Ratio of two quantities

Year 6 programme of study: Ratio and proportion:
Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

This resource introduces the concept of ratio, starting with sharing a given quantity using the visual support of tape diagrams (also called the bar model), then moving on to word based problems.

Worksheets with visual support
Tape diagrams (or bar models) allow students to see the relationships between quantities in a simple graphical format. This visual aid helps students understand the structure of the problem and the relationships between the parts to be shared and how the relationships between quantities change when the ratio changes. They also help to develop a systematic approach to solving ratio problems.

Worksheet Sets 1 to 3
The initial quantity and the ratio for sharing are given. Students must find the value of one unit of sharing, color in the tape diagram accordingly, then find the size of each sharedpart of the original quantity.

You have a choice of 3 ranges of numbers:
Level 1: Under 100
Level 2: to 1000 in multiples of 10
Level 3: to 1000

This gives you the choice of starting with small numbers and focusing on the ratio calculations, then later use the worksheets with larger numbers to bring in extra practice with the 4 operations.

Worksheet Sets 4 to 6
A further set of challenging Worksheets with the visual aid contain questions giving the ratio & one of the final answers with the aim to find the initial quantity. As with Worksheets Sets 1-3 you have a choice of 3 ranges of numbers to work with.

Worksheet Sets 7 to 9
These have a mix of the formats from Sets 1 to 3 and 4 to 6, with the 3 ranges of numbers, and the additional task of determining the width of the tape diagrams before coloring them in according to the ratio of the parts.

Word Problems on Ratio Worksheet Sets
The two Sets contain a mix of questions including sharing a given quantity; given a share and the ratio, find the original quantity etc as outlined above, (but now without the visual support), plus finding the ratio of two quantities in their simplest form (equivalence of ratios). The quantities in Set 1 are 1 & 2-Digit numbers, whilst in Set 2 range quantities are 2 & 3-Digit numbers.

How many worksheets are there in total ?
Virtually unlimited … There are 8 Sets, BUT, at the click of a button numbers are randomised, so the questions change which allows you to create new worksheets at the any level for extra practice or revision throughout the year or even give groups of pupils within your class different sets of questions.

Answers are automatically generated every time.

Note
These resources work with the official Adobe Acrobat Reader on Windows or Mac computers.

Australian Syllabus
ACMEM065 - demonstrate an understanding of the elementary ideas and notation of ratio
ACMEM069 - divide a quantity in a given ratio