RIC-6136 3.1/372
Australian Curriculum Mathematics – Number and Algebra: Fractions Book 1 (Years 1 and 2) Published by R.I.C. Publications® 2015 Copyright© Clare Way 2015 ISBN 978-1-925201-28-4 RIC– 6136
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) 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.
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:
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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 1 Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
Year 2
Teachers notes .............................................................2
Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
Blacklines................................................................ 7–20
Teachers resources ............................................27–31
Assessments ........................................................21–22
Blacklines..............................................................32–54
Checklist .....................................................................23
Assessments ........................................................55–56
Answers.......................................................................24
Checklist .....................................................................57
© R. I . C.Publ i cat i ons Teachers notes ...........................................................25 Warm-up activities......................................................3 •f orr evi ew pur p ose sonl y• Warm-up activities....................................................26 Teachers resources ................................................ 4–6
Answers................................................................58–59
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Fractions (Years 1 and 2)
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Teachers notes
Year 1
Recognise and describe one-half as one of two equal parts of a whole (ACMNA016) For some students just the word ‘fractions’ can be a little daunting. Start by defining the word very simply and displaying it in the classroom, for example:
A fraction is an equal part of a whole. Introduction
Demonstrating
Discuss how we use or talk about fractions in everyday life. Ask students to offer examples, such as: • Last night I only ate half of my dinner. • This morning I ate a whole piece of toast. • My dad ate a whole pizza and I can eat 12 a pizza. • My basketball game has two halves. • A football game is divided into four quarters. • I can swim half the length of a swimming pool. • I can ride my bike half way to school. • The recipe needed 1 cup of flour and 12 cup of sugar. • I drink half a cup of milk before I go to bed each night. • Mum bought 12 dozen eggs at the shops. Students write and illustrate one example of fractions in their lives. These could be presented to the class or displayed around the room.
Demonstrate how whole objects can be divided equally into halves. Use items such as fruit, slices of bread, plasticine, playdough and paper. For example, have students cut a piece of paper into two halves. How can they make sure they are equal? Are they halves if they are not equal? Fractions of groups Discuss how collections of things can be split into equal groups. For example, a farmer may divide his flock in half and put them in two paddocks. Apples picked from a tree could be sorted into two groups—ripe and unripe. Children can be divided into groups; for example, boys and girls, ages, or hair colours. Practise dividing collections of counters into two groups. Point out to students that a number has to be even in order to divide it into two equal halves.
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Above all, convey to your students that fractions are easy and fun!
Fraction symbols Display or make some posters comparing a whole with common fractions such as a half (see teachers resources). Show pictures of objects depicting a half or a whole using an internet based or interactive whiteboard program. Students to suggest what fraction they are viewing.
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Fractions (Years 1 and 2)
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Warm-up activities
Year 1
These activities could be used to introduce fractions as a whole class focus, or small group or individual activity depending on the lesson content. •
What is a whole? Discuss and brainstorm all the ‘whole’ objects you can see in the classroom.
•
How many students are in the whole class? Do a head count and discuss the word ‘whole’. What does it mean to have a ‘whole collection of something’?
•
What is a half? Cut pieces of fruit in half in front of students. What happens when the two halves are put together? How many halves make one whole?
•
Have the students fold and cut a piece of paper in half.
•
Cut a piece of plasticine in half. Compare the two halves—are they exactly the same size? If they aren’t, are they halves?
•
•
Make posters showing one half of shapes or pictures. Students may draw or cut out pictures from a magazine and cut them in half. Display posters.
•
Locate whole shapes in the playground. Have students draw a chalk line through the middle of these shapes to show their halves.
•
Students form a line to represent the halfway line of a netball or tennis court.
•
How many different ways can a netball or tennis court or a square area be divided in half? (Vertically, horizontally, diagonally)
•
Ask students how they could divide a collection of items in half. How could the students in the class be divided in half? Explain that there must be equal numbers in each group for them to be halves.
•
Count out some even numbers using small counters then divide the counters into two equal groups or halves.
•
This game can be played by two or more players. Each player will need, a 50 or 100 grid, small counters and a dice.
© R. I . C.Publ i cat i ons Players take turns to throw a dice and place Trace around each student on a large sheet of • orliner e vi e p r po se son y their counters onl the • number of squares paper. Draw af dotted down thew centre ofu shown on their dice, on their grid.
the outline. Are the sides the same? Discuss the symmetry of the human body.
The first to complete the whole collection wins. (see teachers resources page 6) •
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This game can also be played on a 100 grid with both a ‘first to 50’ and a ‘first to 100’ winner.
Fractions (Years 1 and 2)
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Teachers resources
A whole – 11 or 1
1 1
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1 1
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Fractions (Years 1 and 2)
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Teachers resources
A half – 12
1 2
1 2
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1 2
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1 2
Fractions (Years 1 and 2)
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Teachers resources
Grids – 50 and 100
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Fractions (Years 1 and 2)
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A whole 1. Look at the shape below and colour the whole shape.
