Maths Rescue Series: Book 3

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r o e t s Bworking r For students at risk at e o p o u k Upper Primary levels S

rescue maths Book 3 number: applications

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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By Sandy T asker Tasker c e her r o t s super

© Ready-Ed Publications - 2003.

Published by Ready-Ed Publications (2003) P.O. Box 276 Greenwood W.A. 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes.

However, this permission is not transferable and applies only to the purchasing individual or institution.

ISBN 1 86397 566 7

Information on the Series About The Books

This series has been created for classroom teachers and parents to use for home or class work - with students of a range of abilities taken into consideration. The focus will be on reinforcement of “the basics” in maths, as well as activities aimed at developing understanding of classroom activities in mathematics.

Students with Specific Learning Difficulties experience a range of problems with their academic learning. These aspects include:• Difficulties with word recognition and comprehension • Coping with pages that are too cluttered and with too many differing requirements • Being able to sequence, recall and apply strategies in abstract situations • Striving to process formation - while working to meet deadlines • Having trouble with personal organization with their schoolwork.

The books in this series are designed with these problems in mind, and whilst pages are designed for the student with learning difficulties, they can also be used as a simple and straightforward introduction to concepts or a reinforcement of mathematical strategies for the whole class. The books will follow a basic format, with a variety of homework topics usually containing a choice of two worksheets.

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Content of the Books

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The Three Books in the Series Book One: Number - Written Calculations Book Two: Measurement, Chance and Data Book Three: Number - Applications Curriculum Links and Learning Outcomes The aim of the activities is to focus on one concept per page, therefore, only one outcome in a strand from the relevant Mathematics outcomes will usually be addressed. Strands and outcomes focused on in this book are shown on pages 4 to 6. Learning Outcomes for each page are specified at the top of the page.

Information in Specific Learning Difficulties This section will contain information from a variety of referenced sources including online literature and recommendations from trained and experienced consultants. Information will include descriptions of the various learning difficulties and ideas for strategies in the classroom and at home.

A list of website addresses containing information and ideas is provided for teachers and parents.

Student Lifesavers Many students with Specific Learning Difficulties become overwhelmed when expected to recall basic facts when carrying out more complex calculations. Students may grasp a concept, but be unable to apply the strategy because they are struggling to remember tables and combinations. To focus on the teaching point and alleviate stress for students, these tables and charts can be kept within easy access for the students. Charts include multiplication tables, addition and subtraction charts, number lines, rules and formulas and measurement conversions.

“Parent Power” Pages The information provided on Specific Learning Difficulties at the beginning of this book can also be photocopied and given to parents who are requesting additional information. However, it should be made clear that this is a guide only, and contact with local recognised Specific Learning Difficulty associations or Child Development Centres should be made if there are any particular concerns.

Parent Power pages can be photocopied and sent home at the commencement of each unit and include: • terminology; • mathematical strategies and examples; • learning and practice ideas in the home and community.

It is also suggested that teachers photocopy answers to each section and include these when sending home the Parent Power Page. This enables parents to feel confident in checking their child’s work and giving them valuable, immediate feedback.

Progress Charts It is widely appreciated that success is built on success, and the more students are able to track their own progress, the more likely they are to be motivated to attempt the next stage in their learning. Students can keep these progress charts as an ongoing record of their homework.

Skill Drills Some students work best with structured, timed drills. Drill practice can be very helpful in developing skills in automatic recall. The drill charts in this book are designed so that the length of time and the starting position for the drill can be changed according to the student’s abilities. A record of the score can be kept so that the student can track their progress.

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Contents

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Information on the series ........................................................................................................................ 2 Curriculum Links - State and National Curriculums ........................................................................... 4 - 6 Specific Learning Difficulties .................................................................................................................. 7 How are Individuals With Specific Learning Difficulties Affected? ........................................................... 9 General Strategies for the Classroom .................................................................................................... 9 General Strategies for the Home ........................................................................................................... 11 Internet References .............................................................................................................................. 12 Parent Power Maths Words ............................................................................................................................. 13 Money Skills .............................................................................................................................. 14 Fractions .................................................................................................................................... 15 Decimals .................................................................................................................................... 16 Progress Chart What Can I Do? ......................................................................................................................... 17 Activity Sheets Greater Than / Less Than 1 ....................................................................................................... 18 Greater Than / Less Than 2 ....................................................................................................... 19 Money Skills - Revision 1 .......................................................................................................... 20 Money Skills - Revision 2 .......................................................................................................... 21 Money Skills - Change 1 ............................................................................................................ 22 Money Skills - Change 2 ............................................................................................................ 23 Money Skills - Budgeting 1 ........................................................................................................ 24 Money Skills - Budgeting 2 ........................................................................................................ 25 Rule of Order 1 .......................................................................................................................... 26 Rule of Order 2 .......................................................................................................................... 27 Squared Numbers 1 ................................................................................................................... 28 Squared Numbers 2 ................................................................................................................... 29 Fraction Revision 1 .................................................................................................................... 30 Fraction Revision 2 .................................................................................................................... 31 Mixed Numerals 1 ...................................................................................................................... 32 Mixed Numerals 2 ...................................................................................................................... 33 Equivalent Fractions 1 ............................................................................................................... 34 Equivalent Fractions 2 ............................................................................................................... 35 Ordering Fractions 1 .................................................................................................................. 36 Ordering Fractions 2 .................................................................................................................. 37 Changing Fractions 1 - Whole Numbers to Improper Fractions .................................................. 38 Changing Fractions 2 - Mixed Numerals to Improper Fractions .................................................. 39 Changing Fractions 3 - Practice ................................................................................................. 40 Changing Fractions 4 - Improper Fractions to Mixed Numerals .................................................. 41 Changing Fractions 5 - Improper Fractions to Mixed Numerals .................................................. 42 Adding & Subtracting Fractions 1 .............................................................................................. 43 Adding & Subtracting Fractions 2 .............................................................................................. 44 Fractions of a Number 1 ............................................................................................................. 45 Fractions of a Number 2 ............................................................................................................. 46 Fractions and Decimals 1 .......................................................................................................... 47 Fractions and Decimals 2 .......................................................................................................... 48 Percent 1 ................................................................................................................................... 49 Percent 2 ................................................................................................................................... 50 ANSWERS .......................................................................................................................................... 51

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Curriculum Links - State Curriculum Documents

Activities in this book mainly address the following outcomes in the Number Strand of the relevant curriculum documents.

Activity

New South Wales

Queensland

Greater Than/Less Than 1

Whole Numbers N 3.1

Number Concepts N 3.1

Greater Than/Less Than 2

Whole Numbers N 3.1

Number Concepts N 3.1

Money Skills 1

Applying Number N 3.5

Number Concepts N 3.1

Applying Number N 3.5

Number Concepts N 3.1

Applying Number N 3.5

Number Concepts N 3.1

Applying Number N 3.5

Number Concepts N 3.1

Applying Number N 3.5

Number Concepts N 3.1

Applying Number N 3.5

Number Concepts N 3.1

Rule of Order 1

Number Operations N 3.4

Number Concepts N 3.1

Rule of Order 2

Number Operations N 3.4

Number Concepts N 3.1

Squared Numbers 1

Number Facts N 3.3

Number Concepts N 3.1

Squared Numbers 2

Number Facts N 3.3

Number Concepts N 3.1

Fraction Revision 1

Fractions N 2.2, N 3.2(a)

Number Concepts N 3.1

Fraction Revision 2

Fractions N 2.2, N 3.2(a)

Number Concepts N 3.1

Mixed Numerals 1

Fractions N 2.2, N 3.2(a)

Number Concepts N 3.1

Mixed Numerals 2

Fractions N 2.2, N 3.2(a)

Number Concepts N 3.1

Equivalent Fractions 1

Fractions N 3.2(b)

Number Concepts N 3.1

Equivalent Fractions 2

Fractions N 3.2(b)

Number Concepts N 3.1

Ordering Fractions 1

Fractions N 2.2, N 3.2(a)

Number Concepts N 3.1

Ordering Fractions 2

Fractions N 2.2, N 3.2(a)

Number Concepts N 3.1

Changing Fractions 1

Fractions N 3.2(a)(b)

Multiplication and Division N 4.3

Changing Fractions 2

Fractions N 3.2(a)(b)

Multiplication and Division N 4.3

Changing Fractions 3

Fractions N 3.2(a)(b)

Multiplication and Division N 4.3

Changing Fractions 4

Fractions N 3.2(a)(b)

Multiplication and Division N 4.3

Changing Fractions 5

Fractions N 3.2(a)(b)

Multiplication and Division N 4.3

Add/Subtract Fractions 1

Number Operations N 3.4

Addition and Subtraction N 3.2

Add/Subtract Fractions 1

Number Operations N 3.4

Addition and Subtraction N 3.2

Fractions of a Number 1

Number Operations N 3.4

Multiplication and Division N 3.3

Fractions of a Number 2

Number Operations N 3.4

Multiplication and Division N 3.3

Fractions & Decimals 1

Number Operations N 3.4

Number Concepts N 3.1

Fractions & Decimals 2

Number Operations N 3.4

Number Concepts N 3.1

Percent 1

Fractions N 3.2(b)

Number Concepts N 4.1

Percent 2

Fractions N 3.2(b)

Number Concepts N 4.1

Money Skills 2 Change 1 Change 2

Budgeting 2

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Budgeting 1

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Curriculum Links - State Curriculum Documents

Activities in this book mainly address the following outcomes in the Number Strand of the relevant curriculum documents. (Read Activity names from previous page.)

South Australia

Victoria

Western Australia

Numbers, Counting and Numeration 3.1

Understand Numbers N 3.1(a)

Number 3.7

Numbers, Counting and Numeration 3.1

Understand Numbers N 3.1(a)

Number 3.6, 3.7

Computation and Applying Number 3.2

Understand Numbers N 3.1(a)

Number 3.6, 3.7

Computation and Applying Number 3.2

Understand Numbers N 3.1(a)

Number 3.6, 3.7

Computation and Applying Number 3.2

Understand Numbers N 3.1(a)

Number 3.6, 3.7

Computation and Applying Number 3.2

Understand Numbers N 3.1(a)

Number 3.6, 3.7

Computation and Applying Number 3.2

Understand Numbers N 3.1(a)

Number 3.6, 3.7

Computation and Applying Number 3.2

Understand Numbers N 3.1(a)

Number 3.7

Computation and Applying Number 3.2

Understand Operations N 3.2

Number 3.7

Computation and Applying Number 3.2

Understand Operations N 3.2

Number 3.7

Number Patterns and Relationships 3.1

Reason About Number Patterns N 3.4

Number 3.7

Number Patterns and Relationships 3.1

Reason About Number Patterns N 3.4

Number 3.8

Computation and Applying Number 3.2

Understand Numbers N 3.1(b)

Number 3.8

Computation and Applying Number 3.2

Understand Numbers N 3.1(b)

Number 3.8

Numbers, Counting and Numeration 3.3

Understand Numbers N 4.1(a)

Number 3.8

Numbers, Counting and Numeration 3.3

Understand Numbers N 4.1(a)

Number 3.8

Numbers, Counting and Numeration 3.3

Understand Numbers N 4.1(b)

Number 3.8

Numbers, Counting and Numeration 3.3

Understand Numbers N 4.1(b)

Number 3.8

Numbers, Counting and Numeration 3.3

Understand Numbers N 4.1(b)

Number 3.8

Numbers, Counting and Numeration 3.3

Understand Numbers N 4.1(b)

Number 3.8

Number Patterns and Relationships 4.3

Understand Numbers N 4.1(b)

Number 3.8

Number Patterns and Relationships 4.3

Understand Numbers N 4.1(b)

Number 3.8

Number Patterns and Relationships 4.3

Understand Numbers N 4.1(b)

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Number 3.7

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Number Patterns and Relationships 4.3

Understand Numbers N 4.1(b)

Number Patterns and Relationships 4.3

Understand Numbers N 4.1(b)

Computation and Applying Number 3.3

Understand Operations N 4.2

Number 3.8

Computation and Applying Number 3.3

Understand Operations N 4.2

Number 3.8

Computation and Applying Number 3.3

Understand Operations N 4.2

Number 3.8

Computation and Applying Number 3.3

Understand Operations N 4.2

Number 3.8

Numbers, Counting and Numeration 4.3

Understand Numbers N 4.1(a)

Number 3.8

Numbers, Counting and Numeration 4.3

Understand Numbers N 4.1(a)

Number 4.8

Computation and Applying Number 4.3

Understand Numbers N 4.1(a)

Number 4.8

Computation and Applying Number 4.3

Understand Numbers N 4.1(a)

Number 3.8 Number 3.8

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National Curriculum Links

Activities in this book mainly address the following outcomes in the Number Strand of the curriculum document.

