Students were given the task of distributing gold bars among two people equally. There were 15 pieces (1 whole, 2 halves, 4 quarters, 8 eighths), so they could not give an equal number of pieces to each. They were given fraction strips to work with.
Students had not learnt about equivalent fractions yet. In the solution on the bottom right, the group tried to divide the pieces one by one. They were stuck when they had one whole left. They asked if they could cut it up. I told them it was a gold bar and there was no tool to cut it up. They had to search for other solutions.
Most groups succeeded in coming up with more than one solution.
Solution A: 1 whole + 2 halves = 4 quarters + 8 eighths
Solution B: 1 whole + 2 quarters + 4 eighths = 2 halves + 2 quarters + 4 eighths
Solution C: 1 whole + 4 quarters = 2 halves + 8 eighths
From the solutions, students were led to see relationships such as 1 whole = 2 halves = 4 quarters = 8 eighths, 1 half = 2 quarters = 4 eighths etc.
They were then introduced to the term “equivalent fractions”. They were asked to observe the equivalent fractions and led to deduce the multiplicative relationships.
They then used paper strips to further explore equivalent fractions
The students were given an extension activity on fractions. They had to divide a square into 4 equal parts in as many ways as possible. They could make use of their knowledge on equivalent fractions to do this task. How many ways can you think of?
Students also learnt how to represent fractions using a number line.
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