Australian Curriculum Mathematics: Fractions and Decimals - Book 2 by Teacher Superstore

RIC-6137 4.7/373

Titles in this series: Australian Curriculum Mathematics – Number and Algebra: Fractions Book 1 (Years 1 and 2) Australian Curriculum Mathematics – Number and Algebra: Fractions and Decimals Book 2 (Years 3 and 4) Australian Curriculum Mathematics – Number and Algebra: Fractions, Decimals and Percentages Book 3 (Years 5 and 6)

Copyright Notice A number of pages in this book are worksheets. The publisher licenses the individual teacher who purchased this book to photocopy these pages to hand out to students in their own classes. Except as allowed under the Copyright Act 1968, any other use (including digital and online uses and the creation of overhead transparencies or posters) or any use by or for other people (including by or for other teachers, students or institutions) is prohibited. If you want a licence to do anything outside the scope of the BLM licence above, please contact the Publisher. This information is provided to clarify the limits of this licence and its interaction with the Copyright Act. For your added protection in the case of copyright inspection, please complete the form below. Retain this form, the complete original document and the invoice or receipt as proof of purchase. Name of Purchaser:

is material subject to All material identified by copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2015. For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum. Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors. Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/ This material is reproduced with the permission of ACARA.

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Foreword This three-book series is aimed at immersing students in all aspects of fraction work, including decimals and percentages for the upper levels. Based on Australian Curriculum Mathematics, the books will provide teachers with a comprehensive approach to teaching and helping their students understand fractions. Through the proficiency strands of Understanding, Fluency, Problem-solving and Reasoning, students will experience success in this sub-strand. The series contains a large variety of activities including teachers notes, warm-up activity ideas, hands-on tasks, blackline master worksheets, assessment tasks and a checklist at the end of each Year level. Each Australian Curriculum content description for fractions will be covered in detail, allowing busy teachers to assist their students in gaining confidence in their knowledge of fractions. Titles in this Australian Curriculum Mathematics – Number and Algebra series are: Fractions Book 1 (Years 1 and 2) Fractions and Decimals Book 2 (Years 3 and 4) Fractions, Decimals and Percentages Book 3 (Years 5 and 6)

Contents Year 3

Year 4 1 1

Model and represent unit fractions including 2 , 4 , 1 1 3 , 5 and their multiples to a complete whole

Investigate equivalent fractions used in contexts (ACMNA077)

Count by t quarters, halves © R. I . C.Publ i ca i on sand thirds, including with mixed numerals. Locate and represent these Teachers notes .............................................................2 fractions on as number line (ACMNA078) • f o r r e v i e w p u r p o s e o n l y • Warm-up activities......................................................3 (ACMNA058)

Teachers resources ................................................ 4–7 Blacklines................................................................ 8–36 Assessments ........................................................37–38 Checklist .....................................................................39 Answers................................................................40–42

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

Teachers notes ...........................................................43 Warm-up activities....................................................44 Teachers resources ............................................45–51 Blacklines..............................................................52–83 Assessments ........................................................84–85 Checklist .....................................................................86 Answers................................................................87–90

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Fractions and Decimals (Years 3 and 4)

iii

Teachers notes 1

Year 3

Model and represent unit fractions including 2 , 4 , 3 , 5 and their multiples to a complete whole

(ACMNA058)

A fraction is an equal part of a whole. Introduction Introduce the topic of fractions by asking students to offer examples of fractions in their world. Ask students to suggest as many examples as they can. For example: • An orange can be cut into quarters for a netball game. • An apple can be cut in half. • They had a fifth of a pie for dinner last night because there are five members in their family. • The teacher divides the class in half. • A football game is made up of four quarters. • A large pizza is commonly cut into eighths. These examples can be listed, made into posters or developed in small focus groups then reported back to the class. Display a variety of fractions using an internet-based or interactive whiteboard program. Ask students to suggest what fraction they are viewing. Help them understand that a whole can be divided evenly into parts such as halves, thirds, quarters or fifths. Display or make some posters showing common fractions such as a whole, thirds, halves, quarters, fifths and eighths (see teachers resources). Investigate fractions using the internet and play fraction games on class computers.

and eighths, using materials such as food, plasticine, playdough or paper. The higher the number at the bottom, the smaller the parts become. Compare and order fractions sizes. Fractions of groups and multiples Show students how collections or groups of things can be divided into fractions. For example, a class of students or a group of things can be divided into two halves if the numbers are even, thirds if the numbers are in multiples of three, quarters if the numbers are in multiples of four, fifths if the numbers are in multiples of five or eighths if the numbers are multiples of eight. Discuss how the correct number of multiples must be present in order to divide the whole group evenly or else there would be a remainder or amount left over. For example, a class of 30 students could be divided into halves, thirds, fifths and even tenths evenly, but it could not be divided evenly into quarters or eighths. A class of 24 could be evenly divided into halves, quarters and eighths.

Fraction symbols Look at the fraction symbols 12 , 13 , 14 , 15 and 18 . What does the bottom number represent? What does the top number represent? Introduce to the students the terms numerator (top number of a fraction or how many parts are represented out of a whole) and denominator (bottom number of a fraction or how many parts a whole has been divided into). Ask students to work by themselves or in pairs to create a fraction poster that illustrates the numerator and denominator.

Use counters to demonstrate finding fractions of groups of numbers; for example, find 14 of 20 counters. Bring up the concept of remainders here; although it is not formally part of the curriculum at this level, it can be addressed informally through discussion. For example, what would happen if there are 31 students in a class and the teacher needs three even groups? Will there be a remainder? Teachers can incorporate concepts of multiplication and division into this area and students will recognise and strengthen their understanding of fractions if they have this understanding. Comparing fractions

Demonstrating

Draw a series of number lines that start at 0 and end at 1 whole and show students where fractions would sit on them. Discuss and compare the size of the fractions; for example, can you notice that 13 is smaller than 12 but larger than 14 ?

Demonstrate how whole objects can be divided evenly and cut into halves, thirds, quarters, fifths

Above all, convey to your students that fractions are easy and fun!

Fractions and Decimals (Years 3 and 4)

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Warm-up activities

Year 3

These activities could be used to introduce your fractions lesson. They can be used as a whole class focus, or a small group or individual activity depending on the lesson content. • Start with five equal-sized lengths of polystyrene, plasticine or paper which you will use to cut into equal fractions in front of the students. Point out how they start out whole, then cut the lengths first into halves, then half and half again to make quarters. Ask the students how they could make sure they cut a length of polystyrene into equal thirds. Lead them to suggest that measuring with a ruler or tape measure can help. Cut a whole piece into thirds. Measure and cut a length into fifths, then cut another piece into eighths. Label each fraction piece that is cut if using polystyrene or paper. Compare the fractional pieces with each other. Which is the largest? Which is the smallest? Define the numerator (top number) and denominator (bottom number). Ask questions such as: How many halves make up one whole? How many thirds make up a whole? How many quarters make up a whole? How many fifths make up a whole? How many eighths make up 14 , 12 or a whole?

fifth one into fifths and the last one into eighths. Compare and answer questions about the various sizes of the fractions. Although it is not formally taught at this level, discuss fractions that may be equivalent or the same. • Divide the class into half—how many different ways could that be done? (Boys and girls, hair colour, clothes etc.) If there is an odd number, there cannot be equal halves as there is a remainder. Ask students to suggest numbers or multiples that can be equally divided into two even groups. Lead them to realise that even numbers can be divided equally into halves. • Divide the class into three equal groups—can it be done? If not, why not? What numbers or multiples can be divided evenly into thirds? Lead students to realise that multiples of three can be evenly divided into thirds. Repeat the exercise with quarters, fifths and eighths.

•i Use counters to demonstrate how collections of © R. I . C.Publ c a t i o n s objects can be divided into equal halves, thirds, • Take the students outside and use chalk to divide quarters, fis fthso andn eighths. Relate this to division shapes or areas in the playground into equal • f o r r e v i e w p u r p o s e l y • and sharing. halves, thirds, quarters, fifths and eighths. Look at how a basketball or netball court is divided into equal thirds. Ask students to draw their own shapes on an area and divide them into equal parts. Allow time to view the different fractions they have drawn.

• Look at the multiples of 2, 3, 4, 5 and 8 on a hundreds chart (see teacher resources page 7). Relate these to division and fractions. For example: 12 of 48 = 24, 15 of 40 = 8. Use counters at this year level to assist with this understanding.

• Allow students the opportunity to cut a ball, length of plasticine or playdough into two equal halves. Discuss why it is important that they are equal. Can they be considered half if it hasn’t been divided in the middle? Cut a ball or length of plasticine into thirds. Do the same for quarters, fifths and eighths.

• Look at fractions used in recipes on the internet or in cooking magazines. What fractions are used? What would you need to do if you wanted to halve or double a recipe? Locate 14 , 13 or 12 on a cup. Make a simple batch of biscuits with the class—does the recipe need to be altered so everyone in the class gets a biscuit?

• Relate fractions to story books. Look at a page in a picture book and ask the students what fraction of the page is words and what is pictures? For example, it may be 12 words and 12 picture or 14 words and 34 pictures.

• Relate fractions to vowels and consonants contained within words. For example, a four-letter word such as LIKE contains 12 vowels and 12 consonants, or WORD has 1 3 4 vowels and 4 consonants. A five-letter word such as PLANT has 15 vowels and 45 consonants. Relate thirds to three-letter words, quarters to four-letter words and fifths to fiveletter words.

• Create fraction number lines, six in total (see teachers resources). Leave the first one as a whole, label the second one in halves, the third one in thirds, the fourth one into quarters, the R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Teachers resources

Thirds

1 3

Fractions and Decimals (Years 3 and 4)

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Teachers resources

Fifths

1 5

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Fractions and Decimals (Years 3 and 4)

Teachers resources

Number lines 0

1 whole

Fractions and Decimals (Years 3 and 4)

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Teachers resources

Hundreds chart 1

100

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Fractions and Decimals (Years 3 and 4)

One whole 1. What does the word whole mean to you?

3. Answer the questions about whole collections. (a)

How many people make up your whole family?

(b)

How many students make up your whole class?

(c)

How many coloured pencils do you have in your whole pencil case?

4. Complete the sentence to make it whole. My favourite season is

1 1 1 1

because 5. Colour only the whole objects you see below.

Going further

Choose your favourite sport and investigate, using the internet, what is the duration or time of the whole game. 8

Fractions and Decimals (Years 3 and 4)

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CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Draw at least three whole things you can see in the classroom.

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One half 1

1. Mark and write the symbol 2 on the number line below. Use your ruler to be accurate. 1

2. Complete the sentence: one half + one half =

whole.

4. Complete the missing halves of the pictures to make them whole.

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

3. Mark and shade one half of the shapes below.

Going further

Investigate the term used to describe when two parts of a shape or object are identical. Write the word and meaning and draw an example on the back of this page. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Half a collection 1. Colour half of the group of tennis balls. How many make up half?

(b)

(c)

(d)

(e)

(f)

(g)

(h)

3. Half of the collections are missing, complete the missing halves.

Going further

A pack of cards can be divided into two halves. Name at least three other collections you know that can be divided equally into halves. 10

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

(a)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Circle one half. Write the number that is half of the collection.

One-quarter 1 4

The numerator tells us how many parts are shaded or used. The denominator tells us that this shape is divided into 4 equal parts. 1 4

2. Divide the shapes evenly into quarters and shade one-quarter.

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Shade one-quarter of the shapes.

1 2

8 0

3. Cut out the strip at the bottom of the page and fold it in half and in half 1 again. Label each section 4 . Going further

How many minutes would make up one-quarter of an hour? How many letters make up a quarter of the word denominators?

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Fractions and Decimals (Years 3 and 4)

Quarters 1. How many quarters are shaded? Write the fraction symbol.

(a)

(b)

(c)

(d)

Two-quarters

One-quarter

Three-quarters

4. Use lines to match the clock time to the clock picture and the fraction symbol. quarter past

one hour

three quarters past

half past

2 1 4 or 2

3 4

1 4

4 4 or 1

Going further

Investigate what sporting games have four quarters. What is the duration of each quarter? 12

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

3. Divide and shade the shapes to match the fraction.

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Use your ruler to divide the line evenly into quarters. Label each quarter with its symbol.

Quarter of a collection 1. Colour one-quarter of the swarm of bees. 1

How many make up 4 ?

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Circle one-quarter. Write the number that is one-quarter of the collection.