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Look at the pictures and colour the whole ones.
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3. Locate 3 whole objects in the classroom and draw them.
Going further
On the back of this page draw a whole pizza with your favourite toppings. R.I.C. Publications©
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Fractions (Years 1 and 2)
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Making a whole 1. Complete the other half of the shapes to make them whole.
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3. Colour the whole of each shape.
Going further
Using coloured paper, draw and cut out a whole circle, square and triangle. Paste them on the back of this page. 8
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Complete the other half of the pictures to make them whole.
A whole collection
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
1. Colour the whole collection of each group. How many are in each group?
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2. Draw the whole collections.
5 suns
2 moons
Going further
How many coloured pencils do you have in your whole collection? Check your pencil case. R.I.C. Publications©
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Fractions (Years 1 and 2)
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A half 1. Colour one half of each shape.
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4 7
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© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. Shade one half of each picture.
Going further
Draw your favourite slice of toast on the back of this page, then show how you could divide it into 2 equal halves. 10
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Circle the pictures that are divided in half. Cross the pictures not divided evenly.
Making a half 1. Shade half of each shape.
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Circle the shapes that have one half shaded.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. Draw a line to show the two halves of each picture.
Going further
Draw half a face and ask a friend to draw the other half. Are the two halves the same? R.I.C. Publications©
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Fractions (Years 1 and 2)
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Half and whole One half + one half = one whole
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2. Match the halves. Colour both halves of each shape the same colour. •f orr evi ew pur posesonl y•
Going further
Find a food picture in a magazine. Cut it out and cut it in half. Paste one half on a sheet of paper. Draw its matching half. 12
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
1. Complete the missing half to make a whole.
Dividing shapes in half Some shapes can be divided in half more than one way. A square can be cut in half:
vertically
horizontally
diagonally
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
1. Show two different ways of dividing each shape into half.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 2. Divide each object in half and shade one half.
SOUP 125m 125 mL
Going further
On the back of this page, draw and name a shape that you can divide in half many different ways. R.I.C. Publications©
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Fractions (Years 1 and 2)
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Half a collection 1. Circle half of each collection. How many did you circle? (b)
Half = (d)
(c)
Half =
Half =
(e)
Half =
(f)
Half =
Half =
2. Shade half of each collection. How many did you shade? (a)
© R(b) . I . C.Publ i cat i ons (c) •f orr evi ew pur posesonl y•
Half = (d)
Half =
Half =
(e)
Half =
(f)
Half =
Half =
Going further
How many coloured markers do you have? How many would there be if you had half? Any left over? 14
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
(a)
Sharing a collection 1. Share these collections into two equal groups. How many in each half? (a)
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
(b)
(c)
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2. Divide a deck of playing cards, without the jokers, into 2 equal piles. How many are in each half? 3. (a) How many red cards are in a deck of cards? (b) How many black cards are in a deck of cards? (c)
How many cards are in the whole deck of cards?
Going further
Make a collection of shapes, dominoes, blocks or counters. Share them into two groups. How many are in each half? R.I.C. Publications©
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Fractions (Years 1 and 2)
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Looking at half 1. Look at the playing cards. Circle half of each symbol. Write how many of each you circled.
(a)
(b)
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. The objects below are half a collection. Draw the missing half. (a)
(b)
(c)
(d)
Going further
Imagine you had a collection of 50 buttons. How many would you have if you gave away half? (You may want to use counters to help you solve this problem.) 16
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Circle half of each collection and write the number you have circled.
Complete the collection
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
1. (a) Half of each collection is missing. Draw pictures to complete them.
(b) What is © the R total number each of the collections above? . I . C .Puin bl i ca t i on s
•f or evi ew pur po ses nl y• leaves =o flowers =r trees =
clovers =
2. Cross out half of each collection. How many are left? (a)
(b)
Half =
Half =
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What is half of each number? Use counters to help you. (a) 12 R.I.C. Publications©
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(c) 18
(d) 32 Fractions (Years 1 and 2)
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Whole or half? 1. How have the shapes been shaded? Label them half or whole. (a)
(b)
(c)
(d)
(e)
(f)
(a)
(c)
(b)
© R. I . C.Publ i cat i ons •f orr evi ew pu r posesonl y• (d)
3. Draw lines to match the halves.
4. Complete this sentence:
halves = 1 whole.
Going further
Locate a whole object in the room and draw it in two halves. 18
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Label each picture half or whole.
Making wholes with halves Cut out the shapes. Match the halves to make whole shapes.
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
11 1 10 9 8 7 6
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2 1
6 5
2 3 4
Going further
Find a picture of your favourite animal and cut it in half. Paste it onto paper and draw the missing half. Are the two halves the same? R.I.C. Publications©
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Fractions (Years 1 and 2)
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Fun with fractions
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Going further
Use a computer graphic program to create a fraction picture made up of whole and half shapes. Print it out and show a friend. 20
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
Cut out the whole shapes below to create a robot. You may need to cut some of the shapes in half. Paste your robot onto a colourful background. Be creative!
