The Narrative First Approach: Room on a Broom investigation

Abstract

This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. The Room on the Broom text is used as an example to illustrate how one might structure a lesson using the Narrative-First Approach.

Full text

INTRODUCING THE
NARRATIVEFIRST
APPROACH
Most primary school teachers know
that there are few things students enjoy
more than being read a good picture
storybook. The Narrative-First Approach
to developing mathematical tasks seeks to
capatalise on student engagement in these
stories, building rich, authentic activities
around their themes, characters or plot.
It is not uncommon for storybooks to
be used as a prompt for mathematical
learning, but often the texts are chosen
to support learning around a particular
mathematical concept. In this case
(what we have dubbed ‘Curriculum-First
Approach’), an educator would identify the
area of the curriculum they hope to cover
and then find a relevant text to support the
learning. The Narrative-First Approach
inverts this process: an educator must first
identify an engaging text and then the
mathematical problem can be developed
using the context of the narrative. The
educator can then retrospectively make
connections between the investigation and
the maths curriculum.
AN EXAMPLE: ROOM ON THE
BROOM INVESTIGATION
For this example of the Narrative-First
Approach the text Room on the Broom was
chosen, a picture storybook written by Julia
Donaldson and illustrated by Axel Scheer
that has also been adapted into a short
animated film. The following five stages
outline the process of lesson delivery, which
in this case was for a Year 5/6 class.
STEP : SHARED READING
The lesson began with a teacher-led shared
reading of the text. Room on the Broom
tells the story of a witch who is travelling
on her broomstick with her cat and meets
other animals on the journey: a dog, a bird
and a frog. When all five animals are on
her broomstick it can’t take the weight and
breaks in two. A dragon then chases the
solo-flying witch, who is saved by her new
friends.
STEP : CONNECTING QUESTIONS
At the conclusion of the reading, it was
necessary for the teacher to guide student
discussion towards the mathematical
context of the investigation using
appropriate connecting questions. Some
connecting questions used were:
• Why do you think the broomstick
broke in two?
• Who was responsible for the
broomstick breaking?
• How much weight do you think the
broomstick could take?
STEP : POSING THE PROBLEM
The problem (see red box) was presented
to students who worked on it independently
or in pairs. For the purpose of this
illustration, the weights of the animals
which students were expected to calculate
have been included in parentheses.
The students began by identifying the
relevant mathematics, primarily calculating
the fraction of a quantity and applying
their knowledge of ratios (proportional
reasoning). They then worked
systematically through the problem by
carefully solving and recording the weight
of each animal.
Most students had success in solving
question one, using a range of strategies.
For example, some students quickly
identified division as a way to determine
the weight of the cat (i.e. one tenth of 60
is 60 ÷ 10), while others used a number
line to separate 60 into ten equal parts
and represented the problem as repeated
addition.
Question two required students to
compare their first answer to another
weight, which is based on a simple addition
problem (60kg + 60kg). Once they had
completed the arithmetic, most students
were able to verbally articulate why the two
witches could not sit on the broomstick
together (‘They weigh too much because
60 plus 60 is 120 and the broom can’t even
take 90kg’).
STEP : EXTENDING STUDENT
THINKING
Most of the Year 5/6 students completed
the initial investigation and attempted the
following extension problem (see page 11).
THE NARRATIVE-FIRST APPROACH:
ROOM ON THE BROOM INVESTIGATION
PRIME NUMBER: VOLUME 33, NUMBER 2. 2018
© The Mathematical Association of Victoria
10
Toby Russo, Bell Primary School and
James Russo, Monash University
ROOM ON THE BROOM
INVESTIGATION
By the time the witch’s broomstick
broke in two, there were lots of
creatures on it! There was the witch, her
cat, the dog, a frog and a bird!
Here is a list of how much each
passenger on the broom weighs:
The witch: 60kg
The cat: One tenth the weight of the
witch (6kg)
The dog: Two and a half times the
weight of the cat (15kg)
The bird: A fifth the weight of the dog
(3kg)
The frog: Twice the weight of the bird
(6kg)
1. Can you work out the maximum
weight the old broomstick could take?
2. Could the broomstick take the
witch and her best friend Glenda
(who happens to weigh exactly the
same!) without breaking? Explain
mathematically.

EXTENSION PROBLEM
The witch’s new broomstick was a huge
upgrade and had plenty of room for
everyone. However, everything has a
limit and this broomstick could only
hold 50% more weight than the old
broom.
1. Would the new broomstick take the
witch, frog and four of his friends, the
bird and two of her friends and the dog
and one of his friends? (Let’s assume all
birds, dogs, etc… are the same weight!)
2. What are some combinations of
animals the new broom can take?
Students used various strategies to
determine the maximum weight of the
new broomstick, with most applying their
understanding of 50% as a half (i.e. ‘the
broomstick can hold half as much weight
as the first one, so half 90 is 45 and 90
plus 45 is 135, so it will break with 135kg
on it’). One student used her knowledge
of the relationship between percentages
and decimals, and then multiplication
of decimals, to solve the problem more
eciently (i.e. 90 x 1.5 = 135). Most worked
out that the new broomstick could fit all
the animals, with some weight (6kg) to
spare. The students found the additional
extension question rather challenging:
some began to work through animal
combinations, but only one pair used a
table to systematically identify a number of
the combinations.
STEP : REFLECTIVE
DISCUSSION
At the conclusion of the lesson, there was
an opportunity for the students to reflect
on the mathematical learning and share
the various methods used, as outlined
above. An extensive discussion ensued
about how we could work out the dierent
combinations of animals that would fit
on the new broom, with one student
suggesting a spreadsheet might help!
PRIME NUMBER: VOLUME 33, NUMBER 2. 2018
© The Mathematical Association of Victoria
11
CONCLUSION
The Narrative-First Approach provides
teachers with a tool for integrating
literacy and maths in a meaningful way,
by leveraging student engagement in
a narrative to create rich and authentic
problem solving activities.
Tasks developed using the Narrative-First
Approach lend themselves to broad and
deep links through the curriculum, which
educators can determine after they have
developed the activity.
Above: The witch trialling her new broomstick. Image: Magic Light Pictures.
Below: Students collaborate on the investigation.
In the example provided, the Room on the
Broom investigation is linked to a range of
mathematical content at level 5 through
to 7 (from the Victorian Curriculum),
including the use of ecient strategies
involving the four operations, calculating
fractions of a quantity and solving problems
involving percentages. To find out more
about the Narrative-First Approach and to
access additional activities, go to
bit.ly/narrativefirst.