4. What do you notice about the numbers that can be evenly divided by quarters?

Going further

Write as many numbers as you can think of that can be evenly divided into quarters. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

One-eighth 1 8

The numerator tells us how many parts are shaded or used. The denominator tells us that this shape is divided into 8 equal parts. 1 8

(b)

(c)

(d)

(e)

(f)

(g)

(h)

6 8

5 8

1 8

3. Cut out the strip at the bottom of the page and fold it in half, three times. Label each section 1 8. Going further

Trace and draw a large circle and decorate it to resemble your favourite pizza. Now divide your pizza into 8 equal parts.

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

(a)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. How many eighths are represented below? Write the fraction symbol.

Eighths of a collection 1. What fraction of the groups of 8 is shaded? (a)

(b)

(c)

(d)

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. What fraction is not shaded in the groups above? birds

leaves

caterpillars

butterflies

3. Answer the questions about the socks on the clothes line.

How many eighths are coloured?

(b)

How many eighths have dots?

(c)

How many eighths have stripes?

4. If there were 16 students and 2 were wearing hats, how many eighths would not be wearing hats? (You may wish to draw this problem.)

Going further

Describe the similarities you can see between eighths, quarters and halves. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Whole, halves, quarters and eighths 1

1. Label the fraction strips below with the symbols 1 whole, 2 , 4 and 8 , and shade each strip a different colour.

(a)

How many halves make up one whole?

(b)

How many quarters make up one whole?

(c)

How many quarters make up one half?

(d)

How many eighths make up one-quarter?

(e)

1 1 1 1

3. Use different coloured pencils to circle wholes, halves, quarters and eighths.

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Use the fraction strips to answer the questions.

4. Draw your own example of a whole, half, quarter and eighth and label them correctly. Going further

In one day a café sold 26 serves of pie. If the pies are divided into quarters, how many pies did they sell? 16

Fractions and Decimals (Years 3 and 4)

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One-third 1 The numerator tells us how many parts are shaded or used. 3 The denominator tells us that this shape is divided into 3 equal parts. 1 3

2. Divide the shapes into thirds and shade one-third.

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Shade one-third of the shapes.

3. Use your ruler to measure and mark the strips into equal thirds. How many centimetres make up each third? 1 3 =

1 3 =

Going further

How many minutes would make up one-third of an hour? How many letters make up one-third of the word numerator? R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Thirds (a)

(b)

(c)

(d)

(e)

(f)

2. Use a piece of string to measure around the circle. Measure the string and divide this amount into thirds making small marks on the string. Use the string and markings to divide this circle into even thirds.

3. Divide and shade the shapes below to match the fraction.

1 1 1 1

(a)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. How many thirds are shaded? Write the fraction symbol.

Three-thirds

One-third

Two-thirds

4. Write the time and the fraction these clocks are showing.

Going further

On the back of this sheet, draw a number line 24 cm long. If you were to divide it into thirds, how many centimetres would be in: one-third? 18

two-thirds?

Fractions and Decimals (Years 3 and 4)

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Third of a collection 1. Colour one-third of the lemons. 1

How many make up 3 ?

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Circle one-third. Write the number that is one-third of each collection. (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

4. What do you notice about the numbers that can be divided by thirds?

Going further

Write as many numbers as you can think of that can be divided into thirds. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

One-fifth 1 The numerator tells us how many parts are shaded or used. 5 The denominator tells us that this shape is divided into 5 equal parts. 1 5

2. Divide the shapes into fifths and shade one-fifth.

1 1 1 1

3. Use your ruler to measure and mark the strips into equal fifths. How many centimetres make up each fifth? 1 5 =

1 5 =

Going further

How many minutes would make up one-fifth of an hour? How many letters make up one-fifth of the word centimetre? 20

Fractions and Decimals (Years 3 and 4)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Shade one-fifth of each shape.

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Fifths (a)

(b)

(c)

(d)

(e)

(f)

2. Use a ruler to measure and divide the rectangle evenly into fifths.

3. Divide and shade the shapes below to match the fraction. (a)

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. How many fifths are shaded? Write the fraction symbol.

Four-fifths

Two-fifths

One-fifth

4. What fraction of each clock is shaded?

(a)

(b)

(c)

(d)

Going further

Look at a 1 metre or 100 cm ruler. If you were to divide this ruler into fifths, 1

how many centimetres would 5 equal? R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Fifth of a collection 1. Colour one-fifth of the beans. 1

How many make up 5 ?

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

1 1 1 1

3. One-fifth of each collection is missing. Draw the missing fifth.

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2. Circle one-fifth. Write the number that is one-fifth of each collection.

4. What do you notice about the numbers that can be divided by fifths?

Going further

Write as many numbers as you can think of that can be divided into fifths. 22

Fractions and Decimals (Years 3 and 4)

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Fraction mat

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Create a fraction mat by representing the following fractions: 1 whole, halves, quarters and eighths. Use your ruler to divide the fractions evenly. Use fraction symbols to name each section. Shade each fraction a different colour.

2. Looking at the fraction mat, answer true or false to the statements. (a)

Two-quarters = one half

(b)

Four-eighths = one half

(c)

Four-quarters = 1 whole

(d)

Two halves = 1 whole

(e)

Five-eighths = one half

(g)

Two-quarters = four-eighths

Four-quarters = four-eighths

3. Create another fraction mat representing 1 whole, thirds and fifths. Name and shade it in the same way.

4. Answer true or false. 1

(a) 5 = 3

(b) 5 = 3

(d) 5 = 3

Going further

What does the word equivalent mean when we talk about fractions? On the back of this page, write your own meaning and give at least two examples of equivalent fractions. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Naming fractions (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

2. What fraction part is not shaded above? (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

3. Use fraction words to name the fraction that is missing.

(d)

(e)

1 1 1 1

(a)

(f)

4. What fraction of these groups is shaded? (a)

(b)

(c)

(d)

Going further 1

Name as many fractions you can see around you. For example, a window 4 open, a clock showing half past etc. 24

Fractions and Decimals (Years 3 and 4)

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CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Use fraction symbols to name the fractions.

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Representing fractions 1. Draw lines to match the fraction symbol to the fraction. 1 2

1 5

1 3

1 whole

1 4

1 8

2. Number the fractions above from largest (1) to smallest (6).

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

3. Divide and colour these shapes to represent the fractions. Three-quarters

One-fifth

Two-thirds

One half

One-third

4. Draw and colour the objects to represent the fraction. 1 3 of 12 suns

1 2 of 8 stars

3 4 of 16 crosses

2 5 of 10 circles

5. What fraction is not coloured above? of 12 suns

of 8 stars

of 16 crosses

of 10 circles

Going further

What fraction of boys are in your class? What fraction have brown hair? R.I.C. Publications©

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Girls?

Blonde hair?

Red hair?

Fractions and Decimals (Years 3 and 4)

Comparing fractions

(a)

(b)

(c)

(d)

(e)

(f)

2. The numerator and denominator tell the size of a fraction. Use your knowledge of fractions to complete the sentences by crossing out the incorrect word. (a) (b)

1 1 1 1

3. Number the fraction pictures from smallest (1) to largest (6).

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Compare the fractions. Is the fraction on the left bigger, smaller or equal to the one on the right?

4. Write the fraction symbols in order from smallest to largest. 1 1

4 5

1 2

3 8

1 5

1 4

Going further 2

Tom ate 5 of a pizza, Kyle ate 3 and Jake ate 4 . Who ate the most?

Who ate the least?

Who ate half? 26

Fractions and Decimals (Years 3 and 4)

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Noticing and creating fractions 1. Colour the fractions from this scene. Eighths are yellow, quarters are green, halves are red, wholes are blue.

oil coconut

choc chips

cocoa

sugar

milk

sultanas

2. Draw a house that is made up of many different fractions. Represent wholes, halves, thirds, quarters, fifths and eighths. Show your house design to the class.

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

flour

Going further

Use poster paper or a computer drawing program to design a beach scene with as many different fractions as you can. Show a friend and see if they can spot all the fractions. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Fun with fractions

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Cut out and use the fractions below to create an interesting fraction picture. Paste them onto a colourful background. Be creative!

Going further

Use a computer graphic program to create a fraction picture. Print it out and show a friend. 28

Fractions and Decimals (Years 3 and 4)

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Fractions on a number line 1. Fill in the missing fractions on the number lines. (a)

(b)

2 3

2 4

0 (c)

(d)

5 8

1 8

0 (e)

2. Mark the following fractions on this number line. Show the halves above 1 1 2 3 4 the line and the quarters below the line. 2 , 1, 4 , 4 , 4 , 4 0

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

2 5

3. Looking at your number lines answer true or false to each statement. (a) (c) (e) (g) (i)

1 3 2 4 1 4 2 4 5 8

is larger than 14

(b)

is the same as 12

(d)

is larger than 13

(f)

is larger than 25

(h)

is larger than 12

(j)

3 4 4 5 1 8 1 4 1 2

is smaller than 35 is larger than 23 is larger than 14 is the same as 15 is smaller than 23

Going further

Create your own number line counting by quarters from 0 up to 2 wholes. Mark the halves in a different colour. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

What fraction of the animals is large?

(b)

What fraction of the animals is small?

(c)

What fraction of the animals is elephants?

(d)

What fraction of the animals is bilbies?

2. What fraction of the fruit is shaded? (a)

(b)

(c)

(d)

4. Use the information above to complete these fraction sentences. (a)

1 2 of 20 =

(b) 4 of 20 =

(c)

1 5 of 20 =

Going further

How many different ways could you make equal groups with or share out 60? 30

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

1. (a)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

Fractions of groups

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

Fractions of numbers – 1

1. Answer the questions about the students using fraction symbols.

(a)

of this group is girls.

(b)

of this group is boys.

(c)

is wearing hats.

(d)

is not wearing hats.

(e)

is tall.

1 1 1 (b) 2 of 26 = (c) 2 of 40 = 2 of 18 = 1 1 1 (d) 2 of 34 = (e) 2 of 52 = (f) 2 of 16 = 1 What is 3 of each number? You may wish to use counters. 1 1 1 (b) 3 of 21 = (c) 3 of 12 = (a) 3 of 9 = 1 1 1 (d) 3 of 30 = (e) 3 of 27 = (f) 3 of 36 = 1 What is 5 of each number? You may wish to use counters. 1 1 1 (b) 5 of 25 = (c) 5 of 40 = (a) 5 of 10 = 1 1 1 (d) 5 of 35 = (e) 5 of 60 = (f) 5 of 15 =

(a)

Going further 2

If in a class of 30 students 5 were away sick, how many students would be at school? R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

of the caps is plain.

(a)

(b)

of the caps have stripes.

of the caps have dots. (d)

of the caps have a smiley face.

1 What is 4 of each number? You may wish to use counters. 1 1 1 (b) 4 of 16 = (c) 4 of 24 = (a) 4 of 8 = 1 1 1 (d) 4 of 32 = (e) 4 of 12 = (f) 4 of 48 =

3. What is an eighth of each number? You may wish to use counters. (a) (d)

1 8 of 8 = 1 8 of 32 =

(b) (e)

1 8 of 40 = 1 8 of 64 =

1 8 of 16 = 1 8 of 48 =

4. What numbers can be evenly divided by 8? Make a list of at least 10 you know.

5. Looking at your numbers above, can you divide them by any other numbers?

What are they?

Going further

Find and write five 3-digit numbers that can be evenly divided by 2, 4 and 8. You may wish to use a calculator. 32

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

1. Answer the questions about the caps using fraction symbols.

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

Fractions of numbers – 2

Fractions and multiples 1. If you wanted to divide a number equally in half, what type of number would it need to be? odd

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

even

2. Colour all the numbers that can be divided equally into half yellow. They are called multiples of 2.

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3. Colour all the numbers that are 61 62 63 64 65 66 67 68 69 70 multiples of 3 in red. Which numbers are already coloured in yellow? 71 72 73 74 75 76 77 78 79 80

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

These numbers are multiples of 2 and 3.

4. Put a blue cross on all the multiples of 4. Which numbers are coloured in yellow and red, and have a cross?

These can be multiples of 2, 3 and/or 4. 5. Circle all the numbers that are multiples of 5. Which numbers are coloured in red and yellow, and are circled?

These numbers can be multiples of 2, 5, and in some cases 3 and 4. 6. List 3 numbers that can be divided by thirds and fifths. , 7.

Name the number that can be a multiple of 2, 3, 4 and 5.

