What do you see?
This is a level 4 number activity from the Figure It Out series. It relates to stage 7 of the number framework. 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 regions.
- Use multiplication facts to find fractions of whole numbers.
What do you see?
Achievement objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
Description of mathematics
Number framework links
Use this activity to help students consolidate and apply their knowledge of equivalent fractions (stage 7), using reunitising as a strategy (stage 8).
Required materials
- Figure It Out, Level 3+, Proportional Reasoning, "What do you see?", pages 6–7
See Materials that come with this resource to download:
- What do you see activity (.pdf)
Activity
This activity models a classroom situation in which a number of students share different ways of viewing the shaded part of a rectangle. It doesn’t matter that three of the contributions seem unlikely; they make excellent subjects for discussion. Take particular care with the last two. Your students may not have come across such fractions before, but if they study the illustrations, they will start to put meaning to the tricky notion of a fraction divided by a fraction. Study them carefully before introducing this activity to your students, and think of ways of rewording or teasing out the speech bubbles.
For example, you could expand the last speech bubble to read:
- I can see groups of 6 squares. There are 3 1/3 of these groups. 2 of them are shaded. That’s 2 out of 3 1/3.
When they come to do question 1, the students should draw on the understanding that they have gained from the discussion of the ideas presented in the speech bubbles, particularly the last two.
In question 2, the students write a number of equivalent fractions. Although they are only asked for “at least six”, there are in fact an infinite number of possibilities. Encourage them to find at least one that is a fraction divided by a fraction (for example, (1 1/8) / (4 1/2) ). Students who have encountered algebraic notation may be able to say that all the equivalent fractions can be represented by the term x/4x.
The simplest way of finding out whether an egg tray can be divided into a particular kind of fraction is to check if the denominator is a factor of the number of eggs in the tray (stage 7). In question 3b, the students need to draw egg trays and then divide them up accordingly. Some may like the challenge of finding just how many different ways the trays can be divided into sixths and eighths.
1.
2.
Answers will vary. There are many possibilities, including: 1/4, 2/8, 6/24, 9/36, 10/40, 15/60.
3.
a.
b. Answers will vary. For example, here are 6 ways of dividing the 18-egg tray into sixths:
The quality of the images on this page may vary depending on the device you are using.