate and measure volume/capacity to a suitable degree of accuracy • Understand and use approximate equivalences between metric units and common imperial units • Calculate mentally with integers and decimals • Use formal written methods to add, subtract, multiply and divide integers and decimals

pencil and paper Resource sheet 2: My notes (optional) Resource sheet 3: Pupil self assessment booklet (optional) Resource sheet 18: 1 cm squared paper Resource sheet 19: 2 cm squared paper ruler calculator scissors 1 litre bucket of water weighing equipment computer with Internet access

Teaching support Page 1 At Home • If children do not have a dishwasher at home, you may wish to discuss with them the amount of water that is used when washing dishes by hand. Hand washing dishes can be efficient if you use a bowl and watch how much water you use. However, daily hand washing of dishes typically uses about 63 litres. If dishes are rinsed off under a running tap the total water used can increase to 150 litres. • Children should count the number of times a day (or week) that their family does each of the actions on the list and add up the total amount of water used, using the figures given. • Once the children have completed the activity, ensure that there is an opportunity in class for pairs or groups of children to discuss their results. What’s the Problem? • Explain how to measure one litre of water with the children first, so that they see the method (see Answers). The Puzzler • Discuss with the children trial and improvement strategies for deciding which three or more capacities are likely to give one of the larger amounts.

Page 2 Construct • Ensure children understand what they are required to do for this activity. • Remind children that volume is the space actually occupied by an object or the bulk of some substance. In the case of the activity, it refers to the size of the three-dimensional space enclosed within the sides of each of the boxes. • Also remind the children of the formula for calculating the volume of a cuboid: length × width × height or l × w × h or lwh

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Issue 21 - Volume and capacity At Home • Once the children have completed the activity, ensure that there is an opportunity in class for pairs or groups of children to discuss their results. • Children investigate the cost of petrol and diesel in different countries in Europe. Which is more expensive in each of these countries, petrol or diesel?

Page 3 In the Past • Children investigate other systems for measuring volume and capacity from other civilisations, e.g. Ancient Egyptian. Let’s Investigate • Many children will probably already know that one litre of water has a mass of one kilogram. However, the important aspect of this activity is for them to design an experiment to prove it. In the Past • Children investigate other systems for measuring volume and capacity from other civilisations, e.g. Ancient Egyptian.

Page 4 In the Past • Children investigate other historical measurements for volume and capacity in England, e.g. Mouthful (about 12 ounce) Pony (2 mouthfuls or 1 ounce) Jigger (1·5 ounces) Jack or Jackpot (2 ounces) Pottle or Half Gallon (80 oz) Kenning or Pail (2 pecks or 4 gallons) Strike (2 bushels or 16 gallons) Coomb (2 strikes or 32 gallons) Cask (2 coombs or 64 gallons) Around the World • Children investigate the difference between the UK ton (‘long ton’ – 2240 pounds) and the US ton (‘short ton’ – 2000 pounds).

AfL • How do you calculate volume? What about for a different solid? • What calculations did you perform to work out that answer / approximation? • What can you tell me about how volume and capacity were measured by the Babylonians / Ancient Greeks? • What were the results of your experiment? What conclusions can you make? • What did your investigation discover? Why do you think this is? • What relationships can you see in the different measures? What are the similarities / differences? • How do the words used for some of the measures convey their meaning?

161

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Issue 21 - Volume and capacity

Answers

Page 3

Page 1

In the Past One sila is approximately equal to one litre. One sila was equal to 60 gin. One gin was equal to 180 she.

At Home Answers will vary.

Let’s Investigate True. 1 litre of water weighs 1 kg. 500 ml of water weighs 500 g.

What’s the Problem? 1 litre = Fill the 5-litre and the 3-litre buckets from the 9-litre bucket. 1-litre remains in the 9-litre bucket. 2-litres = Fill the 5-litre bucket. From this bucket ﬁll the 3-litre bucket. 2-litres remain in the 5-litre bucket. 3-litres = Fill the 3-litre bucket. 4-litres = Fill the 5-litre bucket from the 9-litre bucket. 4 litres remain in the 9-litre bucket. 5-litres = Fill the 5-litre bucket. 6-litres = Fill the 3-litre bucket from the 9-litre bucket. 6-litres remain in the 9-litre bucket. 7-litres = Fill the 5-litre bucket from the 9-litre bucket. 4-litres remain in the 9-litre bucket. Then, from the 5-litre bucket ﬁll the 3-litre bucket. Add the 3-litres to the 4-litres remaining in the 9-litre bucket to make 7-litres. 8-litres = Fill the 3-litre and 5-litre buckets from the 9-litre bucket. 9-litres = Fill the 9-litre bucket.

In the Past The cotyle or cotyla ranged from 210 ml to 330 ml (about the capacity of a cup or a can of drink). The choenix was about the volume of a man’s daily ration of grain. A wine amphora held 39 litres of wine.

