Mystery fractions
This is a level 3 number link activity from the Figure It Out series. It is focused on finding fractions of a whole. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Find fractions of a whole.
Mystery fractions
Achievement objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Required materials
- Figure It Out, Link, Number, Book Two, "Mystery fractions", page 21
- multilink cubes or beads, plastic jars (all optional)
See Materials that come with this resource to download:
- Mystery fractions activity (.pdf)
Activity
This activity examines the use of a ratio table or double number line as a tool to find the fractional amounts of a set. The students need to recognise the “whole” to which the fractions refer. The whole in this case is the total number of cubes in the jar, not the jar itself.
Some students may find fractions with a numerator greater than 1 difficult to handle. This is usually because they do not fully understand the meaning of the fractional notation. Check that the students do understand 3/4 as three lots of one-quarter and 3/5 as three lots of one-fifth.
Observe how the students attempt the problem. Look to see if they know to share equally by the number indicated in the denominator. For example, 2/3 will involve equal sharing by 3. If they can make equal shares, do they then use the numerator to decide how many equal shares to consider? Some students may use addition to find the complete fraction while others use multiplication. Have the students share their strategies.
Notice the ratio table device used by Simon. This is an excellent tool for developing proportional thinking in students. This ratio table does not use distance to show the relationships, as the double number line does; it is simply a number table.
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Answers will vary.
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