Going further

Explain what fractions and multiples have in common.

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Fractions and Decimals (Years 3 and 4)

Fractions in recipes 1. Many recipes use fractions to describe how much of an item is needed. Give at least three examples of fractions you have seen in a recipe.

2. This recipe makes 40 coconut biscuits. Rewrite the recipe so that it makes half of this amount. How many would it make? Coconut biscuits – makes 40 Ingredients:

Coconut biscuits – makes Ingredients:

250 g butter 6

1 cup coconut

makes double the amount. How many muffins would it make? Blueberry muffins – makes 12 1 3 cup melted butter 1 4 cup of milk

Blueberry muffins – makes Ingredients:

1 egg 1 2 cup sugar

1 cup SR flour 1 2 cup blueberries

Going further

Using the internet or a magazine, find three examples of recipes that use fractions. Print or cut them out and circle the fractions. 34

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

2 cups SR flour

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1 2 or 4 cups sugar 2 eggs

Fractions around the world When the English talk about fractions they mention the numerator then the denominator; for example, one-third. The French say it the same way. In China they say it is one part of three. In some other countries they say the denominator first. For example: In Japan they say 31 is thirds-one.

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Draw lines to match the English style of writing fractions to the Japanese style (which is the opposite) and the Chinese style. English

Japanese

Chinese

One half

Eights-three

Two parts of three

One-third

Halves one

One part of four

One-quarter

Fifths-one

One part of two

Two-thirds

Thirds-one

Three parts of eight

Quarters-one

One part of three

Three-eighths

done for you. (a)

Two-fifths – Fifths-two

(b)

Four-fifths –

(c)

One half –

(d)

One-third –

(e)

One whole –

(f)

Three-quarters –

(g)

Two-thirds –

(h)

Five-eighths –

3. Write the fraction symbols to match the fraction names above. (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Going further

Choose a different country and use the internet to investigate how they write fractions. Write the country on the back of this page and give some examples. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Fraction problems 1. Solve the fraction story problems by drawing the fractions first. 3

(b) At an afternoon tea 18 halves of scones were covered in jam and cream and served. How many whole scones were there? (c) At a party there were pizzas cut 3 into quarters. If 6 guests ate 4 of pizza each, how many whole pizzas were eaten? 1

(d) A recipe needed 2 cup of 1 sugar, 4 cup of currants, 1 whole 1 cup of flour, 2 cup of oats and 1 4 cup of milk. How many cups of ingredients were needed altogether? (e) If Gemma swam 4 whole laps and 8 half laps of a pool, how many laps did she swim altogether?

1 1 1 1

(f) If a painter completed 8 of a wall, how much does he have left to paint? (g) 24 birds were in a tree. If 16 were white, what fraction were not? (h) A farmer separated his 40 sheep 3 into 2 paddocks. If 8 of the sheep were in one paddock, how many were in the other paddock? Going further

Work out how many pizzas and cups of drink you would need for a party for 1 12 people if you allowed 2 pizza each and 3 drinks. 36

Fractions and Decimals (Years 3 and 4)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

(a) At a café Tom ate 4 of a pie, Kate 1 1 ate 4 and Ben ate 2 . How many pies were eaten altogether?

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Name:

Date:

Assessment 1

1 1 1 1

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

1. Write the fraction symbol to match the shaded pictures. (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

2. Draw fractions to match these symbols. 5I © R. . C.Pub2l i cat i on8s •f orr evi ew pur posesonl y• 1 4

2 3

3. Add the missing fractions to these number lines. 1 2

(a) 0

1 3

(b) 0

3 5

1 1

4. Order these fractions from the smallest to the largest: 2 , 3 , 8 , 5 , 1, 4

Going further 2

If someone offered you 3 of a pizza, 8 of a pizza, 5 of a pizza or 4 of a pizza which one would you choose? Explain why. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Name:

Date:

Assessment 2 1. What fraction of the group is shaded? (a)

(b)

(c)

(d)

2. What fraction is not shaded above? (d)

3. Write at least five numbers that can be divided evenly into: (a)

halves –

(b)

thirds –

(c)

quarters –

(d) (e)

4. Write the fractions in order from the smallest to the largest: 1 7 1 5 3 1 3, 8, 4, 5, 4, 5

5. Draw and solve this fraction problem: At a party, 4 guests 1 each drank 4 cup juice, 6 1 guests drank 3 cup of juice and 2 guests drank a whole cup. How many cups of juice were drunk? Going further

Find a recipe that uses fractions and rewrite the recipe so that it makes double the amount. 38

Fractions and Decimals (Years 3 and 4)

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1 1 1 1

(c)

CONTENT DESCRIPTION: Model and represent unit fractions including 2 , 3 , 4 , 5 and their multiples to a complete whole (ACMNA058)

(b)

(a)

Checklist

Year 3

1 1 1 1

Model and represent unit fractions including 2 , 4 , 3 , 5 and their multiples to a complete whole (ACMNA058)

Name

Models and represents fractions of shapes

Models and Locates represents fractions on Understands fractions of a number multiples collections line

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Fractions and Decimals (Years 3 and 4)

Answers One whole ................................................ page 8 1.–4. Answers will vary. 5. Teacher check Going further – Answers will vary.

One half .................................................... page 9 1. Teacher check 2. one 3.–4. Teacher check Going further – Symmetry or symmetrical. Two halves are identical in size and shape. Teacher check drawing.

Half of a collection ................................. page 10 1. 13 2. (a) 7

(b) 11

(d) 14

(e) 8

(f) 15

(g) 13

(h)17

3. Teacher check

Year 3

Eighths of a collection........................... page 15 2 7 3 1. (a) 8 (b) 8 (c) 8 6 1 5 3 2. 8 , 8 , 8 , 8 4 2 2 3. (a) 8 (b) 8 (c) 8 7 4. 8 Going further – Answers will vary.

5 (d) 8

Whole, halves, quarters and eighths ............................................ page 16 1. Teacher check 2. (a) 2

(b) 4

(d) 2

(e) 4

3.–4. Teacher check

1 Going further – 6 2 pies

One-third ................................................ page 17 1.–2. Teacher check 3. 3 cm, 5 cm

Going further – Answers will vary.

Going further – 20 minutes, 3 letters

One-quarter ............................................ page 11

Thirds ...................................................... page 18

2 1 1. (a) 3 (b) 3 2 2 (d) 3 (e) 3 2.–3. Teacher check

Going further – 15 minutes, 3 letters

1. (a) 4 (b) 4 4 2 (d) 4 (e) 4 2.–4. Teacher check

3 (c) 3 1 (f) 3

1 4. (a) 4 o’clock, 3

Going further – Answers will vary.

Quarter of a collection .......................... page 13

3 (b) 12 o’clock, 3 2 (c) 8 o’clock, 3 Going further – 8 cm, 16 cm

Third of a collection............................... page 19

1. 7 2. (a) 4

(b) 2

(d) 3

1. 5

(e) 5

(f) 8

(g) 7

(h) 10

2. (a) 4 (e) 12

3. 2 leaves, 4 sticks, 1 rock

(b) 6

(d) 7

(f) 9

(g) 5

(h) 8

4. They are multiples of 4.

3. 5 apples, 2 pears, 6 grapes

Going further – Teacher check; e.g. 4, 8, 12, 16 etc.

4. multiples of 3

One-eighth ............................................. page 14 3 8 1. (a) 8 (b) 8 5 1 (e) 8 (f) 8 2.–3. Teacher check

4 (c) 8 7 (g) 8

Going further – Teacher check

Fractions and Decimals (Years 3 and 4)

6 (d) 8 6 (h) 8

Going further – Teacher check/Answers will vary e.g. 3, 6, 9, 12 etc.

One-fifth.................................................. page 20 1.–2. Teacher check 3. 2 cm and 3 cm Going further – 12 minutes and 2 letters

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Answers Fifths ....................................................... page 21 2 1. (a) 5 5 (d) 5 2.–3. Teacher check

1 (b) 5 3 (e) 5

5 1 (b) 5 4. (a) 5 Going further – 20 cm

4 (c) 5 1 (f) 5 3 (c) 5

2 (d) 5

Fifth of a collection ................................ page 22 1. 5 2. (a) 4

(b) 7

(d) 5

(e) 3

(f) 6

(g) 2

(h) 8

Going further – Answers will vary; e.g. 5, 10, 15, 20 etc.

Fraction mat ........................................... page 23 1. Teacher check (b) true

(d) true

(f) true

(g) true

(h) false

(d) smaller 2. (a) larger

(b) smaller

(e) bigger

(f) smaller

(b) smaller

3. 3, 5, 6, 2, 1, 4

1 1 3 1 4 4. 5 , 4 , 8 , 2 , 5 , 1 1 Going further – Kyle, Tom, Jake

Noticing and creating fractions ............ page 27 1.–2. Teacher check Going further – Answers will vary/Teacher check

(d) false

Going further – Teacher check

Fractions on a number line ................... page 29 1 1 1 3 1. (a) 2 (b) 3 (c) 4 , 4 1 4 2 3 4 6 7 (d) 5 , 3 , 5 (e) 8 , 8 , 8 , 8 , 8 5 2. Teacher check

3. Teacher check 4. (a) false

1. (a) bigger

Teacher check

4. multiples of 5

(e) false

Comparing fractions .............................. page 26

Fun with fractions ................................. page 28

3. 1 cup, 3 saucers, 2 bowls

2. (a) true

Year 3

(b) true

Going further – Answers will vary. Teacher check

Naming fractions ................................... page 24 3 3 1 7 1. (a) 5 (b) 4 (c) 2 (d) 8 1 1 3 2 (e) 3 (f) 5 (g) 8 (h) 3 2 1 1 1 2. (a) 5 (b) 4 (c) 2 (d) 8 2 4 5 1 (e) 3 (f) 5 (g) 8 (h) 3 3. one-quarter, one-third, two-quarters, twofifths, one half, three-quarters, one-eighth 3 1 (b) 12 or 4 4. (a) 3 5 4 1 3 1 (c) 8 or 2 (d) 9 or 3 Going further – Answers will vary.

Representing fractions .......................... page 25

3. (a) true

(b) false

(d) true

(e) false

(f) false

(g) true

(h) false

(i) true

(j) true

Going further – Teacher check

Fractions of groups................................ page 30 6 1 6 1. (a) 12 or 2 (b) 12 or 4 1 3 (c) 12 or 3 (d) 12 or 4 1 6 2. (a) 8 or 2 (b) 15 or 12 2 5 (c) 18 or 3 (d) 20 or 3. Teacher check. Groups of: 2’s, 4’s, 5’s, 10’s 4. (a) 10

(b) 5

1 2 1 4 2 5 1 4

Going further – groups of 2, 3, 5, 6, 10, 12, 15, 20, 30, 60

Fractions of numbers – 1....................... page 31

2. 6, 1, 4, 2, 5, 3

1 1. (a) 2 2. (a) 9

1 (b) 2 (b) 13

1 3 (c) 4 (d) 4 (c) 20 (d) 17

1 2 (e) 3 (f) 3 (e) 26 (f) 8

3. Teacher check

3. (a) 3

(b) 7

(d) 10

(e) 9

(f) 12

4. (a) 2

(b) 5

(d) 7

(e) 12

(f) 3

1. Teacher check

4. Teacher check (a) 4 (b) 4

(d) 4

Going further – 18 students

2 1 1 3 5. 3 , 2 , 4 , 5 Going further – Teacher check R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Answers Fractions of numbers – 2....................... page 32 1 1. (a) 2 2. (a) 2

1 (b) 4

1 (c) 8 (b) 4

1 (d) 8 (c) 6

(d) 8

(e) 3

(f) 12

3. (a) 1

(b) 5

(d) 4

(e) 8

(f) 6

4. Teacher check

Year 3

Fractions around the world .................. page 35 1. one half = halves one = one part of two, one-third = thirds-one = one part of three, one-quarter = quarters-one = one part of four, two-thirds = thirds-two = two parts of three, one-fifth = fifths-one = one part of five, three-eighths = eighths-three = three parts of eight 2. (b) fifths-four

5. Yes, 2 and 4

(d) thirds-one

(e) wholes one

Going further – Answers will vary.

