Background

When creating fractions, students generally take a whole and subdivide it to create fractions. This might be called whole to part thinking. It is equally important that the students are required to form the whole from a given part.

Activity

Show seven “lollies” assembled and wrapped up in paper, for example, four are one colour, and three are another. Slide the cubes out of the paper to leave the wrapper intact. Place three cubes on top of the wrapper. Ask what fraction of the packet the three cubes represent (three-sevenths). Show the other four cubes against the packet, and ask what fraction they represent. This will reinforce the idea of fractions adding to one. For example, 3/7 + 4/7 = 7/7 = 1.

Tell a story about the lolly manufacturer deciding to put in another lolly that makes the packet bigger. Show the wrapped packet of eight lollies and put a cube against it. Ask what fraction of  the packet a lolly represents now (one-eighth). Discuss why its fraction name was one-seventh and now is one-eighth, even though the size of each lolly has not altered. Open the packet up

Give the students cubes and get them to make a packet to show (four of one colour and five of another).

Repeat for 2/9, 4/11, 3/4, 9/10, 2/3, 9/16, ...

Record various problems involving fractions and one whole as word stories and equations on the board or modelling book. For example, two-ninths and seven-ninths equals nine-ninths  equals one whole, and  2/9 + 7/9 = 9/9 = 1.

Extension Activity

Make a lolly packet with six of one colour and five of another colour. Hide the five lollies and show the six lollies to the students. Tell them this is six-elevenths of the packet. Record on the board or modelling book. Ask what fraction you are hiding. Repeat for other fractions.

Record 6 elevenths + 5 elevenths = ? elevenths, and the matching equation 6/11 + 5/11 = ?/11

on the board or modelling book.

Repeat for: 2/9 + 7/9 = ?/9,

5/12 + ?/12 = 12/12

?/13 + 4/13 = 13/13 …