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CHALLENGING TASK

WHERE THE WILD THINGS ARE

PRIME NUMBER: VOLUME 33, NUMBER 1. 2018

© The Mathematical Association of Victoria

16

This challenging task has been developed

using the much loved Maurice Sendak

children’s book, Where The Wild Things

Are. This text has been chosen for several

reasons: it is highly engaging for students

of all ages; the story lends itself to a maths

task focused on time and ratios; and,

importantly for us teachers, the book is

readily available in school classrooms and

libraries (as well as read-aloud versions

online).

As suggested by Sullivan et al (2014),

challenging tasks can be an eective

learning tool as they help students ‘build

connections between a network of ideas’

and develop the ‘conﬁdence... to devise

solutions to problems’ by engaging with

‘mathematical tasks that are complex’ (p

124). Furthermore, children’s literature can

help support the learning of mathematical

concepts by helping to contextualise the

maths, promote mathematical reasoning

and engage students (Muir et al., 2017).

THE TASK

The idea for this task stems from my own

childhood curiosity about Max, the story’s

protagonist, and his trip to The Land of

The Wild Things. I couldn’t fathom how,

upon returning from what seemed like

years in the mysterious and wondrous Land

of the Wild Things, Max’s dinner was still

hot! This was the ﬁrst time I had considered

alternative realities and the idea that time

could be relative. How much more quickly

did time pass in the Land of the Wild

Things than it did in the real world? This

key question forms the basis of this task.

Having read the book to my 5/6 class,

I explained that we would be exploring

a mathematical problem about Max.

My students are familiar with my use of

literature as a tool to launch maths tasks

and one enthusiastically stated ‘I bet we will

be looking at how quickly time passes when

Max is away compared to at home!’

In order to explore the relative speed

that time passes in the two worlds, it is

ﬁrst necessary to work out how long Max

spends away and, then, how much time

passed at home. For this investigation it is

necessary to guide students to establish

the following time periods to ensure the

maths is workable (although, coincidentally

my class stated the exact numbers I was

looking for!).

For a digital presentation to guide you

through this part of the task, go to:

bit.ly/wildmaths.

TIME IN THE LAND OF

THE WILD THINGS

Initially, I asked my students to consider

‘How long did Max spend in the Land of

the Wild Things’, by analysing the following

sections of text:

And an ocean tumbled by with a private

boat for Max

and he sailed o through night and day

and in and out of weeks

and almost over a year

to where the wild things are.

We concluded 365 days (‘almost over

a year’) to get to the Land of The Wild

Things.

But Max stepped into his private boat

and waved goodbye

and sailed back over a year

and in and out of weeks

and through a day

SUGGESTION: AN ALTERNATIVE

TASK FOR YOUNGER STUDENTS

An exploration of how much time

Max spent away and how much time

passed at home (without the more

complex ratio task) could be posed as

a challenging task for younger students

(e.g., Year 2). This would draw attention

to the relationship between dierent

units measuring time (i.e., day, week,

year), highlight how mathematical

problems are often embedded within

text, and provide students with a

relatively dicult multi-digit addition

and subtraction task.

Toby Russo, Bell Primary School

We concluded that this period was equal

to one year + two weeks + one day, PLUS

ﬁve days staying at the Land of The Wild

Things or 385 days. Students calculated

this total amount as the ﬁrst part of the

problem.

This makes a total of 750 days (365 + 385).

TIME AT HOME

I then asked my students to consider ‘How

much time do you think passed at home?’,

looking at this section of the text:

Where he found his supper waiting for him

and it was still hot.

Student A: Well his dinner was still hot, so it

couldn’t have been all that long.

Student B: I reckon about ﬁve minutes, no

longer than that.

We agreed that 5 minutes had passed.

POSING THE PROBLEM: HOW

MUCH TIME HAD PASSED?

• In the Land of The Wild Things: 365

days PLUS one year + two weeks +

one day + ﬁve days

• At home: 5 minutes

The above information was recorded for

the students and the following problems

were posed:

Problem

Using this information, how much time

passes in the Land of the Wild Things,

compared with one minute in the real

world?