(f) quarters-three

(g) thirds-two

Fractions and multiples......................... page 33 1. even 2. Teacher check 3. Teacher check – 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96 4. Teacher check – 12, 24, 36, 48, 60, 72, 84, 96 5. Teacher check – 30, 60, 90 6. 15, 30, 45, 60, 75, 90 7. 60

(h) eighths-five

2 3. (a) 5

4 (b) 5 (c) 3 (e) 1 (f) 4 (g) Going further – Teacher check

1 2 2 3

1 (d) 3 5 (h) 8

Fraction problems.................................. page 36 1 1. (a) 1 2

(b) 9

1 (c) 4 2

1 (d) 2 2

1 1 5 (f) 8 (g) 3 (h) 8 or 25 sheep Going further – 6 pizzas and 36 drinks (e) 8 laps

Assessment 1 ......................................... page 37 © R. I . C.Pu bl i c t i o s5 1 a 3n 1 2 4 8 3 1 4 2 5 f orr evi ew ur p4oses nl y Fractions in recipes• ................................ page 34 p 5 o 3 • 5 Going further – Answers will vary; e.g. The denominator can be divided into numbers evenly if they are multiples of that denominator.

1. (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

1. Answers will vary.

2. Teacher check

2. makes 20

1 3 2 (b) 3 , 1 3. (a) 4 , 4 1 1 1 1 1 4. 8 , 5 , 4 , 3 , 2 , 1 Going further – Answers will vary.

3 125 g butter, 4 cup sugar, 1 egg, 1 cup SR 1 1 flour, 2 cup coconut, 4 cup oats, 1 teaspoon vanilla 2 2 1 3. makes 24 – 3 cup butter, 4 or 2 cup milk, 2 eggs, 1 cup sugar, 2 cups SR flour, 1 cup blueberries Going further – Teacher check

or 1

1 2 4 (c) 5 , 5 , 5

Assessment 2 ......................................... page 38 4 2 1. (a) 10 or 5 6 2 (c) 9 or 3 6 3 2. (a) 10 or 5 3 1 (c) 9 or 3 3. Answers will vary.

3 (b) 12 8 (d) 16 9 (b) 12 8 (d) 16

1 or 4 1 or 2 3 or 4 1 or 2

1 1 1 3 7 5 4. 5 , 4 , 3 , 4 , 8 , 5 5. 5 Going further – Teacher check

Fractions and Decimals (Years 3 and 4)

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Teachers notes

Year 4

Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) Introduction

Counting fractions and number lines

At this level students can draw on their knowledge of dealing with fractions in previous years.They have been exposed to hands-on tasks such as cutting objects and paper strips into simple fractions such as halves, quarters, eighths, thirds and fifths. They would have had experience with seeing fractions of shapes and groups, and fractions on a number line. In Year 4 they build on this knowledge and go further to explore how fractions can be equivalent. They will be able to rename equivalent fractions and see how fractions can be placed and counted using number lines. They will be able to compare fraction sizes using their knowledge of equivalence and number lines. Students will come to understand that numbers larger than a whole number are called improper fractions and that these can be converted to mixed numbers (a whole number with a fraction). They will discover the connection between fractions and decimals. Knowledge of place value will help with this concept.

Use number lines to help students count by fractions. Count by halves, quarters, thirds, eighths etc. including over whole numbers to end up with mixed numbers. Define what a mixed number is and change improper fractions to mixed numbers and visa versa. Initially use pictures and number lines to illustrate how an improper fraction can become a mixed number then, as students understand and become more competent, they can use their knowledge of fractions and division to convert improper fractions to mixed numbers. Incorporate division and the use of multiples when talking about fractions and fractions of groups. Place value system and decimals

Introduce decimals tenths to students using strips © R. I . C.Publ i cat i ons of paper divided into ten equal parts. One part out of ten is e thes same saying •f orr evi ew pur p os oasn l y•or 0.1. Relate the

Fractions and equivalence Revisit and define numerator (top number of a fraction) and denominator (the bottom number of a fraction). Look at some fractions on the interactive whiteboard or computer and name them using fraction symbols. Define the word ‘equivalent’ as the same. Make or look at a fraction wall demonstrating equivalence in fractions. Discuss how 12 is the same as 24 or 48 . It is a good idea at this level to still show students this concept using strips of paper or have them make their own fraction wall. Explore the relationship between families of fractions such as thirds and sixths, and halves, quarters and eighths.

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1 10

tenths to fractions with which students should already be familiar. Lead them to understand that whole numbers with decimal tenths are the same as mixed number in fractions. Use base ten material to help students initially visualise decimal tenths and fractions. Match fractions with decimals numbers and visa versa and introduce hundredths in the same way. Visually look at parts shaded out of 100 and compare fractions and decimals. Relate this concept to cents and dollars in our money system. $2.54 is the same as a mixed number 54 fraction 2 100 .

Fractions and Decimals (Years 3 and 4)

Warm-up activities

Year 4

These activities could be used to introduce your fractions lesson. They can be used as a whole class or small group focus, or an individual activity depending on the lesson content. • Make a fraction wall, guiding students through dividing each section to match the fraction denominator then shading and labelling each fraction (see teacher resources page 45). Discuss the most accurate way of making sure each fractional is the same; this may be done by folding each section or measuring it with a ruler.

• Look at how fractions can be used in sharing or dividing groups. Using the internet, investigate how often fractions are used when looking at fraction of groups.

• Define equivalence of fractions (the same) then use the fraction wall to discuss which fractions are equivalent. Play an equivalent fractions match-up game where you match fractions that are equivalent (see teacher resources page 46).

• Using strips of paper divided into ten (see teacher resources page 47), discuss how tenths can be related to decimal numbers. Shade the tenths to match the decimal tenths; for 1 2 = 0.1, 10 = 0.2 etc. example, 10

• Create fraction equivalence posters using circles. For example, 13 = 26 : students would divide and shade two equal sized circles to represent the equivalence.

• Use a hundredths grid (see teacher resources page 49) to illustrate that hundredths can be also related to decimal numbers; for example, 53 100 = 0.53. Shade some decimal numbers to match the fraction hundredths. Relate these hundredths to money. Mixed numbers can be represented; for example, $8.25 is a the same 25 . as the mixed number 8 100

• Use the interactive whiteboard or a fraction maths program to view fraction symbols and suggest whether they are equivalent or not. See <www.mathsisfun.com/fractions-menu.html> for examples. •

© R. I . C.Publ i cat i ons • Play fraction and decimal bingo using the grids • f o r r e v i e w p uprovided r pos eteacher son l y• (see resources page 50). The Count by halves, thirds, quarters, fifths, sixths,

eighths and tenths using number lines. What happens when you get to 1 whole? Lead students to realise that you can count as high as you like using fractions; it just means that you are using mixed numbers (a whole number together with a fraction). • Place common fractions and mixed fractions on a number line. Compare the size of fractions by looking at the number line. Look at equivalent fractions again. • Use the blank number lines to count above the line in mixed numbers and below the line in improper fractions. Illustrate how an improper fraction (numerator is higher than the denominator) can be change to a mixed number by drawing it, or by looking at a number line and using the division method; for example, 19 1 3 = 6 3 (3 can be divided into 19 six times with 1 3 remainder).

• Locate a recipe that requires fractions, including mixed number fractions. Convert these to improper fractions.

Fractions and Decimals (Years 3 and 4)

students write six different tenths on their bingo card and the teacher calls out the matching decimal number. The student who has matched and crossed off all their tenths is the winner. • Play match-ups using decimal tenths or hundredths with fractions (see teacher resources page 51). • Find money amounts in catalogues and cut them out. Convert the money amount (decimal number) to fractions or mixed numbers; for 50 example, $2.50 = 2 100 or 2 12 . Discuss how fractions can be broken down to their lowest common denominator.

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Teachers resources

Fraction wall whole half third quarter fifth sixth eighth tenth

Fraction wall

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Fractions and Decimals (Years 3 and 4)

Teachers resources

Equivalent fractions match-up game 2 8

1 4 2 4 3 4 4 4

4 8 6 8 8 8 3 1 6 2 2 1 6 3 4 2 © R . I . C . P u b l i c a t i o n s 6 3 •3f orr evi ew pur poseson y• 6l 6 3 2 1 10 5 4 2 10 5 6 3 10 5 4 8 5 10 10 5 10 5 2 1 2

Fractions and Decimals (Years 3 and 4)

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Teachers resources

Tenths

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Fractions and Decimals (Years 3 and 4)

Teachers resources

Hundredths

Fractions and Decimals (Years 3 and 4)

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Teachers resources

Hundredths grids

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Fractions and Decimals (Years 3 and 4)

Teachers resources

Bingo cards

Fractions and Decimals (Years 3 and 4)

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Teachers resources

Fraction and tenths match-ups

1 10

2 10

3 10

4 10

5 10

6 10

7 10

8 10

9 10

10 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

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Fractions and Decimals (Years 3 and 4)

1. Draw lines to match the fraction word to its symbol. 3 5 2 3 2 10 3 6 1 8 3 8 4 4 4 5 1 3

One-eighth Four-quarters Four-fifths One-third Two-tenths Three-fifths Two-thirds One whole

Three-eighths

match the fraction name.

symbol.

(a) two-quarters

(a) 1 4

(b) four-eighths

(b) 10

(d) three-tenths (e) two-fifths

(d) (e)

(f) four-sixths (g) one half (h) seven-eighths (i) one whole Going further

(f) (g) (h) (i)

5 5 8 2 3 3 6 2 2 3 4 6 10

Write the fraction symbol to represent how many boys there are in your class today. Then write the fraction symbol to represent the girls. 52

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

Numerator – tells us how many parts are shaded or represented. Denominator – tells us how many parts a shape or object is divided into.

on a number line (ACMNA078)

1 2

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Fractions are equal parts of a whole.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fraction words and symbols

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Divide the rectangle into halves and shade one half. Write the symbol 2 in each part.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Halves, quarters and eighths

2. Divide the rectangle into quarters and shade one-quarter. Write the symbol 1 4 in each part.

3. Divide the rectangle into eighths and shade one-eighth. Write the symbol 1 8 in each part.

4. Name the fractions shaded using fraction symbols. (a)

(e)

(f)

(g)

(h)

5. Can you see any fractions above that are the same? If so, shade them the same colour and name them.

Going further

When fractions are the same they are called e Write a dictionary definition of this word. R.I.C. Publications©

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fractions. Fractions and Decimals (Years 3 and 4)

2. Circle the correct definition of equivalent. sometimes the same size

the same size

not the same size

3. Fill in the missing quarters and eighths on the number line. 1 4

4 4 1 2

1 8 8

(a) (c) (e) (g) (i)

8 8 1 4 3 4 2 2 3 8

= 2

(b)

= 1 2

(d)

= 8

(f)

(h)

= 4

(j)

3 4 2 8 7 8 1 2 3 4

= 8 = 1 4 4

= 4 4

= 8 7

= 8

5. What do halves, quarters and eighths have in common? (Hint: look at their denominators.)

Going further

Investigate the term ‘equivalence in fractions’ using the internet and list some examples of what you found out. 54

Fractions and Decimals (Years 3 and 4)

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CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

4. Use the number line to answer true or false to the fraction statements.

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

What do you notice?

on a number line (ACMNA078)

1. Shade half of the first circle, two-quarters of the next circle and foureighths of the last circle.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Comparing halves, quarters and eighths

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Divide the rectangle into thirds and shade one-third. Write the symbol 3 in each part.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Thirds and sixths

2. Divide the rectangle into sixths and shade one-sixth. Write the symbol 6 in each part.

3. What do the fractions 3 and 6 have in common? (Hint: look at the denominators.)

4. Name the fractions shaded below using fraction symbols.

5. Show the equivalent (same) fractions above by shading them the same colour. Name three pairs of the equivalent fractions.

