Resources

We have specified a problematised situation and its associated spreadsheet in the following PowerPoint document.

Download Collage of Halves

If this is printed on one piece of paper (double-sided) it can be laminated for use by students at the computer.

Target Strategies

halving fractions

making relationships between fractions and decimal numbers

entering and understanding formulae

interpreting data from a spreadsheet

The Activity

Allow time for the students to cut and label the fractional pieces. Some students may be able to label all pieces whereas others may only be able to label the first few. Some will invent notation to help them continue, for instance writing half of an eighth instead of one sixteenth. This will give you important information for future planning.

When the students have created their spreadsheets use the following questions to initiate discussion between students and to ensure that the students develop an understanding of the data presented:

"Why was the formula C3/2 entered in cell C4?" (C3/2 indicates that the value of cell C3 is to be divided by a half)

"What would have happened if the formula C3/4 had been entered?"

"Which cell shows that the fraction is equivalent to one quarter?"

"Which cell has a value closest to one hundredth?"

"Which fractional piece of paper would match this decimal?"

"What fraction do you think 0.125 is equivalent to?"

"Write the equivalent fractions for each of the decimal values using your fraction pieces as a guide?"

Extension

Instead of halving, we might think about doubling, changing the formula in cell C4 to become = C3 * 2. Here the metric paper sizes come into play, as we start with an A4 piece of paper, and doubling makes an A3 sheet. An A1 sheet is exactly 1 square metre.

"How many times do we need to double the piece of paper to cover 1 square kilometre?"

"How many times to cover Brisbane (2,000 sq km)?"

"How many times to cover Australia (7,682,300 sq km)?"