Name:
Date:
Assessment 1 1. Label these pictures whole or half. (a)
(b)
(c)
(d)
(e)
(f)
CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
2. Draw a line through each shape to show two equal halves.
3. Complete the half of shape ton make ©missing R. I . C .P ueach bl i c at i o s it whole.
•f orr evi ew pur pose sonl y• 1 11 10 9 8 7 6
4. Divide and shade half of each object.
125 mL
5. Complete this sentence: one half + one half = Going further
Name and draw three objects in the classroom that you can divide equally into halves. R.I.C. Publications©
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Fractions (Years 1 and 2)
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Name:
Date:
Assessment 2 1. Shade the whole of each collection.
2. Shade half of each group. (b)
y Happ ay Birthd
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3. Look at the group of children and answer the questions.
(a) How many children are there in the whole group? (b) How many boys are there? (c) Do the girls make up half of the whole group? Going further
If you had 30 pencils in your pencil case, and you gave away half, how many would you have left? 22
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)
(a)
Checklist
Year 1
Recognise and describe one-half as one of two equal parts of a whole (ACMNA016) Name
Understands Understands whole half
Comment
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Fractions (Years 1 and 2)
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Answers A whole .................................................... page 7 1. Teacher check 2. whole apple, square, banana, pear, cupcake 3. Teacher check Going further – Teacher check
Making a whole ....................................... page 8 1.–3. Teacher check
1. 6 bees, 9 snails, 3 trees, 10 ladybugs, 5 butterflies, 8 caterpillars
A half....................................................... page 10
1. (a) Teacher check
(b) 11 flowers
Going further – (a) 6 (b) 13 (c) 9 (d) 16
1. (a) half
Going further – Teacher check
Making a half ......................................... page 11
(d) half 2. (a) half
1.–3. Teacher check
(b) whole
(c) whole
(e) half
(f) half
(b) whole
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• (c) whole
Going further – Teacher check
Half and whole ....................................... page 12
(d) half
3. Teacher check 4. 2
Going further – Teacher check
Going further – Teacher check
Dividing shapes in half .......................... page 13
Making wholes with halves.................. page 19 Teacher check
1.–2. Teacher check
Going further – Teacher check
Going further – Teacher check
Half a collection ..................................... page 14 (b) 2
(c) 8
(e) 10
(f) 7
(b) 3
(c) 9
(e) 11
(f) 7
Sharing a collection ............................... page 15 (b) 13 in each
Fun with fractions ................................. page 20 Teacher check Going further – Teacher check
Assessment 1 ......................................... page 21 1. (a) half (d) whole
Going further – Teacher check
1. (a) 12 in each
Complete the collection ........................ page 17
Whole or half? ........................................ page 18
1.–3. Teacher check
(d) 12
(b) 11 dogs
2. (a) 8 leaves
Going further – Teacher check
2. (a) 6
2. (a) 9 cats
(b) 8 flowers, 14 leaves, 4 trees, 16 clovers
2. Teacher check
(d) 5
1. diamonds – 2 clubs – 3 spades – 4 hearts – 5
Going further – 25 buttons
A whole collection ................................... page 9
1. (a) 4
Looking at half ....................................... page 16
3. Teacher check
Going further – Teacher check
1.–2. Teacher check
Year 1
(c) 11 in each
(b) whole
(c) whole
(e) half
(f) half
2.–4. Teacher check 5. one whole Going further – Teacher check
2. 26 3. (a) 26
(b) 26
Going further – Teacher check
(c) 52
Assessment 2 ......................................... page 22 1. Teacher check 2. (a) 7
(b) 5
3. (a) 12
(b) 6
(c) yes
Going further – 15 pencils
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Fractions (Years 1 and 2)
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Teachers notes
Year 2
Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
Fractions are equal parts of a whole. Introduction
Demonstrating
Begin your fraction topic by allowing students to brainstorm what their understanding of a fraction is. Draw on their knowledge of what they remember learning in Year 1. Look at their understanding of the words ‘whole’ and ‘half’. Discuss how fractions are used in everyday life. Ask students to offer examples, such as: • Last night I only ate half of my dinner. • This morning I ate a whole piece of toast. • My dad ate a whole pizza and I can eat 12 a pizza. • My birthday cake was divided into 8 pieces this year. • Mum divided our pie last night into quarters. • An orange can be cut into quarters. • My basketball game has two 20-minute halves. • A football game is made up of four quarters. Students write and illustrate one example of fractions in their lives. These could be presented to the class or displayed around the room.
