NAME AND SURNAME:
CHAZELIWE THULILE
HADEBE
STUDENT NUMBER: 65881834
MODULE CODE: OPM1501
DATE: JAN/FEB 2020
Question 1
1.1.
Main Idea: In this step, the student is a reader, a thinker, and an analyzer. First, the student reads over
the problem and finds any proper nouns (capitalized words). If unusual names of people or places
cause confusion, the student may substitute a familiar name and see if the question now makes
sense. It may help the student to re-read the problem, summarize the problem, or visualize what is
happening. When the student identifies the main idea, he or she should write it down, using words or
phrases; that is, complete sentences are unnecessary. Students need to ask themselves questions
such as the ones shown below.
Details: The student reads the problem again, sentence by sentence, slowly and carefully. The student
identifies and records any details, using numbers, words, and phrases. The student looks for extra
information that is, facts in the reading that do not figure into the answer. In this step, the student
should also look for hidden numbers, which may be indicated but not clearly expressed. (Example: The
problem may refer to “Frank and his three friends.” In solving the problem, the student needs to
understand that there are actually four people, even though “four” or “4” is not mentioned in the
reading.) Students ask themselves the following kinds of questions.
Strategy: The student chooses a math strategy (or strategies) to find a solution to the problem and
uses that strategy to find the answer/solve the problem. Possible strategies, as outlined in the Texas
Essential Knowledge and Skills (TEKS) curriculum, include the following.
How: To make sure that their answer is reasonable and that they understand the process clearly,
students use words or phrases to describe how they solved the problem. Students may ask
themselves questions such as the following.
 “How did I solve the problem?”
 “What strategy did I use?”
 “What were my steps?”
1.2. The mathematical tasks with which students become engaged determine not only what substance they
learn but also how they come to think about, develop, use, and make sense of mathematics. Indeed, an
important distinction that permeates research on academic tasks is the differences between tasks that
engage students at a surface level and tasks that engage students at a deeper level by demanding
interpretation, flexibility, the shepherding of resources, and the construction of meaning.
Lower-level demands (Memorization):
 Involve either reproducing previously learned facts, rules, formulas, or definitions or committing facts,
rules, formulas or definitions to memory.
 Cannot be solved using procedures because a procedure does not exist or because the time frame in
which the task is being completed is too short to use a procedure.
 Are not ambiguous. Such tasks involve the exact reproduction of previously seen material, and what is
to be reproduced is clearly and directly stated.
 Have no connection to the concepts or meaning that underlies the facts, rules, formulas, or definitions
being learned or reproduced.
1.3. Allow for productive struggle time. ‰
Circulate as students work independently and then collaboratively in pairs or groups. ‰
Ask questions to focus, assess, and advance student thinking. ‰
Decide which solutions will be selected for sharing.
1.4. State Of Knowledge
The following review of the state of knowledge in cognitive aspects of school learning first examines
literacy development and then content learning.
Literacy Development
Like work on language acquisition, research on literacy forms a continuum whose endpoints represent
quite different definitions of the phenomenon. At one end of this continuum, literacy is defined as a
psycholinguistic process involving component sub processes such as letter recognition, phonological
encoding, decoding of grapheme strings, word recognition, lexical access, computation of sentence
meaning, and so on; at the other end, it is defined as a social practice of meaning construction with distinct
characteristics among different groups.
1.5. Engage the class in discussion. Rule number one is that the discussion is more important than hearing
an answer. Learners must be encouraged to share and explore the variety of strategies, ideas and solutions
and then to communicate these ideas in a rich mathematical discourse. List the answers of all groups on
the board without comment. Unrelated ideas should be listened to with interest, even if they are
incorrect. These can be written on the board and testing the hypothesis may become the problem for
another day until additional evidence comes up that either supports or disproves it. Give learners space to
explain their solutions and processes.
A suggestion here is to begin discussion by calling first on children who are shy, passive or lack the ability
to express themselves because the more obvious ideas are generally given at the outset of a discussion.
These reticent learners can then more easily participate and thus be valued. Allow learners to defend their
answers, and then open the discussion to the class. Resist the temptation to judge the correctness of an
answer. In place of comments that are judgmental, make comments that encourage learners to extend
their answers, and that show you are genuinely interested. For example: ‘Please tell me how you worked
that out.’
Make sure that all learners participate, that all listen, and that all understand what is being said. Encourage
learners to ask questions, and use praise cautiously. You should be cautious when using expressions of
praise, especially with respect to learners’ products and solutions. ‘Good job’ says ‘Yes, you did that
correctly’. However, ‘nice work’ can create an expectation for others that products must be neat or
beautiful in order to have value it is not neatness, but good mathematics that is the goal of mathematics
teaching.
1.6. 1. The After Phase
1.6.2. The After Phase
1.6.3. The After Phase
Question 2
2.1 .
Hundreds
3
Tens
5
Units
1
2.2 . Five hundred sixty-seven million two hundred thirty-four thousand eight hundred ninety
2.3 . The value refers to the worth of each digit depending on where it lies in the number while the total value
refers to the quantity represented by the digit.
Question 3
3.1.
Number set
1; 5; 9; 13; …..
4; 9; 9; 15; 14; …..
Pattern or Not Pattern
Pattern
Not Pattern
3.2.
Number of folds
Number of triangles when folded
0
0
1
1
2
2
3
3
4
4
10
10
11
11
12
12
3.4.1. 6
3.4.2. 2
3.4.3. 23
3.4.4. 79
3.4.5. 98
3.4. The Van Hiele theory describes the way in which the understanding of a new topic may develop. MALATI
has chosen to use three levels appropriate for school mathematics, namely the visual, analysis and
ordering levels. We begin by describing these three levels and typical learner responses for each level.
3.5. Hexahedron.
3.6. A nnet of a Triangular prism
3.7.1. True
3.7.2. False
3.8. A hexahedron: is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all its
faces square, and three squares around each vertex. There are seven topologically distinct convex
hexahedra, one of which exists in two mirror image forms.
A hexagon is a polygon with 6 straight sides. It's commonly found in nature, because it's a particularly
efficient shape. A regular hexagon has sides that are all congruent and angles that all measure 120 degrees.
This means the angles of a regular hexagon add up to 720 degrees.
3.9. Kite (two pairs of adjacent sides equal)
A Quadrilateral One pair of opposite angles equal
A parallelogram (One diagonal bisect angles and the other perpendicular each other perpendicularly)
Question 4
4.1. 1. Image A has been translated 3 units to the left and 1 unit up
4.1.2. Image A has been rotated 180 degrees clockwise
4.2. 1) = d
2) = e
3) = c
4) = a
4.4.1.
Stem
2
4.4.2. Mode = 37
4.2.3. Median = 58 + 61/2
= 59.5
4.2.4. Mean = 1058/20
= 52.9
leaf
7
3
7; 7; 7; 9
4
3
5
5; 8; 8
6
1; 2;
7
3; 5;
8
7; 8;
9
1; 1;2