Activity

Count & Order 3.11

Greater Than/Less Than 1

4.11

Equations 3.13

4.13

Applying Numbers 3.14

4.14

Mental Written Calculators Computation Computation 3.15

4.15

3.16

4.16

3.17

4.17

O O

Greater Than/Less Than 2

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Money Skills 1

O

Money Skills 2

O

Change 1

O

Budgeting 1

O

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Change 2

O

Budgeting 2

Rule of Order 1

O

Rule of Order 2

O

Squared Numbers 1

O

Squared Numbers 2

O

Fraction Revision 1

O

Fraction Revision 2

O

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Mixed Numerals 1

O

Mixed Numerals 2

O

Equivalent Fractions 1

O

Equivalent Fractions 2

O

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Changing Fractions 1

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Changing Fractions 2 Changing Fractions 3 Changing Fractions 4 Changing Fractions 5

Adding & Subtracting Fractions 1 Adding & Subtracting Fractions 2

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Ordering Fractions 1

O O O

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O O

Fractions of a Number 1

O

Fractions of a Number 2

O

Fractions & Decimals 1

O

Fractions & Decimals 2

O

Percent 1

O

Percent 2

O

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Specific Learning Difficulties (SLDs) What are Specific Learning Difficulties?

Specific Learning Difficulties ARE: • A range of conditions including dyslexia, dyscalculia, dyspraxia and dysgraphia.

• Significant difficulties in one or a few areas of learning, whilst demonstrating average to above average abilities in most or all other areas.

Specific Learning Difficulties ARE NOT: • A result of global low intelligence, physical conditions such as visual or hearing impairments, or a lack of appropriate parenting or teaching.

• Attention difficulties (or behavioural disorders) such as Attention Deficit Disorder (ADD) and Attention Deficit Hyperactivity Disorder (ADHD). Specific Learning Difficulties are founded on a reduced capacity to learn, and attention difficulties stem from a reduced capacity to concentrate and attend to tasks when learning.

Specific Learning Difficulties CAN: • Appear to overlap, as learning areas often merge. For example, a person with reading difficulties may struggle in maths in the presence of lengthy word problems or poorly set-out activities (www.dyslexia-speld.com).

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Descriptions of the Types of Specific Learning Difficulties

(www.dyslexia-speld.com)

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Dyslexia is the most commonly recognised and well-researched SLD, characterised by difficulties in: • Recognising, reading and spelling words; • Comprehension of written information; • Relating new written concepts to stored ideas and existing knowledge; • Phonological coding, the process of associating sounds with letter groups; • Producing written work (sequencing letters, recognising letter reversals).

Dyscalculia describes significant difficulties in the area of mathematics. People with dyscalculia may possess average to above average linguistic skills but struggle with: • Mental recall of basic facts; • Accurate calculation; • Understanding and applying mathematical concepts, rules and formulas; • Awareness of time, direction (such as spatial and mapping skills) and sequence; • The ability to estimate and recognise errors in maths work; • Money and budgeting; • Games that involve strategic planning or complex scoring.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• (www.dyscalculia.org)

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Dysgraphia outlines difficulties with the production of written language which may occur in isolation or in conjunction with other SLDs. Underlying causes include difficulties with sequencing and ordering of letters and words, attention difficulties leading to poor fine motor and organisational skills and reduced auditory processing. (www.ldonline.org) Dyspraxia describes difficulties in the ability to plan and execute new or unfamiliar movements in a coordinated manner. During early childhood, many new tasks are being learned, so this is a time where dyspraxia can significantly impact upon daily living. Problems can appear with performing fine and gross motor tasks (Motor Dyspraxia) and / or speech-related tasks (Verbal or oral Dyspraxia). (www.dyspraxiafoundation.org.uk)

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Associated Difficulties

Visual and Visual-Perceptual Difficulties (Source: www.children-special-needs.org)

These difficulties may occur in conjunction with, or as a result of, other learning or attention difficulties. The problems listed below can also place a considerable strain on the reading process for a child, and can often go unnoticed until the child is in primary school, where the he / she spends longer periods of time focusing on print.

Myopia (short-sightedness) - may lead to difficulties in reading information written on the blackboard or on charts around the classroom, if not rectified with glasses or contact lenses.

Binocular coordination - the action of both eyes moving together, a process required to read effectively.

Convergence - the movement of both eyes inwards, reaching an accurate point of focus.

Fixation - where the eyes meet on a specific point so that the image is clear.

Pursuit - smoothly tracking across an image or follow a moving object.

Saccades - a “jump” from one point of focus to another without losing place. This is particularly important as skilled reading involves a series of fixations on words across a line rather than one continuous movement.

• Children who have difficulty with any of the above may show signs such as skipping or re-reading lines, misreading small words, using their finger or moving their head as they read.

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Directionality - A convention of the English language is that information is written from left to right. Some children confuse or reverse this direction and may also confuse letters that are the same shape in a different direction, such as d and b, or p and q.

Visual Figure-Ground is the ability to distinguish certain forms, words or features amongst irrelevant visual information such as reading print on a cluttered page, successfully scanning for key words within a block of text and editing work for errors.

Visual Discrimination relates to the distinction of similar words. Some children, for example, may consistently confuse similar words such as bad and bed, through and thorough.

Visual Form Constancy describes the recognition of the same object image or word in a different form, for example, being able to read the same sentence correctly in a variety of fonts, or understanding that a word is the same whether it is represented in capital or lower case letters.

Visual Closure can be demonstrated by mentally or physically completing “gaps” in visual images, such as writing the end of a word where only part of it is given or doing “dot-to-dot” and jigsaw puzzles.

Visual Memory aids in both reading and writing, as familiar words can be recognised, pronounced and spelt more automatically once they are retained. Students with poor visual memory take longer to learn new words.

Visual Sequential Memory refers to the recall of a sequence of shapes, images or words, and the ability to apply what is recalled. For example, looking up at the board to remember and write down a list of spelling words.

Visual Motor Integration is the process of integrating visual input with motor output – the coordination of “seeing, planning and doing”. In the classroom context, this skill is used in accurate copying of images and words, staying on the lines when writing and correctly aligning maths calculations, to name a few examples.

Auditory Processing

Auditory processing problems affect the learner’s ability to interpret auditory information. Often under the broad category of Central Auditory Processing Disorder (CAPD), this group of disorders are caused by a dysfunction of the brain, rather than of the ear, and include symptoms such as: • A slower rate of processing auditory information due to a perceived distortion of the incoming sounds; • A sensitivity to excessive noise or background noise – inability to concentrate and distractibility; • Difficulty locating directionality of sound; • Confusion of similar words or sounds; • Poor memory of verbal instructions; • Difficulty interpreting intonation such as jokes, sarcasm, questions, etc.; • Apparent hearing loss, e.g. saying “What?” often despite normal results on hearing tests; • Poor reading and/or writing as a result of some of the above problems.

There are several subgroups, which more specifically describe auditory processing disorders and like visual perceptual problems, these can exist in conjunction with other learning or attention difficulties.

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Attention Deficit Disorder

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Attention Deficit Disorder or ADD is a neurological disorder that has been a focus of media attention over the last decade. There are two types that are commonly recognised: Attention Deficit Hyperactivity Disorder (ADHD) is characterized by: • Constant fidgeting or moving about in a seat; • Having trouble waiting a turn; • Impulsivity; • Difficulty listening to and following instructions.

Attention Deficit Disorder (ADD) is evident in individuals who: • Are quiet, withdrawn and sluggish; • Demonstrate low self-esteem; • Are often described as “daydreamers”; • Need constant prompting to remain on task.

Both types tend to be: • Easily distracted • Forgetful • Disorganised As previously mentioned, Attention Deficit Disorder is a separate entity to Specific Learning Difficulties and each requires some unique strategies to best approach the difficulties. There are, however, instances where an individual may experience both conditions to a certain degree.

Initially, it may be difficult for the untrained individual to pinpoint the “cause”. A student with attention difficulties may appear dyslexic because their distractibility leads them to constantly lose their place when reading. Conversely, a student with a specific learning difficulty may become so frustrated that they avoid work or give up easily, appearing to “lose concentration”.

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Source: http://add.about.com

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How are Individuals With Specific Learning Difficulties Affected?

Some of the obstacles that students with SLDs can face are: • Being branded as “lazy” because they are capable in most areas, and their difficulties often do not correspond with expectations based on their intelligence; • Becoming frustrated that they understand a concept, but are not able to read or write about it; • Developing a low self-esteem as they struggle to keep up with their peers; • Missing out on educational support and resources during the time it takes to identify their problems.

On the positive side, having a SLD can also mean that the individual: • Is constantly seeking out alternative ways of thinking and learning, thus becoming a creative and innovative thinker or a strong leader; • Is an intelligent, capable individual, who can be educated at any level if approached with understanding and a willingness to provide appropriate learning opportunities and strategies; • Can overcome learning difficulties to become successful in their chosen fields. Some examples of these people can be found at: www.nald.ca and www.dyslexiaonline.com

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General Strategies for the Classroom

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Below are some ideas that may be of assistance with any of the areas of difficulty listed above. They are not intended to be specific strategies for any one area. These suggestions are provided as a guide only and it is recommended that teachers and parents seek specialised, individualised assessment and intervention for students who have SLDs. Location - Seat the student where they can: • Read the board; • Hear instructions clearly; • Easily access teacher assistance; • Locate reference charts; • Find personal belongings; • Be free from potential distractions.

Organisation - Encourage a desk that: • Is clear of “clutter”; • Contains daily work items in a clear pencil case or a tin (contains only the “essentials” such as pencils, ruler, eraser, scissors, glue and a calculator).

A daily or weekly checklist to ensure that all stationery is available may help the student to keep track of when things need to be tidied or replaced.