Demonstrate how objects, shapes and paper can be divided into halves, quarters and eighths. Show students that a piece of paper cut in half gives two halves, cut in half again gives four quarters and if the quarters are cut in half again they give eight eighths. Plan as many hands-on activities as possible to allow students to visualise and understand these concepts. Display a variety of fractions using an internet-based or interactive whiteboard program. Fractions of groups Discuss how collections of things can be split into two equal groups (halves), four equal groups (quarters) and eight equal groups (eighths). For example, a pack of cards can be divided into two equal colours of red and black or divided into quarters using the four suits (spades, clubs, diamonds and hearts). If a group of objects has an even number it can always be divided into halves. Multiples of four can always be divided into quarters, as can multiples of eight. The concepts of multiplication and division can easily be related to this area. Students will strengthen their understanding of fractions if they recognise this relationship.
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Fraction symbols Display or make some posters comparing a whole with common fractions such as halves, quarters and eighths (see Teachers resources). Numerator: The number above the fraction line tells how many parts of the named fraction are shaded or being considered. (Or, more simply, the ‘top number’.) Denominator: The number below the fraction line that tells how many parts the whole has been divided into. (Or, more simply, the ‘bottom number’.) Introduce the terms above and relate the fraction discussions to symbols; for example, if you poured three quarters of a glass of milk, what would this look like as a fraction symbol? If you ate half of a sandwich, what would be the fraction symbol for this? If you ate three slices of a pizza that had been cut into eight, how much did you eat and what fraction was left? R.I.C. Publications©
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Fractions (Years 1 and 2)
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Warm-up activities
Year 2
These activities could be used to introduce a fractions lesson as a whole class focus, small group or individual activity depending on the lesson content. • Cut up pieces of fruit in front of students. Point out how they start out whole then cut them into halves, quarters and eighths. Ask students to guess how many pieces you would have if you cut the eighths in half again. What is happening to the numbers? (doubling)
• Create a fraction mat. Give each student 4 strips of paper (see teachers resources page 30). Shade each strip a different colour and cut out. Follow these instructions:
• Allow students the opportunity to cut a ball or length of plasticine or playdough in half. Discuss why it is important that the halves are equal. Can they be considered halves if the whole hasn’t been equally divided? Discuss. Cut a ball or length of plasticine into four quarters. Do the same for eighths. Mention that symmetrical things can be divided evenly in half.
2. Fold the next strip in half, draw a line on the fold, label each part ‘half’ and paste it underneath the whole strip.
1. Label the first strip ‘whole’ and paste on a sheet of paper.
3. Fold the next strip in half twice and draw lines on each fold. Label each piece ‘quarter’ and paste it under the halves. 4. Take the final strip and fold in half three times open the strip out and count the eight equal sections. Draw lines on the folds and label each piece ‘eighths’. Paste the strip under the quarters strip.
© R. I . C. Publ i cat i ons Whole •f o rr evi ew pur poses onl y• Half Half Quarter Eighth
Eighth
Quarter Eighth
Eighth
• Match fraction words to fraction symbols in a game of memory (see teachers resources page 31).These fraction symbols and words can also be used to sort into equivalent groups of fractions. • Divide the class in half—how many different ways can that be done? If there is an odd number, the group cannot be divided equally; there must be an even number of students.
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Fractions (Years 1 and 2)
Quarter Eighth
Eighth
Quarter Eighth
Eighth
• Divide the class into four equal groups. Are the groups even? If not, why not? Convey to the students that we need even numbers and multiples of four for this to work out exactly. • Divide the class into eight equal groups. Can it be done? If not, why not? • Use counters to demonstrate how collections of objects can be divided into halves, quarters and eighths. Relate this to division and sharing. Talk about remainders if numbers are uneven.
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Teachers resources
Quarters
1 4
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1 4
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Fractions (Years 1 and 2)
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Teachers resources
Eighths
1 8
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1 8
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Fractions (Years 1 and 2)
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Teachers resources
Whole, half, quarters and eighths
1 1
1 2
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Fractions (Years 1 and 2)
29
Teachers resources
Fraction strips
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30
Fractions (Years 1 and 2)
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Teachers resources
Fraction words and symbols 1 One whole 1 1 One half 2 2 Two halves 2 1 One-quarter 4 2 Two-quarters 4 3 Three-quarters 4 4 Four-quarters I . C.Publ i cat i on s 4© R. 1rr •f o evi ew pur poseso nl y• One-eighth 8 2 Two-eighths 8 3 Three-eighths 8 4 Four-eighths 8 5 Five-eighths 8 6 Six-eighths 8 7 Seven-eighths 8 8 Eight-eighths 8 R.I.C. Publications©
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Fractions (Years 1 and 2)
31
Whole
2. Draw the missing half of each shape to make it whole.
© R. I . C.P12ubl i cat i ons 11 10 •f orr evi ew pur posesonl y• 9
8 7
6
3. Draw two whole objects you can see outside the classroom window.
Going further
How many different ways can a whole can be divided? Draw some examples on the back of this page. 32
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Shade each shape to show one whole.
One half When a shape is divided into two equal parts, each part is called a half.
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1 1. Draw a line to halve each shape. Shade one half and label it 2 .
