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Where The Wild Things Are Challenging Task

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  • Fitzroy North Primary School

Abstract and Figures

This article takes readers through a challenging maths task built around the children's book, Where the Wild Things Are. Using the Narrative First Approach, the author has developed a task centred around Max's journey to the land of the wild things which explores concepts of relative time and proportional reasoning. The article provides student work samples based on the delivery of the lesson in an upper primary classroom in Australia, and ideas about how the activity could be used for younger students.
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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 eective
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 dierent
units measuring time (i.e., day, week,
year), highlight how mathematical
problems are often embedded within
text, and provide students with a
relatively dicult 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 dierent 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
dierent 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
18
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 ecient mental and written
strategies and apply appropriate digital
technologies to solve problems
Level 6
Number and Algebra
Select and apply ecient 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).
... It is important to consider that these are potential benefits and, as with any other pedagogical tool, story picture books may be interpreted and implemented in ways which limit their impact. Sometimes teachers might superficially link a story picture book with a topic they are teaching (Russo & Russo, 2018). Similarly, not all story picture books are appropriate for teaching mathematical concepts and may even lead to children developing misconceptions (Flevares & Schiff, 2014;Nurnberger-Haag, 2017). ...
... Enabling prompts can be posed to children having difficulty with the main task and extending prompts aim to extend the children's responses to the main task, such as making a generalisation (Sullivan, 2018). There are many other examples of rich, challenging tasks targeted at upper primary-age children developed around narratives that include enabling and extending prompts in an aim to optimise the level of challenge for all children participating in the lesson (e.g., Russo, 2018;Russo & Russo, 2019). Such lessons also demonstrate teachers' purposeful and meaningful context and connections between literacy and mathematics. ...
... The literature supports this belief reporting that children can be highly motivated when the story provides a hook for mathematical learning. In addition, teachers are engaged because they can choose stories they enjoy and the task or investigation can be engaging for children because it includes a range of mathematical ideas (Russo & Russo, 2018). Others agree that engagement should be fostered through careful selection of appropriate literature and purposeful mathematical tasks that might also promote problem solving and reasoning (e.g., Muir et al., 2017;NCTM, 2018). ...
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... An adaptation to this lesson structure is noted elsewhere in the literature (e.g., see [79] and their instructional model incorporating (re)launch, re(explore), (re)summarize/review). Note that the core tasks used in each of the lessons are briefly summarized in Table 1, whilst the full tasks have been published elsewhere (Where the Wild Things Are, [80]; We're Going on a Bear Hunt, [81]; Despicable Me and Coin Operated, [63]). ...
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Engaging with Mathematics through Picture Books
  • T Muir
  • S Livy
  • L Bragg
  • J Clark
  • J Wells
  • C Attard
Muir, T., Livy, S., Bragg, L., Clark, J., Wells, J., & Attard, C. (2017). Engaging with Mathematics through Picture Books. Albert Park, Australia.: Teaching Solutions.
  • J Russo
  • T Russo
Russo, J., & Russo, T. (2017a). Harry Potterinspired Mathematics. Teaching Children Mathematics, 24(1), 18-19.