B1.4 Use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems.
Activity 1: Let's Compare Numbers (Fractions, Decimals, Percents)
Materials
- small blank cards
- black felt-tip pen
- concrete materials: paper for folding, fraction strips, relational rods, etc.
Students are given five small blank square cards (approximately \(5\;{\rm{\;cm}}\; \times \;{\rm{5}}\;{\rm{\;cm}}\)).
Ask students to write one number on each card and include one of each of the following: a whole number, an integer, a fraction, a decimal and a percent. Target certain students to ensure that there are percentages over 100% and under 1%.
Ask students to prepare a table with three columns like this:
| Fractions | Decimal Numbers | Percents |
|---|---|---|
Ask students to exchange five cards with another student in the class. Each student will then place their new set of five numbers in the correct column of their chart and then convert them into the other forms, making sure to maintain equivalence.
Activity 2: What's the Best Deal? (Solving Problems Involving Percents, Decimals and Fractions)
Prepare paper strips with statements about purchasing goods.
Place the strips (10-12) in an envelope. The same statements can be repeated in the other envelopes.
Form teams of two to three people.
Distribute an envelope to each team. In turn, each student chooses a strip, and places it in view of everyone. Individually, the student chooses the statement that represents the best discount. Then, as a team, they justify their choice with calculations or by explaining their reasoning. Students who choose the correct statement receive a point.
Review the problem statements as a class. It is important to highlight students' different computational strategies.
Examples of statements
Strip 1: A ski jacket is on sale. The store offers two purchase options:
- The store is offering a 10% discount on the original price of the jacket.
- The store sells the jacket for 85% of the original price.
Which option do you choose? Justify your choice.
Strip 2: A pair of sneakers can be purchased at a discount at the sports store.
Options:
- The store sells the sneakers at \(\frac{3}{4}\) of the original price.
- Sneakers are 20% off.
Which option do you choose? Justify your choice.
Strip 3: The local music store advertises an electric guitar for sale.
Options:
- The guitar is half price.
- The guitar is sold at 60% of the original price.
Which option do you choose? Justify your choice.
Activity 3: Unusual Percents (% Greater Than 100% and Smaller Than 1%)
Prepare a deck of cards (minimum 20 cards) with numbers written in % (more than 100% and less than 1%) on one card and with the equivalent decimal representations on a second card. Divide students into teams of two. One student shuffles the cards, placing them face down with the number hidden. In turn, each student picks two cards. They must find two equivalent numbers to form a pair. The student with the most pairs wins.
Examples of cards
Card 1: 150%
Card 2: 0.05%
Card 3: 250%
Card 4: 0.2%
Equivalent card: 1.5
Equivalent card: 0.0005
Equivalent card: 2.5
Equivalent card: 0.002
Extension
Once the pairs are completed, ask students to find the fraction equivalent to the numbers in the chosen pair.
Activity 4: To Learn More
Materials
- Appendix B (To Learn More)
This activity integrates concepts in numbers, health and physical education and Language Arts.
Today's youth are bombarded with information. Critical reading of excerpts from informational and advertising articles and pamphlets contributes to the development of good judgment and enables students to make informed decisions about their health.
Have students read excerpts from various documents (see Appendix B) and encourage them to think about the numbers presented by asking questions such as:
Excerpt A
- There is a 10% gap between boys and girls. Is that a lot?
- Using our class as a model, how many girls and boys are not active enough, according to these results?
Excerpt B
- The excerpt could have read, "Since 1981, childhood obesity rates have increased from 5% to 16.6% for boys and from 5% to 14.6% for girls." What effect does the addition of the term tripled have?
- If we triple the number 5, we get 15. Why is the term tripled used?
- Why are the 16.6% and 14.6% data presented?
Excerpt C
- Do the majority of Canadians believe that children and youth spend too much time on non-physical activities?
- Approximately what fraction of the Canadian population shares this opinion?
Excerpt D
- Why did the author calculate the grams to the nearest hundredth?
- What is the apple made of?
Excerpt E
- What does the decimal number 2.4 represent in the excerpt?
- What is the advantage to the reader of expressing this quantity using a decimal number (2.4 million) instead of a whole number (2 400 000)?
- How many adults used food banks in 1995?
Excerpt F
- Why is the expression "most" used in the extract?
- What percent of Canadians floss daily?
Excerpt G
- What do the expressions 2.7 times more and 2.5 times more mean in this excerpt?
- Why do we use a decimal number in these expressions?
Excerpt H
- Which is greater: 1 in 6 in 2025 or 1 in 10 in 2000?
- At the current rate, how many millions will the number of deaths from smoking increase in 25 years?
Excerpt I
- Why can a product marked "sugar free" contain sugar?
- What could weigh about 0.5 g?
- Why not use milligrams as the unit of measurement?
Excerpt J
- From these statistics, is it possible to tell how many 10- to 14-year-old pedestrians have died?
- What does the 27.5% represent?
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 3, Nombres décimaux et pourcentages, p. 122-123.