B1.6 Use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts.
Activity 1: The Special Snack
The students in the class have to prepare a special delicious snack. At each table, the teacher placed different foods with plastic bowls and knives to cut into portions if necessary. There should be a fair share of food in each bowl. Dividing the food between a number of bowls, what do you notice?
Example 1
Jonas and Hadi are sharing the bananas equallly. There are 6 bowls and 8 bananas.
Strategies
Area Model
There are 6 bowls and 8 bananas, so on a grid paper I drew 8 rectangles. Each rectangle represents 1 whole banana. I distribute the bananas into the bowls.
There are 2 rectangles left, which represents 2 whole bananas. I need to cut the 2 bananas and divide the pieces into the 6 bowls. If I divide the bananas into 3 equal parts, or thirds, I will be able to put one piece in each bowl.
The sharing will be equal if in each bowl, Jonas and Hadi place 1 whole banana and \(\frac{1}{3}\) of 1 other banana.
Example 2
Kamal and Maria are sharing 2 pieces of licorice into 8 equal portions. Afterwards, the 2 students will help assemble the entire special snack.
Strategies
Linear Model
2 licorice pieces need to be divided into 8 equal parts. I folded a strip of paper into half three times to represent the eighths.
This made 8 equal parts, or eight eighths, which I cut into equal pieces. I put one piece into each bowl. I repeated this with another strip of paper, as there are 2 pieces of licorice to share. So after that, each bowl will have two one-eighth pieces of licorice.
Source: translated from En avant les maths! 3e, CM, Nombres, p. 3-5.
Activity 2: Fraction as Division
Example 1
At an end-of-season party, the 8 players on a soccer team must share 5 subs. If the division is to be equal, what portion of the subs will each player receive?
Possible answer:
Each submarine is separated into 8 pieces.
Each of the 8 players is given a first piece (one eighth of the submarine). Then, they are given a second piece (one eighth of the submarine), and so on, until the fifth piece. So, each of the players will receive five eighths of a submarine.
Example 2
At Lili's restaurant, 2 litres of maple syrup must be divided equally into 8 containers. How much syrup will be in each container?
Possible answers:
2 litres divided into 8 containers means 2 litres divided by 8 or \(\frac{2}{8}\).
Strategy 1
Separate each of the 2 litres into 4 parts (fourths) to make 8. So, each container will hold one fourth of a litre of syrup.
Strategy 2
Separate each of the 2 litres into 8 parts (eighths). Pour \(\frac{1}{8}\) of a litre (from the first litre) into each of the containers. Pour another \(\frac{1}{8}\) (from the second litre) into each of the containers. Therefore, each container will contain \(\frac{2}{8}\) of a litre of syrup.
Source: translated from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).