Going further

On the back of this page, draw and label three other fractions that you know are equivalent. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

(c)

2. Complete the equivalent sentences. (a)

-sixths

(b)

two-thirds =

-sixths

one-third = three-thirds =

-sixths

2 3

1 1 6

4 6

4. Use the number line to answer true or false to the fraction statements.

(e)

2 5 3 = 6 2 1 6 = 3 1 1 3 = 2

(g)

3 6 3 = 6

(a) (c)

(b) (d) (f) (h)

4 2 6 = 3 1 1 3 = 6 6 6 =1 3 1 3 = 6

Going further

One-third is larger than one-sixth. Explain if this statement is true or false and draw an example. 56

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

(b)

on a number line (ACMNA078)

(a)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Shade the sixths to be equivalent to the thirds already shaded.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Comparing thirds and sixths

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Divide the rectangle into fifths and shade one-fifth. Write the symbol 5 in each part.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fifths and tenths

2. Divide the rectangle into tenths and shade one-tenth. Write the symbol 1 10 in each part.

3. What do the fractions 5 and 10 have in common? (Hint: look at the denominators.)

4. Name the fractions shaded below using fraction symbols.

5. Show the equivalent (same) fractions above by shading them the same colour. Name three pairs of the equivalent fractions. Going further 5

At a local café during lunch hour 10 of carrot cake, 10 of lemon cake and 2 10 of chocolate cake was ordered. How many fifths of cake were ordered altogether? R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

(c)

(d)

2. Complete the equivalent sentences. (a)

one-fifth =

(c)

three-fifths =

-tenths

(b) two-fifths =

-tenths

(d) four-fifths =

-tenths

five-fifths =

3 5

5 5

1 1 10

3 10

8 10

4. Use the number line to answer true or false to the fraction statements. (a) (c) (e) (g)

7 4 = 10 5 4 2 = 10 5 3 6 = 5 10 8 2 = 10 5

(b) (d) (f) (h)

4 8 = 5 10 9 4 = 10 5 3 1 = 10 5 1 2 = 5 10

Going further 4

If you had 10 of $1.00, how much money would you have? 7

If you had 10 of $1.00 how much money would you have? 58

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

(b)

on a number line (ACMNA078)

(a)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Shade the tenths to be equivalent to the fifths already shaded.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Comparing fifths and tenths

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Complete the fraction wall by first shading each fraction line a different colour. Write the fraction name in the first part, then write the fraction symbols in each other section. The fifths are done for you as an example. whole

1 5

fifth

1 5

2. Use the fraction wall to help you write the equivalent fraction. 1

(a) 3 = 6 3

(d) 5 = 10

(e) 2 = 6

(f) 6 = 3

(g) 8 = 4

(h) 3 = 2

(i) 8 = 2

(j) 5 = 10

(l) 2 = 8 4

(k) 4 = 2

3. Write all the equivalent fractions you can see on the fraction wall for each fraction. 1

(a) 1 4 =

(b) 2 =

(d) 5 =

(e) 1 whole = on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fraction wall

Going further

Play the equivalent fraction match-up game or explore equivalent fractions using the internet. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

(e) If a painter painted 5 of a wall made up of 10 panels, what fraction does he have left to paint?

(d) At a party, 10 of a cake was eaten. How many fifths were left?

(f) Before getting a lift, John walked a third of the way home from school one day and a third more each day. How many days would it take him to walk the whole distance?

1 (g) If a store assistant packed 1 4 of (h) The bath was only 3 filled and a shelf and another assistant Mum came along and filled 1 another 2 packed 2 shelf, how much of 6 with water. What fraction of the bath has now the shelf is left to fill? been filled? 2

(i) On Monday Lara wrote 5 of a page at school and today she 6 wrote 10 . How much has she written altogether?

(j) A pie was cut into 8 pieces. If 1 Dad ate 1 , Jack ate 4 4 and Chloe 1 ate , how much of the pie is 8 left?

Going further

Imagine you were planning a party for 12 guests and you decided to have pizzas. Work out how many pieces you would allow for each person and how many whole pizzas you would need to order. 60

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

(b) Kate ran 8 of a kilometre and Beth ran 7 . Who ran the 10 furthest?

on a number line (ACMNA078)

(a) Charlie ate 4 of a chocolate bar and Harry ate 5 . Who ate 6 more?

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Solve the problems using your knowledge of equivalent fractions. (Hint: you may wish to use drawings to help you.)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Equivalent fraction problems

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. What fraction of each group is shaded?

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fractions of groups (a)

(b)

(c)

(d)

(e)

(f )

(g)

(h)

What fraction is kiwi fruit?

(b)

What fraction is apples?

(c)

What fraction is grapes?

(d)

What fraction is strawberries?

(e)

What fraction would remain if someone ate the kiwi fruit and the apples?

(f)

What fraction would remain if someone ate the grapes and the strawberries?

Going further

Looking at the contents of your pencil case, what approximate fraction of the total is: coloured pencils? textas? pens? scissors? erasers? R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

2. Find one half of each number you circled above. (a) (c) (e) (g)

1 2 1 2 1 2 1 2

(b) 2 of

(d) 2 of

(f)

(h)

1 2 of 1 2 of

= =

3. Circle the numbers that can be evenly divided by thirds. (multiples of 3) 12

4. Find one-third of each number you circled above.

1 3 of 1 1 (c) 3 of = (d) 3 of = 1 1 (e) 3 of = (f) 3 of = 1 1 (g) 3 of = (h) 3 of = 5. Find 1 4 of the numbers. (Hint: Divide the four into the whole number.) (a) 1 (b) 1 (c) 1 4 of 16 = 4 of 24 = 4 of 40 = 1 1 (d) 1 of 28 = (e) of 48 = (f) 4 4 4 of 12 = 1 6. Find 10 of the numbers. (Hint: Divide the 10 into the whole number.) 1 1 1 (a) 10 of 40 = (b) 10 of 70 = (c) 10 of 20 = 1 1 1 (d) 10 of 110 = (e) 10 of 90 = (f) 10 of 250 =

(a)

Going further

What numbers could be evenly shared into eighths? Make a list. 62

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

on a number line (ACMNA078)

1. Circle the numbers that can be evenly divided by half (multiples of 2).

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Fractions, division and multiplication are closely related. For example, if you 1 wanted to find 5 of a group of 25, you would divide the group of 25 into 5 (fifths) to find the answer: 5. To divide evenly the numerator has to be a multiple of the whole number.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fractions and division

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Counting by halves We can count by fractions but once we count over one whole, the fraction becomes a mixed number. This means it is made up of a whole number and 1 a fraction; for example, 2 2 . 1. Complete the number line counting by halves. 1 2

2. You can also count by halves without using whole numbers. When the numerator is higher than the denominator it is called an improper 9 fraction; for example, 2 . Use improper fractions to count by halves. 1 2

2 2

3. Change the improper halves into mixed numbers. For example: 2 = 6 2 (a) (c) (e) (g)

4 2 = 8 2 = 11 2 = 9 2 =

(b)

7 2 = 3 2 = 18 2 = 21 2 =

4. Solve the problems dealing with halves. (a)

If 24 half pizzas were consumed at a restaurant, how many whole pizzas were eaten?

(b)

A fruit store cut and sold 1 watermelon halves. If they sold 13 2 watermelons, how many halves did they sell?

(c)

If Ethan completed 19 half sprints, how many whole sprints did he run?

Going further

When do people need to count by halves? Write examples on the back of the page. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

2. When the numerator is equal to or higher than the denominator, it is 12 called an improper fraction; for example, 4 . (a) 1 4

Use improper fractions to count by quarters. There are

(b)

quarters.

How many wholes do the quarters you counted equal?

3. Change the improper halves into mixed numbers by dividing the bottom number into the top number. The remainder becomes the fraction. If the fraction can be broken down further to a half, show that in your answer. 18 2 1 For example: 4 ÷ = 4 4 or 4 2 (a) (d) (g)

8 4 = 14 4 = 19 4 =

4 24 4 = 29 4 =

(f)

4 10 4 =

4. Solve these problems dealing with quarters. (a)

If 48 orange quarters were consumed at a football match, how many whole oranges were cut?

(b)

A deli sold 6 2 wheels of cheese in one day. If the cheese was cut into quarters, how many quarters were sold?

(c)

If a whole concert went for 3 hours and each act went for a quarter-hour, how many acts were there?

Going further

When do people need to count by quarters? Write examples on the back of this page. 64

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

on a number line (ACMNA078)

1 4

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Complete the number line counting by quarters above the line and by halves below the line.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Counting by quarters

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Complete the number line counting by eighths above the line and by quarters and halves below the line.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Counting by eighths

1 8

4 8

2. (a) 8 8

Write improper fractions to match the mixed numbers on the number line.

1 18 18 18 18 18 18 18 (b)

8 2

28 28 28 28 28 28 28

8 3

How many quarters equal 3 wholes?

3. Change these improper eighths into mixed numbers by dividing the bottom number into the top number. The remainder becomes the fraction. If the fraction can be broken down further to a quarter or half, show that in your answer. 42 2 1 For example: 8 ÷ = 5 8 or 5 4

(a) (d) (g)

24 8 = 16 8 = 49 8 =

(b) (e) (h)

17 8 = 20 8 = 64 8 =

34 8 = 35 8 =

4. Solve these problems dealing with eighths. (a)

A large pizza is cut into eighths. If 60 pieces of pizza were consumed at a party, how many whole pizzas were there to begin with?

(b)

At a local bakery 52 slices of cake were sold. If each cake was divided into eighths how many whole cakes did they sell?

(c)

How many times would you need to fold a length of string to make eighths?

Going further

When do people need to count by eighths? Write examples on the back of this page. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

1 3

2 3

2. Count by sixths using improper fractions, then using mixed numbers. The first few are done for you. 1 6

2 6

3 6

1 6

2 6

3 6

4 6

5 6

3. How many thirds or sixths are represented below? Write your answer in improper fractions and mixed numbers. (a)

(b)

(c)

(d) 4. Change the improper fractions into mixed numbers by dividing the bottom number into the top number. The remainder becomes the fraction. If the fraction can be broken down further to a third or half, show that in your answer. 20 2 1 For example: 6 ÷ = 3 6 or 3 3 (a) (d) (g)

9 3 = 29 3 = 31 6 =

(b) (e) (h)

16 3 = 18 6 = 38 6 =

22 3 = 27 6 =

Going further

Explain how thirds and sixths are related. 66

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

2 3

on a number line (ACMNA078)

1 3

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Count by thirds using improper fractions, then using mixed numbers. The first few are done for you.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Counting by thirds and sixths

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Count by fifths using improper fractions, then using mixed numbers. The first few are done for you.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Counting by fifths and tenths

5 5

6 5

2. Count by tenths using improper fractions, then using mixed numbers. The first few are done for you. 10 10

11 10

12 10

1 10 1 10 3. How many fifths or tenths are represented below? Write your answer in improper fractions and mixed numbers. (a)

(b)

(c)

(d) 4. Change the improper fractions into mixed numbers by dividing the bottom number into the top number. The remainder becomes the fraction. If the fraction can be broken down further to a fifth or half, show that in your answer. 45 5 1 For example: 10 ÷ = 4 10 or 4 2 (a) (d) (g)

20 5 = 51 5 = 75 6 =

(b) (e) (h)

37 5 = 60 10 = 87 6 =

19 5 = 43 10 =

Going further

Explain how fifths and tenths are related. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

(b)

2 3

1 3

3 3

6 3

5 3

4 3

1 5

3 5

2 5

4 5

7 4

8 4

(d) 0

1 4

2 4

3 4

4 4

5 4

6 4

2. Change the improper fractions on numbers lines (b) and (d) to mixed numbers. Write the mixed numbers in red pencil. 3. Divide the number line below into 8 parts and mark in the halves, quarters and eighths.

4. Divide the number line below into 5 parts and mark in the fifths and tenths.

Going further

Cut a strip of paper 30 cm long and make a number line that counts by halves, thirds, quarters, fifths, sixths and tenths. 68

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1 2

on a number line (ACMNA078)

(a)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Write the missing fractions on the number lines.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fractions and number lines

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

When working with fractions it is best to break down larger fractions to their lowest form. For example: The highest multiple each number can be divided by is 6, therefore 6 ÷ 6 = 1

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Breaking down fractions

12 ÷ 6 =

1. Break the fractions down by using the highest common multiple provided. (a)

8 ÷8 =

(b)

3 ÷3 =

16 ÷ 8 = (d)

4 ÷2 =

4 ÷4 =

9 ÷3 =

16 ÷ 4 =

5 ÷5 =

(f) 12 ÷ 6 =

15 ÷ 5 =

18 ÷ 6 =

(e)

6 ÷2 =

(c)

2. Write the highest multiple the two numbers can be divided by. (a)

6 and 9 =

(b) 8 and 16 =

(e)

(g)

14 and 21 =

(c)

10 and 60 =

(h) 32 and 34 =

3. Use the highest common multiple to break the fractions down to their lowest form. For example: 16 ÷ 8 = 2 24 ÷ 8 = 3 (a) (d) (g) (j)

2 4 = 8 16 = 35 40 = 32 40 =

(b) 9 =

(c)

(e) 21 =

(f)

(h) 80 =

(i)

36 54 =

(l)

(k)

12 15 16 20 12 24 36 48

= = = =

Going further 160

How many different ways could you break down 240 ? Suggest at least three. (There are five.)