Collaboration - A peer tutor needs to know how to: • Prompt and set good examples for the student; • Help without “spoon-feeding” them with the answers; • Avoid distractions.

Support Success - Building self-esteem by: • Drawing attention to any success, even if partial, e.g. “Well done! You are using the formula correctly, you just might like to check your final calculation again”.

• Drawing on student’s strengths, e.g. asking them to dictate answers verbally if extended writing is difficult.

Break It Down - Aid learning by breaking tasks down into manageable components.

• Help the student to plan each stage of a task with a familiar “plan of attack” can be helpful.

For example, when approaching a word problem, asking “What sort of sum is this”, then “What numbers will be in the sum”, then “Write the sum”, etc.

Allow Extra Time - allowing students additional time in situations such as tests is a fair means of compensating for their difficulties. Additional time can also be given to a student by spending a few minutes explaining a new concept in advance before introducing it to the class, so that the information is consolidated, rather than lost in a panic.

Easy On Eyes - Try some of the following and ask the student what they prefer.

• Font: simple, clear font with no serifs, such as “Arial”. (This book is typeset in Arial.)

• Size: Medium to larger size, for example 14 point.

• Line Length: 45 - 75 characters including spaces and punctuation.

• Paragraphing: wide margins (1.5 - 2.0 cm), 1.5 or double spacing, short, clearly separated paragraphs.

• Alignment: Do not justify - it leads to uneven spacing on the line.

• Emphasis: simple headings, using bold instead of italics. Use boxes to highlight information.

• Points: Use bullets or numbers to identify a list.

• Paper: Use matt paper, and try cream or other pastel colours, as many students with SLDs find white paper harder to read from.

• Limit irrelevant pictures, background print and borders.

• Additional space for ease of working out.

• Guiding lines, boxes and cues to assist students with setting out their work.

• Simple pictures, only used to reinforce concepts or problems, not as additional decoration on the page.

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Multisensory Learning - Students with SLDs often learn more successfully if provided with a variety of sensory experiences. To consolidate a concept use some of these – it will help ALL students learn: Look at it; write it in six different colours; write it in the air; trace it on sandpaper; show classmates on the blackboard; sing it or make it into a rhyme; say it to a partner; draw it; act it out; use counters, MAB blocks and plastic money or other real objects.

1x9 bend first finger down

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4x9 5

3

• Reversals, e.g. 6 + 4 = 4 + 6 • “Tens pairs” (pairs of numbers adding up to 10) e.g. 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 …

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Keep On Track - To avoid “losing track of time”: • Issue regular warnings about how much time is left; • Try a timer on the student’s desk (if this does not cause additional stress); • Highlight a number of items that they should aim to complete before the next time you pass by their desk.

Room To Move - Provide an outlet for excess energy by: • A small “fidget toy” such as a palm sized squeeze ball; • Asking the student to take messages to other classrooms.

Memory Strategies • Reference charts; • Mnemonics, poems; • Visualising in pictures; • The “9 x table finger” technique, i.e.

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General Strategies for the Home Some of the strategies below may be of assistance when supporting your child in their mathematics homework.

• Short and Sweet - Shorter, more frequent sessions of homework minimise the risk of your child losing concentration. Practising a task over a number of days will help to reinforce the concept, so try 10 - 15 minutes of homework each day rather than one hour, once a week.

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• A Friendly Place - Create an environment that is consistent, quiet, comfortable and well lit, with plenty of space for both you and your child to work together. Have a glass of water for your child to drink. Some students also work best if they have small snacks to nibble on whilst they work.

• The Right Stuff - Make sure your child has all the necessary equipment before starting. Some handy things to have include highlighters (to emphasise important parts of the homework or examples), eraser (so that mistakes can easily be corrected and there is no mess of scribbling out), sharpener (so that writing is clear and easy to read), lined scrap paper (with relevant sized lines and plenty of space for working out and examples).

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• • In Tune - Background music has been found to be beneficial for some

• Write it Big - A whiteboard may be a useful way of working out problems. It is easy to see, easy to rub out, and another way of introducing a different sensory experience to the child. learners. Classical (Baroque) music has been researched quite extensively and may be of assistance.

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• Check it Off - Using a checklist to tick off tasks that have been done give your child a sense of achievement as well as helping them to keep their place.

• Charts are not Cheating - A chart with rules, formulas, definitions and basic maths facts can help your child enormously. Remember that integrating several concepts at once can be overwhelming, and it is best to “isolate” the new skill being learned until your child is confident. For example, if your child is learning how to calculate area, a multiplication chart may be useful until he / she has learned how to use the length x width formula.

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o c . che e r o t r s super • Success is the Best Foundation - Remember that every time your child

gets something correct, even if it is just one part of a larger task, praising them for their success is the most effective way to increase their self esteem and to motivate them to continue. Vary your positive comments, make them specific: “Good work for writing the 3 in the correct column!” and give them small rewards for reaching their goals: “You finished the whole page! Let’s go and kick the footy!”

Ready-Ed Publications

Book 3

Page 11

Internet References The following can be used as alternatives for parents who wish their child to practise basic mathematics online. http://www.math.com - Go to “Homework Help” for a range of explanations on a variety of maths skills. http://schooldiscovery.com - Visit sections such as “Parents”, “Brain Boosters” and “Webmath” for a range of activities.

r o e t s Bo r e p ok u S

www.discover.tased.edu.au - A Tasmanian education site with links to mathematics activities

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www.kevinsplayroom.co.uk - Visit the “Maths” section and explore activities such as the Maths Dictionary, A-Plus Math (including online flash cards), Curious and Useful Maths with interesting tricks and puzzles, and Math Baseball. www.yahooligans.com - Follow the links from School Bell > Math > Real World Math to discover activities for sites such as Math in Daily Life, Cadbury Learning Zone, Cool Math and Figure This.

www.awesomelibrary.org - Follow the links from Maths > Elementary School for a range of activity and article sites.

© ReadyEdPubl i cat i ons Sites with more information on learning difficulties: • f o r r e v i e w p u r p o s e s o nl y• www.dyslexia-speld.com - Western Australian organisation for people with learning difficulties.

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www.ldonline.org - Contains many links for a range of informative sites. www.interdys.org - International Dyslexia Association website.

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www.bda-dyslexia.org.uk - British Dyslexia Association website with ideas for parents and educators.

o c . www.dyscalculia.org c - Information on dyscalculia (specific learning difficulties e her r in maths). o t s s r u e p Contact your local organisation that caters for people with dyslexia and specific learning difficulties, or ask your local Child Development Centre or Child Health service for more information.

Page 12

Book 3

Ready-Ed Publications

Parent Power Maths W ords Words R Here are some meanings for words that you might read in maths work.

Examples are underneath.

Addition - Plus, add or “what is the sum of?” e.g. 2 + 4 = 6 Subtraction - Minus, take away or “how much is left?” e.g. 5 - 2 = 3

r o e t s Bo r e p ok u S

Multiplication / Multiplied by - Times, “lots of” or “what is the product of?” e.g. 3 x 5 = 15

Teac he r

Whole Number - 0, 1, 2, 3, 4 … (counting numbers as well as zero) Even Numbers - 2, 4, 6, 8, 10 … (numbers divisible by 2) Odd Numbers - 1, 3, 5, 7, 9 … (numbers not divisible by 2) Prime Numbers - A number that can only be divided by 1 and itself. e.g. 1, 3, 5, 7, 11, 13, 17, 19, 23, 29

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Division / Divided by - Shared into groups or “how many times does x go into y?” e.g. 10 ÷ 2 = 5 or 10 shared into groups of 2 = 5 groups

© ReadyEdPubl i cat i ons Composite Numbers - Numbers that have more than 2 numbers (factors) that divide into it, • f orr evi ew pur posesonl y• e.g. 2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

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Rounding - Finding the closest 10, 100 or 1000 for the number. e.g. Round 46 to the nearest 10 = 50 Round 530 to the nearest 100 = 500 Round 2978 to the nearest 1000 = 3000

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e.g. Factors of 16 are 1, 2, 4, 8 and 16 so it is a composite number.

o c . che e r o t r s super

> If the number to be rounded is “in the middle”, e.g. 35 is in between 30 and 40, most sources agree that it is best to round up, i.e. round 35 to 40. It is best to check with individual teachers on what they expect and why.

Ready-Ed Publications

Book 3

Page 13

Parent Power Money Skills R When are money skills used?

•

Banking - working out balances, amounts required to save, credit, debits, etc.

•

Shopping - estimating amount required, giving correct notes and coins, working out change.

•

Budgeting at home - estimating weekly or monthly amounts spent on items, dividing up monthly bills into weekly usage, working out amount of money available for other spending. With children, budgeting pocket money will develop money skills.

•

Socialising - paying for outings, keeping tabs on expenses throughout the day, splitting bills at restaurants.

r o e t s Bo r e p ok u S

Teac he r

R Activities at Home

Allow your child to keep small change in a piggy bank. This will encourage them to count up the money that they have and work out if they have enough to buy certain items.

•

Take your child shopping with you and ask them to round each item to the nearest dollar and mentally add to get a rough estimate of the total bill.

•

During food shopping, ask your child to help you work out the best value for money by doubling, halving, e.g. Is it better to get 6 eggs for $2.50 or a dozen eggs for $4.75?

•

At the checkout, ask your child to tell you which coins and notes will be needed (once the total is given) and how much change should approximately be expected.

•

Add up items eaten at a family meal at a restaurant. How much will the meal cost? What notes / coins should be given?

•

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•

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Allow your child to be responsible for coins during outings when public transport or

parking must be paid for, so they get used to planning the correct makeup of required coins.

•

Enquire about the service that banks have for children’s accounts. Many banks offer special programs that assist children in using forms and familiarising them with keeping track of their account.

•

Allow your child to use calculators for larger sums of money. This is realistic in terms of what is done in adult life and using the calculator is an important skill. One way to practise this is to have your child view your monthly bills and add up how much expenses will cost. This will also enable them to get a more realistic idea of how much things cost and help develop an appreciation of the value of money.

•

Play games at home that use money concepts, such as “Monopoly” or “The Game of Life” to help your child learn about keeping money in order, spending wisely, giving portions to “the banker”, etc.

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Make use of newspapers, junk mail and brochures to encourage your child to add up costs of Christmas gifts, toys that they wish to buy with pocket money, or food items for a dinner party.

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o c . che e r o t r s super

Book 3

Ready-Ed Publications

Parent Power Fractions •

Fraction - Part of a whole number or part of a group.

•

Proper Fraction e.g. ½ The numerator (top number) is smaller than the denominator (bottom number).

r o e t s Bo r e p ok u S

Numerator Denominator •

Improper Fraction

Teac he r

e.g. 4⁄2 •

Mixed Numeral or Mixed Number e.g. 2 ½

A whole number and a fraction.

•

Equivalent Fractions e.g. Fractions which show the same amount in different ways.

⁄ © Rea dyEdPubl i cat i ons Fraction Rules •only f o rfractions r evi pur p os eso n l y • You can add ife thew denominators (bottom number) are the same: ½ = 2⁄4 = 4⁄8 =

•

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The numerator (top number) is larger than the denominator (bottom number).

10

⁄20 =

50

100

e.g. you cannot easily add 1⁄3 and 2⁄4.

You can easily add 2⁄4 and ¼.

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Add the numerators (top number).

