TMN3704/102/0/2021
Tutorial Letter 201/0/2021
TEACHING MATHEMATICS IN THE INTERMEDIATE PHASE
TMN 3704
Department of Mathematics Education
This tutorial letter contains important information
about your module.
, ASSIGNMENT 2 TMN3704/102/0/2021
2.1 NB: Describe each concept
Key concept Example
Symbols 16 + 23 = 39
Notations 13>10 also
operations and equal
sign
Numerical 1;2;3;4;…
Geometric
(shapes)
Graphical
2.2 Set model
2
( two third, meaning two sets of heads are part of the three sets)
3
Area model
4
( four fifths, meaning the four shaded blocks are part of the five blocks)
5
2.3 1. b 2. a, b and d 3. a
2.4
Content area General content focus Intermediate phase specific content focus
, TMN3704/201/0/2021
Space and The study of Space and The learner’s experience of space and shape in
Shape Shape improves this phase moves from
(Geometry) understanding and recognition and simple description to classification
appreciation and more detailed
of the pattern, precision, description of characteristics and properties of two-
achievement and beauty dimensional shapes
in natural and cultural and three-dimensional objects.
forms. It focuses on the • Learners should be given opportunities to:
properties, relationships, • draw two-dimensional shapes and make
orientations, positions models of three-dimensional objects
and
• describe location, transformations and
transformations of two-
dimensional shapes and symmetry
three-dimensional
objects.
2.5 Explain, with illustrations, how you would use rounding off and compensation as calculation techniques to judge the reasonableness of solutions. Give
one example in each case. (Guidelines: Use addition of four 3-digit numbers as an example; simplify the problem using any method; judge the
reasonableness of the answer using (i) rounding off and (ii)compensation techniques) (Refer to mathematics CAPS document on page 132 for more
information)
(i) Rounding off: (ii) Compensation:
1. 𝟐𝟏𝟑 + 𝟗𝟔𝟐 1. 𝟐𝟏𝟑 + 𝟗𝟔𝟐
= 𝟐𝟎𝟎 + 𝟏𝟎𝟎𝟎 = 𝟐𝟏𝟑 + 𝟕 + 𝟗𝟔𝟐 − 𝟕
= 𝟐𝟐𝟎 + 𝟗𝟓𝟓
= 𝟏𝟐𝟎𝟎
= 𝟏𝟏𝟕𝟓
𝑫𝒐 𝒏𝒖𝒎𝒃𝒆𝒓 𝟐 Do number 2
2. 𝟒𝟔𝟕 + 𝟗𝟔𝟒 + 𝟔𝟏𝟐 + 𝟒𝟗𝟎 2. 𝟒𝟔𝟕 + 𝟗𝟔𝟒 +612+ 490
Learners should be trained to judge the reasonableness of solutions. One way to do this is to estimate their answers before calculating. They can round off any
number involved in the calculations. When adding or subtracting numbers, learners can round off to the nearest whole number. When multiplying two numbers that
are close to each other, learners can use doubling and halving as a way of estimating answers(see page 84 of CAPS.
2.6 Each content area in Mathematics contributes towards the acquisition of specific skills. One focus area emphasised is that “the learner should
recognize and describe properties of numbers and operations, including (i) identity properties, (ii) factors, (iii) multiples, and (iv) commutative; (vi)
associative and (vii) distributive properties” Describe in brief, what the identity property entails and provide two relevant examples. (Hint: use different
basic operations to clarify your answer)
Real numbers are an ordered set of numbers that possess unique properties. The basic properties are commutative, associative, distributive, and identity. The identity property is
named ‘identity property’ because when applied to a number, the number keeps its identity.
Examples
1. The identity property of addition is that when a number n is added to zero, the result is the number itself i.e. n + 0 = n. Zero is called an additive identity(identity element for
addition) and it can be added to any real number without changing its value.
4 4
3+0=3 (Positive Integers) +0= (Fractions)
5 5
0,5 + 0 = 0, 5 (Decimals) x + 0 = x (Algebraic notation)
3
, TMN3704/201/0/2021
2. The identity property of multiplication is that when a number n is multiplied by one, the result is the number itself i.e. n × 1 = n
One is called the multiplicative identity, and it can be multiplied with any real number without changing its value.
4 4
3×1=3 (Positive Integers) ×1= (Fractions)
5 5
0,5 × 1 = 0,5 (Decimals) a×1=a (Algebraic notation)
2.7 Check the clarification notes for each grade in Section 3 of the CAPS document
2.8 The topic ‘Common Fractions’ in Grade 4 is allocated 16 hours (See the table on page 34 of the CAPS document)
2.9 Refer to page 119 of the CAPS document
2.10 Refer to Section 1.8 of your study guide. You are expected to paraphrase, write in your own words and support your arguments with examples
2.11
Teaching Strategy More/less effective Elaborate
teaching strategy
Mrs Barileng asks learners More effective teaching The strategy requires learners to explain and justify their arguments.(NB: Think of other
the question that begins strategy reasonable elaborations)
with, “What would happen
if..?”
To keep learners interested Less effective teaching It is more useful in strengthening computational skills, but never in presenting a new
in Mathematics, Mrs. strategy concept
Naidoo works problems for
her learners and
“magically” comes up with
answers.
