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INTRODUCING THE

NARRATIVEFIRST

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 Scheer

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

eciently (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 dierent

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 ecient 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.