2

⁄4 + ¼ = ¾

This rule is the same for subtraction. Multiplying and dividing fractions are usually covered in upper primary/secondary school.

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R When are fractions used?

•

Cooking, especially in measurements, such as ½ a cup, ¼ of an apple, etc.

•

Everyday language, e.g. sports and games (the score was 134 points in the third quarter), telling time (half past three), travel (we are half way there), estimates (about a third of our class have a pet), etc.

R Activities at home •

Use a variety of utensils and measuring devices in cooking to help your child to see measurements, e.g. how much is ¼ of a cup, 1/3 of a tablespoon or ½ a kg of flour?.

•

Convert recipe amounts by using fractions, e.g. if the recipe is for 12 cupcakes and you only want to make 6, ask your child to halve each ingredient.

•

Encourage the interchange of terminology when your child is confident, e.g. point out that ½ a litre is 500ml.

Ready-Ed Publications

Book 3

Page 15

Parent Power •

Use cake or pizza to show fraction concepts, e.g.

How many cuts do I have to make to divide the cake into 8ths? (4 cuts) How many quarters does 2/8 make? (1/4 = 2/8) If I took away 3/8 of the cake, how many 8ths are left? (5/8)

•

Incorporate fractions into daily language, e.g.

“Give me half of your dirty laundry.”

“There are three children in this family. Can you divide the lollies into thirds to share them?”

“How old were you when you were half your age?”

“Can you please fold the blanket into quarters?”

“How much cordial is left in the bottle?”

Decimals

r o e t s Bo r e p ok u S

Teac he r

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R When are decimals used?

• Money is expressed in decimals, e.g. $3.50 means $3 plus .5 of one dollar.

• Fuel prices, odometer distances, Olympic distance measurements or anything else that needs to be expressed with precision can be written as a decimal.

R Activities at home

• • • •

Help your children to understand the relationship between money and decimals. This will help them to understand that $3.50 is more than $3.05.

Use a calculator when working out complex decimal sums, but also round to whole numbers and estimate to check the answer, e.g. 4.7892 + 7.9835 can be estimated as 5 + 8 = 13. The exact answer is 12.7727.

Use measurement activities to encourage precision by using decimals, e.g. “Can you measure out 1.5m of material to make this tablecloth?”

Discuss distances, sports results, etc. with your child in decimal amounts.

Ask your child to read thermometers, petrol rates, etc. and compare on a daily basis.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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•

How To Use The Following Activity Pages

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Each topic will focus on a single maths concept with a choice of two separate activity sheets. The teacher is able to introduce and explain the sheet to the whole class and then select which worksheet is assigned to each student. As both worksheets focus on the same content, only differing by the level of complexity, there is no need to isolate students by giving them separate instructions. Teachers may also choose to give all students the first sheet, and then follow up with the second sheet if the student is able to complete the first with minimal difficulties.

Some topics in this book have 3 or 4 sheets. These should be completed in sequential order.

Note: Although the second worksheet is designed for the more “able” students in the classroom, this certainly does not discount students with learning difficulties.

Research shows that many students with Specific Learning Difficulties can work at an average to above average level, provided that their needs are taken into consideration. With this in mind, both worksheets have been designed so that ALL students have the opportunity to be extended.

Page 16

o c . che e r o t r s super

Book 3

Ready-Ed Publications

Progress Chart

What Can I Do? O Colour the lines in as you learn something new: Encourage your child to use their own judgement for colouring in. The first square can be coloured in straightaway.

Getting some right: Approx 4/10; Getting most right: Approx 6/10 to 8/10; I can do this: Consistently getting more than 8/10 and confidently trying more complex problems

I can do this!!

Money Skills Starting to learn

Getting some right Getting most right

I can do this!!

Change Starting to learn

Getting some right Getting most right

I can do this!!

Budgeting Starting to learn

Getting some right Getting most right

r o e t s Bo r e p ok u S

Rule of Order

Starting to learn

Getting some right Getting most right

Squared Numbers

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Teac he r

Greater Than / Less Than Starting to learn Getting some right Getting most right

I can do this!!

I can do this!!

© Re ady Eright dP ubl i ca t i on sdo this!!

Getting some Getting most right I can Mixed Numerals •f orr evi ew pur posesonl y• Starting to learn Starting to learn

Getting some right Getting most right

I can do this!!

Equivalent Fractions Getting some right Getting most right

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Getting some right Getting most right

Ordering Fractions

. t e Starting to learn Starting to learn

I can do this!!

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Starting to learn

I can do this!!

Io can do this!! c . che e Adding and Subtracting Fractions r oright I can do this!! t r s su Starting to learn Getting some right most er pGetting Changing Fractions

Getting some right Getting most right

Fractions of a Number Starting to learn

Getting some right Getting most right

I can do this!!

Fractions and Decimals Starting to learn

Getting some right Getting most right

I can do this!!

Getting some right Getting most right

I can do this!!

Percent Starting to learn Ready-Ed Publications

Book 3

Page 17

Learning Outcome: Students will use > or < to show which number is greater than / less than between two whole numbers up to 999 999.

Name:

Greater Than / Less Than 1 > means “greater than”

< means “less than”

The “small pointy bit” always points to Do these two steps: the smaller number, and the “big, wide 1. Which number has MORE place values (before the decimal point)? open part” opens to the larger number.

O Compare 460 and 4007

r o e t s Bo r e p ok u S

Thousands Hundreds Tens 6

Nothing

Thousands Hundreds Tens

Ones

0

4

7

0

0

More

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Teac he r

4

Ones

460 does not have anything in the Thousands, so 4007 is larger.

460 < 4007

2. If both numbers have the same number of place values, start comparing from the left until you find the number that has the FIRST largest place value.

Read toi right. © ReadyE dPu bfrom l i cleft at ons ° ° Thousands • Hundreds Tens Ones Thousands Hundreds Tens f or r evi e w pu r pos eso nl yOnes • O Compare 4570 and 4507.

5

7

0

Same

Same

Larger

4

5

0

Same

Same

Smaller

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7 is larger than 0, so 4570 is larger.

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4

This is written as 4570 < 4507.

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O Place the symbols in between these sets of numbers to show which is greater.

276 ______ < 982

986 ______ > 709

401 ______ 410

1872 ______ 1287

780 ______ 708

1457 ______ 999

2790 ______ 2900

3000 ______ 2899

44 ______ 1200

9778 ______ 9807

45 961 ______ 45 916

49 876 ______ 49 878

415 987 ______ 415 899

986 002 ______ 986 020

788 987 ______ 98 987

O Use a separate piece of paper to write your own.

Page 18

Book 3

Ready-Ed Publications

Learning Outcome: Students will use > or < to show which number is greater than / less than between two decimal numbers up to two decimal places

Name:

Greater Than / Less Than 2 > means “greater than”

< means “less than”

1. Which number has MORE place values (before the decimal point)? e.g.

45.98 > 4.998

6.999 < 23.1

24.67 < 246.00

r o e t s Bo r e p ok ° ° u S

2. If both numbers have the same number of place values, start comparing from the left until you find the number that has the FIRST largest place value.

Read from left to right.

Teac he r

O Compare 4.570 and 4.507.

Ones . Tenths Hundredths Thousandths

4

4

. 5

Same . Same

7

0

Larger

. 5

0

Same . Same

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Ones . Tenths Hundredths Thousandths

7

Smaller

The first number to have a larger digit is 4.570.

This is written as 4.570 > 4.507.

Ones

from left to right. © ReadyEd bl i ca t i o ns° °PuRead f or r evi ew puOnes r po esHundredths onl yThousandths • .• Tenths Hundredths Thousandths . s Tenths

0

. 0

O Compare 0.09 and 0.55.

9

0

5

Same . Larger

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Same . Smaller

. 5

The first number to have a larger digit is 0.55.

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This is written as 0.09 < 0.55.

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O Place the symbols in between these sets of numbers to show which is greater.

4.8 _____ < 5.8

4.90 _____ > 4.09

5.8 _____ 8.5

13.4 _____ 11.9

3.99 _____ 3.09

6.35 _____ 6.53

8.35 _____ 3.99

7.38 _____ 3.87

8 _____ 7.99

1 _____ 0.008

3.987 _____ 11.002

20.67 _____ 26.6

8.227 _____ 8.12

11.87 _____ 7.912

6.022 _____ 6.020

4.80 _____ 4.8

O Use a separate piece of paper to write your own.

What is the trick in this one?

Ready-Ed Publications

Book 3

Page 19

Learning Outcome: Students will identify appropriate coins and notes to use for items, given an exact price up to $1000.00.

Name:

Money Skills - Revision 1 O Here are the coins and notes that you see being used every day:

r o e t s Bo r e p ok u S

Teac he r

Amount $100 $50

$20

$10

$5

$2

$1

50c

$8.65

$16.90

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O Tick in the boxes to show which coins you will use to make up these amounts. There may be more than one right answer! You can make 2 ticks in one box.

20c

10c

5c

© ReadyEdPubl i cat i ons $106.40 •f orr evi ew pur posesonl y• $47.70

$0.75

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$11.60 $243.20 $86.15

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o c . che e r O Most people do not give ther exact money when paying.

What notes would o t s s r u e p you use for these items?

Cost: $2.75

Cost: $17.50

Cost: $48.00

Cost: $187.99

Pay with: _______ Pay with: _______ Pay with: _______ Pay with: _______ Page 20

Book 3

Ready-Ed Publications

Learning Outcome: Students will order amounts of money from least to most, written in values of up to $100.00 and use a calculator to add given amounts up to $10.00.

Name:

Money Skills - Revision 2 O Colour in the box in each row that shows the most money. $2.25

$2.30

$3.20

$2.35

$4.55

$6.55

$6.40

$46.00

$5.20

r o e t s Bo r e p ok u S $4.60

$9.20

$0.99

$2.40

$25.60

$5.25

$2.05

$25.55

$18.33

$4.20

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Teac he r

O Write the numbers underneath from least to most.

$10.25

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O Add the prices up for these shopping bills on your calculator.

Apples $1.99 kg

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© ReadyEdPubl i cat i ons O Challenge: Order these boxes by writing numbers from 1 (Least) to 4 (Most).

•f orr evi ew pur posesonl y•

Watermelon $2.20 each

Pineapple $1.80 each

Strawberries $3.00 punnet

Oranges $2.50 kg

Sam: 1 kg apples 1 punnet strawberries 1 watermelon

Jan: 2 kg oranges 1 pineapple

Ted: 2 pineapples 2 watermelons

Cost: _________________

Cost: _________________

Cost:__________________

Whose bill was the most? ____________ Ready-Ed Publications

Whose bill was the least? ______________ Book 3

Page 21

Learning Outcome: Students will use simple written calculations to work out change when given the price and the amount paid, and identify correct change in notes and coins.

Name:

Money Skills - Change 1

O Change is the money that is given back to you when you pay more money than the cost.

Cost = 60 c Pay – Cost = Change If you pay = $1.00 Change = 40 c

r o e t s Bo r e p ok u S

O Use Pay – Cost = Change to work out these. Use scrap paper to work out the sum: You Pay

$10.00

Sum

Change

$0.80

5.00 – 0.80 = $4.20

$4.20

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Teac he r

$5.00

Cost

$3.50

$20.00

$17.65

$50.00

$1.25

$20.00

$10.95

O Use these coins and notes to show how the change will be made up.

