What do you see?

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Purpose

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.

Achievement Objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
Student Activity

  

Click on the image to enlarge it. Click again to close. Download PDF (1205 KB)

Specific Learning Outcomes

find fractions of regions

use multiplication facts to find fractions of whole numbers

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 Resource Materials
FIO, Level 3+, Proportional Reasoning, What do you see? pages 6-7
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.
 

Answers to Activity

1.

answers.

2. Answers will vary. There are many possibilities, including: 1/4, 2/8, 6/24, 9/36, 10/40, 15/60
3. a.

answers.
b. Answers will vary. For example, here are 6 ways of dividing the 18-egg tray into sixths:

egg trays.

Attachments
Add to plan

Log in or register to create plans from your planning space that include this resource.


Level Four