How many people?
This is a level 2 number activity from the Figure It Out theme series. 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 whole numbers.
How many people?
Achievement objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Required materials
- Figure It Out, Level 2–3, Theme: Gala, "How many people?", page 3
- a classmate
- a calculator
See Materials that come with this resource to download:
- How many people activity (.pdf)
Activity
Using fractions in this context will help the students to work out how to find fractions of larger whole numbers. Some students may have some difficulty visualising fractions of larger numbers, such as 1000. You could use a metre ruler or a number line and show the students halves, quarters, fifths, and so on. You could record your findings in a table.
Discussing concrete examples such as 1/2 of a pack of cards, 1/4 of a packet of pebbles, 1/2 of your height, 1/2 of a kilogram, and 3/4 of a packet of biscuits may also be useful.
Point out to the students the connections between fractions, division, and multiplication so that they are able to see how to calculate the answers. For example:
- 1/2 of 20 is 20 divided by 2.
- 2/3 of 21 is 21 divided by 3, and that answer is multiplied by 2.
The students will learn to use a calculator to find the fractional part of a larger number like 1000. For example, 3/4 of 1000 is 1000 divided by 4, and then that answer is multiplied by 3.
You could also explain that 2/3 means 2 ÷ 3. The students need to understand that the line separating the numerator and the denominator of a fraction is the division operator. If the students grasp this at an early stage, many of their problems in later algebra will be solved. You could then discuss the following examples:
- 12/3 is the same as 12 ÷ 3 = 4.
- 100/4 is the same as 100 ÷ 4 = 25.
- 20/4 of 100 is the same as 100 divided by 4 and that answer is multiplied by 20.
- or 20/4 of 100 is 20 ÷ 4 and that answer is multiplied by 100.
In question 2, encourage the students to use mental reasoning by explaining how they worked their classmate’s problem out and why they know their answer is right.
The students also deal with fractions of sets in question 2, Activity 2, page 18.
Page 20 of Number, Figure It Out, Levels 2–3, deals with finding fractions of two-digit numbers. This page and its teachers’ notes could tie in well with "How many people?"
1.
a. 250
b. 200
c. 500
d. 250
e. 750
2.
Answers will vary.
The quality of the images on this page may vary depending on the device you are using.