Smith_Jason_Fractions lessons – Stage 2

3 Differentiated Fractions Lessons – Stage 2

Maths Lesson 1 (1 hour)

Equivalent fractions (ACMNA077)

Learning objectivesBy the end of this lesson children will be able to:

Make a fraction wall to show relationships between halves, thirds and fourths.

Explain why one fourth of an item is smaller than one third of the same item.

Resources2cm x 20cm strips of paper

IntroductionDiscount dilemma. A family netball pass costs $60. CheapTix is offering a one-third discount

off the price. EzyTix is offering a one-fourth discount off the price. Which one is offering the

biggest saving? How can you prove your answer?

Main BodyChildren fold a 2cm x 20cm strip of paper into fourths. Use IWB to demonstrate, provide a

worked example, invite children to show on the IWB. All strips checked by peers and the

teacher for accuracy and understanding. Remind children of ‘equal sized parts’.

Children fold a 2cm x 20cm paper strip into thirds. Scaffold and check as before.

Children colour one-fourth of the first strip and one-third of the second strip. Children in pairs

use the strips to explain why one-third is bigger than one-fourth.

Continue with paper strips to build a Fraction Wall of one, halves, thirds, fourths, fifths and

sixths.

Differentiation: Build a Fraction Wall showing one, halves, thirds, and fourths (decreasing);

extend the Fraction Wall to include sevenths, eighths, ninths and tenths (increasing).

Are two halves equal to one (whole)? Justify your answer.

What other fractions are equal to half? Justify your answer.

Differentiation: Identify the fractions that are less than half. Justify your answer

(decreasing); identify the fractions that equal two-fifths. Justify your answer (increasing).

Introduce the terms ‘equivalence’ and ‘equivalent fractions’.

ConclusionGlue the Fraction Wall into your Maths Journal.

Return to the Discount dilemma. Which company is offering the bigger discount on netball

tickets? Explain your answer to your partner. Write and illustrate your explanation in your

Maths Journal.

ReflectionIn your Maths journal, write one interesting fact you learned today.

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Smith_Jason_Fractions lessons – Stage 2

You cut a Hawaiian pizza into six equal pieces, and a Pepperoni pizza into five equal pieces.

Which pizza has the bigger pieces? Discuss this with your partner.

How can you explain to mum or dad the meaning of equivalent fractions?

Maths Lesson 2 (1 hour)

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Smith_Jason_Fractions lessons – Stage 2

Equivalent fractions (ACMNA077)

Learning ObjectivesBy the end of this lesson children will be able to:

Show and explain why the same fractions can be represented in various ways.

Resources20cm x 20cm paper/cardboard sheets; small red, green, yellow and blue tiles for fractions

activity

IntroductionShow 3 squares of equal size cardboard divided differently, and unusually, into fourths.

Which one of these is divided equally into fourths? Stimulate whole class discussions.

Main BodyChildren have multiple sheets of 20cm x 20cm paper or cardboard

Children fold one sheet in half horizontally and vertically, another sheet three times vertically,

and another sheet three times horizontally so all sheets are folded in fourths.

Ask children to shade one fourth of each sheet. What do you notice? Are they all one-fourth?

Are they identical? Are they equal? What is the difference? Whole class discussions.

Children cut off one strip (one fourth) from the paper folded vertically. How can you prove

that it is equal to one-fourth of the other two sheets? Children work in pairs. Scaffold as

required.

Children fold remaining sheets into eighths and find equivalent fractions (1/2 = 4/8; 1/4 =

2/8).

Differentiation: identify half of the sheet and count the number of eighths that make up that

half, and how many eighths make up the whole (decreasing). What fraction of one fourth is

one eighth? What fraction of six eighths is one fourth? (increasing).

Students fold again to make sixteenths. Identify fourths, eighths and sixteenths, looking for

equivalent fractions (3/4 = 6/8 = 12/16).

Differentiation: identify half of the sheet and count the number of sixteenths that make up

that half; identify how many sixteenths are in one fourth of the sheet; find how many

sixteenths make up the whole (decreasing); use different colours to show how many different

ways you can shade one eighth of the sheet; what fraction of 12/16 is 2/8? (increasing).

Children have 20cm x 20cm sheets marked several ways in halves, fourths, eighths and

sixteenths. Shade half of each sheet. Explain what you notice.

Repeat the above activities for thirds, sixths and ninths. Children provide explanations to

peers and whole class. Record understandings in Maths Journals.

