the doorbell rang - Informit

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. 15 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 different 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.

Grandma could have made 60 cookies to share between 12. 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 different 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?

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EXPLORE (APPROX. 25-30 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. 10-15 MINS) Facilitate a discussion of the different 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 48 cookies to share between 12. •

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, different 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 differentiate 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?

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?

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,

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© The Mathematical Association of Victoria

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