Ratios with Whole Numbers 2

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Purpose

These exercises and activities are for students to use independently of the teacher to practise number properties.

Achievement Objectives
Specific Learning Outcomes

Ratio problems set in different ways. All problems work with ratios with three numbers. Note that in all activities there is a basic recipe (lowest equivalent ratio) based on 10 people. The equivalent ratios needed then are for 20, 30, 40 people etc. This means that the multiplier is 2, 3, 4 etc and not 20, 30…

Description of Mathematics

Proportions and Ratios, AP (Stage 8)

Required Resource Materials
Practice exercises with answers (PDF or Word)
Activity

Prior knowledge:

  • Multiplication basic facts
  • Multiply any two digit number by a single digit number
  • Find fractions of numbers
  • Work with equivalent fractions

Background:

In this activity students explore equivalent ratios.  It is helpful is students are familiar with the concept of equivalent fractions. 

Comments on the Exercises

The exercises have been set up in the following way.

Exercise 1
Asks students to find equivalent ratios from given ratio written in ratio form (20, 50, 100).

Exercise 2
Asks students to make up their own ratios and finding equivalent ratios (30, 80, 200 people).

Exercise 3
Asks students to write ratios from a word problem where the numbers are given, finding lowest equivalent ratios, finding equivalent ratios (50 people).

Exercise 4
Asks students to make their own problem like in Exercise 3, and find lowest equivalent ratio.

Exercise 5
Asks students to write ratios from a word problem where the information is given as the number of red for every white and black, and find equivalent ratios (30 people).

Exercise 6
Asks students to write word problems as in Exercise 5 from a given ratio.

Exercise 7
Asks students to make up their own salads and describing as in Exercise 5.

Exercise 8
Asks students to write ratios from a word problem where the information is given as white is twice red and black is three times red (for example),and finding equivalent ratios (40 people).

Exercise 9
Asks students to write word problems as in Exercise 8 from a given ratio.

Exercise 10
Asks students to make up their own salads and describe as in Exercise 8.

Exercise 11
Asks students to write ratios from a word problem where the information is given as a fraction, and find equivalent ratios (70 people).

Exercise 12
Asks students to write word problems as in Exercise 11 from a given ratio.

Exercise 13
Asks students to make up their own salads and describing as in Exercise 11.

Exercise 14
Asks students to combine salads to get new ratio, and find equivalent ratios (60 people, from 20 people).

Exercise 15
Asks students to make up own salads as in Exercise 14.

Number generalisation:

Build the ideas that a:b:c and 3a:3b:3c are the same. See Book 8 page 42.

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Level Five