B1.4 Use equivalent fractions to simplify fractions, when appropriate, in various contexts.
Activity 1: Equivalent Fractions
Materials
- envelopes
- paper strips
- felt pen
- have access to relevant manipulatives for understanding the concept of fractions (for example, fraction strips, grid sheets, tokens)
Write 2 scenarios per paper strip related to equivalent fractions. Each strip will have a situation with a simplified fraction (in lowest terms) and another with a fraction that can be simplified.
The student will need to determine if the fractions represent equivalent situations.
Consider different scenarios in the examples (drawings, fractions in symbolic notation, written problems). Be sure to have examples where fractions are equivalent and others are not. Place a dozen strips of paper in an envelope. Reproduce to meet the needs of the class.
Divide students into pairs. Distribute one envelope per team.
In turn, one of the students takes a paper strip from the envelope. Each student must decide: Equivalent: yes or no? They must then justify their choice.
Examples
Paper Strip 1:
Situation A: A student has traveled \(\frac{2}{3}\) of the route.
Situation B: A student has traveled \(\frac{{18}}{{24}}\) of the route.
Paper Strip 2:
Situation A:
Situation B:
Paper Strip 3:
Situation A: The seamstress chooses \(\frac{3}{4}\) from all available buttons.
Situation B: The seamstress chooses \(\frac{{24}}{{32}}\) of all available buttons.
Paper Strip 4:
Situation A : \(-\frac{4}{18}\)
Situation B : \(-\frac{1}{6}\)
Paper Strip 5:
Situation A : The elapsed time represents \frac{{15}}{{60}} of an hour.
Situation B: The elapsed time represents \frac{1}{4} of an hour.
Activity 2: Keep It Simple (Simplify Fractions to Lowest Terms)
Materials
- one whiteboard per student with erasable felt-tip pen
Project on the board, a statement with an unsimplified fraction.
The student must write the simplified fraction (where the numerator and denominator have no common whole number factor other than 1) on their whiteboard.
Important: Question students regarding their strategies:
- How did you find the simplified fraction?
- How do you know that the fraction in the statement is equivalent to your simplified fraction?
- What model did you use to find the simplified fraction?
Examples of statements
- Situation A : The elapsed time represents \(\frac{{45}}{{60}}\) of an hour.
- Jacques ate \(\frac{{15}}{{18}}\) of the cake.
- The student got \(\frac{4}{{20}}\) answers incorrect.
- The marathon runner has covered \(\frac{{25}}{{100}}\) of the race.
- The painter has finished \(\frac{{4,5}}{9}\) of his project.
Activity 3: It's a Question of Equivalence (Simplified Fractions and Equivalent Fractions)
Materials
- whiteboards
- erasable felt-tip pen
Group students into teams of 3 or 4.
Write an unsimplified fraction on the board. (alternative: distribute an envelope with a set of cards)
Each student in the team must write on their board 2 fractions equivalent to the one listed, one of which must be the simplified fraction. Students compare their answers.
Important: Question students about the two fractions:
- How did you find the simplified fraction?
- How do you know that the fraction in the statement is equivalent to your simplified fraction?
- Are your teammates' fractions the same as yours? If not, are these fractions equivalent?