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The Doorbell Rang: Learning Maths Through Picture Story Books

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This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. Read the classic story by Pat Hutchins, The Doorbell Rang and use this story as an opportunity to introduce this corresponding challenging task. The task, which has been used with Year 1 and 2 students, introduces the sharing model of division, and provides a chance to explore the connections between addition, multiplication and division.
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PRIME NUMBER: VOLUME 32, NUMBER 3. 2017
© The Mathematical Association of Victoria
10
THE DOORBELL RANG:
LEARNING MATHS THROUGH PICTURE STORY BOOKS
James Russo
Belgrave South Primary School and Monash University
Read the classic story by Pat Hutchins,
The Doorbell Rang and use this story
as an opportunity to introduce this
corresponding challenging task. The task,
which has been used with Year 1 and 2
students, introduces the sharing model
of division, and provides a chance to
explore the connections between addition,
multiplication and division.
It is open-ended – there are many
acceptable answers and approaches – and
it is aimed at the whole class. A potential
lesson structure for tackling the task as
a class is presented, with enabling and
extending prompts included at the end of
the article.
LAUNCH APPROX.  MINS
Begin reading The Doorbell Rang. Stop at
the beginning of the story (p. 1), and get
children to estimate how many cookies
Mum might have baked.
Turn the page, and physically model the
problem to work out how many cookies
Mum actually baked if the two children
receive six cookies each (using paper plates
and counters, to represent the cookies). As
the teacher, model three dierent number
sentences which could be used to describe
this problem situation:
6 + 6 = 12: Because six cookies and
another six cookies equals twelve
cookies altogether
2 × 6 = 12: Because two groups of six
cookies equals twelve altogether
12 ÷ 2 = 6, Because twelves cookies
shared between two children equals
six each.
Continue the story, stopping at the relevant
parts to introduce more plates as more
children arrive, and work with students to
model the redistribution of the cookies.
Encourage children to link the physically
modelled problem to the three dierent
types of number sentences (i.e., addition,
multiplication and division). Explore how
all three types of number sentences could
be used to describe each of the problem
situations.
Read the second last page of the story.
Ask students: Can you estimate how many
cookies are on Grandma’s tray? Do not read
the last page of the story.
Tell students that Grandma, coming to the
rescue at the end of the story, has brought
the perfect number of cookies on her tray
to share them equally amongst the 12
children. Ask students:
How many cookies do you think each child
might get? How many cookies must be on
Grandma’s tray?
EXPLORE APPROX.  MINS
Get students to attempt to answer these
two questions by creating their own model
of the problem situation. Encourage
students to record the relevant number
sentences.
DISCUSS APPROX.  MINS
Facilitate a discussion of the dierent
student solutions to the problem. To
support students to make connections
between division and more familiar
mathematical operations (e.g., addition,
skip-counting, multiplication), ask
stimulating questions such as:
How did you go about trying to solve the
problem?
What did you decide first: how many
cookies each child gets [framed as a
multiplication problem], or how many
cookies were on Grandma’s tray [framed
as a sharing problem)?
Grandma could have made 60 cookies to share between 12.
PRIME NUMBER: VOLUME 32, NUMBER 3. 2017
© The Mathematical Association of Victoria
11
How can we check if our answer makes
sense? Depending on how students
framed the problem originally,
encourage them to use either some
form of equal sharing, multiplication,
dierent skip-counting sequences
and/or repeated addition to check
their answer. Discuss how there are
multiple acceptable strategies for
verifying the total number of cookies.
DIFFERENTIATING THE
LESSON
Enabling and extending prompts can
be used to further dierentiate the
investigation.
ENABLING PROMPT
Both these enabling prompts provide
students with a less challenging
mathematical problem through simplifying
the task and making it more explicit. The
two enabling prompts are interconnected.
The first prompt encourages students to
represent the problem multiplicatively,
whilst the second prompt requires students
to model a sharing (division) problem.
A) What if each of the 12 children get
exactly three cookies. How many cookies
are on Grandma’s tray altogether?
B) Oh no, the family dog, Golly, has
jumped up onto the table and devoured
some of the cookies before mum had a
chance to share them out! Now there are
only 24 cookies left on Grandma’s tray.
How many cookies does each of the 12
children get now?
EXTENDING PROMPT
This extending prompt encourages
students to informally explore the idea of
common factors.
Briefly read the last page of the story
to students. It turns out that there were
exactly 60 cookies on Grandma’s tray,
which, along with Mum’s original cookies,
makes 72 cookies altogether. But oh no,
what’s this?! The doorbell has rung again,
and some extra children have arrived! It
turns out, rather luckily, that, even with
these extra children, the cookies can still be
shared equally so that each child gets the
same number of cookies. How many more
children might have arrived at the door?
Grandma could have made 48 cookies to share between 12.
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