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Fractions and Decimals (Years 3 and 4)

. (b)

A fraction that contains a whole number and a fraction is called .

2. Name these fractions using improper fractions and mixed numbers. (a)

(b)

(c)

(d)

(e) 3. Change these improper fractions into mixed numbers by dividing the denominator into the numerator to find the whole number. If there is a remainder, it becomes the numerator for the fraction part. 13 1 For example: 2 ÷ = 6 2 (a) (d) (g) (j)

5 2 = 25 4 = 42 10 = 30 6 =

(b) (e) (h) (k)

9 4 = 19 3 = 19 8 = 49 5 =

15 3 27 5 17 2 51 4

= = = =

Going further

Which do you find easier to understand, mixed numbers or improper fractions? Explain your answer. 70

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

A fraction where the numerator (top number) is equal to or larger than the denominator (bottom number) is called

on a number line (ACMNA078)

(a)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Write the correct type of fraction: mixed number or improper fraction.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Improper fractions to mixed numbers

1. Write mixed numbers to match the improper fractions on the number lines. 1 2

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

(a) 0

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Mixed numbers to improper fractions 2 2

3 2

4 2

5 2

6 2

7 2

8 2

9 2

10 2

1 1 3

(b) 0

2 3

3 3

4 3

5 3

6 3

7 3

8 3

9 3

10 3

11 3

12 3

4 4

5 4

6 4

7 4

8 4

9 4

10 4

11 4

12 4

1 1 4

2 4

3 4

1 5 5

(d) 0

6 5

7 5

8 5

9 5

10 5

11 5

12 5

13 5

14 5

15 5

9 8

10 8

11 8

12 8

13 8

14 8

15 8

16 8

17 8

18 8

1 8 8

(e) 0

18 = 8

24 = 4

3. Change the mixed numbers to improper fractions. (Multiply the denominator with the whole number then add the numerator.) For example: 3 11 2 4 = 4 (4 [denominator] x 2 = 8, then 8 + 3 [numerator] = 11) ×

(a)

12 = 2

(d)

46 = 6

(g)

28 = 8

3 7

(b) 3 3 = 3 9

(e) 1 10 = 10 1

(h) 5 5 = 5

(f)

35 = 5

(i)

43 = 3

Going further

Using the internet, investigate where mixed numbers are commonly used. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Bolognaise sauce 1 kg mince meat 8 4 cups tomato puree 3 2 cups chopped onion 1 clove garlic 4 3 cups beef stock basil and parsley (chopped)

3. (a)

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• The baker needs to make a larger batch of biscuits. Rewrite the recipe so he can make double the amount. Write the amounts as mixed numbers or improper fractions in column 2. How many biscuits does this recipe make?

Anzac biscuits: makes 24

Anzac biscuits: makes

6 8 cup melted butter 1 4 cup boiling water 1 teaspoon bicarb soda

1 tablespoon golden syrup 6 8 cup plain flour 2 3 cup coconut 6 4 cups oats

(b)

Rewrite the recipe in column 3 so that it makes half a batch of biscuits.

Going further

Find a large recipe in a newspaper, magazine or on the internet to cut out or print. Rewrite the recipe to make half the quantity. 72

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

2. Rewrite the recipe changing the improper fractions to mixed numbers.

on a number line (ACMNA078)

Banana and choc-chip muffins 1 2 2 cups SR flour 1 1 2 cups mashed banana 1 1 4 cups sugar 2 eggs 1 2 cup milk 3 4 cup chocolate chips

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Mixed numbers are often found in recipes. Rewrite the recipe using improper fractions where you can.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fractions and cooking

(a)

0.57

•

(b)

8.4

•

(c)

42.65

•

(d)

279.5

•

(e)

5288.10

•

(f)

41.78

•

(g)

73 822

(h) (i)

hundredths

tenths

•

ones

tens

hundreds

thousands

1. Place the numbers on the place value grid. Tens of thousands

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

Whole numbers always appear to the left of the decimal point. Decimal numbers or fractions are to the right of the decimal point. For example: 25.68 = 25 whole ones and 68 tenths (or 6 tenths and 8 hundredths).

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Decimals and place value

82 463.02

2. Write the numbers from question 1 in order from smallest to largest.

3. Write the value of the number that is underlined. For example: 5378.03 3 hundredths. (a)

42.86

(b) 521.7

(c)

375.68

(d) 4 216.94

(e)

8 920.3

(f)

(g)

2 156.04

(h) 12 548.41

705.23

Going further

Find out if numbers can be broken down further than hundredths. If they can, explain how and give an example. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

8 = 10 1 = 10 5 = 10 7 = 10

2. Write the fraction to match the decimal number. 8 For example: 0.8 = 10 (a)

0.5 =

(e)

0.6 =

10 10

(b) 0.2 = (f)

0.4 =

10 10

(d) 0.1 = (h) 1.0 =

10 10

Going further

If a 10-metre path was divided into tenths, how many metres would need to be laid if 0.4 was already laid? 74

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

3 = 10

on a number line (ACMNA078)

1. Shade the tenths to match the fraction. Write the matching decimal number.

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Fractions and decimals are closely related. A fraction is an equal part of a 2 whole. A decimal is part of a whole number. For example: 10 is the same as the decimal number 0.2

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fractions and decimals – tenths

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

Cut and match the fractions with their pictures and decimal numbers.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Matching fractions and decimal tenths

1 2

0.6

4 10

1.0

7 10

0.9

2 10

0.5

3 10

0.8

0.7

9 10

0.2

10 10

0.4

8 10

0.1

6 10

0.3

Going further

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Fractions and Decimals (Years 3 and 4)

2 10

10 2. (a)

0.4

5 10

0.7

8 10

1.0

Complete the missing decimal tenths.

0.1 (b)

0.2

Use your knowledge of equivalent fractions to write the decimal number to match the fractions. 1 5 = 0.

2 5 = 0.

3 5 = 0.

4 5 = 0.

5 5 =

3. What is the decimal number for 2 ? 0.

4. Make a list of other fractions that are equivalent to one half or 0.5.

5. Make a list of ten fractions that are equivalent to 1.0.

6. Write true or false next to these statements. (a) (d) (g) (j)

4 10 = 0.4 4 5 = 0.8 3 10 = 0.1 2 5 = 0.2

(b) 2 = 0.5

(i)

7 10 = 0.6 3 5 = 0.6 5 5 = 1.0

(l)

5 10 = 0.5

(c)

(e) 5 = 0.3

(f)

(h) 10 = 0.8 10

(k) 10 = 1.0

Going further 2

If a painter had painted 5 of one wall one day and 10 of the wall the next day, how much did he have left to paint? Write your answer as a decimal. 76

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

0.1

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

1. Write the missing fractions and the matching decimals on the number line.

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Tenths and equivalent fractions

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fractions and decimals – hundredths If one whole is divided into 100 equal parts, each part is called one hundredth and can be written as a fraction or a decimal. 27 For example: 100 = 0.27

1. Shade the hundredths to match the fraction and write the decimal number. 62

(a) 100 or 0.

(b) 100 or 0 .

(d) 100 or 0.____

(e) 100 or 0.0

2. Write the decimal to match the fraction. (a) (d) (g)

95 100 = 0. 8 100 = 0. 14 100 = 0.

(b) 100 = 0. 75

(e) 100 = 0. 88

(h) 100 = 0.

54 100 = 0. 41 100 = 0. 38 100 = 0.

Going further 50

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Fractions and Decimals (Years 3 and 4)

(c)

48 hundredths =

(e)

9 hundredths =

(g)

81 hundredths =

100 100

100

or 0.

(b) 13 hundredths =

or 0.

(d) 67 hundredths =

or 0.

100

(f)

or 0.

39 hundredths =

(h) 77 hundredths =

100 100 100 100

or 0. or 0. or 0. or 0.

2. Write the fractions to match the decimal hundredths. (a)

0.18 =

(d)

0.27 =

(g)

0.03 =

3. (a)

100 100

(b) 0.94 = (e) 0.05 = (h) 0.29 =

100 100 100

0.84 =

(i)

0.58 =

100 100 100

Draw lines to match the fraction to its decimal. 76 100 14 100 73 100 4 100 98 100 67 100 26 100 6 100 37 100 41 100

(b)

100

0.06 0.98 0.37 0.14 0.04 0.73 0.67 0.76

Write the decimal numbers in order from smallest to largest.

Going further

What similarities are there between tenths and hundredths? 78

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

21 hundredths =

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

(a)

on a number line (ACMNA078)

1. Write the hundredths as a fraction and a decimal number. 54 For example: 52 hundredths = 100 or 0.54

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Hundredths

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Comparing tenths and hundredths 1. Tenths and hundredths are related because 1 tenth can be divided into 10 1 10 hundredths; so 10 is the same as 100 and 0.1 is the same as 0.10. Shade each tenth on the hundredths chart a different colour and complete the missing fraction and decimal number. The first one is done for you. 10

(a) 100 = 0.10 or 0.1 20

(b) 100 = 0.20 or 0. (c) (d) (e) (f) (g)

30 100 40 100 50 100 60 100 70 100 80 100 90 100 100 100

= 0.

or 0.

= 0.

or 0.

= 0.

or 0.

= 0.

or 0.

= 0.

or 0.

or 0. or 0.

= 1.

or 1.

2. Change the hundredths to tenths. For example: 0.40 = 0.4 (a)

0.90 = 0.

(b) 0.10 = 0.

(d) 0.70 = 0.

(e)

0.80 = 0.

(f) 0.30 = 0.

(g) 0.60 = 0.

(h) 0.20 = 0.

3. Explain what you had to do to change the hundredths to tenths.

4. Order the tenths and hundredths from smallest to largest. 0.4 0.71 0.15

0.8

0.54

0.7

0.26

0.82

0.1

0.5

0.95

0.43

Going further

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Fractions and Decimals (Years 3 and 4)

3 10

3.8

3.7

3.6

3.3

3.5

3.1

2. Write the decimal number to match the mixed number fractions. 2 78 For example: 6 10 = 6.2 and 5 100 = 5.78 1

(a)

42 =

(d)

2 10 =

(g)

3 100

(j)

9 100 =

(b) 7 10 =

100 18 (k) 7 100 =

(l)

100 81 5 100 =

3. Write the decimal numbers as mixed number fractions. 6 For example: 3.06 = 3 100 (a)

1.5 =

(b) 4.2 =

(d)

9.3 =

(e) 5.6 =

(f)

2.03 =

(g)

5.12 =

(h) 9.35 =

(i)

4.88 =

(j)

7.06 =

(k) 2.84 =

(l)

11.59 =

4. Write the decimal numbers above from smallest to largest.

Going further

Explain the difference between 4.05 and 4.50. Write them as fractions. 80

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

3 10

on a number line (ACMNA078)

1. Match the mixed numbered fractions to their decimal number by shading them both in the same colour.

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Mixed number fractions can also be written as decimal numbers. The whole number remains the same and is to the left of the decimal point. The fraction becomes a decimal number and is to the right of the decimal point. 1 For example: 2 2 is the same as 2.5

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Decimals and mixed numbered fractions

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Name the fractions represented below. Write the matching decimal number. The first one is done for you.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Representing mixed fractions and decimals Representation (a)

Fraction

Decimal

4.1

4 10 (b)

(c)

(d)

(e)

2. Represent the fractions by drawing them. Write the matching decimal number. Fraction

Representation

Decimal

(a)

2 10

(b)

(c)

3 10

Going further 1

John ran sprints of an oval 3 days in a row. The first day he sprinted 2 2 lengths, the second day he sprinted 3.2 lengths and the third day he sprinted 4 5 10 . How many lengths did he sprint altogether? Write your answer in decimals and fractions. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

$2.00 =

(b) 50c =

(d)

$1.75c =

(e) $5.20c =

(f)

$9.50c =

2. Colour code to match the money to its decimal number and fraction. 1

$6.50

6.7

$4.75

6.5

9 100

$1.25

5.4

4 100

$9.85

4.15

$5.40

1.25

3 10

$4.15

3.1

6 10

$6.70

9.85

85 15

1 7

3. Write the decimal amount (money) to match the fractions. (a) (d) (g)

1 4 = 2 10 = 9 7 10 =

(b) 1 2 = 85

(e) 100 = 3

(h) 15 10 =

(f)

65 =

(i)

5 100 =

Going further

Use the internet to investigate other world currencies. Do any other countries use fractions to describe their amounts of money? 82

Fractions and Decimals (Years 3 and 4)

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

(a)

on a number line (ACMNA078)

1. Write the fraction to match the amounts. 75 For example: $4.00 = 4 and 75c = 100

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

We use decimals to represent amounts of money. Any number to the left of the decimal point is a whole dollar. Numbers to the right of the decimal point are cents which are parts or fractions of a dollar (100 cents). 1 For example: $2.50 = 2 dollars + 0.5 or 2 dollar or 50 cents

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Relating money to fractions

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1. Solve the problems using your knowledge of fractions and decimal numbers.

on a number line (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Fraction and decimal problems

(a) At the long jump event Cara jumped 2.75 m and Lily 4 jumped 2 5 m. Who jumped the further?

