is in transition

AND, you will soon be too!

Join the Maths Department as we explore Harry Potter’s world in transition.

Have a go at the questions, when you see the symbol

And, don’t fret if you get stuck – the world of magic canbe dauntingly challenging, but always exciting.

If you have any queries or would like to share/check your answers,send an email to Mrs Dixon (sdixon@wykhampark-aspirations.org).

This Transition Project has been adapted by Ms Richards and Mrs Dixon from materials created by Mathslover(http://www.boxedrockets.co.uk/blog/harry-potter-in-transition-add-a-bit-of-magic-to-your-year-6-transition/) –TES Website: https://www.tes.com/teaching-resource/maths-transition-project-harry-potter-in-transition-11318582. All images used are under Creative Commons Sharealike copyright.

Getting to Hogwarts …

A muggle overheard someone talking about the sign for

Platform 93

4, so this unfortunately now needs to be changed.

Think of three different ways to write this platform number?

Be creative, think about words, pictures, symbols, other fractions, decimals, additions, subtractions etc. that all equal 9 ¾.

For example, the new sign could read: Platform 10 - point 25

Which options are equivalent to this platform number?

Platform 81

2+ 1

1

4

Platform 9 ×3

4

Platform 39

4

Platform 27

4

Platform 9.75 Platform 9.34

Platform 6

8+ 9

Platform 32 +3

4

Platform 11 − 2 +1

4× 3Platform

1

4× 3 + 9

17 Knuts = 1 Sickle 29 Sickles = 1 Galleon.

How many Knuts are there in a Galleon?

Knut

SickleGalleon

Hagrid has asked the Goblins to exchange 1 Galleon for Knuts.

Imagine you are a Goblin at Gringotts Bank…..

1 Galleon = 29 Sickles

1 Galleon = 493 Knuts

1 Sickle = 17 Knuts

Work out how many Knutseach of Gringotts’ clients has in their vaults?

Hagrid’s Vault 82 Sickles

Lupin’s Vault 624 Sickles

Sirius Black’s Vault 100 Sickles + 50 Knuts

The Malfoy’s Vault 4 Galleons + 20 Knuts

Rita Skeeta’s Vault 8 Galleons + 8 Sickles

Olivander’s Vault82 Galleons + 47 Sickles + 1 Knut

Can you convert their money into Sickles and Galleons?

Snape has 4404 Knuts

Dumbledore has 8095 Knuts

1 Galleon = 29 Sickles

1 Galleon = 493 Knuts

1 Sickle = 17 Knuts

1. What is 3 Galleons in pounds sterling?

2. What is 20 Sickles in Danish Kroner?

3. What is 42 Knuts in Swiss Francs?

4. £1 = _______ Knuts

5. £1 = _______ Sickles (round your answer off to the nearest Sickle).

6. £100 = ______ Galleons (round your answer off to the nearest 10)

Wizard Challenge

Making Muggle money work for you

In order to buy your Hogwarts items in Diagon Alley, you must first change your Muggle money into Wizard money at Gringott’s bank.

Shopping List

Owl (12 Galleons)Nimbus 2000 (150 Galleons)

6 X bottles of butter beer (2 Sickles + 9 Knuts)Quill (8 Sickles + 12 Knuts)

How much will these items cost in Muggle money?

The Time-Turner is a device used by Hermione Grainger. This device is used for time travel, which allows a wizard or witch to fit a lot more into their already very busy day!

The number of times one turns the hourglass corresponds to the number of hours one travels back in time.

Can you put these times in order: shortest time to longest time?

3 hours92mins

6000 seconds

2 minutes

2.6 hours150 minutes

23

4hours

600 seconds2hr 20mins

125 minutes

1.5 hours

What are your Time-Turner skills?

Can you help Hermione?

One turn on the time-turner moves her forward or back 1 hour. Can you work out what time she is on in each case?

Harry has borrowed the Time-Turner. Help him to complete his morning plan, using the device when necessary

(he isn’t as good at Hermione at using it!)Harry gets up at 8am.

He needs to allow 15min between activities to get to each venue.When he uses the Time-Turner, he does this after an activity.

Time Activity Time turner?

8:00 Wake-up Back 30min

7:30 Wash & Get ready (15min) Not used

8:00 – 8:30 Breakfast (30min) Forward 15min

9:00 – 10:30 Quidditch (1hr30min)

10:00 – 11:00 Potions Lesson (1hr)

11:00 - _____ Herbology Lesson (45min)

12:00 - _____ Charms Lesson (1hr15min)

_____ - _____ Reading the Quibbler (30min)

13:00 – 13:30 Lunch (30min) Not used

It’s a matter of time!

Question A:Ron has to catch the Hogwarts Express at 10:25am. It takes him 20 minutes to shower, ¾ hour to pack, 10 minutes to have his breakfast and 2 minutes to travel by floo powder to the station. What is the latest time he can roll out of his bed?

