Part and Whole (ACMNA078) MAG 4.4.2
Draft-This is a work in progress. MAG Writing Project Year 4 2013
Australian Curriculum YR 4
ACMNA078 Count by quarters halves and thirds, including
with mixed numerals. Locate and represent these fractions on a
number line
● Identify and describe ‘mixed numerals’ as having a wholenumber part and a fraction part
● Count by halves, thirds and quarters
● Place halves, quarters, eighths and thirds on a number line
between 0 and 1
● Place halves, thirds and quarters on number lines that extend
beyond 1
● Compare unit fractions using diagrams and number lines and
by referring to the denominator
● Recognise and explain the relationship between the value of
a unit fraction and its denominator
2. Show students different shapes and identify them as one
whole. Invite three student to divide different shapes equally
into two parts.
1 whole = 2 equal parts of two = 2/2= two halves
Invite three students to divide different shapes into 3 equal
parts
1 whole = 3 equal parts of 3 = 3/3 = three thirds
Invite three students to divide different shapes into 4 equal
parts. identify and explain language options
1 whole= 4 equal parts of four= 4/4 = four quarters
Key Idea
●
●
●
●
Fractions are ways of writing parts of whole numbers.
Fractions are formed by splitting a whole into any
number of pieces of equal size.
It doesn’t matter how many equal pieces a whole is
split into, if all the pieces are combined, we have the
whole again.
Fractions may appear in many equivalent forms.
3. Introduce the terms
denominator - shows into how many equal parts the whole has
been divided
numerator - shows how many of the equal parts have been
used.
Resources
● FISH problem solving kit
Introductory Activity Process
1. Display a fraction on the board, invite students to provide any
words they know about the fractions. Collect information on
Word Collage iPad app for display to class or in group work
situations with groups taking their turn to display.
4. Students practise fraction given by teacher into their
workbooks. Teacher should mix up the way the fraction is
delivered to students allowing
- folding (represent visually)- drawing (represent visually)
- representing (represent symbolically)
- naming (representing orally)
A nominated fraction given by teacher for this purpose. Teacher
should mix up the way the fraction is delivered to students
Use the language of numerator and denominator. eg Say - show me 2/4
where students need to show fractions
Extension:
One approach to paper folding is origami. Origami uses geometric shapes
which are not always the same size. The folds create shapes which are
fractions of a whole. Ask students to investigate what shapes they can
create with a basic tri-fold using a standard A4 piece of paper.
Activity Process - introduce students to mixed number fractions and
placing in positions on number line.
1. Show students the large number line on the floor, ask them to place
whole numbers onto the marks where they think they should go.
2. Explain, like the shapes we used to show fractions, the space between the
numbers on the number line are one whole number with each jump and
can be divided into fractions. Practice placing faction tags (below one) into
the correct position
3. Revise fractions looked at, ½, ⅓ and 1/4, how many of each in one whole
jump (use numerator and denominator terminology). Give selected students
fraction cards to place on the number line where they think they should be.
As as a group discus reasoning for placement - why put there? why not?
where should it go? Why?
1
Activity Process - students recognise and place mixed number
fractions on number line.
1. Introduced the lesson by assigning each student a fraction or
mixed number card. Divide students into two groups and
discuss that they are in groups which represent half. Each group
races against the clock (discuss a fraction of the lesson in time)
to put the numbers in order from least to greatest.
2. Discuss placing fractions and mixed number on a number
line. Remind students that a their fraction cards have mixed
numbers - a number that has a mixture of whole numbers and
fractions . Remind students of the number of each fraction in
each jump - 4/4 in each whole jump for quarters, 3/3 in each
whole jump for thirds etc. count in fractions to place mixed
numbers on the number line.
eg 2¼
following ordinary situations:
¾ of the distance from …... to …....
2/3 of the houses in the neighborhood
⅛ of a pizza
All these examples use the word of, and all the fractions
represent part of some object, collection of objects, or quantity.
Activity Process- Introduce improper fractions
An improper fraction has the numerator larger that the
denominator.
1. Show students flashcards with mixed number fraction in
quarters. Ask student to identify the mixed number they
represent.
2¼
2. Ask students to work out how many quarters there are
altogether, for the mixed number fraction. Practice colouring
pictorial representations showing quarters, thirds and halves.
4. display a number of fractions on the board for students to -orally name
fraction, identify the denominator, the numerator and colour number of
equal parts the written fraction represents.
Extensions and Variations
Students can practice changing mixed number fractions to improper
fractions or improper fraction to mixed number fractions.
Check that students are identifying the different fraction by the correct
name.
Which is the mixed fraction? How many wholes are there?
Which is the improper fraction? ‘Top heavy’
Which is the proper fraction? ‘Bottom heavy’
The Fraction Fill Game is an effective way to monitor and consolidate
students understanding. The link below provides a video explanation of the
paper based game.
http://www.sharemylesson.com/teaching-resource/Fraction-GameFraction-Fill-50005655/
How do I get one quarter?