(b) Alex found $4.50 in the bottom of his drawer. If he already had 1 5 of $1.00, how much does he have now?

(c) Two builders measured a wall. (d) Two family-size pizzas were 3 ordered and cut into eighths. One builder measured 3 4 3 1 metres, the other measured If 4 of one pizza and 2 of the other were eaten, what 3.75 metres. Are their measurements the same? fraction was left?

(e) A wall needed to be rendered. (f) 4 If the renderer got 10 done one day and 0.3 completed on another day, how much does he have left to do? (g)

© R. I . C.Publ i cat i ons •f orr evi ew pur p osesonl y• On Monday the farmer sold (h) There were 100 passengers 15.68 barrels of grain and on 73 Tuesday he sold 15 100 . On which day did he sell more?

(i)

If Liam got 100 for a test and Jake got 0.86, whose score was higher?

A restaurant had five cakes, (j) each cut into 10 slices. At the end of the day the following 1 3 1 fractions were left; 10 , 10 , 2 , 2 4 and 10 10 . What part of each cake was sold? What was the total number of cakes sold?

on a train. At the first stop 32 100 of them got off. Then 0.27 of them left, followed by 0.18. How many passengers remained on the train? 37

If a bricklayer had laid 100 of bricks, how much does he have left to lay? Write your answer in decimal numbers.

Going further

If a person was 1.58 m tall, what does this mean? (What does the 1 stand for? What does the .58 stand for?) Write this length in fractions. Now find out how tall you are. Write your height in fractions and decimals. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

7 8

3 4

1 2

1 8

5 8

1 4

0 2. Count by thirds and sixths on the number line below. 1 3

1 6

0 3. (a)

6 6 6 6 An improper fraction is

(b)

A mixed number fraction is

(c)

Write the improper fractions from question 2 as mixed numbers.

4. Answer true or false to the equivalent fractions. (a) (d) (g) (j)

2 4 = 3 6 6 3 = 10 5 7 5 = 8 6

(e) 4 = 8 6

(f)

(h) 10 = 2 (k)

(i)

4 2 = 4 2

(l)

1 1 = 10 5 3 6 = 4 8 2 4 = 3 5

5. Write the improper fractions as mixed numbers. (a) (e)

9 8 = 21 4 =

15 6 = 27 (g) 8 =

(b) 3 = (f)

(c)

37 5 =

6. Find the fraction of each whole number. (a) (c) (e) (g) 84

1 3 1 2 1 8 1 4

of 12 =

(b)

of 32 =

(d)

of 32 =

(f)

of 48 =

(h)

Fractions and Decimals (Years 3 and 4)

1 4 1 5 1 3 1 6

of 20 = of 45 = of 36 = of 54 =

(d) (h)

13 2 = 31 3 =

Going further

On the back of this page count by halves, quarters and eighths to 2 wholes using a number line. Write three examples of equivalent fractions. R.I.C. Publications©

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation. (ACMNA079)

1. Place the fractions in order on the number line below.

on a number line. (ACMNA078)

Assessment 1

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Date:

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts. (ACMNA077)

Name:

Date:

Assessment 2 Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation. (ACMNA079)

1. Shade the tenths to the fraction. Write the equivalent decimal number.

on a number line. (ACMNA078)

CONTENT DESCRIPTIONS: Investigate equivalent fractions used in contexts. (ACMNA077)

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions

Name:

7 10 = 4 10 = 9 10 =

2. Write the fractions as decimal numbers. (a)

1 10 = 0.

(b) 10 = 0.

(d) 10 = 0.

3. Shade the hundredths to match the fraction and write the decimal number. 57

(a) 100 or 0.

(b) 100 or 0.

(d) 100 or 0.

4. Write the fraction to match the decimal numbers. (a)

0.31 =

(e)

0.04 =

(a)

1 10 =

(d)

8 10 =

100

(b) 0.11 =

100

(f) 0.82 = (g) 0.30 = 100 100 100 5. Write the mixed fractions as decimal numbers. 3 5

(d) 0.79 = (h) 0.17 =

100 100

(b) 5 100 =

(e) 2 100 =

(f)

9 10 =

Going further 37

On the back of this page represent the fraction 10 . Write this amount in a mixed number fraction and as a decimal number. R.I.C. Publications©

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Fractions and Decimals (Years 3 and 4)

Checklist

Year 4

Counts by Understands Understands Relates and locates equivalent tenths and fractions to fractions using fractions hundredths decimals number lines

Fractions and Decimals (Years 3 and 4)

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Answers Fraction words and symbols ................ page 52

Year 4

Comparing thirds and sixths ................ page 56 (a) 2 (b) 4 6 6 2. (a) two-sixths (b) four-sixths

1. Teacher check

1. Shaded:

2 4 (b) 8 2. (a) 4 2 (e) 5 (f) 4 6 3. (a) one-quarter

1 (c) 3 (d) 3 10 1 7 (g) 2 (h) 8 (b) nine-tenths

(d) five-eighths

(e) two-thirds

(f) three-sixths

(g) two-halves

(h) three-quarters

(i) 1

3. Teacher check 4. (a) false

(b) true

(d) false

(e) false

(f) true

(g) true

(h) false

Going further – True. Teacher check

Fifths and tenths .................................... page 57 1.–2. Teacher check

(i) six-tenths

3. common multiples of 5

Going further – Teacher check

Halves, quarters and eighths ................ page 53 1.–3. Teacher check

4 1 1 1 (b) 2 (c) 2 or 4 (d) 4 4. (a) 8 8 1 2 1 4 (e) 5 (f) 2 (g) 4 or 2 (h) 1 or 4 8 4 2 1 1 5. 8 , 4 , 2 and 2 and 4 8 Going further – equivalent fractions. Teacher check; e.g. equivalent fractions have different names for the same number or value.

5 3 4. 10 , 2 , 9 , 5 , 10 , 10 10 10 2 5 4 8 5 5 , 5 , 10 , 10 , 10 , 2 , 7 , 3 , 1, 4, 1 10 10 10 5 5 10 5. Teacher check e.g. 1 = 2 , 2 = 4 , 3 = 6 , 10 5 10 5 10 4 = 8 , 5 = 10 5 5 10 5 10 4 Going further – 5

Comparing fifths and tenths ................. page 58

Comparing halves, quarters and eighths .................................................... page 54

1. Shaded:

(a) 2

2. (a) two-tenths

1. Teacher check. They are the same/equivalent.

2. the same size

(e) ten-tenths

3. Teacher check

4. (a) true

(b) false

(d) true

(e) true

(f) false

(g) true

(h) true

(i) false

(j) false

5. They are even numbers. Quarters and eighths have common multiples of 2 and 4. Going further – Teacher check

Thirds and sixths ................................... page 55 1.–2. Teacher check 3. common multiples of 3

1 4. 2 , 1 , 4 , 2 , 3 , 1 , 6 , 3 , 1 whole, 2 3 3 6 6 3 6 6 6 5. Teacher check e.g. 2 = 4 , 1 = 2 , 3 = 6 3 6 3 6 3 6 Going further – Answers will vary.

(b) 8

4. (a) false (e) true

(d) 4 10 (b) four-tenths (d) eight-tenths

(b) true

(d) false

(f) false

(g) false

(h) true

Going further – 40c, 70c

Fraction wall........................................... page 59 1. Teacher check (b) 6 (c) 2. (a) 2 6 8 2 (e) 3 (f) 3 (g) 6 1 (i) 2 (j) 8 (k) 10 2 4 5 3. (a) 2 (b) 4 , 3 , 8 , 10 8 6 2 2 3 (d) (e) , , 4 , 5 , 6 , 10 2 3 4 5 6 Going further – Teacher check

2 5 1 4 1 2

(d) 6 10 (h) 2 2 4 (l) 8 (c) 2 6

8 , 10 8 10

Equivalent fraction problems ............... page 60 2 (c) 4 1 (e) 2 or 1 (f) 3 days (g) 4 10 5 3 (i) 10 or 1 page (j) 8 10 Going further – Answers will vary. 1. (a) Harry

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(b) Kate

Fractions and Decimals (Years 3 and 4)

(d) 1 5 2 (h) 3

Answers Fractions of groups................................ page 61 4 1 5 1 9 3 1. (a) 8 or 2 (b) 25 or 5 (c) 12 or 4 (d) 2 or 1 (e) 10 or 2 (f) 5 or 1 20 10 25 5 15 3 5 1 3 1 (g) or (h) or 30 6 24 8 2. (a) 4 or 1 (b) 2 or 1 24 6 24 12 1 1 12 6 (c) or 2 (d) or 4 24 24 18 3 6 1 (e) 24 or 4 (f) 24 or 4 Going further – Answers will vary.

Fractions and division ........................... page 62

Counting by eighths .............................. page 65 1. Teacher check.

2, 3, 5, 6, 7,11,13,14,15,16 8 8 8 8 8 8 8 8 8 8 1 2 3 1 2 3 4, 4, 4,14,14,14 1 1 2,12 2. (a) 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 8 8 8 8 8 8 8 8 8 18 , 19 , 20 , 21 , 22 , 23 , 24 8 8 8 8 8 8 8 (b) 12 1 (b) 2 8

1 (c) 4 4

(d) 2

1 (e) 2 2

3 (f) 4 8

1 (g) 6 8

(h) 8

1 4. (a) 7 2

1 (b) 6 2

3. (a) 3

1. 68, 26, 32, 50, 84, 12, 46, 58 2. (a) 34 (e) 42

(b) 13 (c) 16 (f) 6

(d) 25

(g) 23 (h) 29

Going further – Answers may vary; e.g. pizza or cake slices.

3. 12, 36, 45, 27, 66, 39, 18, 15 4. (a) 4 (e) 22

(b) 12 (c) 15

(d) 9

Counting by thirds and sixths .............. page 66

(f) 13

(h) 5

3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 3 3 3 3 3 3 3 3 3 3 2 1 2 1 2 1 3 , 2, 2 3 , 2 3 , 3, 3 3 , 3 3 , 4 2. 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 6 6 6 6 6 6 6 6 6 1 2 4 5 1 ,1 ,1 ,1 ,2 6 6 6 6 1 7 or 2 3 (b) 15 or 5 3. (a) 3 3 4 24 16 (c) or 2 (d) or 4 6 6 6 1 1 2 (c) 7 3 (d) 9 3 4. (a) 3 (b) 5 3 1 1 (e) 3 (f) 4 3 or 4 2 (g) 5 1 (h) 6 2 or 6 3 6 6 6 Going further – Both are multiples of 3.

(g) 6

5. (a) 4

(b) 6

(d) 7

(e) 12

(f) 3

6. (a) 4

(b) 7

(d) 11

(e) 9

(f) 25

Going further – Teacher check

Counting by halves ................................ page 63 1. Teacher check. 1, 1

2. 3 , 4 , 5 , 6 , 7 , 8 , 9 , 2 2 2 2 2 2 2 14 , 15 2 2 1 3. (a) 2 (b) 3 2 1 (e) 5 2 (f) 9 4. (a) 12

(b) 27

, 3, 4, 4

10 , 11 , 12 , 13 , 2 2 2 2

1 (d) 1 2

1 (g) 4 2

1 (h) 10 2

1 (c) 9 2

Going further – Answers will vary; e.g. cooking.

