B1.7 Describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, in various contexts.
Activity 1: Area Model
Area models are very useful for showing the relationship between the 3 representations.
Example
16 of the 25 plots in one field are cultivated with wheat and 9 with barley.
- Represent the situation semi-concretely.
- Represent the situation symbolically.
- What decimal number and percent do the wheat plots represent?
- What decimal number and percent do the barley plots represent?
Interactive Lesson: L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).
Activity 2: Concentration
Group students in pairs and give each team 18 small blank cards. Ask them to make 6 sets of 3 cards, one of which displays a percent, the other the corresponding decimal fraction and the last the corresponding decimal number.
Example of a set of cards
Then explain the Concentration game:
- The cards are randomly placed upside down. One person turns over a card and then turns over two others, trying to find the two numbers that match the first one. If they succeed, they get a point and can continue. If they fail, they turn the cards over, and it is their opponent's turn to play. The game continues until all the cards are turned over. The person with the most points wins the game.
Invite teams to exchange sets of cards and play again.
Source: Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, p. 177.
Activity 3: What is the Criterion?
This activity integrates concepts in Number as well as in Data.
In order to be more effective in formulating survey questions, constructing various graphs, and managing data, students must learn to determine classification criteria.
To develop this skill in students, teachers show them a set of ten different objects and ask them to find criteria for classifying them (other than colour or shape, which have been covered in previous grades). Students then divide the objects into subsets according to their classification criteria. Students are then asked to determine the fraction of the original set represented by each subset (for example, many of the objects are made of plastic, which is equivalent to 0.3 or 30%). Classification of 10 objects allows students to easily relate a fraction, a decimal number, and the corresponding percent.
For example, present this set of ten objects: a tennis ball, a pencil, a water bottle, a highlighter, post-it notes, a pair of shoes, a sheet of paper, a calendar, a box of tissues, and a cup.
Then ask students to create a classification criterion to use to create subsets, and then to determine the fraction, decimal number, or percent that the subset represents.
Here are 2 examples.
- The pencil and the highlighter are both used for writing or drawing, so \(\frac{2}{{10}}\), 0.2 or 20% of the objects are used for writing or drawing.
- The sticky notes, the sheet of paper and the calendar serve as a writing medium, so \(\frac{3}{{10}}\) or 0.3 or 30% of the objects serve as a writing medium.
There are several other classification criteria such as texture, material of construction, mass, utility. In the junior grades, the criteria do not have to be observable as are colour and size.
This classification activity can be repeated throughout the year with different objects which a group of students is responsible for choosing. The number of objects can increase to 20, 25, or even 50. Depending on the grade, students apply equivalence relationships to determine fraction, decimal, or percent. For example, if 13 of the 20 objects are plastic, they can determine that \(\frac{{13}}{{20}}\), \(\frac{{65}}{{100}}\), 0.65 or 65% of objects are plastic; if 10 of the 25 objects or \(\frac{{10}}{{25}}\) objects are removed from the set, they can say that it is \(\frac{2}{5}\), 0.4 or 40% of the objects.
To extend the activity, a group of students can classify a set of objects according to a chosen criterion. For example, students can announce that \(\frac{4}{{10}}\) or 0.4 or 40% of the objects, namely the tissue box, the highlighter, the calendar, and the pencil have something thing in common. The other students then try to determine which criterion was chosen to carry out the classification (these 4 objects included lettering). Note that several criteria can be accepted.
Source: Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, p. 116-117.