2. Complete this sentence: Two halves equal one
.
3. Draw a line to show each object divided into halves.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
125 mL
4. Draw something that is on your desk you can divide in half.
Going further
If a builder had to saw a plank of wood in half, explain how he could make sure each half was equal. R.I.C. Publications©
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Fractions (Years 1 and 2)
33
Matching halves
2. Complete the missing half to make the picture whole.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. Match the halves. Colour both halves of each shape the same colour.
Going further
Find a picture of a piece of furniture in a magazine and cut it out. Cut it in half, paste it on a sheet of paper and draw the missing half. 34
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Draw lines to match the halves.
Representing one half
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Circle the shapes that are divided in half.
2. Mark where you think half should be on the line below. Then check that it is half using your ruler. You may want to remark it.
3. Use your ruler to find the half mark of each piece of wood. How many centimetres is each half? (a)
© R. I . C.Publ i cat i ons (b) •f orr evi ew pur poseso nl y• Half =
cm
Half =
cm
(c)
cm
Half = (d)
Half =
cm
Going further
Measure your pencil with a ruler. How many centimetres is half of your pencil? Do the same with your glue stick. R.I.C. Publications©
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Fractions (Years 1 and 2)
35
Half of a collection 1. (a) How many apples are there? (b) How many bananas are there? (c) One half of the fruit collection is and the other half
2. Shade half of each collection. How many make up a half? (a)
(b)
Half = (d)
(c)
Half =
Half =
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• (e)
Half =
(f)
Half =
Half =
3. Half of each collection is missing. Draw the missing halves. (a)
(b)
(c) Going further
If you had a collection of 54 AFL cards and you gave half to a friend, how many would you have left? (Use cards or counters to help you.) 36
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
.
is
Finding one half 1. Circle one half of each group. How many make up half? (a)
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
(b)
(c)
(d)
2. What is half of each number? You may use counters to help you.
© R. I . C.Pub l i cat i ons (b) half of 22 = •f orr evi ew pur posesonl y•
(a) half of 26 = (c) half of 16 =
(d)
half of 30 =
3. (a) Circle the numbers that can be divided in half. (b) Are the numbers you circled odd or even? 1
2
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48
Going further
A movie theatre sold 42 tickets. If half of the tickets were sold to adults, how many were sold to children? (Use counters to help you.) R.I.C. Publications©
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Fractions (Years 1 and 2)
37
One-quarter When a shape is divided into four equal parts, each one is called a quarter.
1. 4
2. Divide each shape into quarters.
DRAGONS
3.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Divide each object into quarters and shade one-quarter.
Going further
Find three objects in the classroom that can be evenly divided into quarters. Draw them on the back of this page. 38
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Shade one-quarter of each shape and label it
Quarters When representing fractions with a symbol: The number below the line tells how many parts a 3 shape has been divided into. 4 The number above the line tells how many parts have been shaded.
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Shade each shape to match the fraction symbol.
2.
(a) 3 4
(b) 1 4
(c) 2 4
(d) 1 4
(e) 4 4
(f) 3 4
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Write the fraction symbols. (a)
(b)
(c)
(d)
(e)
(f) 10
11
12 2
1
8
2 3
9 7
6
5
4
Going further
4 shapes above and explain what you notice about Look at the 4 these fraction shapes. Explain what you notice about the 2 shapes. 4 R.I.C. Publications©
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Fractions (Years 1 and 2)
39
Representing quarters
2. (a) Divide the objects into quarters. Shade two-quarters of each one.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
(b) True or False? You shaded half of each of the objects. 3. Divide the line into quarters. Label each with 1 . 4
Going further
There are
quarters in one whole.
There are
quarters in a half.
40
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Circle the objects divided into quarters. Shade one-quarter of each object.
Quarters of a collection
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Answer the questions about the children. (a) One-quarter of the children are wearing a cap. What fraction is not wearing a cap? (b) Three-quarters of the children are not wearing shorts. What fraction is wearing shorts? (c) What fraction is wearing long pants?
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
2. (a) How many quarters of each collection are circled? caps 4
T-shirts
4
shoes
4
shoes
4
(b) How many quarters are not circled? caps 4
T-shirts
4
Going further
If there were 20 students in your classroom and one-quarter of them were away sick, how many would be left? (Hint: It may help to draw the students on the back of this page.) R.I.C. Publications©
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Fractions (Years 1 and 2)
41
Finding one-quarter (a)
(b)
(c)
(d)
(e)
(f)
2. Circle one-quarter of each group and write the number you circled.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
(a) (b) (c)
3. Multiples of 4 can be divided into quarters, e.g. 4, 8 and 12. Circle all the numbers that are multiples of 4. 1
2
3
4
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47
48
Going further
Find five more numbers that are multiples of 4. 42
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Shade one-quarter of each group.
One-eighth When a shape is divided equally into eight, each part is called an eighth.
2. Divide each shape into eighths.
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. Divide and shade one-eighth of each object.