5. Divide class into groups and provide fraction cards writeon
blanks, (use non permanent markers)fraction tags and number
lines to record positions.
Digital Learning
A range of simple fraction games
Explain this can be written as a fraction called an improper
fraction - where the numerator is more than the denominator.
use the same definitions for numerator and denominator.
the numerator has how many quarters there are shaded or used
and goes on the top.
the denominator shows how many equal groups the whole
shape has been divided into
http://www.sheppardsoftware.com/math.htm
3. Provide students with laminated shapes or number lines.
Write an improper fraction on the board and ask students to
show this number on their cards by colouring the number of
parts identified on the numerator. Ask what does the bottom
number tell us? what is it called?
what does the top number tell us? what is it called? how do you
say the fraction? what type of fraction is it?
Context for Learning Real life experiences:
Discuss with students that much of the information we receive in daily life is
presented in terms of fractions. Eg recipes ‘a half a cup of’. A news report
might begin, ‘Nearly three quarters of the people surveyed . . . ‘,
Fractions arise naturally whenever we want to consider one or more parts
of an object or quantity that is divided into parts.
Consider how fractions are used in the real world and make a list of
examples
2
Extension Activities
'Create 'Mondrian-esque' works of art based
on repeated application of a fraction'
Display the powerpoint
‘Piet Mondrian and Fractions’
What shapes are the coloured blocks? What
shapes are the white blocks?
What fraction of the shapes in this painting are
red, blue, yellow?
The Art of Fractions
http://www.teachmathematics.net/activities/the-art-offractions.htm
What other fractions can you see?
Use the painting Komposition to explore simple
fractions. Using scissors cut out all the pieces
and find those that are ¼ of the red square,
those that are half the yellow oblong, those that
are 1/8 of the red square and so on. Ask
learners to investigate the question, how many
of the different fractions will make a whole?
Create a list of the common features of
Mondrian’s work and use that as a starting point
for an independent composition in the style of
the artist.
Resources
The Art of Piet Mondrian
https://www.ncetm.org.uk/resources/16792
Assessment Year 4 Achievement Standard
By the end of Year 4, students choose appropriate strategies for calculations
involving multiplication and division. They recognise common equivalent
fractions in familiar contexts and make connections between fraction and
decimal notations up to two decimal places. Students solve simple
purchasing problems. They identify unknown quantities in number
sentences. They describe number patterns resulting from multiplication.
Students compare areas of regular and irregular shapes using informal units.
They solve problems involving time duration. They interpret information
Mondrian is best known for his compositions
using only vertical and horizontal lines at 900
angles, primary colours against a white
background. His influence can be seen in
industrial design and advertisements from the
1030s onwards.
Ask learners what they notice. Develop their
observation by asking if all the lines are the
same thickness? How are the lines arranged?
contained in maps.
Students identify dependent and independent events. They describe different
methods for data collection and representation, and evaluate their
effectiveness.
Students use the properties of odd and even numbers. They recall
multiplication facts to 10 x 10 and related division facts. Students locate
familiar fractions on a number line. They continue number sequences
involving multiples of single digit numbers. Students use scaled instruments
to measure temperatures, lengths, shapes and objects. They convert
3
between units of time. Students create symmetrical shapes
and patterns. They classify angles in relation to a right
angle. Students list the probabilities of everyday events.
They construct data displays from given or collected data
Background
Assessment Task:
Simple explanations for fractions
http://www.bbc.co.uk/skillswise/factsheet/ma17frac-l1-f-equivalent-fractions
Students create a matching games for mixed fractions and
improper fractions
Fractions are used in different ways: to describe equal parts of a whole; to
describe equal parts of a collection of objects; to denote numbers, eg.half is
midway between 0 and 1, and as operators related to division eg. dividing a
number in half
http://www.havefunteaching.com/flash-cards/math/fraction-flashcards.pdf
Digital Resources
1. Explain to students they will use the template to create
a snap or memory game where they need to match and
improper fraction to the same proper fraction.
http://www.communication4all.co.uk/Numeracy/Fractions%20Mat.pdf
http://home.centurytel.net/cdefreese/foldables/folding_the_flipper.htm
2. students to write fraction onto the number part
3. students to draw a pictorial representation of the
fraction on the reverse.
4. students play games in pairs providing peer feedback
about
Possible Criteria
http://www.helpingwithmath.com/printables/others/3nf1Fraction-
Use appropriate terminology and symbols to represent,
mathematical fraction ideas
● Check accuracy of a statement and explains the
reasoning used
● Represents, models and compares commonly used
fractions
Dominoes0.htm
Word Wall: part, whole, less than, more than, numerator,
denominator, quarters, halves, thirds, mixed, improper
4