Fraction tiles activity. Children work in similar ability pairs. Children make shapes using

specified number of tiles displaying required fractions. For example, use 9 tiles to make a

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Smith_Jason_Fractions lessons – Stage 2

shape that is one-third yellow and one third green; use 12 tiles to make a shape that is one-

fourth blue; use 15 tiles to make a shape that is two thirds green.

Differentiation: use 4 tiles to make a shape that is half red; use 6 tiles to make a shape that

is one-third yellow (decreasing). What fraction will be green when you use 16 tiles to make a

shape that is three-fourths yellow and one-eighth blue?; make a shape using 15 tiles that is

two-sixths green; why can’t a 15 tile shape be one-fourth blue? (increasing).

ConclusionFractions activity. Students work in similar ability pairs to match fraction symbols to

equivalent regions, such as matching ½ to a 2 x 2 region with two regions shaded.

Differentiation: Provide symbols and regions using halves, thirds and fourths (decreasing);

provide symbols and regions using fractions up to tenths (increasing).

ReflectionExplain how different fractions of the same object are equivalent. Use words and drawings to

show your thinking.

How do equivalent fractions relate to our learning about number lines? Draw a number line

from zero to one and mark it with some of today’s fractions. What other fractions can you

mark on the number line?

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Smith_Jason_Fractions lessons – Stage 2

Maths Lesson 3 (1 hour)

Equivalence and sharing (ACMNA077 and ACMNA078)

Learning ObjectivesBy the end of this lesson children will be able to:

Show how improper fractions can be expressed as mixed numerals, and vice versa;

Share the same item or number of items equally among differing numbers of people.

ResourcesJugs of water; plastic cups

IntroductionDonut problem! I have 3 donuts to share between 3 people. I have 4 donuts to share

between 4 people. I have 2 donuts to share between 2 people. What about 2 donuts

between 4 people? What about 2 donuts between 3 people? 4 donuts between 6 people?

Relate to equivalence. Stimulate discussions.

Main BodyBirthday party, 3 cakes cut into fourths. Children draw the 3 cakes cut into fourths. How

many fourths in each whole cake? How many fourths in total? Justify.

3 people ate one fourth each. How many fourths did they eat?

How many fourths are left? Draw diagrams to show. Explain/justify to your peer.

Differentiation: draw 3 cakes each divided into halves, then progress to fourths

(decreasing); draw 3 cakes each divided into fifths and sixths (increasing).

Explicitly introduce improper fractions and mixed numerals. Relate this to the cakes.

Stimulate and scaffold discussions about how the improper fraction 9/4 might be written

(thought of) as a mixed numeral (2 and one fourth).

Children shade their cake drawings and write the improper fractions and mixed numerals to

demonstrate understanding.

Two more pieces have been eaten. How many quarters have been eaten in total? (5 fourths;

5/4; 1 and one fourth). Children to draw diagrams and write symbols to prove and explain to

peers/teacher/whole class.

How many fourths are left? (7 fourths; 7/4; 1 and three fourth cakes). Diagrams and symbols

show understanding.

Continue examples and scaffold for understanding.

Differentiation: modify the activity based on halves (decreasing); extend the activity to fifths

and sixths (increasing).

Children individually choose a number of fourths to be eaten from 4 cakes and pose a

problem for a peer to solve (eg: 5 fourths of the cakes have been eaten, how many fourths

remain?). Peers write the problem in their Maths journal and draw diagrams to solve it.

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Smith_Jason_Fractions lessons – Stage 2

Answers to be given in words and symbols using improper fractions and mixed numerals.

Differentiation: cut 4 cakes into halves (decreasing) or cut 5 cakes into fifths (increasing)

before children pose the problem for their peers

ConclusionChildren work in mixed ability triads. They pour the water from the jug to make sure each

person gets an equal share (DEWA, 2013b, p. 107). Pour the water back into the jug, add

another cup and repeat. Continue for a fifth and a sixth cup. How do you know everyone’s

share is equal? What do you notice when you add more cups. Record observations in Maths

journals.

ReflectionReturn to the donut problem. How do you share 4 donuts between 6 people? What fraction

does each person get? How do you know your answer is right? Work in pairs and record

your thoughts and answers in your Maths journal.

On a number line from zero to four, locate the improper fractions 9/4 and 5/4, and the mixed

numerals 1 ¾ and 2 ¼.

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