Work out the sums on a spare piece of paper.

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You Pay $1.00 $5.00

$10.00 $20.00

Cost

Notes / Coins

75 c 25 c 20 c + 5 c . te$3.25 o c . che $8.90 e r o t r s super $16.40

$30.00

$28.05

$50.00

$16.35

$100.00

$76.45

$70.00

$61.10

$200.00

$148.30

Page 22

Change

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Book 3

Ready-Ed Publications

Learning Outcome: Students will use simple written calculations to work out the appropriate amount to pay and the correct change in notes and coins, when given the price of an object.

Name:

Money Skills - Change 2 O Circle the money that you would use to pay for the item in the picture.

Write the change you would get in the last column.

Item

Circle what you would pay

Change to be given

r o e t s Bo r e p ok u S $50

$20

$10

$5

$1

$100

$50

$20

$10

$5

$2

$1

50 c

20 c

10 c

5c

50 c

$10 © Ready$50 Ed$20Pub l i cat i ons $5 $2 $1 •f orr evi ew p20ucr p5o sesonl y• 50 c c

$8.80

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$100

$50

$20

$10

$5

$2

$1

20 c

$50

$20

$5

$1

$50

$20

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$47.30

$87.90

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$25.50

o c . che e r o t r s super $10

$0.75 $10

$5

Ready-Ed Publications

Book 3

Page 23

Learning Outcome: Students will select appropriate items from a list, keeping within a designated budget and calculating the total amount spent with a calculator.

Name:

Money Skills - Budgeting 1 O Your class has a budget of $60.00 for the class party. Choose items from the list below and use the budget columns to add the amounts up. You cannot go over budget, so choose wisely!

You can buy more than one of each item.

Item

Number

r o e t s Bo r e p ok u S

Cost

10 paper plates $1.15

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40 plastic cups $3.00 Chips 500g $4.25

Chips multi-pack of 12 $6.00 Lollies mix $ 3.00 Chocolate cake $5.00

© ReadyEdPubl i cat i ons Large pizza •$8.00 f orr evi ew pur posesonl y• Chocolate block $3.20

20 frozen sausage rolls $ 6.50

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Tomato sauce $1.30 2L soft drink $2.15

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Total che e r o t r s super

Hint: Use a calculator and check costs along the way.

Challenge: See if you can find a “menu” which uses the most of the money that you have.

Page 24

Book 3

Ready-Ed Publications

Learning Outcome: Students will select appropriate items from a list, keeping within a designated budget and calculating the total amount spent with a calculator.

Name:

Money Skills - Budgeting 2 O You have a budget of $9 000 to furnish a house for a family of 4. Choose items from the list below and use the budget columns to add the amounts up. You cannot go over budget, so choose wisely!

Item

Bookshelf $480.00

Number

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Cost

Double couch $570.00

Single couch $380.00 each

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Coffee table $150.00 TV wall unit $299.00

Display cabinet $320.00 Bean bags $60.00 each Woollen rug $300.00

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Stereo $827.70 Television $550.99

DVD player $670.65

Fridge $620.00

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Washing machine $465.99 Dishwasher $286.50

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Dryer $313.80

Microwave $299.99

Double bed $600.00

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Single beds $360.00 each Bed linen for 4 $563.99

Total

Bedside cabinets $50.00 each Dining table with chairs $ 700.00 Study desk $506.00 Computer with all parts $1,500.00 Ready-Ed Publications

Hint: Use a calculator and check costs along the way.

Challenge: See if you can find a “list” which uses the most of the money that you have.

Book 3

Page 25

Learning Outcome: Students will work out a mixed calculation by carrying out multiplication and division before addition and subtraction.

Name:

Rule of Order 1 Sometimes sums have more than one thing to do in them.

The rule of order states that you must do × and ÷ before + and – .

r o e t s Bo r e p ok u S

Look at this sum:

Look at this sum:

6+3×4

10 – 16 ÷ 4

Teac he r

You do the x first, i.e. 3 × 4 = 12

You do the ÷ first, i.e. 16 ÷ 4 = 4 So 10 – 16 ÷ 4 = 10 – 4

6 + 12 = 18

10 – 4 = 6

O Re-write these sums and then solve them:

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So 6 + 3 × 4 = 6 + 12

8+7 = ___________________ = __________

5×6+3

= ___________________ = __________

8×2+5

= ___________________ = __________ 3 + 12 = ___________________ = __________

4+3×5

= ___________________ = __________

8+4×9

= ___________________ = __________

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3+2×6

9–2×4 4÷2+6 6÷3+5

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© ReadyEdPubl i cat i ons 2 × 3 + 2 = ___________________ = __________ •f orr evi ew pur posesonl y• 4×2+7

o c . = ___________________ che = __________ r e o r st su 2+6 = ___________________ =p __________ er = ___________________ = __________

10 ÷ 5 – 2 = ___________________ = __________ 12 – 3 12 – 9 ÷ 3 = ___________________ = __________ 20 – 24 ÷ 6 = ___________________ = __________ Page 26

Book 3

Ready-Ed Publications

Learning Outcome: Students will work out a mixed calculation by carrying out multiplication and division before addition and subtraction.

Name:

Rule of Order 2 The rule of order states that you must do × and ÷ before + and – .

6+3×4

10 – 16 ÷ 4

So 6 + 3 × 4 = 6 + 12 = 18

So 10 – 16 ÷ 4 = 10 – 4 = 6

r o e t s Bo r e p ok u S

O Re-write these sums and then solve them:

Teac he r

15 + 7 5 × 3 + 7 = _______________ = _________

ew i ev Pr

9 × 3 + 6 = _______________ = _________ 7 × 8 + 9 = _______________ = _________ 6 + 49 6 + 7 × 7 = _______________ = _________

11 + 9 × 5 = _______________ = _________ 30 – 4 × 4 = _______________ = _________

© ReadyEdPubl i cat i ons 60 – 42 ÷• 6= f _______________ =w _________ orr evi e pur posesonl y• 45 ÷ 5 – 7 = _______________ = _________

. te

m . u

w ww

O If the sum has more than one × or ÷ part to it, you just do them in the order they appear: 4 × 5 ÷ 10 + 3 = 65 – 30 ÷ 5 × 3 = 4 × 5 ÷ 10 + 3 = 20 ÷ 10 + 3 = 2 + 3 = 5

65 – 30 ÷ 5 × 3 = 65 – 6 × 3 = 65 – 18 = 47

Multiply First

Divide first

o c . che e r o t r s super

Then divide

Then add

Then multiply

Then subtract

O Solve these sums by following the rule of order.

3×4+2×7

12 + 2 × 7 12 + 14 = ________________ = ________________ = __________

30 ÷ 3 + 4 × 5 = ________________ = ________________ = __________ 7 + 16 ÷ 4 × 3 = ________________ = ________________ = __________ 40 ÷ 8 × 2 – 3 = ________________ = ________________ = __________ 24 ÷ 6 + 48 ÷ 8 = ________________ = ________________ = __________ Ready-Ed Publications

Book 3

Page 27

Name:

Learning Outcome: Students will calculate squared numbers under 10 mentally and squared numbers under 100 on the calculator by multiplying the given number by itself.

Squared Numbers 1 When there is a small 2, to the right of a number, e.g. 4², it means that the number is squared.

This means that you multiply the number by itself.

r o e t s Bo r e p ok u S

So 4² = 4 × 4 = 16

O Here are some other examples:

2² = 2 × 2 = 4

O Try these ones: 1²

= ______ × ______ = ______

5²

= ______ × ______ = ______

7²

= ______ × ______ = ______

8² 9²

3² = 3 × 3 = 9

ew i ev Pr

Teac he r

6² = 6 × 6 = 36

© R e a d y E d P u b l i c a t i o n s = ______ × ______ = ______ •f orr evi ew pur posesonl y• = ______ × ______ = ______

w ww

m . u

10² = ______ × ______ = ______

O Try these on your calculator. The answers will be large numbers in their 100’s or 1000’s.

. te 18² = __________

Page 28

o c . che e r o t r s super 21² = __________

Book 3

25² = __________

Ready-Ed Publications

Learning Outcome: Students will calculate squared numbers under 10 mentally and squared numbers under 100 on the calculator by multiplying the given number by itself and use the rule of order to add squared numbers by multiplying them prior to adding.

Name:

Squared Numbers 2 When there is a small 2, to the right of a number, e.g. 4², it means that the number is squared.

This means that you multiply the number by itself.

So 4² = 4 × 4 = 16

r o e t s Bo r e p ok u S

O Here are some other examples:

2² = 2 × 2 = 4

O Try these examples:

7² = ______ × ______ = ______

3² = 3 × 3 = 9

ew i ev Pr

Teac he r

6² = 6 × 6 = 36

9² = ______ × ______ = ______

O Try these on your calculator. The answers will be large numbers in their 100’s or 1000’s.

37² = ___________

57² = ___________

89² = ___________

© ReadyEdPubl i cat i ons The rule • of order that numbers before orl –y them: f omeans rr e vyou i emust wsquare pur pos esyouo+n • e.g. 3² + 5² = 9 + 25 = 34 Not 3² + 5² = 8² = 64

w ww

4² + 6² = ______ + ______ = ______

. te

8² + 2² = ______ + ______ = ______

2² means 2 × 2.

7² + 5² = ______ + ______ = ______ 4² + 7² = ______ + ______ = ______

o c . che e r o t r s super

9² + 1² = ______ + ______ = ______

O Challenge:

m . u

O Try these:

3² + 6² = ______ + ______ = ______

2³ is 2 cubed, or 2 × 2 × 2 = 8.

3³ = 3 × 3 × 3 = 27.

What is 4³? _________

Ready-Ed Publications

Book 3

Page 29

Learning Outcome: Students will shade correct areas given simple fractions and write simple fractions given clear diagrams.

Name:

Fraction Revision 1 O Follow this pattern.

1

1

⁄2

Look at the fraction 1⁄2

⁄2 How many pieces? 2

1

1

⁄3

⁄3

How many pieces? 3

1

1

1

1

1

⁄4

⁄4

⁄4

Look at the fraction 1⁄4 How many pieces? 4

O When you make fractions, each piece is the same size.

Use the rule to shade in the boxes:

ew i ev Pr

Teac he r

⁄3

⁄4

r o e t s Bo r e p ok u S

Look at the fraction 1⁄3

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

⁄3

1

⁄4

2

⁄2

⁄3

2

⁄3

3

w ww

⁄4

3

⁄4

1

. te

m . u

2

o c . che e r o t r s super

O Challenge: Write a fraction for each of the following:

= ______ Page 30

= ______

= ______ Book 3

= ______ Ready-Ed Publications

Learning Outcome: Students will shade correct areas of pies or sets given simple fractions and write simple fractions given clear diagrams of pies or sets.

Name:

Fraction Revision 2 O Write down a fraction for the shaded parts:

2

_______ ⁄4

Teac he r

_______

_______

O Colour in these fractions on the shapes:

7

⁄8

_______

ew i ev Pr

r o e t s Bo r e p ok u S

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 5

2

⁄10

⁄3

1

⁄5

Tick the one which also looks like 1⁄2 (one half).

w ww

. te

_______

m . u

O Write down a fraction for the shaded parts of each set:

o c . che e r o t r s super _______

_______

_______

O Colour in these fractions on the sets:

5

⁄8

2

1

⁄10

⁄3

3

⁄6

O Tick the one which also looks like 1⁄2 (one half).