AUSTRALIA 60c
ESTERN W
Steffie Chang 19 Honeycherry Lane Tilba Tilba NSW 2546 Y
23•JULY•2012
SYDNE
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Shade one-eighth of each shape and label it 1 . 8
Going further
Find three objects in the classroom that can be evenly divided into eighths. Draw them on the back of this page. R.I.C. Publications©
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Fractions (Years 1 and 2)
43
Eighths The number below the line of the fraction symbol tells us how many parts a shape is divided into. The number above the line tells us how many parts are shaded. For example: 5 8
(a)
= 8
(b)
= 8
(c)
= 8
(d)
© R. I . C.Publ i cat i ons = •f orr evi ew pur posesonl y•
8
2. Colour the fraction strip to match the symbol. = 5 8 = 1 8 = 8 8 = 4 8 Going further
Trace a circle on the back of this page and divide it evenly into eighths. Shade or decorate five-eighths. 44
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. How many eighths are shaded?
Representing eighths 1. How many eighths are shaded in each shape? (a)
(b)
(c)
8 CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
(d)
8 (e)
8 (f)
8
8
8
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
2. Shade the shape to match the fraction symbol.
(a)
2 8
(b) 5 8
(c)
7 8
(d) 4 8
3. Divide the line into eighths. Label each with 1 . 8 Going further
There are
eighths in one whole.
There are
eighths in a half.
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Fractions (Years 1 and 2)
45
1. Answer the questions about the dogs. (a) What fraction is wearing a bow?
=
(b) What fraction is wearing a coat?
=
(c) What fraction has long hair?
=
8 8 8
(d) What fraction short hair? ©has R. I . C. Publ i cat i o=n8s
•f orr evi ew pur posesonl y•
2. (a) What fraction of each collection is shaded? cats
fish birds 8 8 8 (b) What fraction is not shaded? cats
8
fish
8
birds
8
rabbits
8
rabbits
8
Going further
Looking at the collection of rabbits above, what other fraction could you use to describe the rabbits shaded? 46
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
Eighths of a collection
Finding one-eighth 1. Shade one-eighth of each shape.
S NG SO
24
All NEW double cd set
W NE
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
2. Divide each object into 8 equal parts and shade 1 . 8
©R . I . C.group. Publ i cat i ons 3. Circle one-eighth of each
•f orr evi ew pur posesonl y•
4. Circle the tacks to make 8 equal groups. How many tacks in one-eighth?
Going further
Find
1 of 64 and 1 of 96. (Use counters to help you work these out.) 8 8
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Fractions (Years 1 and 2)
47
Comparing fractions
2. Look at the fraction strips and complete the sentences. halves inu one whole. © R. I . C.P bl i cat i ons quarters in whole. There• are f orr ev i ew p uone r po sesonl y•
(a) There are (b)
(c) There are
eighths in one whole.
(d) There are
quarters in one half.
(e) There are
eighths in one half.
(f)
eighths in one-quarter.
There are
3. Fill in the missing fractions on the number line.
1 2
0
1 8
4 8
1 whole
6 8
8 8
Going further
On the back of this page draw and write three fractions that are the same size (equivalent). 48
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Divide the strips below to show a whole, halves, quarters and eighths. Label each section with the correct fraction symbol. Colour each fraction strip a different colour.
Naming fractions
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Name the fractions shaded using words; for example, seveneighths. (a)
(b)
(c)
(d)
2. Draw a line to match each fraction symbol with its name. 1 One half • • 4 1 Three-quarters • • 2 7 Five-eighths • • 8 3 Three-eighths • • © R. I . C.Publ i cat i ons 46 One-quarter • •f orr evi e•w pur poseso nl y8• 5 Seven-eighths • • 8 3 One-eighth • • 8 1 Six-eighths • • 8 3. What fraction of each group is shaded? (a)
(b)
(c)
Going further
1 Find fractions on this page that are equivalent, for example: 4 and 2 . 8 R.I.C. Publications©
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Fractions (Years 1 and 2)
49
Creating fractions 1. Draw lines to match the fractions to the symbols.
1 4
3 8
3 4
1 8
2. Divide and shade each shape to match the fraction symbol.
2 4
1 8
3 4
5 8
1 2
1 4
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
3. Show each fraction.
3 4 of a pizza
1 2 block of cheese
5 8 of a pie
Going further
1 2 4 On the back of this page draw the fractions 2 , 4 and 8 . What do you notice about them? 50
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
2 8
Fractions of groups 1. Draw lines to match the fractions and groups.
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
3 8
1 2
3 4
1 8
2. Name the fraction shaded in each group. (a)
(b)
(c)
(d)
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. Draw three collections. Circle some of each one to show the fraction.