The Puzzler a. 475 litres + 1538 litres – 1837 litres = 176 litres b. 1538 litres – 846 litres + 1837 litres = 2529 litres c. 2338 litres – 846 litres + 1837 litres – 475 litres = 2854 litres d. 2338 litres – 475 litres – 1538 litres + 846 litres = 1171 litres e. 846 litres + 1538 litres – 1837 litres + 2338 litres = 2885 litres Page 2 Construct Volume of the ﬁrst box is 1 cm × 8 cm × 8 cm = 64 cm3 Volume of the second box is 2 cm × 6 cm × 6 cm = 72 cm3 Volume of the third box is 3 cm × 4 cm × 4 cm = 48 cm3 Volume of fourth box is 4 cm × 2 cm × 2 cm = 16 cm3 So, the fourth box has the smallest volume. So, the second box has the greatest volume. At Home Answers will vary. Diesel is more expensive than petrol.

Page 4 In the Past 60 minims

1 ﬂuid drachm

8 ﬂuid drachms

1 ﬂuid ounce

20 ﬂuid ounces

1 pint

4 gills

1 pint

2 pints

1 quart

4 quarts

1 gallon

2 gallons

1 peck

4 pecks

1 bushel

8 bushels

1 quarter

36 bushels

1 chaldron

9 gallons

1 ﬁrkin

4 ﬁrkins

1 barrel

52 1 gallons

1 hogshead

26 2 ﬂuid ounces

1 bottle

2 3

Around the World gallon

pint

ﬂuid ounce

UK 8 UK pints or ≈ 4·55 litres 0·568 litre 1 UK pint or ≈ 28·41 ml 20

US 8 US pints or ≈ 3·79 litres 0·473 litre 1 US pint or ≈ 29·57 ml 16

Inquisitive ant

hectolitre Equal to 100 litres.

162

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Issue 22 - Time

Issue 22 Time Prerequisites for learning

Resources

• Solve problems involving converting between units of time • Use simple expressions and formulae in symbols • Calculate mentally with integers and decimals • Use formal written methods to add, subtract, multiply and divide integers and decimals

pencil and paper Resource sheet 2: My notes (optional) Resource sheet 3: Pupil self assessment booklet (optional) analogue clock with geared hands (optional) calculator map of the world showing time zones coloured pencils computer with Internet access

Teaching support Page 1 Around the World • Ensure children are familiar with the terms longitude, latitude and Greenwich Mean Time (GMT). • Referring to the time zone map, you may wish to discuss with the children that numbers written as +1, +2, +3 … refer to the number of hours ahead of GMT, and that numbers written as –1, –2, –3 … refer to the number of hours behind GMT. Around the World • Ensure the children are familiar with a 24-hour timeline. • This activity relies on children having completed the Around the World activity above, and realising the time difference between their current time zone and the current time zone in Sydney, Australia.

Page 2 Famous Mathematicians • Work through one child’s birthday so that the children understand how to use the tables.

Page 3 Let’s Investigate • This activity relies on children having completed the Famous Mathematicians activity on page 2. • When the children have completed this activity and the Famous Mathematicians activity on page 2, discuss with them which method (and why) they preferred for working out on which day of the week a person was born.

Page 4 Let’s Investigate • You may wish to ask the children to work out the ﬁrst ten DDMMYYYY palindromic dates in the 21st century (see Answers). What’s the Problem? • One method of working out this investigation is to time how long it takes to count 100 or 200 numbers and multiply up. Discuss with the children which numbers they should use for this method and why, e.g. the numbers 145 601 to 145 700 as opposed to 1 to 100.

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Issue 22 - Time At Home • Children can complete this activity just as effectively in school as at home. • If the children do undertake this activity at home, once they have completed the task, ensure that there is an opportunity in class for pairs or groups of children to discuss their results. What’s the Problem? • Assuming that Lisa’s great-grandma is 80 years old she could be 30 000 days old. 365 × 80 = 29 200 days (365 days a year) × (80 years old) • Assuming that Lisa’s great-grandma sleeps eight hours a day on average and that she is 80 years old, then she could have slept for over 200 000 hours during her lifetime. 8 × 365 × 80 = 233 600 hours (8 hours of sleep a day) × (365 days a year) × (80 years old).

AfL • Can you explain to me how the world’s time zones work? • How did you work out the answer to the problem / puzzle? Talk me through your calculation. How did you work that out? • Explain to me the formula for ﬁnding out on which day of the week a person was born. • How does this method for ﬁnding out on which day of the week a person was born differ from the formula devised by Carl Gauss? Which method do you think is best? Why?

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Issue 22 - Time

Answers Page 1 Around the World Answers will vary. Around the World Answers will vary. Page 2 Famous Mathematicians Answers will vary.

Page 4 Let’s Investigate There are 29 in total, the ﬁrst 10 are: 10 February 2001 (10022001) 20 February 2002 (20022002) 1 February 2010 (01022010) 11 February 2011 (11022011) 21 February 2012 (21022012) 2 February 2020 (02022020) 12 February 2021 (12022021) 22 February 2022 (22022022) 3 February 2030 (03022030) 13 February 2031 (13022031)

Page 3

What’s the Problem? Answers will vary.

Let’s Investigate Answers will vary.

At Home Answers will vary. What’s the Problem? Lisa’s great-grandma could almost be 30 000 days old if she is approximately 80 years old. She would have slept for more than 200 000 hours. Explanations and other ‘amazing facts’ will vary.

Inquisitive ant

CET Central European Time. CET is 1 hour ahead of Greenwich Mean Time (GMT).

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