Ready-Ed Publications

Book 3

Page 31

Learning Outcome: Students will identify and write correct mixed numerals given simple diagrams; and shade correct areas given simple mixed numerals.

Name:

Mixed Numerals 1

A mixed numeral is made up of a whole number and a fraction.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

11⁄2 pizzas would look like this:

O Write down a fraction for the shaded parts. One has been done for you.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• ___________

___________

w ww

O Shade these fractions on the shapes:

. te

Shade 17⁄8

___________

m . u

12

/4 ___________

o c . che e r o t r s super Shade 25⁄10

Shade 32⁄3 Page 32

Book 3

Ready-Ed Publications

Learning Outcome: Students will identify and write correct mixed numerals given simple diagrams; and shade correct areas given simple mixed numerals.

Name:

Mixed Numerals 2 A mixed numeral is made up of a whole number and a fraction.

Teac he r

22⁄3 sets of tennis balls would look like this:

r o e t s Bo r e p ok u S

ew i ev Pr

O Write down a fraction for the shaded parts of each set. One has been done for you.

© ReadyEdPubl i cat i ons 1/ ___________ ___________ ___________ •f orr evi ew pur posesonl y• 2

5

w ww

. te

Shade 11⁄3

m . u

O Shade these fractions on the sets:

o c . che e r o t r s super Shade 22⁄6

Shade 31⁄3

O Read these instructions carefully for the pizzas below: Shade 11⁄2 red; Shade 31⁄2 green; Shade 2 blue.

Ready-Ed Publications

Book 3

Page 33

Learning Outcome: Students will shade areas to show how two equivalent fractions are the same; identify patterns between numerators and denominators of equivalent fractions and use this understanding to complete written equivalent fractions.

Name:

Equivalent FFractions ractions 1 Equivalent means the same.

O Shade in these shapes to show that 1 ⁄2 is the same as 2⁄4.

They are equivalent.

⁄2 = 2⁄4

Teac he r

1

r o e t s Bo r e p ok u S

/4 = 1/2

ew i ev Pr

O Shade the shapes below to show equivalent fractions:

/8 = 3/4

6

2

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• /3 = 2/6

1

w ww

1 2

m . u

O Look at the numbers in each fraction. Each part of the fraction has a special name: = numerator = denominator

. tany pattern between the equivalent fractions? o O Can you seee c . che e r o t r s1 = 5 su r 1 = 2 2 = 4 3 =p 6e Both × 2

Both × 2

×2

×2

2

4 ×2

4

Both × 3

Both × 5

×3

8 ×2

6

×5

12 ×3

2

10 ×5

Both × 9 ×9

1 = 9 2 18 ×9

O Try writing in the missing numbers: Whatever you do to the numerator, do to the denominator. ×4

1 = 4 2 Page 34

× 10

1 = 10 2

×2

÷2

÷2

2 = 4 3

4 = 2 12

10 = 5 10

Book 3

Ready-Ed Publications

Learning Outcome: Students will identify patterns between numerators and denominators of equivalent fractions and use this understanding to complete written equivalent fractions and write equivalent fractions of shaded areas of a diagram.

Name:

Equivalent FFractions ractions 2 1 2

= numerator = denominator

O Can you see any pattern between the equivalent fractions?

Both × by 2

Both × by 2

×2

Both × by 3 ×3

2 = 4 4 8

×5

2 = 6 4 12

×2

1 = 5 2 10

×3

÷3

9 = 3 15 5

×5

O Try writing in the missing numbers.

Whatever you do to the numerator, do to the denominator.

1 = 8 2

1 = 12 2

2 = 8 3

4 = 1 12

2 = 10 4

1 = 6 4

1 = 3 3

4 = 16 4

÷3

ew i ev Pr

Teac he r

×2

Both ÷ by 3

r o e t s Bo r e p ok u S ×2

1 = 2 2 4

Both × by 5

10 = 2 15 9 = 12 4

w ww

. te

Ready-Ed Publications

__________

=

__________

m . u

© ReadyEdPubl i cat i ons f o r evfractions i ewforp ur pos esonl y• O Write • down ther equivalent these shaded diagrams:

o c . che e r o t r s super __________

=

__________

__________

=

__________

Book 3

Page 35

Learning Outcome: Students will identify the larger of two fractions with like denominators, with diagrams to support.

Name:

Ordering FFractions ractions 1

(Like denominators)

O Shade in the boxes to show which is larger.

Which is larger?

2

3

⁄4

⁄4

r o e t s Bo r e p ok u S

________

Which is larger?

4

2

⁄8

________

ew i ev Pr

Teac he r

⁄8

Rule: If the denominator is the same, then the one with the HIGHER numerator is larger.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• ⁄ , ⁄ , ⁄ , ⁄ , ⁄ , ⁄ , ⁄ , ⁄ , =__________________________________________

O Put these fractions into order:

⁄4, 2⁄4, 1⁄4, 3⁄4 = _____________________________

4

7

8

4

8

1

8

5

8

3

8

2

8

8

8

6

8

. te

⁄3 _____ < 2⁄3

1

4

⁄8 _____ 2⁄8

Page 36

m . u

w ww

O Using the symbols > (more than) and < (less than), show which fraction is larger.

o c . che e r o t r s⁄ ⁄ _____ ⁄s ⁄r ⁄ _____ ⁄ _____ upe 6

7

3

5

7

5

⁄9 _____ 9⁄9

10

3

8

10

⁄6 _____ 2⁄6

Book 3

3

6

1

6

7

⁄9 _____ 3⁄9

Ready-Ed Publications

Learning Outcome: Students will identify the larger of two fractions with like denominators, with diagrams to support.

Name:

Ordering FFractions ractions 2

(Like numerators)

O Shade in the boxes to show which is larger.

2

1

⁄5

r o e t s Bo r e p ok u S

________

Which is larger?

1

⁄6

________

ew i ev Pr

Teac he r

⁄8

Which is larger?

2

⁄4

Rule: If the denominator is the same, then the one with the HIGHER numerator is larger.

O If you like pizza, would you rather have 1⁄4 of a pizza or 1⁄2?

1

© ReadyEdPubl i cat i ons ⁄ is smaller ⁄ is larger •f orr evi ew pur posesonl y• 1

4

The denominator is smaller.

m . u

The denominator is larger.

2

w ww

O Using the symbols > (more than) and < (less than), show which fraction is larger.

. te

1

⁄4 _____ 1⁄3

4

⁄5 _____ 4⁄8

Ready-Ed Publications

o c . che e r o t r ⁄ _____s ⁄u ⁄s ⁄ _____ ⁄ _____ ⁄ per 2

7

2

5

4

5

⁄9 _____ 5⁄7

10

3

5

6

⁄6 _____ 3⁄9

Book 3

3

5

3

6

7

⁄8 _____ 7⁄10 Page 37

Learning Outcome: Students will change whole numbers to improper fractions by multiplying the whole number by a given denominator.

Name:

Changing FFractions ractions 1 -

Whole Numbers to Improper Fractions How many quarters in one whole pizza?

An improper fraction is where the numerator is MORE than the denominator.

1 = 4 quarters or 4 4

r o e t s Bo r e p ok u S e.g.

2 = 8 quarters or 8 4

= proper = improper

ew i ev Pr

Teac he r

How many quarters are in two whole pizzas?

2 4 5 4 2 5 8 5

How many thirds in three whole pizzas?

3 = ___ thirds or 3

= proper

= improper

© ReadyEdPubl i cat i ons How many eighths are in three whole pizzas?

•f orr evi ew pur posesonl y• 3 = ___ eighths or

w ww

Rule:

Whole number × denominator

=

numerator

m . u

8

slices . te × 8 slices (eighths) = total number of o c 3 × 8 = 24 slices 3 = 24 . che e 8r o t r There are 24 in three pizzas. s s r u e p 8 3 pizzas

whole number

numerator

×3

denominator

O Try this one: How many fifths are in three whole pizzas?

3= ×

Page 38

Now draw a picture to check.

5 Book 3

Ready-Ed Publications

Learning Outcome: Students will change whole numbers to improper fractions by multiplying the whole number by a given denominator.

Name:

Changing FFractions ractions 2 -

Mixed Numerals to Improper Fractions How many quarters are in 21⁄4 pizzas?

21⁄4 = 9 quarters or 9 4

r o e t s Bo r e p ok u S 32⁄3 = ___ thirds or

3

e.g. 21⁄2 32⁄3 54⁄6

ew i ev Pr

Teac he r

How many thirds in 32⁄3 pizzas?

A mixed numeral is a combination of a whole number and a fraction:

Rule: Whole number × denominator + numerator = new numerator

3 ×

2 3

+

3 × 3 + 2 = numerator

©R ead yEdPubl i cat i ons = ⁄ (denominator stays the same) 3⁄ •f orr evi ew pur posesonl y• 9+2 2

3

= 11 11

3

O Try these. Draw some pizzas to help you with your working.

w ww

. te

m . u

How many eighths are in 31⁄8 pizzas?

31⁄8 =

o c . che e r o t r s super

8

How many quarters are in 22⁄4 pizzas?

22⁄4 =

4

24⁄6 =

6

How many sixths are there in 24⁄6 pizzas?

Ready-Ed Publications

Book 3

Page 39

Learning Outcome: Students will change whole numbers and mixed numerals to improper fractions by multiplying the whole number by a given denominator and adding the existing numerator.

Name:

Changing FFractions ractions 3 A mixed numeral is a combination of a whole number and a fraction:

2

1 2

3

2 3

2 = proper 4

5 = improper 4

4 6

2 = proper 5

2

8 = improper 5

4

. te

4=

2

6=

5

3=

6

1=

7

8= 4=

3= o c . che e r o t r s supe r O Change the mixed numerals to improper fractions: 2=

7

9=

5=

2

4

m . u

3

w ww

6=

1 = 7 3 3

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 15

O Change the whole numbers to improper fractions:

5=

15 3

ew i ev Pr

5

5=

r o e t s Bo r e p ok u S e.g.

Teac he r

e.g.

An improper fraction is where the numerator is MORE than the denominator.

Practice

3

8

9

2

1 = 7 3 3

4

3 = 4 4

6

1 = 5 5

2

5

1 = 7 7

5

4 = 6 6

7

7 = 9 9

2 = 6 10 10

Page 40

Book 3

7 = 8 8

Ready-Ed Publications

Learning Outcome: Students will change improper fractions to mixed numerals by dividing the numerator by the denominator.

Name:

Changing FFractions ractions 4 -

Improper Fractions to Mixed Numerals How many whole pizzas can you get out of 9⁄4 pizzas?

9 = 4

2

1 pizzas 4

2. Divide the pizzas into quarters.

Teac he r

4. How many wholes and quarters do you have?

Rule:

ew i ev Pr

2 r o e t s Bo 3 r e p ok u S 5

1. Draw some fillings on the pizza bases above.

3. Shade 9⁄4.

A mixed numeral is a combination of a whole number and a fraction: 1 e.g.

2 2 3 4 6

Numerator ÷ denominator = whole numbers. Remainders are the new numerator.