1 (a) 2 of 10 squares
3 (b) 4 of 8 circles
3 (c) 8 of 12 triangles
Going further
Look at a deck of playing cards. What fraction of the cards is: black? R.I.C. Publications©
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hearts?
spades? Fractions (Years 1 and 2)
51
Looking at fraction sizes 1. Number the fractions from the smallest (1) to the largest (4). (a) (b) (c) (d) 2. Number the fractions from the smallest (1) to the largest (8). (a) (b) (c) (d)
(f)
(g)
(h)
3. Complete the statement with smaller than, larger than or the same as. (a) (b)
is
©isR. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
(c)
is
(d)
is
(e)
is
4 1 3 1 4. (a) Shade and label these four fractions 4 , 2 , 4 , and 4 .
(b) Write the fractions from smallest to largest.
Going further
On the back of this page, draw six squares. Shade them to show 7 1 3 1 2 1 these fractions in order from smallest to largest. 8 , 2 , 4 , 8 , 2 , 4 52
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
(e)
Fun with fractions
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
Cut out and use the shapes and fractions of them to create an interesting fraction picture. It might be an animal, fish, building or robot. Paste them onto a colourful background. Be creative!
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
Going further
Use a computer graphic program to create a fraction picture. Print it out and show a classmate. R.I.C. Publications©
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Fractions (Years 1 and 2)
53
Fraction problems 1. Solve the fraction problems by drawing them first.
3 (c) If 8 of a cake is eaten, what fraction is left?
(d) Two pies were cut into quarters. If seven-quarters were eaten how much was left?
(e) Sarah, Ben and Alex each ate 1 (f) If 22 football players ate 2 three-quarters of a sandwich © R . I . C . P u b l i c a t i o n s an orange each, how many and Faith ate one-quarter. oranges were eaten? How many sandwiches were •f o rr evi ew pur p oses on l y• eaten altogether?
2. If a bricklayer needed 24 whole bricks, 10 half-bricks and 8 quarter-bricks, how many bricks does he need altogether?
1 3. If a baker used five 2 dozen cartons of eggs, how many eggs did he use?
Going further
Locate a recipe in a newspaper or magazine that uses fractions. Cut it out and circle the fractions. 54
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
(a) If 5 out of 10 students are (b) If 9 out of 12 apples are wearing a hat, what fraction picked from a tree, what is not wearing a hat? fraction of apples is left?
Name:
Date:
Assessment 1
CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. Name the fractions shaded. (a)
(b)
(c)
(d)
(e)
(f)
2. Name the fractions above that are not shaded. (b)
(a) (d) 3. (a)
(c)
(f) © R. I . C(e) .Publ i cat i ons •f o rr e vi ethe w shapes pur ptoomatch seso nfraction l y• symbols. Divide and shade the (The number below the line tells how many parts the shape is divided into. The number above the line tells how many parts are shaded.)
1 4
5 8
1 2
7 8
(b) Write the fractions in order from smallest to largest:
Going further
Find and name fractions on this page that are the same (equivalent). R.I.C. Publications©
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Fractions (Years 1 and 2)
55
Name:
Date:
Assessment 2 (a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
2. What fraction of each group of toys above has not been shaded? (a) (e)
(b) (c) © R. I . C.Pub l i cat i ons(d) (g) (h) •f or(f)r evi ew pur posesonl y•
3. Draw the shapes and shade them to match the fraction. 1 2 of 4 circles
5 3 1 8 of 8 squares 4 of 4 diamonds 8 of 8 rectangles
4. What fraction of 8 dogs are girls if four of them are boys?
Going further
3 1 On the back of this page, draw 20 mice; 4 are grey and 4 are white. 56
Fractions (Years 1 and 2)
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CONTENT DESCRIPTION: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