2.12 Refer to the study guide and write in your own words
&2.13
4
Tutorial Letter 201/0/2021
TEACHING MATHEMATICS IN THE INTERMEDIATE PHASE
TMN 3704
Department of Mathematics Education
This tutorial letter contains important information
about your module.
, ASSIGNMENT 2 TMN3704/102/0/2021
2.1 NB: Describe each concept
Key concept Example
Symbols 16 + 23 = 39
Notations 13>10 also
operations and equal
sign
Numerical 1;2;3;4;…
Geometric
(shapes)
Graphical
2.2 Set model
2
( two third, meaning two sets of heads are part of the three sets)
3
Area model
4
( four fifths, meaning the four shaded blocks are part of the five blocks)
5
2.3 1. b 2. a, b and d 3. a
2.4
Content area General content focus Intermediate phase specific content focus
, TMN3704/201/0/2021
Space and The study of Space and The learner’s experience of space and shape in
Shape Shape improves this phase moves from
(Geometry) understanding and recognition and simple description to classification
appreciation and more detailed
of the pattern, precision, description of characteristics and properties of two-
achievement and beauty dimensional shapes
in natural and cultural and three-dimensional objects.
forms. It focuses on the • Learners should be given opportunities to:
properties, relationships, • draw two-dimensional shapes and make
orientations, positions models of three-dimensional objects
and
• describe location, transformations and
transformations of two-
dimensional shapes and symmetry
three-dimensional
objects.
2.5 Explain, with illustrations, how you would use rounding off and compensation as calculation techniques to judge the reasonableness of solutions. Give
one example in each case. (Guidelines: Use addition of four 3-digit numbers as an example; simplify the problem using any method; judge the
reasonableness of the answer using (i) rounding off and (ii)compensation techniques) (Refer to mathematics CAPS document on page 132 for more
information)
(i) Rounding off: (ii) Compensation:
1. 𝟐𝟏𝟑 + 𝟗𝟔𝟐 1. 𝟐𝟏𝟑 + 𝟗𝟔𝟐
= 𝟐𝟎𝟎 + 𝟏𝟎𝟎𝟎 = 𝟐𝟏𝟑 + 𝟕 + 𝟗𝟔𝟐 − 𝟕
= 𝟐𝟐𝟎 + 𝟗𝟓𝟓
= 𝟏𝟐𝟎𝟎
= 𝟏𝟏𝟕𝟓
𝑫𝒐 𝒏𝒖𝒎𝒃𝒆𝒓 𝟐 Do number 2
2. 𝟒𝟔𝟕 + 𝟗𝟔𝟒 + 𝟔𝟏𝟐 + 𝟒𝟗𝟎 2. 𝟒𝟔𝟕 + 𝟗𝟔𝟒 +612+ 490
Learners should be trained to judge the reasonableness of solutions. One way to do this is to estimate their answers before calculating. They can round off any
number involved in the calculations. When adding or subtracting numbers, learners can round off to the nearest whole number. When multiplying two numbers that
are close to each other, learners can use doubling and halving as a way of estimating answers(see page 84 of CAPS.
2.6 Each content area in Mathematics contributes towards the acquisition of specific skills. One focus area emphasised is that “the learner should
recognize and describe properties of numbers and operations, including (i) identity properties, (ii) factors, (iii) multiples, and (iv) commutative; (vi)
associative and (vii) distributive properties” Describe in brief, what the identity property entails and provide two relevant examples. (Hint: use different
basic operations to clarify your answer)
Real numbers are an ordered set of numbers that possess unique properties. The basic properties are commutative, associative, distributive, and identity. The identity property is
named ‘identity property’ because when applied to a number, the number keeps its identity.
Examples
1. The identity property of addition is that when a number n is added to zero, the result is the number itself i.e. n + 0 = n. Zero is called an additive identity(identity element for
addition) and it can be added to any real number without changing its value.
4 4
3+0=3 (Positive Integers) +0= (Fractions)
5 5
0,5 + 0 = 0, 5 (Decimals) x + 0 = x (Algebraic notation)
3
, TMN3704/201/0/2021
2. The identity property of multiplication is that when a number n is multiplied by one, the result is the number itself i.e. n × 1 = n
One is called the multiplicative identity, and it can be multiplied with any real number without changing its value.
4 4
3×1=3 (Positive Integers) ×1= (Fractions)
5 5
0,5 × 1 = 0,5 (Decimals) a×1=a (Algebraic notation)
2.7 Check the clarification notes for each grade in Section 3 of the CAPS document
2.8 The topic ‘Common Fractions’ in Grade 4 is allocated 16 hours (See the table on page 34 of the CAPS document)
2.9 Refer to page 119 of the CAPS document
2.10 Refer to Section 1.8 of your study guide. You are expected to paraphrase, write in your own words and support your arguments with examples
2.11
Teaching Strategy More/less effective Elaborate
teaching strategy
Mrs Barileng asks learners More effective teaching The strategy requires learners to explain and justify their arguments.(NB: Think of other
the question that begins strategy reasonable elaborations)
with, “What would happen
if..?”
To keep learners interested Less effective teaching It is more useful in strengthening computational skills, but never in presenting a new
in Mathematics, Mrs. strategy concept
Naidoo works problems for
her learners and
“magically” comes up with
answers.
2.12 Refer to the study guide and write in your own words
&2.13
4