Extending prompt

Max went to sleep, after eating his supper,

at 9pm and woke up at 6.30am. He then

went straight back to the Land of the Wild

Things. How much time has passed there?

The next time Max returned it was four

years later, at age 12. How much time had

passed now?

Enabling prompt

If 750 days passed in the The Land of

the Wild Things compared with only ﬁve

minutes in Max’s world, how can we work

PRIME NUMBER: VOLUME 33, NUMBER 1. 2018

© The Mathematical Association of Victoria

17

out how many days passed during one

minute in Max’s world? What operation

would help you solve this problem?

SOLVING THE PROBLEM

Students worked in pairs or independently

to tackle the problem. Generally students

found the ﬁrst part of the problem straight

forward: applying their knowledge of

the length of a year and week, as well as

addition and subtraction to determine the

total time in The Land of the Wild Things

(750 days). Some solved this problem

mentally, while others recorded their

process (see Figures 1 and 2).

The next stage of the problem was to

determine the relative time that had passed

at home (5 minutes) compared with The

Land of the Wild Things (750 days). Most

students immediately recognised the need

to use division (750 ÷ 5) to solve the ratio

of 1 minute = 150 days, although some

required peer or teacher guidance (through

the enabling prompt).

The majority of students attempted the

extension problems, making dierent levels

of progress. For example, one student

used the ratio (150 days : 1 minute) to

determine that one hour in Max’s world

was the equivalent to 9000 days. Using

a table to organise their working out, she

extrapolated this amount to determine

9.5 hours (the time he was asleep) was the

equivalent to 85,500 days or 234.24 years

(see Figures 3 and 4). It should be noted

that this student initially made an error in

the total amount of days passed by a factor

of 10, until this was highlighted by a peer.

Another student took an alternative

approach, solving the length of time Max

was asleep as 9.5 hours or 570 minutes

and multiplying this by 150 days to solve

the total number of days passed (85,500).

They then divided this number by 365 to

get 234.2 years (see Figure 5).

A number of students found the extension

problem challenging and worked through

it as part of a teacher-focus group. In order

to elicit their thinking, I asked ‘How many

hours was Max asleep for?’ Students used

dierent techniques to determine the

amount of time lapsed between 9pm and

6.30am, including mental processes (‘Well

there’s three hours until midnight and then six

and a half more hours, which makes nine and

a half hours’) while others drew a timeline.

Once we established he was asleep for

9.5 hours, we revisited what we already

knew from the ﬁrst problem: one minute in

Max’s World is 150 days. I asked the group

‘How will we work out how much time has

passed in The Land of The Wild Things’

and a student responded ‘First we need to

work out how many minutes nine and half

hours is. Then we times it by 150 to work

out how many days all up’. Students were

able to multiply 9.5 by 60 independently

(either by using the distributive property,

partitioning 9 x 60 and 0.5 x 60 and

then adding the products, or by using an

algorithm) to determine the total minutes

Max was asleep as 570 minutes. I asked,

‘If one minute for Max is 150 days for

The Wild Things, then 570 minutes is…?’

Students realised they needed to multiply

570 by 150 to work out how many days had

Figures 1 and 2: Varied approaches to solving

the ﬁrst part of the problem.

passed. Some students were comfortable

attempting this problem using an algorithm

(one student stated ‘We can do 57 x 15 and

then add two zeroes to our answer’) and

others elected to use a calculator and could

verify their peers answer: 85,500 days had

passed for The Wild Things!

I asked my group, ‘So we know the number

of days, how do we work out the number of

years that have passed?’ One students was

quick to suggest ‘We can divide the days

by 365 because there are 365 days in a year.’

Using calculators, the group determined

that it was 234.25 years! The students were

amazed at how much time had passed for

the Wild Things and were concerned that

some of Max’s friends were still around to

play with him. I reassured them they live for

a very long time!

