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, teachers 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 responsible for sharing the bananas fairly. There are 6 bowls and 8 bananas.
Strategies
Area Model
There are 6 bowls and 8 bananas, so on a grid sheet I draw 8 rectangles. These rectangles represent 1 whole banana. I distribute the bananas into the bowls.
There are 2 rectangles left, which is 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, namely thirds, I will be able to put one piece in each bowl.
The sharing will be fair if in each bowl, Jonas and Hadi place the equivalent parts of 1 whole banana and \(\frac{1}{3}\) of 1 other banana.
Example 2
Kamal and Maria are responsible for fairly sharing 2 pieces of licorice into 8 bowls. Afterwards, the 2 students will help assemble the entire special snack.
Strategies
Linear Model
2 licorice should be divided into 8 equal parts. I fold a strip of paper to represent the eighths of a licorice by folding it into halves 3 times.
This makes 8 equal parts, or eight eighths. Next, cut the licorice into 8 equal parts. In all, there are 8 one eighth pieces. I repeat this with another strip of paper, as there are 2 pieces of licorice. Each bowl will have two one-eighth pieces of licorice.
Source: En avant les maths! 3e année, 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 fair, 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 1st piece (one eighth of the submarine). Then, they are given a 2nd piece (one eighth of the submarine), and so on, until the 5th 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 (in eighths). Pour \(\frac{1}{8}\) of a litre (from the 1st litre) into each of the containers. Pour another \(\frac{1}{8}\) (from the 2nd litre) into each of the containers. Therefore, each container will contain \(\frac{2}{8}\) of a litre of syrup.
Source: L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).