Fractions of Amounts

Calculating the fractions of amounts or sets brings together a number of concepts that includes the unit fraction, quantities of objects in rectangular arrays (multiplication), connecting the unit fraction of a quantity and division, and finally the step by step numerical calculation to obtain the final result and word based problems.

The following (almost) unlimited, no-prep worksheets combine and connect all these ideas providing you with material to differentiate from the very beginning, and plan a structured development of understanding and practice.

Worksheets Sets

• WS1: Unit fraction of amounts with rectangular arrays - the visual approach, counting

• WS2: Unit fractions & fraction of amounts with rectangular arrays - mix with small denominators (2-5)

• WS3: Fraction of amounts with rectangular arrays with larger denominators ( 6 - 9)

• WS4: Coloring in fractions of amounts with rectangular arrays

• WS 5-7: Unit fractions of amounts - numerical exercises - with guiding steps
  3 levels of increasing range of denominators & quantities

  denominators 2-8 & amounts 4 to 112 

  denominators 4-10 & amounts 12 to 160 

  denominators 5-12 & amounts 30 to 240 

• WS 8-10: Unit fractions of amounts - numerical exercises - without guided steps

3 levels of increasing range of denominators & quantities

denominators 2-8 & amounts 4 to 112

denominators 4-10 & amounts 12 to 160

denominators 5-12 & amounts 30 to 240

• WS 11-13: Fractions of amounts - numerical exercises - with guiding steps
  3 levels of increasing range of denominators & quantities

denominators 3-10 & amounts 6 to 120

denominators 4-12 & amounts 15 to 180

denominators 5-15 & amounts 50 to 450

• WS14-16: Fractions of amounts - numerical exercises - without guided steps
  3 levels of increasing range of denominators & quantities

denominators 3-10 & amounts 6 to 120

denominators 4-12 & amounts 15 to 180

denominators 5-15 & amounts 50 to 450

• WS17-18: Word Problems

denominators 3-6 & amounts 18 to 108

denominators 5-20 & amounts 40 to 500

How is 'almost unlimited' worksheets possible ?
At the click of a button numbers ( and pictures with the arrays) are randomised, so the questions change every time. This will allow you to create as many new worksheets your students need for practice throughout the year (classwork, homework, revision, fillers, assessments etc) or even give small groups of students in your class different sets of questions either at the same level or differentiated .

There will certainly be enough material to keep the skill alive throughout the year.

Answers found on the second page of every worksheet are automatically generated when you create a new worksheet.

Self Checking Interactive Presentation

Ideal for a whole class activity as an introduction to the worksheets. Pupils can come to the Whiteboard and enter solutions and get immediate feedback.

There are 2, one covering the arrays, and the other the numerical method.

All of the above is accompanied by a Guide.

Note
These resources are PDF documents and work with the official Adobe Acrobat Reader on Windows or Mac computers with the randomising buttons also working via a touchscreen (PC or Mac)or on an Interactive Whiteboard.

Curriculum links

Common Core

CCSS.MATH.CONTENT.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

CCSS.MATH.CONTENT.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Australia - Year 6

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

UK National Curriculum
Year 3 - Number Fractions
Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Notes and guidance (non-statutory)

Pupils understand the relation between unit fractions as operators (fractions of), and division by integers.

Year 4: Fractions of amounts
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number