This is an activity based on the picture book **Spaghetti and Meatballs for All! A Mathematical Story**

Students will be able to find and discuss the multiplicative relationships between elements in simple ratios.

Students will be able to represent relationships in sequential patterns in both tables and line graphs.

Ratios allow you to create sequential patterns which can be used to explore multiplicative relationships.

Scrap paper and hula-hoops

Meatball Multiplication

This activity is based on the picture book Spaghetti and Meatballs for All! A Mathematical Story

Author: Marilyn Burns

Illustrator: Debbie Tilley

Publisher: Scholastic (1997)

ISBN: 978-0-545-04445-5

**Summary:**

When you have a family reunion you need to make plans for lots of elements especially when you need to feed and seat a large group of people.

**Lesson Sequence: **

This book explores the plans for the seating arrangements in great detail through a humourous constant changing of table arranging. There are very good teacher notes at the end of the book explaining the maths involved in the table arranging and there are suggested activities for modeling and extending these concepts. The following activity supports the investigation of the multiples related to the menu elements.

- Warm up with some practice of multiplication basic facts with focus on common multiples. For example organise students into 9 groups each small group representing a times table sequence. Have them create a set of 10 cards on scrap paper with their table’s multiples (2x-10x). Give each group a hula-hoop and make table pairs and give them a minute to create a Venn diagram showing the common multiples between them in the hoop overlap. For example, if you pair 3x and 5x and their hoops they should have the cards 15 and 30 in the overlap and the rest of the multiples in either the 3x hoop or the 5x hoop. Ask them to come up with 3 more common multiples there would be if they weren’t limited to the 10x10 multiplication grid. Switch pairings and repeat several times asking for observations and extensions each time.
- Introduce the book and ask students to have their eyes and ears open for examples of multiplication in the story. Share the book and stop for discussion on occasions when the multiplication jumps out at the audience.
- Revisit page 5 where Mr. Comfort is preparing the food. On the board place the number 32 in a circle. Around it write the other numbers that are given on the page (16 garlic bread; 8 pasta; 8 sauce; 96 meatballs). Ask students to discuss the multiplicative relationships they can find between 32 and the other numbers. Go to page 7 where he is setting out 8 plates of celery and olives. Ask students to solve problems related to the number of elements required - for example if each plate has 12 olives and 8 celery sticks or other combinations.
- On another day revisit the story and create a table with the title: Meatball Multiplication (see Copymaster 1). Ask students to recall what ratio of meatballs to people Mr. Comfort has prepared (96:32 or 3:1). What is the ratio of sauce to pasta to meatballs? (8:8:96 or 1:1:12) Note: the book uses imperial measurements so you could simply replace pounds with kilograms and quarts with litres or if students are able to work well with fractions a pound could be 0.5 kg which is more accurate (so ratio would then be: 1/2:1:12)
- Ask students to fill in what they know from the story and then figure out the missing values and predict values based on the multiplicative relationships they find within the table and between the elements. For example:
*We know that Mr. Comfort made 8 litres of sauce for 32 people so he must be thinking about feeding 4 people per 1 litre. How many meatballs is that per litre? Can we work back from the 1 litre and figure out how much sauce is required for 3, 2, and 1 person? Now let’s move ahead and figure out how much would be needed for 16 people, 100 people? What is the multiplicative relationship between the people and meatballs and sauce?* - There are other versions of the tables in the copymaster that students can work on independently or in supported groups exploring the quantities required based on the ratios within the story. Further exploration can be done by graphing the results of their tables, using line graphs with different colours for each element and looking at the graphic representation of the ratios and using the lines to calculate how much would be needed for certain numbers of people.