Working with Equivalent Fractions MAG 4.3.8
Draft-This is a work in progress. MAG Writing Project Year 4 2013
Australian Curriculum YR 4
Activity Process-Extending equivalence to other fractions
ACMN077 Investigate equivalent fractions used in contexts
1. In pairs, give each pair some sentence strips as used in the
previous lesson.
2. Students are to create ½ using fourths, fifths, sixths, eighths,
tenths and twelfths.
3. Let students share what they discovered. What was easy?
What was hard? etc.
4. Re-examine the idea of equivalence by explaining to the
students that they are called equivalent fractions because they
are all equal to the same value.
INDEPENDENT PRACTICE:
5. In their pair, have students find the equivalent fractions for ⅓
using the fraction strips.
6. Allow them for them to report back their findings.
Key Ideas
● understand numbers, ways of representing number,
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relationships among numbers and number systems
develop an understanding of fractions as parts of
wholes and as locations on a number line
understanding that there are different ways to
represent the same quantity
recognise and generate equivalent forms of
commonly used fractions
Resources
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FISH problem solving kit
Pizza Story Teacher Resource
butchers paper
marker pens
fraction strips
fraction wall - another way of using fraction strips
(http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/k
s2/maths/fractions/wall.htm)
Introductory Activity Process
Review: Area Diagrams
1. Review with students how we can represent fractions by
shading areas.
● The total of the shape (E.g. square) is considered to be
1 or 1 whole.
● The shaded part represents a fraction of the whole.
The shaded area represents the fraction ⅔.
Activity Process-Simple Equivalence using ½ ,¼ and ⅛
PART A:Pizza Story
1. Read to the students the “Pizza Story”.
2. Split the students into small groups (3 or 4).
3. Direct the students to discuss who had the correct answer Scott or Sam.
4. On a piece of butchers paper, each group will complete the
sentence - We know _____ is correct because _____.” They can
use words, numbers and/or pictures to show their thinking.
5. Allow time for each group to report back to the class about
their finding.
PART B: Pizza Story
1. Explain to the students that they will be using fraction strips
to help them understand fractions. At the end of the lesson,
they will have the chance to change their answer from the
previous lesson using the Pizza Story about who ate more pizza.
2. In pairs, give each pair the two strips that make ½.
3. Ask them to find how many ¼ strips equal ½.
4. Have pairs share what they have discovered and record
answers (picture and fraction) on butcher’s paper.
5. Have them repeat the process with the ⅛.
6. Using what they have found, get the students to come up
with their own way of converting between the three fractions.
The idea of equivalence.
½ is the same as 2/4 is the same as 4/8.
7. Have them record their thinking and process in their Maths
Journals and change their answers as required.
¼ is the same as 2/8 - Sam was right!
Activity Process-Extending equivalence to number lines
1. Show the students the 1 whole piece from the fraction strips.
2. Ask them how they could represent that in a different way.
Eg. 3/3, 4/4, 5/5 etc
3. Draw a picture below on the board. (create a number line)
4. Write at each end the digits 0 and 1.
5. Ask the students, if the whole line was representing 1 - then
where half would be. (split into two)
6. Where would ⅓ be? (split into three pieces) Where would ¼
be? (Half of a half) etc.
7. Record these on multiple number lines to help show
equivalence in pictorial mode. Examples see below.
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Extensions and Variations
Assessment Year 4 Achievement Standard
By the end of Year 4, students choose appropriate strategies for
calculations involving multiplication and division. They recognise
Extension (from MAG 4.1.4) - Fraction Monkey App for iPad
Hang the monkey by putting the hook on its tail into the rings
on the number line. The game helps you to match equivalent
fractions. The game also helps with ordering fractions.
common equivalent fractions in familiar contexts and make
FRACTIONS: Smart Pirate App for iPad
The App teaches children to read, compare, find equivalent and
add fractions in a fun and easy way. There are four activities,
each with 3 levels of difficulty.
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.
Context for Learning
Real life experiences:
Review and Extension (various levels to work through)
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks
2/maths/fractions/index.htm
Includes support material to aid the teaching of fractions. Also
has problem solving with fractions - be aware it does use
pounds instead of dollars for one of the questions.
Digital Learning
informal units. They solve problems involving time duration.
They interpret information 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
Using the Explain Everything iPad App:
The Explain Everything App allows you to record your voice
whilst drawing on a blank canvas.
numbers. They recall multiplication facts to 10 x 10 and related
Students describe events in their lives (at home or at school)
that require the use of fractions or equivalent fractions.
single digit numbers. Students use scaled instruments to
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Fraction Walls App for iPad (Highly recommended)
Uses an interactive fraction wall rather than paper strips or
Cuisenaire rods to show equivalent fractions. Includes a
teacher’s teaching tool option, fill the fraction wall, two-player
equivalent fraction game and addition with fractions.
Students compare areas of regular and irregular shapes using
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division facts. Students locate familiar fractions on a number
line. They continue number sequences involving multiples of
measure temperatures, lengths, shapes and objects. They
convert between units of time. Students create symmetrical
Some suggestions include in a recipe - if you are
required to double a batch - two ¼ equal ½
dividing a birthday cake up between the whole class.
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.
They record their thoughts whilst illustrating the point.
Assessment
Assessment
Students are asked to draw a picture to show two equivalent
fractions for 2/8. Students will need to:
● name the fractions they used
● say how they knew they were equivalent
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Draw a small rectangle . Draw a bigger recyangle that
the smaller one is part of. Tell what fraction of the
bigger rectangle the small on is. Justify your answer
with a diagram.
Choose two fractions with different denominators.
Explain how to compare them.
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Possible Assessment Criteria
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Uses appropriate terminology to describe, and symbols to
represent, mathematical ideas
Selects and uses appropriate mental or written strategies,
or technology, to solve problems
Checks the accuracy of a statement and explains the
reasoning used
Uses mental and informal written strategies for fractions
Background
Traditionally, the term ‘fraction’ was used to describe a part of
a whole. The word comes from the Latin frango − I break.
Fractions arise naturally in everyday situations involving
sharing, cutting up and proportions. For example, the bathtub
was one-third full, three quarters of the class walk to school.
Fractions between 0 and 1 describe parts of a whole. Fractions
extend the whole numbers to a number system in which
division by a non-zero number always makes sense. While
decimals can be used to represent fractions, many numbers are
Word Wall:
fraction, part, whole, area model, numerator, denominator,
number line
simpler in fraction notation. For example,
0.142857....
compared to
Links to other MAGs
MAG 4.1.4 Fractions
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