Question B:The Weasley’s car travels at 60 miles per hour. Hogwarts School is approximately 300 miles from London – How long will it take them to drive to the school? The Nightbus travel at 200 miles per hour – how much faster would it be to go by nightbus?

Ingredients are listed, but even if Muggles would gather and brew the correct herbs, insects, and other materials (some of which are poisonous), they would not be able to create the potions listed here.

The most important ingredient to any magic is the magical power of the wizard creating the effect.

Don’t try this at home!

Imagine you are a student in Snape’s Potions class…..

Potions WARNING!

Forgetfulness Potion(Makes enough for 5 people)

10 tablespoons of powdered Griffin claw2.5 tablespoons of Salamander blood

30 rat tails

Make an ingredient list for:

a) 10 people b) 1 personc) 3 people

Can you do any of these calculations in your head?

Shrinking PotionIngredients:

5 chopped daisy roots, 3 skinned shrivel fig1 sliced caterpillar

one rat spleendash of leech juice(Makes 2 Doses)

1. If Ron only has 20 daisy roots, how many people can he make the potion for?

2. Ron wants to buy exactly the right number of daisy roots and shrivel figs. The daisy roots are bought in packs of 10 and the shrivel figs in packs of 2. What is the minimum number of doses Ron can make?

Wit-Sharpening PotionIngredients:

40 ground Scarab beetles2 tablespoons Armadillo bile

1 ginger root20g of Knotgrass(Makes 10 doses)

Hi I’m Dobby. Dobby is a free

house-elf.Dobby has come to chat about worded

problems

PROBLEM 1

A packet of Bertie Botts beans contains 560 sweets. Dobby shares them between himself and 3 other friends. How many do

they each get?

PROBLEM 2

Harry has 36 boxes of 6 Quidditch balls. He shares the balls between himself and 2 friends. How many Quidditch balls do they each get?

PROBLEM 3

There are 1550ml of butter beer in a large glass. Ron accidentally spills 275ml. He then shares the rest of the butter beer

between 5 friends. How much butter beer do they each get?

PROBLEM 4

There are 7 chocolate frogs in a pack. Hagrid has 35 packs. He shares them

between 5 friends. How many chocolate frogs do they get each?

PROBLEM 5

Hermione has read 456 books. During the

first term she reads 282 more books. How

many has she read altogether?

The Negative Cauldron

… with Severus Snape

(Professor of Potions)

When carrying out our work in protecting

against the dark arts, the temperature of the

cauldron is essential!

For this reason, when preparing the cauldron for a spell, we will use traditional fire cubes

and ice cubes.

Even Potter would know that when adding a single ice cube to a

cauldron, it will lower the temperature of the cauldron by one

degree...

And of course, when adding a fire cube...

...the temperature will increase by one degree.

And of course a fire cube is worth

positive one

Mathematically speaking – if you

must – an ice cube is worth negative one

Imagine, if you will, that our cauldron begins at the

temperature of 10 degrees.

What will happen if I add4 fire cubes and then add 6

ice cubes?

10℃

10 + (+4) + (–6) = 810 + 4 – 6 = 8

What would happen if I now add 10 more ice

cubes?

8 + (–10) = -28 – 10 = -2

Add Fire CubesWarmerAdding

Add Ice CubesCooler

Subtracting

Add Ice CubesCooler

Subtracting

What will the cauldron’s temperature be in each situation?

1. Original temperature of cauldron is 𝟏𝟐℃.Fifteen ice cubes are added.

2. Original temperature of cauldron is 𝟏𝟐℃.Eight fire cubes are added.

3. Original temperature of cauldron is −𝟑℃.Seven ice cubes are added.

4. Original temperature of cauldron is −𝟑℃.Five fire cubes are added.

5. Original temperature of cauldron is 𝟐℃.Four ice cubes are added and six fire cubes are added.

Imagine, if you will, that our cauldron begins at the temperature of 10

degrees.

What will happen if I subtract5 fire cubes?

10℃

10 – (+5) = 510 – 5 = 5

What would happen if I now subtract 10 more

ice cubes?

8 - (–10) = 188 + 10 = 18

Remove Fire Cubes … Cooler

Subtracting

Remove Ice Cubes … WarmerAdding

What will the cauldron’s temperature be in each situation?

1. Original temperature of cauldron is 𝟏𝟐℃.Fifteen ice cubes are subtracted.

2. Original temperature of cauldron is 𝟏𝟐℃.Eight fire cubes are subtracted.

3. Original temperature of cauldron is −𝟑℃.Seven ice cubes are subtracted.

4. Original temperature of cauldron is −𝟑℃.Five fire cubes are subtracted.

5. Original temperature of cauldron is 𝟐℃.Four ice cubes are subtracted and six fire cubes are subtracted.

Calculating Probabilities

We are going to learn how to calculate the probability of an event happening.

