J u l y 2 0 1 5 m e i . o r g . u k I s s u e 4 8

Click here for the MEI

Maths Item of the Month

Disclaimer: This magazine provides links to other Internet sites for the convenience of users. MEI is not responsible for the availability or content of these

external sites, nor does MEI endorse or guarantee the products, services, or information described or offered at these other Internet sites.

Curriculum Update

GCSE

Ofqual has announced the publication of revised GCSE maths sample assessment materials by AQA, OCR, Pearson and WJEC Eduqas.

Commenting on the announcement, Glenys Stacey, Chief Regulator, said:

“The new sample papers are now judged to be very similar, in terms of expected difficulty, and also likely to differentiate across the full range of students. They meet our requirements.

We appreciate that teachers will want to choose a specification that best suits their students and the way that they teach, with the assurance that, whichever board they choose, standards will be comparable when students sit their exams in 2017 and beyond.”

You can read more in the Ofqual press

release.

M4 is edited by Sue Owen, MEI’s Marketing Manager.

We’d love your feedback & suggestions!

End of term update

We have a different format of M4

magazine this month as we know that

the end of the term is nigh!

We recently held our annual

conference and wanted to share some

of it with you, especially if you were

unable to attend, so on the next page

you’ll find a few photos from the three-

day event, and an adapted version of

the Delegate Challenge for you to use

with students (or to try yourself!). This

was devised by Carol Knights, the MEI

Extension and Enrichment Coordinator.

The original activity, targeted at

teachers, included QR codes for

participants to scan to find more

information related to the questions.

The QR codes (and resources) were

available on each of the exhibition

stands on the Friday of the conference.

Overall winner of the Delegate

Challenge was a team from Peter

Symonds College, with Howard Fay

coming a very respectable second. The

winning team shared a prize of two

Dynakars to add to their existing one!

You can see

the Dynakar

in action on

YouTube.

Howard was presented

with a prize of a Casio

Edifice men’s watch by

Tatiana Bowskill,

Education Project

Manager of Casio UK.

We also

awarded

other

prizes:

some

delegates

spotted a gold label on a leaflet in their

delegate bag, which won them a prize

from that organisation.

In this issue

Curriculum Update: New GCSE

specimen assessments available

on exam boards’ websites

July focus: End of term update

KS3-KS5 Teaching Resource:

Summer Challenge

Delegate ideas

Delegate Ideas

We asked MEI Conference Delegates

to share what ideas they would take

away from the conference and share

with their colleagues back at their

school/college. The response to this

was great: some delegates Tweeted

their #MEIConf2015 #Ideas (follow the

link to read these), while others wrote

their ideas onto sheets and pinned

them onto a

noticeboard.

We will put all

of these ideas

together onto a

document and

upload these to

our MEI

Conference

2015 archive,

where in due

course some of our session resources

will also be uploaded.

You can read more about

the conference by

searching for

#MEIConf2015 on Twitter.

MEI Conference 2015

New end of term

resource

The final teaching and

learning resource of

the academic year is

a replica of the

delegate challenge

from MEI’s Annual

Conference.

There are 15

challenges, presented

in approximate order

of difficulty, for you

and your students to

enjoy. You should

find some questions

are suitable for KS3

students whilst others

will challenge A level

students.

Some hints are

provided after the

relevant question and

all answers are given

in the teacher notes

at the end of the

resource.

The PowerPoint

version of the

resource can be

downloaded from the

Monthly Maths web

page - you can then

remove the teacher

notes and solutions

before sharing it with

your students!

Have fun! M4 Magazine will return next term, when it will change to a half-termly issue.

Challenge 1 Arrange all the digits 1 to 9, using

them once each only, to form a

fraction equivalent to 1/3

Challenge 1 Hint What could the 2 numbers end in?

What could the first digit of the

bottom number be?

Challenge 2

A handywoman is going to fix numbers onto

bedroom doors in a very large hotel. The

numbers are supplied as individual digits.

There are 1000 rooms, how many 7’s does she

need?

Challenge 3

Why is the number 8,549,176,320 special?

Challenge 4

What are the smallest integer values of A, B and

C such that the product of any two of the values

added to the third gives a square number?

Challenge 5

Find the three 4 digit numbers that equal the

square of the sum of the two 2-digit numbers

formed from the 1st and 2nd digits and 3rd and

4th digits.

e.g. one that doesn’t work:

1546 ≠ (15+46)2

Challenge 5 Hint

Can you use a spreadsheet to help you find

them?

Challenge 6

.-- .... .- - -.. --- -.-- --- ..-

--. . - .. ..-. -.-- --- ..-

-- ..- .-.. - .. .--. .-.. -.--

... .. -..- -... -.-- -. .. -. .

Help here

Challenge 7

A set of 15 dominoes (all combinations of 1 to 5)

is placed on a square grid as shown – except that

the outlines haven’t

been given…

What number is on the

other half of the domino

with the ‘1’ highlighted?

2 2 3 5 4 3

2 1 3 2 5 4

4 1 5 5 3 4

3 3 2 2 4 1

4 5 1 5 1 1

Challenge 7 Hints

What are all the possible dominoes?