9 4 = 9 ÷ 4 (How many times does 4 go into 9) = 2 r 1 whole number new numerator 1 i.e.

4

©2ReadyEdPubl i cat i ons 5f 5 o • orr evi ew pur p sesonl y• Change to a mixed numeral. Shade in to help you check your answer.

3

3

w ww

Change

Change

Change

5 = 3

1

2 3

m . u

÷

6 6 to a mixed numeral. Shade in to help you check your answer.

4 4

. te

9 3

o c . c e herShade in 93 s r to a mixed numeral. to help you check your answer. o t super ÷

6 = 4

÷

9 = 3

16 16 to a mixed numeral. Shade in to help you check your answer.

5 5 ÷

Ready-Ed Publications

Book 3

16 = 5 Page 41

Learning Outcome: Students will change improper fractions to mixed numerals by dividing the numerator by the denominator.

Name:

Changing FFractions ractions 5 -

Improper Fractions to Mixed Numerals A mixed numeral is a combination of a whole number and a fraction:

5

4 6

2 4 5 4 2 5 8 5

5

5

1 3

16 ÷ 3 = 5 r 1

= proper

= improper = proper = improper

© ReadyEdPubl i cat i ons •f orr evi ew pur p osesonl y9 • 10 16

O Change the improper fractions to whole numbers: 15 3 =

16 = 3

ew i ev Pr

3

÷

r o e t s Bo r e p ok u S e.g.

2 3

remainder

5

w ww

12 = 6

. te

=

4

21 = 7

=

36 = 9

3

=

m . u

2

Teac he r

e.g.

1 2

An improper fraction is where the numerator is MORE than the denominator.

40 = 8

o c . che e r o t r s smixed r pe O Change the improper fractions tou numerals: 20 = 5

17 = 3 19 = 6 Page 42

5

2 3

30 = 6

48 = 12

12 = 5

19 = 4

14 = 3

25 = 7

30 = 9

28 = 8

Book 3

33 = 11

Ready-Ed Publications

Learning Outcome: Students will add or subtract two fractions with like denominators by adding or subtracting the numerators.

Name:

Adding & Subtracting FFractions ractions 1 Rule: You can only add or subtract fractions easily if the denominator is the same: 3

⁄4 + 1⁄4 - can add easily

⁄3 + 4⁄5 - cannot add easily Thirds and fifths are different.

2

You + or – fractions by + or – the numerator (top number).

Do not change the bottom number.

1 1 2 + = 3 3 3

3 1 + = 7 7 7

ew i ev Pr

Teac he r

O Add these

r o e t s Bo r e p ok u S

3 4 + = 9 9 9

© ReadyEdPubl i cat i ons 1 3 3 1 5 1 + = + = + = 6 •f 6o 5 p 5r 8n 8 • rr evi ew u poseso l y

w ww

. te

m . u

O Subtract these:

6 2 4 – = 6 6 6

7 1 – = 9 9 9

5 4 – = 8 8 8

3 – 2 = 7 7

1 – 1 = 4 4

4 – 2 = 10 10 10

o c . che e r o t r s super

O Try these examples without pictures: Add: 3 1 1 1 + = + = 5 5 8 8 Subtract: Ready-Ed Publications

8 3 – = 12 12

9 3 – = 10 10 Book 3

1 1 + = 2 2 5 3 – = 5 5 Page 43

Name:

Learning Outcome: Students will add or subtract two mixed numerals with like denominators by adding or subtracting the whole numbers and the numerators.

Adding & Subtracting FFractions ractions 2 Rule: You can only add or subtract fractions easily if the denominator is the same.

Add whole numbers and fractions separately.

r o e t s Bo r e p ok u S

11⁄2 + 51⁄2 = 6 + 2⁄2 = 6 + 1 = 7

e.g.

Sum

+ or – whole numbers and fractions separately

Change any improper fractions

+ or – all parts

None

6

Add these: 2 + 3

4

5 + 8

2

5 + 6

4

3

1 3

3 3

© R e a y E d P u b i c a t i o n 12 d 4 l 4s 1 + and 1 5 5 18 6 8 or 6 2 8 •2f orr evi ew pur posesonl y• 5

6

3 + 7

2

5 7

4 + 5

4

3 5

3 + 4

5

3 4

. te

Subtract these:

3

3 – 6

1

2 6

3

8 – 9

2

2 9

8

5 and

7 8

w ww

2

2

m . u

3

ew i ev Pr

Teac he r

You + or – fractions by + or – the numerator. Do not change the denominator.

o c . che e r o t r s super

2 and

1 6

None

2

1 6

7

4 10 – 3 10 Page 44

Book 3

Ready-Ed Publications

Learning Outcome: Students will calculate a simple fraction of a given number by dividing the number by the denominator of the requested fraction.

Name:

Fractions of a Number 1 Shade in 1⁄2 of these spots:

Shade in 1⁄4 of these spots:

r o e t s Bo r e p ok u S

This shows that 1⁄2 of 8 is 4.

Teac he r

To get ONE fraction of any number, DIVIDE the number by the DENOMINATOR. 1 of 9 = 9 ÷ 3 = 3 3 ÷ 1 of 10 = 10 ÷ 5 = 2 2

ew i ev Pr

Rule:

This shows that 1⁄4 of 8 is 2.

1 of 20 = 20 ÷ 5 = 4 5 ÷ 1 of 16 = 16 ÷ 4 = 4 4

÷

÷

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

w ww

1

⁄5 of 30 = 30 ÷ 5 = ______

. te

1

m . u

O Divide the number by the denominator to get the answers. Shade in the correct fraction of spots.

⁄4 of 12 = 12 ÷ ______ = ______

o c . che e r o t r s super

1

⁄3 of 15 = ____________ = ______

1

⁄6 of 24 = ____________ = ______

1

⁄8 of 32 = ____________ = ______

1

⁄9 of 45 = ____________ = ______

Ready-Ed Publications

Book 3

Page 45

Learning Outcome: Students will calculate a simple fraction of a given number by dividing the number by the denominator of the requested fraction and multiplying by the numerator.

Name:

Fractions of a Number 2 Shade in 1⁄4 of these spots. This shows that 1⁄4 of 8 is 2.

r o e t s Bo r e p ok u S

Now shade in another 1⁄4 of the same set. How many spots is 2⁄4 of 8? ⁄4 of 8 is ________

ew i ev Pr

Teac he r

2

Rule: To get MORE THAN ONE fraction of any number, DIVIDE the number by the DENOMINATOR, then MULTIPLY it by the NUMERATOR. numerator

number

2 of 9 = 9 ÷ 3 = 3 × 2 = 6 3 denominator

3 of 16 = 16 ÷ 4 = 4 × 3 = 12 4

Fraction

w ww

3 of 30 5 3 of 12 4 2 of 18 3

Number ÷ denominator

Answer × numerator

Final Answer

30 ÷ 5

6×3

m . u

© ReadyEdPubl i cat i ons O Divide the number by the denominator to get the answers. Multiply the answer by the numerator.

•f orr evi ew pur posesonl y•

. te

18

o c . che e r o t r s super

5 of 36 6 6 of 40 8 5 of 54 9 Page 46

Book 3

Ready-Ed Publications

Learning Outcome: Students will convert fractions of tenths and hundredths to decimals and vice versa.

Name:

Fractions and Decimals 1 Both decimals and fractions show PART of a whole number.

Decimals are usually shown in tenths or hundredths, so the easiest fractions to convert are tenths and hundredths.

Decimal point

Tenths

Hundredths

6

.

5

2

6

.

0.5

0.02

Teac he r

Ones

r o e t s Bo r e p ok u S

Fraction

Decimal

OR

⁄10

0.10

0.1

⁄10

0.20

0.2

1

2

⁄10

3

ew i ev Pr

O Follow the pattern to change the fractions to decimals. The fractions are all tenths, so the decimal number goes in the tenths column.

O

OR

Fraction

0.60

0.6

6

3

w ww

Decimal

0.3

⁄100

0.01

⁄100

0.02

0.30 0.70

⁄10 ⁄10

. te

m . u

© ReadyEdPubl i cat i ons •the f o rr e i ewthep ur ptoo sesonl y• Follow pattern tov change decimals fractions.

⁄10

4

o c O Follow the pattern to change the fractions to decimals. . che e r o Fraction Decimal r st super 0.40

1

2

⁄100

3

⁄100

10

0.10

⁄100

30

Ready-Ed Publications

Book 3

Page 47

Learning Outcome: Students will convert fractions of tenths and hundredths to decimals and vice versa.

Name:

Fractions and Decimals 2 Both decimals and fractions show PART of a whole number.

Follow the pattern to change the fractions to decimals. The fractions are all tenths, so the decimal number goes in the tenths column.

Fraction ⁄10

1

Decimal

OR

0.10

0.1

⁄10

2

⁄10

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3

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O Follow the pattern to change the decimals to fractions.

Decimal

OR

Fraction

0.60

0.6

6

⁄10

0.30

© ReadyEdPubl i cat i ons O Follow the to r change the decimals fractions. fractions all hundredths.

•pattern f or evi e w ptou r poThe se soare nl y • 0.70

Fraction

Decimal

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⁄100

5

⁄100

7

⁄100

80

0.03

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⁄100

90

⁄100

20

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Look how:

⁄100

3

⁄100 = 0.02 (small)

2

o c . che e r o t r s super ⁄100 = 0.20 (larger)

20

Good ones to remember: 1

⁄2 = 5⁄10 = 0.5

1

⁄4 = 25⁄100 = 0.25

2

⁄4 = 50⁄100 = 0.5

3

⁄4 = 75⁄100 = 0.75

1

⁄5 = 2⁄10 = 0.2

2

⁄5 = 4⁄10 = 0.4

3

⁄5 = 6⁄10 = 0.6

Page 48

Book 3

4

⁄5 = 8⁄10 = 0.8

Ready-Ed Publications

Learning Outcome: Students will convert a given fraction to a fraction of a hundredth, convert to a decimal and then to a percentage.

Name:

Percent 1 Percent means “Out of 100”, so if you get 75⁄100 in a test, you would get 75%.

This grid has 100 squares in it.

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Colour in 2 squares red.

O

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This is 0.02, or 2 hundredths, or 2⁄100, or 2%.

Colour in 20 squares green.

This is 0.20 or 20 hundredths, or 20⁄100 or 20%.

Remember that 0.2 is the same as 0.20.

© ReadyEdPubl i cat i ons See if you can fill out this chart to compare fractions, decimals and percent.

•f orr evi ew pur posesonl y• Imagine that each fraction is a score in a test, e.g. 4/10 means you got 4 correct out of ten questions.

⁄10

3

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⁄10

8

⁄10

7

⁄10

6.5

⁄10

9.5

Out of 100 ⁄100

30

Decimals

Percent

0.3

30%

⁄100

80

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o c . ⁄ 0.65 che e r o t r ⁄ s super 65

95

100

100

⁄100

73

0.12 0.85 20% 50% Ready-Ed Publications

Book 3

Page 49

Learning Outcome: Students will convert a given fraction to a fraction of a hundredth, convert to a decimal and then to a percentage.

Name:

Percent 2 Percent means “Out of 100”, so if you get 75 /100 in a test, you would get 75%.

Use these fractions and decimals to help you fill out the chart underneath.

