Equivalent Fractions

(擴分和約分)

A Lesson on Equivalent Fractions

Level: P4

Lesson Time: 1 hour 10 minutes

Resources:

Worksheet 1	Worksheet 1′
Worksheet 2	Worksheet
Worksheet	Printed on a transparency

 

Objectives:

Students are

1. to explore to see that fractions of different numerators and denominator can be of the same value;
2. to expand a fraction into other equivalent forms by multiplying an appropriate number to the numerator and the denominator.

Strategies:

1. Overlay transparencies are used to divide the ‘whole’ into different number equal portions. The shaded part is thus represented in different form of fractions.
2. Practice the steps in expanding and demonstrate the examples using the Geogebra program https://www.geogebra.org/m/PCfbqmVP(Appendices: Worksheets p.1-4)

Learning Activities

1. (Anticipatory Set) A story on dividing a pizza. “For the same piece of pizza, will I have more when it is further divided into more parts?”
2. Each student is given a worksheet (工作紙一) and a set of three labelled transparency pieces.
   For questions (1a) and (1b)
   1. Students are instruction to overlay the transparencies onto the corresponding figures.
   2. Copy and draw the patterns in the boxes.
   3. Discuss with partner and write down the fractions that describe the corresponding shaded part.

   For question (1c), students can choose to shade some parts in the original figure before the overlaying work.

3. Whole class discussion: receiving answers from students.
   Lead students to see that the fractions might look different (different denominator and numerator) butrepresent the same shaded portion.
4. Each student is given a worksheet (工作紙二). Teacher leads the discussion on expanding fraction with the first two overlay examples. “When the numerator and the denominator are multiplied by the same number, the resulting fraction is equal to the original one.”
5. Geogebra program is used to demonstrate practice question (1).
6. Students are instructed to discuss and work on question (2). Check with demonstration in Geogebra.
7. Whole class discussion on question (3) to find an appropriate multiplier to expand to an equivalent fraction of given denominator.
8. Students work on (4)-(6) and (10), (11). Whole class discussion about answers.

 

Comments and Suggestions:

1. The transparency set is a very handy manipulatives. Through the activity, the students see that the shaded portion remains the same though it is partitioned into more parts.
2. When working with the number sentences without concrete manipulative, students might lost the sense of the equivalence of the fractions at the two ends. Might give reminders from time to time.
3. Can work more on the easier question types: .
   Might also ask students to write down the pair of equal fractions after the working steps.