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3.2 Which of them ate the same quantity of shortbread?

4. Amos looked after the vines at the end of his grandfather’s vegetable garden. When the grapes were ripe, Amos picked 15 kilograms of delicious Hanepoot grapes. His grandfather said he could put them in packets that held 1 1 2 size 12{ size 11{1 { {1} over {2} } }} {} kg of grapes each, and sell them for R6 each, or he could put the grapes in boxes which held 5 kg of grapes, and sell each box for R20. Amos wanted to make as much money as possible.

4.1 How many packets would Amos need if he chose packets?

4.2 How many boxes would he need if he chose boxes?

4.3 Would he make more money by using the packets or the boxes, and if so, how much more would he make? Explain your answer.


Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment standards(ASs)
We know this when the learner:
1.1 counts forwards and backwards in a variety of intervals;
1.3 recognises and represents the following numbers in order to describe and compare them: common fractions with different denominators, common fractions in diagrammatic form, decimal fractions and multiples of single-digit numbers;
1.3.2 common fractions with different denominators, including halves, thirds, quarters, fifths, sixths, sevenths and eighths;
1.3.3 common fractions in diagrammatic form;
1.3.4 decimal fractions of the form 0,5; 1,5 and 2,5; etc., in the context of measurement;
1.3.6 multiples of single-digit numbers to at least 100;
1.5 recognises and uses equivalent forms of the numbers including common fractions and decimal fractions;
1.5.1 common fractions with denominators that are multiples of each other;
1.5.2 decimal fractions of the form 0,5; 1,5 and 2,5, etc., in the context of measurement;
1.7 solves problems that involve comparing two quantities of different kinds (rate);
1.7.1 comparing two or more quantities of the same kind (ratio);
1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve addition of common fractions, multiplication of at least whole 2-digit by 2-digit numbers, division of at least whole 3-digit by 1-digit numbers and equal sharing with remainders;
1.8.3 addition of common fractions in context;
1.8.6 equal sharing with remainders;
1.9 performs mental calculations involving:
1.9.2 multiplication of whole numbers to at least 10 x 10;
1.12 recognises, describes and uses:, and
1.12.1 the reciprocal relationship between multiplication and division (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3;
1.12.2 the equivalence of division and fractions (e.g. 1 ÷ 8 = ⅛);
1.12.3 the commutative, associative and distributive properties with whole numbers.
Learning outcomes(LOs)
LO 2
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment standards(ASs)
We know this when the learner:
2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules;
2.1.1 represented in physical or diagrammatic form;
2.1.2 not limited to sequences involving constant difference or ratio;
2.1.3 found in natural and cultural contexts;
2.1.4 of the learner’s own creation;
2.2 describes observed relationships or rules in own words;
2.3 determines output values for given input values using verbal descriptions and flow diagrams;
2.3.1 verbal descriptions;
2.3.2 flow diagrams.


ACTIVITY 1: comparing fractions

1.1<1.2<1.3 . 1.4<

2.1 five (or six, seven, eight, nine) tenths

2.2 four

2.3 seven (or six, five, four, three, two, one) tenths

  • two (or three, four, five) fifths
  • four-fifths
  • two-fifths

2.7 five-tenths

  • three (or two, one)
  • two (or three, four)
  • eighths

ACTIVITY 2: counting in fractions

1.1 Group discussion

ACTIVITY 3: equivalent fractions

1.1 shading; 2 quarters

1.2 3 sixths 1.3 four eighths 1.4 own

  • shading
  • half = two-quarters = four-eighths
  • shading
  • one-third = two-sixths = four-twelfths = eight twenty-fourths
  • two-thirds = four-sixths = eight-twelfths = sixteen twenty-fourths

4. Fifths

4.1 shading

4.2 ; ; ;

4.3 ; ; ;

4.4 ; ; ;

4.5 ; ; ;

Discuss patterns

5. Patterns

5.1 Missing parts: 2; 4; 16; 32

  • Pattern
  • Missing parts: 2; 3; 18; 4
  • Class discussion: patterns for making equivalent fractions.

ACTIVITY 4: using equivalent fractions

1. Joan; =

2. David; = , David had more carrots left over.

3.1 Len: one third; Bruce three-sixths (i.e. half); Dad: four-twelfths so Bruce ate the most.

  • Len and his father.

4.1 1 x 10 = 15; 10 packets

4.2 5 x 3 = 15; 3 boxes

4.3 10 x R6 = R60; 3 x R20 = R60He’d get the same amount of money whether he used boxes or packets.

3. 1 - = - =

4. + = + = = 1

0 1 2

Questions & Answers

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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