1

⁄2 = 5⁄10 = 0.5

1

⁄4 = 25⁄100 = 0.25

1

⁄5 = 2⁄10 = 0.2

r o e t s Bo r e p ok u S 2

⁄4 = 50⁄100 = 0.5

3

⁄4 = 75⁄100 = 0.75

2

⁄5 = 4⁄10 = 0.4

3

⁄5 = 6⁄10 = 0.6

4

⁄5 = 8⁄10 = 0.8

Fraction

Out of 100

⁄10

30

⁄10

80

3

8

⁄100

Decimals

Percent

0.3

30%

⁄100

⁄10

7

⁄10

9.5

⁄4

3

2

⁄5 = ⁄10

4

⁄5 = ⁄10

0.65

©R adyEdPub l i cat i ons ⁄ e 0.95 95% •f orr evi ew pur posesonl y• 95

100

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⁄5

5

⁄100

65

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⁄10

6.5

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Remember that 0.2 is the same as 0.20.

o c . che e r o t r s super

Sometimes, it is too difficult to convert a fraction to be out of 100.

Use your calculator to divide the numerator by the denominator. This will give you a decimal with hundredths, which you can then convert to a percentage. e.g. 18⁄40 on the calculator is 18 ÷ 40 = 0.45 or 45%.

O Try these: 16

⁄25 = 0.64 = ______%

18

⁄30 = ______ = ______%

63

⁄70 = ______ = ______%

48

⁄52 = ______ = ______%

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Book 3

Hint: Round the decimal to 2 places.

Ready-Ed Publications

ANSWERS

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All answers are for the questions as they read across the page from left to right. Sums have not been numbered on the pages in order to limit visual clutter.

Page 18 - Greater Than / Less Than 1 <; >, >, >; <, >, <; <, >, <; >, <, > Page 19 - Greater Than / Less Than 2 <, >; >, <, >, >; >, >, <, <; >, >, >, = Page 20 - Money Skills Revision 1 Answers will vary for the first part. Pay with: $5, $20, $50, 2 x $100 or $100, $50, $20 x 2 or $100 + $50 x 2, etc.

Page 21 - Money Skills Revision 2 Most money: $ 3.20, $46.00, $9.20; $2.05, $2.40, $4.20, $5.25; $10.25, $18.33, $25.55, $25.60; Boxes, in order = 3 (80c), 2 (70c), 1 (25c), 4 (90c); Sam = $7.19, Jan = $6.80, Ted = $8.00; Ted paid the most, Jan paid the least.

Page 22 - Money Skills - Change 1 $6.50, $2.35, $48.75, $9.05; 1.75 = $1.00 + 50c + 20c + 5c $1.10 = $1.00 + 10c; $3.60 = $2.00 + $1.00 + 50c + 10c; $1.95 = $1.00 + 50c + 20c + 20c + 5c; $33.65 = $20.00 + 10.00 + $2.00 + $1.00 + 50c + 10c + 5c; $23.55 = $20.00 + $2.00 + $1.00 + 50c + 5c; $8.90 = $5.00 + $2.00 + $1.00 + 50c + 20c + 20c; $51.70 = $50.00 + $1.00 + 50c + 20c Page 23 - Money Skills - Change 2 Answers may vary - Pay = $100.00, Change = $12.10; Pay = $50.00, Change = $2.70; Pay = $50 + $20 + $10, Change = $1.85; Pay = $10.00, Change = $1.20; Pay = $5.00, Change = $4.25 Page 24 - Budgeting 1 Answers will vary. Check with calculator.

Page 25 - Budgeting 2 Answers will vary. Check with calculator.

Page 26 - Rule of Order 1 15, 6 + 2 = 8, 30 + 3 = 33, 16 + 5 = 21; 15, 4 + 15 = 19, 8 + 36 = 44, 09 – 8 = 1; 8, 2 + 5 = 7, 2 – 2 = 0; 9, 20 – 4 = 16 Page 27 - Rule of Order 2 22, 27 + 6 = 33, 56 + 9 = 65; 55, 11 + 45 = 56, 30 – 16 = 14, 9 – 7 = 2, 60 – 7 = 53 26, 10 + 20 = 30, 7 + 4 x 3 = 7+ 12 = 19, 5 x 2 – 3 = 10 – 3 = 7, 4 + 6 = 10 Page 28 - Squared Numbers 1 1 x 1 = 2, 5 x 5 = 25, 7 x 7 = 49, 8 x 8 = 64, 9 x 9 = 81, 10 x 10 = 100; 324, 441, 625 Page 29 - Squared Numbers 2 7 x 7 = 49, 9 x 9 = 81; 1369, 3249, 7921; 16 + 36 = 52, 49 + 25 = 74, 64 + 4 = 68, 16 + 49 = 65, 81 + 1 = 82, 9 + 36 = 45; 64 Page 30 - Fraction Revision 1 1 Boxes should be shaded in appropriately; ⁄2, 3⁄4, 1⁄3, 1⁄4 Page 31 - Fraction Revision 2 2 ⁄4 or 1⁄2, 5⁄8, 3⁄9 or 1⁄3, 4⁄6 or 2⁄3; Fractions should be shaded in correctly. 5⁄10 also looks like 1⁄2; 2 ⁄4 or 1⁄2, 5⁄8, 3⁄9 or 1⁄3, 4⁄6 or 2⁄3; Fractions should be shaded in correctly. 3⁄6 also looks like 1⁄2 Page 32 - Mixed Numerals 1 25⁄8, 13⁄9, 31⁄2; Fractions should be shaded in correctly.

Page 33 - Mixed Numerals 2 12⁄5, 35⁄8, 23⁄9 or 21⁄3; Fractions should be shaded in correctly.

Page 34 - Equivalent Fractions 1 4 Fractions should be shaded in correctly; ⁄8, 10⁄20, 4⁄6, 2⁄6, 5⁄5 Page 35 - Equivalent Fractions 2 8 1 ⁄16, 12⁄24, 8⁄12, 1⁄3, 2⁄3, 10⁄20, 6⁄24, 3⁄9, 1⁄4, 3⁄4; ⁄4 = 4⁄16, 4⁄8 = 2⁄4, 3⁄6 = 1⁄2 Page 36 - Ordering Fractions 1 3 1 1 ⁄4 is larger, 4⁄8 is larger; ⁄4, 2⁄4, 3⁄4, 4⁄4; ⁄8, 2⁄8, 3⁄8, 4⁄8, 5⁄8, 6⁄8, 7⁄8, 8⁄8; >, <, >, >, <, >, > Page 37 - Ordering Fractions 2 2 ⁄4 is larger, 1⁄6 is larger; <, <, <. >, >, <, >, >.

Page 38 - Changing Fractions 1 9 15 ⁄3, 24⁄8; ⁄5 Page 39 - Changing Fractions 2 11 25 ⁄ 3; ⁄8, 10⁄4, 16⁄6

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s super

Book 3

Page 51

Page 40 - Changing Fractions 3 ⁄2, 30⁄5, 32⁄4, 24⁄4, 18⁄6, 7⁄7, 32⁄8, 14⁄7, 18⁄2, 15⁄3, 27⁄9; Page 41 - Changing Fractions 4 12⁄4 or 11⁄2, 3, 31⁄5 Page 42 - Changing Fractions 5 2, 4, 3, 2, 3, 4, 5, 4, 5, 4, 3; Page 43 - Adding and Subtracting Fractions 1 4 ⁄7, 7⁄9, 4⁄6, 4⁄5, 6⁄8, 6⁄9, 1⁄8, 1⁄7, 0⁄4 or 0, 2⁄10; Page 44 - Adding and Subtracting Fractions 2 Sum + or - whole numbers and fractions separately 25⁄6 + 52⁄6 7 and 7⁄6 43⁄7 + 25⁄7 6 and 8⁄7 24⁄5 + 43⁄5 6 and 7⁄5 3 3 3 ⁄4 + 5 ⁄4 8 and 6⁄4 38⁄9 - 22⁄9 1 and 6⁄9 8 7 4 ⁄10 - 3 ⁄10 1 and 1⁄10

19

⁄4,

31

⁄5,

23

⁄8,

36

⁄7,

34

⁄6,

70

⁄9,

62

⁄10

22⁄5, 43⁄4, 42⁄3, 31⁄6, 34⁄7, 33⁄9 or 31⁄3, 34⁄8 or 31⁄2 ⁄5, 2⁄8, 2⁄2 or 1;

⁄12, 6⁄10, 2⁄5

4

5

Change any improper fractions 7 + 1 = 1⁄6 6 + 1 = 1⁄7 6 + 1 = 2⁄5 8 + 1 = 2⁄4 None None

+ or - all parts

Answer × numerator 6×3 3×3 6×2 6×5 5×6 6×5

Final answer 18 9 12 30 30 30

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Page 45 - Fractions of a Number 1 Answers only: 6, 3, 5, 4, 4, 5 Page 46 - Fractions of a Number 2 2 ⁄4 of 8 is 4 Fraction Number ÷ denominator 3 ⁄5 of 30 30 ÷ 5 = 6 3 ⁄4 of 12 12 ÷ 4 = 3 2 ⁄3 of 18 18 ÷ 3 = 6 5 ⁄6 of 36 36 ÷ 6 = 6 6 ⁄8 of 40 40 ÷ 8 = 5 5 ⁄9 of 54 54 ÷ 9 = 6

81⁄6 71⁄7 72⁄5 92⁄4 or 91⁄2 16⁄9 or 12⁄3 11⁄10

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8

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Decimals 0.80 0.70 0.65 0.95 0.73 0.12 0.85 0.20 0.50

Percent 80% 70% 65% 95% 73% 12% 85% 20% 50%

Page 50 - Percent 2 Fractions 8 ⁄10 7 ⁄10 6.5 ⁄ 10 9.5 ⁄ 10 3 ⁄4 2 ⁄5 = 4⁄10 4 ⁄5 = 8⁄10 5 ⁄5 = 10⁄10

Decimals 0.80 0.70 0.65 0.95 0.75 0.40 0.80 1.00

Percent 80% 70% 65% 95% 75% 40% 80% 100%

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0.03, 0.3

0.05, 0.07, 0.90, 0.20

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Page 47 - Fractions and Decimals 1 0.30 or 0.3, 0.40 or 0.4; 0.7 or 7⁄10, 0.4 or 4⁄10; Page 48 - Fractions and Decimals 2 0.20 or 0.2, 0.30 or 0.3; 0.3 or 3⁄10, 0.7 or 7⁄10; Page 49 - Percent 1 Fractions Out of 100 80 8 ⁄10 ⁄100 7 70 ⁄10 ⁄100 6.5 65 ⁄ 10 ⁄100 9.5 95 ⁄ 10 ⁄100 7.3 73 ⁄ 10 ⁄100 1.2 12 ⁄ 10 ⁄100 8.5 85 ⁄ 10 ⁄100 2 20 ⁄10 ⁄100 5 5 ⁄10 ⁄100

o c . che e r o t r s super

Out of 100 ⁄100 70 ⁄100 65 ⁄100 95 ⁄100 75 ⁄100 40 ⁄100 80 ⁄100 100 ⁄100 80

64%, 0.6 = 60%, 0.9 = 90%, 0.92 = 92% Page 52

Book 3

Ready-Ed Publications