Harry has a coin. He tosses it.

There are two likely outcomes: heads or tails.

The probability of getting a tail is 1 out of 2. We write Probability (tail) = ½ or P(tail) = ½

Probability Scale

You can mark probability of an outcome

happening on a probability scale

Impossible unlikely even chance likely certain

0 ¼ ½ ¾ 1

Something that definitely won’t happen has a

probability of 0 and something that definitely will

happen has a probability of 1.

0 ¼ ½ ¾ 1

Lets mark the following outcomes on the scale:

1. Boris Johnson will be an extra in the next Harry Potter movie.

2. If they brought out another movie, no-one would watch it.

3. There is a person in Britain called Ronald Weasley

4. Harry tosses a coin and it lands heads up.

5. Someone at your school has watched all the Harry Potter films.

6. Someone in this classroom has not read any of the Harry Potter books.

The sorting hat is trying to decide which house at Hogwarts to put someone in.

The 4 possible, equally likely, outcomes are:

Gryffindor Ravenclaw Slytherin Hufflepuff

What is the probability that a new pupil will be placed in Ravenclaw?

What is the probability that a new pupil will be placed in EITHER Ravenclaw OR Hufflepuff?

The letters of the name HERMIONE are placed in a hat.

What is the probability that the letter H will be pulled out of the hat?

What is the probability that the letter E will be pulled out?

Probability of something happening and nothappening

Ron has a packet of Bertie Botts Every Flavour beans. In his packet he has 5 sweets left: strawberry, apple, chocolate, pepper and a chilli flavour sweet.

Ron chooses a sweet at random. What is the probability that he will choose a chilli sweet?

• What is the probability that Ron will choose a sweet which is not a chilli flavour?

In order to cast spells we need to know how to

expand brackets

Here are 8 of my spells …

Colovaria (Colour Change Charm; Sunshine, daisies, butter mellow, Turn this stupid, fat rat yellow)

Expecto Patronum (Patronus Charm) Imperio (Imperius Curse; used on Bogrod the goblin; Lumos

(Wand-Lighting Charm) Petrificus Totalus (Full Body-Bind Curse) Reducto (Reductor Curse) Riddikulus (Boggart Banishing Spell) Slugulus Eructo (Slug-vomiting Charm;

Ron was able to cast this non verbally with a broken wand)

Wingardium Leviosa (Levitation Charm)

Weasley’s Warm ups…

Colovaria spell: 2(3 + 2) = 6 + 4 = 10

Expecto Patronum spell: 3(5 - 1) = 15 – 3 = 12

Imperio spell: 3(2 + 2) = 6 + 6 = 12

Petrificus Totalus spell: 7(9 – 5) = 63 – 35 = 28

Look carefully at how Ron did his warm-up exercise.

Hagrid’s Have-a-go…

Expand the following brackets.

Reducto: 3(a + 2) = _______

Riddikulus: 2(a – 3) = _______

Slugulus Eructo: 5(3 + a) = _______

Wingardium Leviosa: 4(4 - a) = _______

The Centaur’s Challenge!

These are the spells I don’t know yet – can you work them out by expanding and come up with a name

2(3 + 2a) =

4(2a + 1) =

5(b – a) =

2(4a – b) =

Harry and his friends often get into lots of trouble at Hogwarts – lets see if you can help them to solve a few of their problems!

In the following questions, 𝒂 = 𝟓, 𝒃 = 𝟏𝟐 and 𝒄 = 𝟑.

1. Ron has left his charms homework a bit late, and can’t remember what page the questions were on! He remembers the page number was equal to 2(𝑏 + 1). Can you work out what page number it was?

2. Hagrid has lost his herd of Hippogriffs in the forbidden forest! He went to look for them, but couldn’t remember how many he started off with. He thinks the number was around 25 + (𝑎 + 𝑐). How many hippogriffs would this be?

3. Hermione answered so many questions in one day that she couldn’t even count them! She answered (𝑏 − 2)2 questions. How many questions was this?

Hogwarts Homework

Time for Potions Class again!

a = squirmy snailb = niggly newtc = juicy bugd = butterfly wing

Answer the questions to work out how many of each ingredient your potion needs.

a(2+1) = 3a …. So, 3 squirmy snails3(a+2b) = _____________________3(4d) = _____________________2(3b+2c) = _____________________

A large bag of money was stolen from Hogwarts late last night.

The only clue is a dirty hand print left on the door of the Hidden Chamber (only a few people know about this).

Can you solve the crime?

What do we know?

* money was stolen* a handprint of the robber was found* finger prints are unusable* CCTV was turned off at the time of the crime.

So, we only have the outstretched handprint (handspan) to go on.