1. What fraction of each group of toys has been shaded?
Checklist
Year 2
Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)
Name
Recognises and demonstrates 1 ’s of 2 shapes and collections
Recognises and demonstrates 1 ’s of 4 shapes and collections
Recognises and demonstrates 1 ’s of shapes and 8 collections
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•
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Fractions (Years 1 and 2)
57
Answers Whole...................................................... page 32 1.–3. Teacher check
One half .................................................. page 33
2. (a) Teacher check
(b) True
4. Teacher check Going further – 4, 2
1. Teacher check
Quarters of a collection ......................... page 41
2. whole 3.–4. Teacher check Going further – Answers will vary, e.g. measure it
Matching halves .................................... page 34 1.–3. Teacher check Going further – Teacher check/Answers will vary
Representing one half ........................... page 35 1.–2. Teacher check (b) 2 cm
(c) 6 cm
(d) 8 cm
Going further – Teacher check/Answers will vary
Half of a collection ................................. page 36 1. (a) 5
(b) 5
2. (a) 3
(b) 5
(c) 7
(d) 4
(e) 11
(f) 8
(c) apples/bananas
1. (a) 3 (b) 1 4 4 1 2. (a) caps 4 (b) caps 3 4 Going further – 15
1 (c) 2 4 or 2 T-shirts 3 shoes 2 4 4 1 T-shirts 4 shoes 2 4
Finding one-quarter ............................... page 42 1. (a) 1
(b) 3
(c) 2
(d) 4
(e) 6
(f) 5
2. (a) 2 football boots
(b) 3 ballet shoes
(c) 1 ski boot 3. 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 Going further – Answers will vary
One-eighth ............................................. page 43
© R. I . C.Publ i cat i ons •f orr evi ew pEighths ur p.................................................... osesonl y• page 44 1.–3. Teacher check
Going further – Teacher check/answers will vary
3. Teacher check (a) 5 squares
(b) 2 stars
(c) 9 circles
1. (a) 6 (b) 3 8 8 2. Teacher check
Going further – 27 cards
Finding one half ..................................... page 37 1. (a) 5
(b) 3
(c) 6
(d) 9
2. (a) 13
(b) 11
(c) 8
(d) 15
3. (a) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48
(c) 7 8
(d) 2 8
Going further – Teacher check
Representing eighths ............................ page 45 1. (a) 3 8 (d) 6 8
(b) 7 8
(c) 4 8
(e) 2 8
(f) 8 8
2.–3. Teacher check
(b) even
Going further – 8, 4
Going further – 21
One-quarter ............................................ page 38 1.–3. Teacher check Going further – Teacher check/Answers will vary
Quarters .................................................. page 39 1. Teacher check 2. (a) 2 4 (d) 3 4
Representing quarters........................... page 40 1. kite, sandwich, pie
Going further – Teacher check/Answers will vary
3. (a) 5 cm
Year 2
(b) 1 4
(c) 4 4
(e) 2 4
(f) 1 4
Eighths of a collection........................... page 46 1. (a) 2 8 (c) 3 8
(b) 1 8
2. (a) cats 6 8
fish 3 8
birds 5 8
rabbits 4 8
(b) cats 2 8
fish 5 8
birds 3 8
rabbits 4 8
(d) 5 8
Going further – 1 2
Going further – Answers may vary, e.g. 4 4 is the 1 is the same as same as 1 whole, 2 4 2
58
Fractions (Years 1 and 2)
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Answers Finding one-eighth ................................ page 47 4. 3 Going further – 8, 12
1. Teacher check (b) 4
(c) 5 8 (f) 11
3. 30 Going further – Teacher check/Answers will vary
(c) 8
(d) 2
(e) 4
(f) 2
3. Teacher check Going further – Teacher check/ Answers will vary
Naming fractions ................................... page 49 1. (a) three-quarters
(b) five-eighths
(c) one half
(d) three-eighths
2. Teacher check 3. (a) 3 4
3 (b) 12 or 1 4 (e) 2 1 2
2. 31
Comparing fractions .............................. page 48 2. (a) 2
Fraction problems.................................. page 54 1. (a) 1 2 (d) 1 4
1.–3. Teacher check
Year 2
1 (b) 2 4 or 2
3 (c) 6 8 or 4
Going further – Teacher check/Answers may vary
Creating fractions .................................. page 50 1.–3. Teacher check Going further – Teacher check (They are the same or equivalent.)
Assessment 1 ......................................... page 55 1 1. (a) 4 8 or 2 (d) 3 8
(b) 1 4
(c) 1 2
(e) 3 4
1 2. (a) 4 8 or 2 (d) 5 8
(b) 3 4
1 (f) 2 4 or 2 (c) 1 2
(e) 1 4
1 (f) 2 4 or 2
3. (a) Teacher check 1 5 7 (b) 1 4, 2, 8, 8 Going further – Answers may vary
Assessment 2 ......................................... page 56 1. (a) 3 8 (d) 1 4
(b) 3 4
(c) 1 2
(e) 2 2 or 1
3 (f) 6 8 or 4
3 (g) 12 or 1 4 5 2. (a) 8
8 (h) 16 or 1 2 1 (b) 4
(c) 1 2
(e) 0
1 (f) 2 8 or 4
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Fractions of groups................................ page 51
(d) 3 4
1. Teacher check
1 (b) 1 2. (a) 4 8 or 2 4 3. Teacher check
(c) 7 8
(d) 1 2
1 1 1 Going further – 1 2, 2, 4, 4
Looking at fraction sizes ....................... page 52 1. (a) 2
(b) 4
(c) 3
(d) 1
2. (a) 3
(b) 8
(c) 5
(d) 7
(e) 2
(f) 4
(g) 1
(h) 6
3. (a) smaller than
(b) larger than
(c) smaller than
(d) larger than
9 8 (g) 3 (h) 16 or 1 4 or 12 2 3. Teacher check 1 4. 4 8 or 2 Going further – Teacher check
(e) the same as 4. (a) Teacher check shading 1 3 4 (b) 1 4, 2, 4, 4 1 1 3 7 2 Going further – Teacher check – 1 8, 4, 2, 4, 8, 2
Fun with fractions ................................. page 53 Teacher check/Answers will vary Going further – Teacher check/ Answers will vary
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Fractions (Years 1 and 2)
59