Finally, we then discussed what a quarter

of a year was and worked out it was about

91 days - one student even suggested that

we should consider leap years (an extra day

every 4 years), which gives a more precise

answer of 234 years and 33 days!

A small group of students attempted the

second extension problem: The next time

Max returned it was four years later, at

age 12. How much time had passed now?

Another prompt was provided to support

students: How many minutes passed in

Max’s world over four years? Most students

understood the process and attempted to

work out how many minutes in Max’s life

across four years. Once they established

this, they returned to the ratio of 1 minute:

150 days. However due to the sheer size

of the numbers and the challenge of

organising their thinking in a structured

way, only two students were able to solve

the problem. For the record, 4 years in

Max’s world is exactly 864,000 years in the

Land of the Wild Things!

CURRICULUM LINKS

The curriculum links for this task are varied

and are somewhat dependent on the

strategies used by individual students. This

task is suitable for upper primary students

(Years 5-6) and lower secondary students

(Years 7-8), and the breadth of curriculum

coverage indicates the varied entry and

exit points that a rich task such as this one

facilitates. Broadly this task covers the

following content descriptors from the

Victorian Curriculum:

PRIME NUMBER: VOLUME 33, NUMBER 1. 2018

© The Mathematical Association of Victoria

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CHALLENGING TASK

WHERE THE WILD THINGS ARE (CONT.)

Figures 3 and 4: One student’s approach to

the ﬁrst extension question.

Figure 5: An alternative approach to the

extension problem.

PRIME NUMBER: VOLUME 33, NUMBER 1. 2018

© The Mathematical Association of Victoria

19

Level 5

Number and Algebra

• Solve problems involving division by a

one digit number, including those that

result in a remainder

• Use ecient mental and written

strategies and apply appropriate digital

technologies to solve problems

Level 6

Number and Algebra

• Select and apply ecient mental and

written strategies and appropriate

digital technologies to solve problems

involving all four operations with whole

numbers

Measurement and Geometry

• Measure, calculate and compare

elapsed time

Level 7

Number and Algebra

• Recognise and solve problems

involving simple ratios

Level 8

Number and Algebra

• Solve a range of problems involving

rates and ratios, including distance-

time problems for travel at a constant

speed, with and without digital

technologies

CONCLUDING THOUGHTS

The success of this lesson stemmed from

a high level of student engagement.

Although Where The Wild Things Are is

more obviously suited to younger students,

my upper-primary class loved being read

this book; I believe their enjoyment in

tackling this task was due to the way it was

embedded in the narrative. It is common

for children’s literature to be used in

connection with mathematical learning, but

often the maths is superﬁcially linked to the

text or a text is chosen for its mathematical

focus. This lesson is based on a ‘Narrative-

First Approach’ to lesson planning,

whereby key ideas, themes, and characters

from well-known children’s stories are

reconstructed through a mathematical lens.

For other examples of attempts to employ

this approach, see Russo and Russo (2017a,

b, c). If you’d like to ﬁnd out more about

the lesson, please feel free to email the

author at russo.toby.t@edumail.vic.gov.au.

REFERENCES

Muir, T., Livy, S., Bragg, L., Clark, J., Wells,

J., & Attard, C. (2017). Engaging with

Mathematics through Picture Books. Albert

Park, Australia.: Teaching Solutions.

Russo, J., & Russo, T. (2017a). Harry Potter-

inspired Mathematics. Teaching Children

Mathematics, 24(1), 18-19.

Russo, J., & Russo, T. (2017b). One Fish,

Two Fish, Red Fish, Blue Fish. Teaching

Children Mathematics, 23(6), 338-339.

Russo, J., & Russo, T. (2017c). Problem

solving with the Sneetches. Teaching

Children Mathematics, 23(5), 282-283.

Sullivan, P., Askew, M., Cheeseman,

J., Clarke, D., Mornane, A., Roche, A.,

Walker, N. (2014). Supporting teachers in

structuring mathematics lessons involving

challenging tasks. Journal of Mathematics

Teacher Education (pp. 123-140).