Handspan = 20.5cm

What if you knew that a person's height was 8 times as big as their handspan?

Or that their shoulders are twice as wide as their handspan?

Five people were spotted around the scene of the crime at the time of the incident. Based on your calculations, who do you think is the most likely culprit?

Height: 166cmWidth: 41cm

Height: 185cmWidth: 34cm

Height: 154cmWidth: 32cm

Height: 133cmWidth: 41cm

Height: 126cmWidth: 39cm

Tom Riddle

BellatrixLestrange

VoldemortLuciusMalfoy

DoloresUmbridge

Horcrux Hunt

A Horcrux is a normal object that Dark Wizards hide part of their souls inside. They must be destroyed in order to be able to kill the Dark Wizards.

You are going to go on a Horcrux Hunt! You must solve a question to destroy the Horcrux, and the use the answer to find the next clue.

Record both the object that the horcrux was hidden in and the numerical answer to the question

Horcrux Hunt Rules

• No calculators allowed!• Work out the answer to the first Clue Card. Write down this

number.• Use this number to find the next Clue Card.• Work out the answer to this Clue Card. Write down this number.• Repeat the process until you’ve looked at each clue card.• Consult the list of classroom objects and use your answers to

identify the horcrux objects.

Horcruxhunt clue!

? To the next clue

Magic Maths!

Think of a number,Double it,

Add 6.Halve it.

Take away your first number.What is left?

46

Previous Answer

Horcruxhunt clue!

? To the next clue

Time-Turner

If Harry uses the time-turner to take him from 10am back to

8:30am,How many turns will he need

(1 hour = 1 turn)

3Previous Answer

To the next clue

Previous Answer

Horcruxhunt clue!

?

Sorting Hat!

There are 184 new first years to be sorted equally

into the four houses.

How many will be in each house?

35Horcrux

hunt clue!

? To the next clue

Magical Numbers

A palindromic number, is a number that is the same number whether written

forwards or backwards. Eg. 535 or 222.

How many palindromic numbers are there between 100 and

150?

2

Previous Answer

Horcruxhunt clue!

?

Previous Answer

To the next clue

Wizard Money!

There are 17 Sickles in a Galleon.

9

Ron has 34 Sickles, how many Galleons is this?

Horcruxhunt clue!

?

Previous Answer

To the next clue

How many wands will be in the next pattern (fig 4) ?

1.5

Wands

Horcruxhunt clue!

? To the next clue

30 young Wizards and Witches take Herbology in their first

year.

2/3 of the class have bought the correct textbook.

How many students have not brought the correct textbook

32

Previous Answer

Herbology

48

Previous Answer

Horcruxhunt clue!

? To the next clue

(for 8 people)

7 Cheetah’s Spots4 wings of a golden snitch10 Spoons of a tidal wave

How many cheetahs spots will Ron need to make enough for 40

people?

Super Speed Potion

Horcruxhunt clue!

?

Previous Answer

To the next clue

More Quills

10

As she is working hard, Hermoine finds a spell that multiplies all of her quills by 700. She completes the spell

and ends up with 13,300 quills?

How many quills did she start with?

Horcruxhunt clue!

? To the next clue

A game of quidditch between Ravenclaw and Hufflepuff is currently

halfway through!

The scoreboard says:Ravenclaw 90 points

Hufflepuff 170 points.

How many more goals have hufflepuffscored than Ravenclaw?

Hint: A goal is worth 10 points in a game of Quidditch.

19

Previous Answer

Quidditch

Horcruxhunt clue!

?

Previous Answer

To the next clue

Winning the cup!

So far the scores for the house cup are as follows:

Ravenclaw: 670 points Slytherin 470 points

Hufflepuff 863 pointsGryffinder 426 points

If Gryffindor gain 92 more points for bravery, how many

more points will they have than Slytherin?

8Horcrux

hunt clue!

?

Previous Answer

To the next clue

Flying Potion!(for 5 people)

5

3 Dragon eyelashes2 teaspoons of unicorn blood8 feathers

How many feathers will Harry need to make the potion for 20 people?

1.5 = compasses3 = cuboid6 = hexagonal prism46 = cube9 = cone2 = triangular-based pyramid5 = square-based pyramid12 = calculator11 = projector10 = protractor32 = cylinder4.2 = whiteboard19 = pair of compasses8 = graph paper4 = teacher’s desk48 = isometric paper35 = ruler

HERCRUX HUNT SHEETWhich classroom objects have Dark Wizards hidden their souls in?

Thank you for joining us on this ‘transition journey.’

If you have any questions/concerns mathematically-speaking, please contact Mrs Dixon: sdixon@wykhampark-aspirations.org.

(and you) have transitioned!

We look forward to meeting you in September and joining you on your next learning voyage ~ Y7 Maths Teachers.