Counting by quarters ............................ page 64 2 3 1 2 1 3 1. Teacher check. 4 , 4 , 1 4 , 1 4 , 2, 2 4 , 2 4 1 1 1 2,12,22 2. (a) 16 2 3 4 5 4, 4, 4, 4, 13 , 14 , 15 , 4 4 4 (b) 4

6 , 7 , 8 , 9 , 10 , 11 , 12 , 4 4 4 4 4 4 4 16 4

3. (a) 2

3 (b) 2 4

1 (d) 3 2

(e) 6

1 (f) 2 2

3 (g) 4 4

1 (h) 7 4

(b) 26

4. (a) 12

Year 4

Counting by fifths and tenths ............... page 67 7 8 9 10 11 12 13 14 15 5, 5, 5, 5 , 5 , 5 , 5 , 5 , 5 3 4 1 2 3 4 1 5 , 1 5 , 2, 2 5 , 2 5 , 2 5 , 2 5 , 3 13 14 15 16 17 18 19 20 2. 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 1 3 ,1 4 ,1 5 ,1 6 ,1 7 ,1 8 ,1 9 ,2 10 10 10 10 10 10 10 14 4 25 (b) 5 or 5 3. (a) 5 or 2 5 39 9 (c) or 3 (d) 35 or 3 5 10 10 10 10 2 4. (a) 4 (b) 7 (c) 3 4 5 5 1 (d) 10 (e) 6 (f) 4 3 5 10 1 1 3 3 (g) 12 or 12 2 (h) 14 or 14 2 6 6 Going further – Both are multiples of 5. 1.

Going further – Answers will vary. 88

Fractions and Decimals (Years 3 and 4)

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Answers Fractions and number lines .................. page 68 1 3 1 3 1. (a) 4 , 4 , 1 4 , 1 4 (b) 1 , 3 , 5 , 7 , 9 , 11 6 6 6 6 6 6 (c) 1 , 3 , 5 , 7 , 9 , 1 1 , 1 3 , 1 5 , 10 10 10 10 10 10 10 10 1 7 ,1 9 10 10 (d) 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 8 8 8 8 8 8 8 8 2. (b) 1 1 , 1 3 , 1 5 6 6 6 (d) 1 1 , 1 3 , 1 5 , 1 7 8 8 8 8 3.–4. Teacher check Going further – Teacher check

Breaking down fractions ....................... page 69 1 1. (a) 2 2 (d) 3 2. (a) 3

1 (b) 3 1 (e) 3 (b) 8

1 (c) 4 2 (f) 3 (c) 10

(d) 3

(e) 4

(f) 15

(g) 7

(h) 2

1 3. (a) 2 1 (e) 3 1 (i) 2

Year 4

Mixed numbers to improper fractions ................................. page 71 1 1 1 1 1. (a) 1 2 , 2, 2 2 , 3, 3 2 , 4, 4 2 , 5 1 2 1 2 1 2 (b) 1 3 , 1 3 , 2, 2 3 , 2 3 , 3, 3 3 , 3 3 , 4 1 2 3 1 2 3 (c) 1 4 , 1 4 , 1 4 , 2, 2 4 , 2 4 , 2 4 , 3 2 4 2 4 (d) 1 1 , 1 5 , 1 3 , 1 5 , 2, 2 1 , 2 5 , 2 3 , 2 5 , 3 5 5 5 5 1 3 4 7 1 (e) 1 8 , 1 2 , 1 8 , 1 8 , 1 5 , 1 6 , 1 8 , 2, 2 8 , 2 2 8 8 8 8 9 15 2. 4 , 8 3. (a) 3 (b) 11 (c) 23 2 3 4 19 19 27 (d) (e) 10 (f) 5 6 23 26 14 (g) 8 (h) 5 (i) 3 Going further – Teacher check

Fractions and cooking ........................... page 72

2 4 (b) 3 (c) 5 4 7 (f) 5 (g) 8 4 2 (j) 5 (k) 3 80 40 20 10 2 Going further – 120 , 60 , 30 , 15 , 3

1 (d) 2 (h) 5 8 3 (l) 4

5 SR flour, 3 banana, 5 sugar 2 2 4 1 2. 2 cups tomato puree, 1 2 cups onion, 1 1 3 cups beef stock 3. (a) Makes 48 biscuits 1.

Improper fractions to mixed numbers ...................................... page 70 1. (a) an improper fraction (b) a mixed number (b) 12 and 1 2 2. (a) 15 and 1 7 8 8 10 10 7 1 19 (c) and 2 (d) and 3 1 3 3 6 6 17 1 (e) 4 and 4 4 1 1 1 3. (a) 2 2 (b) 2 4 (c) 5 (d) 6 4 1 2 3 (e) 6 3 (f) 5 5 (g) 4 2 (h) 2 8 10 1 4 3 (i) 8 2 (j) 5 (k) 9 5 (l) 12 4 Going further – Answers will vary.

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or 1

cups melted butter

cup boiling water

2 tsp bicarb soda 2 tbsp golden syrup

12 or 1 1 cups plain flour 2 8 4 or 1 1 cups coconut 3 3 12 or 3 cups oats 4 (b) Makes 12 biscuits 3 cup melted butter 8 1 8 cup boiling water 1 2 tsp bicarb soda 1 2 tbsp golden syrup 3 cup plain flour 8 1 3 cup coconut 3 4 cup oats Going further – Answers will vary/Teacher check

Fractions and Decimals (Years 3 and 4)

Answers Decimals and place value ..................... page 73 1. Teacher check 2. 0.57, 8.4, 41.78, 42.65, 279.5, 5288.1, 15 632.50, 73 822, 82 463.02 3. (a) 8 tenths

(b) 2 tens

(d) 4 thousands

(e) 3 tenths (g) 4 hundredths

Year 4

Fractions and decimals – hundredths ............................................. page 77 1. (a) 0.62

(b) 0.15

(d) 0.83

(e) 0.06

(f) 0.42

(g) 0.76

(h) 0.91

Teacher check shading 2. (a) 0.95

(b) 0.23

(f) 7 hundreds

(d) 0.08

(e) 0.75

(f) 0.41

(h) 1 tens of thousands

(g) 0.14

(h) 0.88

(i) 0.38

2 1 Going further – Answers will vary; e.g. 0.5, 4 , 2

Going further – Yes; e.g. thousandths.

Fractions and decimals – tenths........... page 74 1. 0.3, 0.8, 0.1, 0.5, 0.7, 0.9, 0.6, 0.4, 1.0 Teacher check shading (b) 2 2. (a) 5 10 10 (e) 6 (f) 4 10 10 Going further – 6 metres

(d) 1 10 (h) 10 10

Matching fractions and decimal tenths ....................................... page 75 Teacher check

Hundredths ............................................ page 78 1. (a) 21 or 0.21 100 (c) 48 or 0.48 100 (e) 9 or 0.09 100 (g) 81 or 0.81 100 2. (a) 18 (b) 100 (d) 27 (e) 100 (g) 3 (h) 100 3. Teacher check

(b) 13 or 0.13 100 (d) 67 or 0.67 100 (f) 39 or 0.39 100 (h) 77 or 0.77 100 94 (c) 66 100 100 5 (f) 84 100 100 29 (i) 58 100 100

1, 2, 3, 4, 5 5 5 5 5 5

4. 0.04, 0.06, 0.14, 0.26, 0.37, 0.41, 0.67, 0.73, 0.76, 0.98

Going further – Answers will vary.

1. 0.2, 0.3, 0.5, 0.6, 0.8, 0.9

1 , 3 , 4 , 6 , 7 , 9 , 10 10 10 10 10 10 10 10 2. (a) 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 (b) 0.2, 0.4, 0.6, 0.8, 1.0 3. 0.5

Comparing tenths and hundredths ...... page 79 1. (b) 0.20 or 0.2

(d) 0.40 or 0.4

(e) 0.50 or 0.5

(f) 0.60 or 0.6

(g) 0.70 or 0.7

(h) 0.80 or 0.8

(i) 0.90 or 0.9

(j) 1.00 or 1.0

Teacher check shading

4. Answers may vary, e.g. 2 , 4 , 3 , 5 , 6 4 8 6 10 12 5. Answers may vary,

2. (a) 0.9

(b) 0.1

(d) 0.7

4 13 e.g. 2 , 3 , 4 , 5 , 6 , 8 , 10 , 11 , 12 , 13 2 3 5 6 8 10 11 12 6. (a) true (b) true (c) false

(e) 0.8

(f) 0.3

(g) 0.6

(h) 0.2

3. Drop the zero which represents hundredths.

(d) true

(e) false

(f) true

(g) false

(h) false

(i) true

(j) false

(k) true

(l) true

4. 0.1, 0.15, 0.26, 0.4, 0.43, 0.5, 0.54, 0.7, 0.71, 0.8, 0.82, 0.95 Going further – Answers will vary; e.g. timing, measuring.

Going further – 0.3

Fractions and Decimals (Years 3 and 4)

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Answers Decimals and mixed numbered fractions ............................... page 80 1. Teacher check 2. (a) 4.5

(b) 7.2

(d) 2.7

(e) 5.9

(f) 24.3

(g) 3.25

(h) 1.73

(i) 6.32

(j) 9.03

(k) 7.18

(l) 5.81

(b) 4 2 (c) 8 1 (d) 9 3 3. (a) 1 5 10 10 10 10 6 3 12 (e) 5 (f) 2 (g) 5 (h) 9 35 10 100 100 100 6 88 84 (i) 4 (j) 7 100 (k) 2 (l) 11 59 100 100 100 4. 1.5, 2.03, 2.84, 4.2, 4.88, 5.12, 5.6, 7.06, 8.1, 9.3, 9.35, 11.59 Going further – 4.05 is smaller than 4.50 with a difference of 0.45. 4.05 = 4 5 100 4.50 = 4 5 or 4 50 10 100

Representing mixed fractions and decimals .......................................... page 81 1. (b) 2 3 , 2.3 10 (d) 3 9 , 3.9 10 2. (a) 2.7 (b) 2.5

Year 4

Assessment 1 ......................................... page 84 1, 8 2 2. 3 , 2, 6 3. (a) 1.

1 1 5 3 7 4, 2, 8, 4, 8 3, 4, 5, 6 3 3 3 3 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 6 6 6 6 6 6 6 6 6 6 A fraction where the numerator is the same or greater than the denominator.

(b) A fraction with a whole number and a fraction part.

1 2 (c) 1, 1 3 , 1 3 , 2 1, 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 2 6 6 6 6 6 4. (a) true (b) true (c) false

(d) true

(e) false

(f) false

(g) true

(h) false

(i) true

(j) false

(k) true

(l) false

5. (a) 1 1 8 1 (e) 5 4 6. (a) 4 (e) 4

(b) 5

1 1 (c) 2 3 or 2 2 (d) 6 2 6 3 1 (g) 3 8 (h) 10 3 (c) 16 (d) 9

(f) 12

(g) 12

(b) 2

2 (f) 7 5

(h) 9

Going further – Teacher check

Assessment 2 ......................................... page 85 © R. I . C.Publ i cat i o ns 1 •f o rr evi ew pur posesonl y• 10

Teacher check drawings

1. 0.7, 0.4, 0.9

Going further – 11

or 11.1

Teacher check shading

Relating money to fractions ................. page 82 1 (b) 50 or 5 or 2 100 10 3 (d) 1 75 or 1 4 100 1 (f) 9 50 or 9 2 100

1. (a) 2

1 (c) 25 or 4 100 (e) 5 20 or 5 2 or 5 1 100 10 5 2. Teacher check 3. (a) 25c

(b) $1.50

(d) 20c

(e) 85c

(f) $6.80

(g) $7.90

(h) $15.30

(i) $5.65

Going further – Answers will vary.

2. (a) 0.1

(b) 0.5

(d) 0.3

3. (a) 0.57

(b) 0.91

(d) 0.68

Teacher check shading 4. (a) 31 100 (e) 4 100 5. (a) 1.3 (d) 8.5

(b) 11 100 82 (f) 100 (b) 5.34

45 (c) 100 (g) 30 100 (c) 3.25

(e) 2.71

(f) 9.3

(d) 79 100 (h) 17 100

Going further – 3 7 , 3.7 10 Teacher check drawing

Fraction and decimal problems ............ page 83 1. (a) Lily (e) 0.3

(b) $4.70

(f) Liam

(g) Tuesday

3 (d) 4 (h) 23

1 1 (i) 9 , 7 , 2 , 8 , 6 total = 35 or 3 2 10 10 10 10 10 (j) 0.63 Going further – 1 58 or 1 m 58 cm. Students’ 100 heights will vary.

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Fractions and Decimals (Years 3 and 4)