Are there any dominoes

that have to be in a

certain place?

2 2 3 5 4 3

2 1 3 2 5 4

4 1 5 5 3 4

3 3 2 2 4 1

4 5 1 5 1 1

Challenge 8

Cherries are naturally 80% water.

Dried cherries are made by leaving them in the

sun until they have lost 75% of their water.

What is the percentage water content

of dried cherries?

Challenge 9 Mia uses an escalator at a railway station.

If she runs up 8 steps of the escalator, then it

takes her 55 seconds to reach the top. If she runs

up 15 steps of the escalator, it takes her 37.5

seconds to reach the top.

How many seconds would it take

Mia to reach the top if she did not

run up any steps at all?

Challenge 10

Each side of the triangle ABC is divided into 5

equal parts.

What is the ratio of the area of the blue triangle to

the area of ABC?

A

B

C

Challenge 10 Hints

A

B

C

A

B

C

Challenge 11

A boat carries rocks on a small, still lake making

the depth of water in the lake D.

The rocks are released and sink to the bottom of

the lake.

Is the level of water in the lake now greater than,

less than or the same as D?

Challenge 11 Hint

Think about a small marble made of gargantuan –

a (fictitious) metal which is 1000 times as ‘heavy’

as lead.

Challenge 12

A large number of sweets need to be eaten.

Eating alone, it takes Hannah an hour to eat a jar

of them, Mike 3 hours, Nat 5 hours and Oscar 7

hours.

Eating together, how long, to the nearest

minute, does it take them to eat their

way through 3 jars of sweets?

Challenge 12 Hints

In 15 hours, Mike will have eaten 5 jars and Nat

will have eaten 3 jars.

Can you find a whole number of hours in which

they will all have eaten full amounts of jars?

Challenge 13

A symmetrical yellow crescent is formed from two

circles as shown with O being the centre of the

larger circle.

AB = 5cm and CD = 9cm

What are the diameters of

the two circles?

Challenge 14

The circumference of a circle is divided into n

equal arcs and semi-circles constructed as

shown.

Can the blue shapes at the edge ever be equal in

area to the orange petals?

If so, what should n be?

Challenge 14 Hint

Try looking at just one blue shape and orange

petal.

Challenge 15

What is the internal side length of the smallest

hollow cube which can wholly contain 4 identical

spherical chocolates, each of diameter 10cm?

Challenge 15 Hint

Think about how the chocolates could be

arranged. Some ping pong balls or tennis balls

might be helpful.

Teacher notes: Summer Challenge The final edition of the academic year is a replica of the delegate

challenge from MEI’s Annual Conference.

There are 15 challenges, presented in approximate order of difficulty,

for you and your students to enjoy. You should find some questions

are suitable for KS3 students whilst others will challenge A level

students.

Some hints are provided after the relevant question and all answers are

given in the teacher notes below.

Enjoy!

Teacher notes: Summer Challenge Challenge 1

Challenge 2 300

Challenge 3 All the digits are in alphabetical order

Challenge 4 1, 7 and 9

5832 or 5823

17496 17469

Teacher notes: Summer Challenge

Challenge 5 2025 3025 9801

Sample spreadsheet columns below, searching for zero values in

column G.

For this solution it helps to work ‘backwards’ through the problem.

Start with a number (A) and square it (B), split the square numbers into

first pair and second pair (C leading to D&E), add them together (F),

compare with original number (G).

A B C D E F G

44 1936 19.36 19 36 55 11

45 2025 20.25 20 25 45 0

n n^2 B/100 int( C ) (C-D)*100 D+E F-A

Teacher notes: Summer Challenge Challenge 6 What do you get if you multiply six by nine? 54

Challenge 7 4.

Challenge 8 50%

Challenge 9 75 seconds

Challenge 10 8:25 look for triangles of equal base and height.

Challenge 11 Less than D.

When the rocks are in the boat, the mass of water displaced is equal to

the mass of the rocks, when in the water, the volume of water displaced

is equal to the volume of the rocks.

Since the rocks sink, their density is greater than 1, hence more water

is displaced when the rocks are in the boat than when they are in the

water.

Teacher notes: Summer Challenge Challenge 12 1 hour and 47 minutes

Find the lowest common multiple of the number of hours for each

person to eat a jar.

In 105 hours, Hannah eats 105 jars, Mike 35, Nat 21 and Oscar 15.

That’s 176 jars between them.

176 jars in 105 hours (6300 minutes), so use proportional reasoning to

find how long it takes to eat 3 jars.

Challenge 13 50cm and 41 cm

Teacher notes: Summer Challenge Challenge 14 8

Consider the circle to have a radius of 2r, then the

area of the circle is 4πr2

Looking at a single sector and ‘petal’,

blue area=orange area

only if

area of sector = area of semicircle

Area of semicircle is 0.5πr2

Area of sector = 0.5πr2

when there are 8 sectors

Teacher notes: Summer Challenge Challenge 15 10+5√2 or an equivalent expression

The chocolates should be arranged as a tetrahedron with each

chocolate nestling in a vertex. This means that 2 chocolates will sit

diagonally at the bottom of the box and 2 at the top. Use this 2d

diagram to calculate the size of the square.