MIP2601 Assignment 2 2025 - DUE12 June 2025, Exams of Nursing

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QUESTION 1: GEOMETRIC THINKING

1.1 Van Hiele"s Levels (1-3)

Level 1: Visualisation (Recognition Level) At this level, learners recognise shapes based on their appearance without

understanding properties. They identify figures visually as whole objects rather than

by individual attributes. Example: A learner identifies a shape as a "square" simply because it looks like one. If it's rotated or skewed, they might not recognise it as a square anymore.

Level 2: Analysis (Descriptive Level)

Learners begin recognising and describing geometric figures by their properties,

like sides and angles. They do not yet understand relationships between these

properties. Example: A learner can state a square has four equal sides and four right angles, but may not realise all squares are rectangles.

Level 3: Informal Deduction (Abstraction Level)

Learners begin understanding relationships between properties. They can classify

shapes based on logical reasoning, making connections between properties.

Example: A learner understands all squares are rectangles because squares share all properties of rectangles (four right angles, opposite sides equal), plus have all sides equal.

1.2 Hierarchical Nature of Van Hiele"s Levels

The Van Hiele levels are hierarchical, meaning:

o Each level builds logically upon the previous level.

(a) Early evidence of geometry:

Ancient Egypt, specifically along the Nile Valley.

(b) Approximate date: Around 2900 BCE (about 5000 years ago). (c) How geometry was practised: Egyptians used practical geometry for surveying land, measuring agricultural fields,

and building structures such as the pyramids. They calculated areas of triangles

and rectangles practically, aiding taxation and construction. (d) Coverage in CAPS: This type of practical geometry (e.g., measuring and calculating areas) is covered under the CAPS Intermediate Phase Mathematics curriculum in "Measurement and

Geometry (Space and Shape)".

QUESTION 2: MEASUREMENT

2.1 Five places in the world with historical evidence of measurement:

1. Mesopotamia (Ancient Sumerians)
2. Ancient Egypt

3. Ancient Greece

4. Ancient China

5. Rome (Ancient Roman Empire)

o Evidence of a calendar system with 12 lunar months, occasionally adding a 13th month.

o Early length measures such as chi (Chinese foot), standardised to facilitate

construction and agricultural practices.

Ancient Rome (*1st century BCE onwards):

o Length measured using the pace (a double step), roughly 5 feet.

o Systematic measurements, roads measured in miles (1 mile = 1,000 paces). e Mass measured using balances and scales, fundamental for trade and commerce. 2.4 Measurement coverage within CAPS curriculum:

In the Curriculum and Assessment Policy Statement (CAPS) for South African

schools, this historical form of measurement aligns specifically with the Foundation Phase (Grades R-3), under:

e Grade 1: Measurement (informal/non-standard units)

Using everyday items, body parts (hands, feet), and verbal descriptors (long,

short, heavier, lighter).

o Grade 2: Measurement (transitioning to standard units)

Informal measuring continues but introduces basic standard units, preparing learners for formal measurement.

o Grade 3: Measurement (introduction of standard units)

Formal units such as metres and kilograms introduced, replacing informal

body-based measurement. e Intermediate Phase (Grades 4-6): Measurement (formal/standard units)

Learners measure using metres, centimetres, kilograms, litres, and other

standardised units; calculations include conversions and reporting precise numerical measurements.

REFERENCES

Department of Basic Education (2011). Curriculum and Assessment Policy Statement (CAPS), Mathematics Foundation and Intermediate Phases. Pretoria:

DBE.

QUESTION 3: POLYGONS

3.1.1 Grade 4 In Grade 4, learners start with basic polygon recognition. They learn to: Identify and name basic polygons (triangles, quadrilaterals, pentagons,

hexagons, and octagons).

Describe polygons according to the number of sides and vertices (corners). Recognise and categorise polygons based on similarities and differences (e.g., regular or irregular shapes).

Understand and describe shapes using informal language and visual

observation. Draw and describe simple polygons using straight edges. 3.1.2 Grade 5

Assessment Type: Written and practical (worksheet) Instructions to Learners: You are a junior park designer! Your task is to plan a triangular flower garden for a community park. Use the measurements provided below to complete the questions. You are given a triangle with the following dimensions:

e SideA=6m

e SideB=5m

e SideC=7m

e Height from base (Side B) =4 m

Diagram provided on the worksheet.

Questions:

1. Calculate the perimeter of the triangle.

Show your steps clearly. (2 marks)

2. What does the word ,,perimeter* mean? (Explain in your own words.) (2 marks)

3. Use the formula to calculate the area of the triangle:

Area = 2 x base x height Use Side B as the base. (3 marks)

4. What does the word ,,area” mean? (Explain in your own words.) (2 marks)
   5. Why do you think it"s important to know the difference between area and perimeter when designing a park or garden?

(Give one reason.) (1 mark)

Total: 10 Marks

Lesson Phase Teacher Activities Learner^ Activities Introduction (^) Begin the lesson by asking learners Answer the questions based (¥10 min) questions such as: "Have you ever seen on their experiences. reflections in water?" "Have you moved e Participate actively by objects from one place to another?" "Have observing visuals and you ever turned a book or your body sharing examples. around?" e Use examples and visuals (drawings, pictures) of translation, reflection, and rotation from everyday life. o Clearly state lesson objectives. Body (¥25 | Step 1: Explanation (¥10 min) e Pay attention, take notes and min) _ ask questions for clarity. e Clearly explain and demonstrate each type _ _ of transformation (translation, reflection, » Work collaboratively during : : guided practice. rotation) using concrete examples.

. e Perform translations, e Use classroom resources like books, _. reflections, and rotations with mirrors, and geometric shapes. _ provided materials. e Clarify new vocabulary. e Complete the independent worksheet activity. Step 2: Guided Practice (10 min Y e Conduct guided activities: a) Translation: Learners slide shapes along grid paper. b) Reflection: Learners use mirrors to see reflections of shapes. c) Rotation: Learners rotate cut-out shapes around a fixed point. Step 3: Independent Practice (5 min) e Distribute worksheets to learners to practice transformations individually. Conclusion e Summarize key concepts learned. e Listen and recap concepts (10 min) e Ask learners to demonstrate a learned. transformation of their choice and explainit | Volunteer to demonstrate

briefly to the class.. transformations. e Provide quick oral questions for informal |e Answer informal assessment assessment. questions. 4.4 Learners" Prior Knowledge: Before this lesson, learners should already know:

1. Basic geometric vocabulary (shapes, lines, points).
2. Familiarity with grid systems or graph paper.
3. Understanding directions (up, down, left, right).
4. Basic measurement concepts (distance and angles). 4.5 Resources from the Environment:

1. Mirrors: to practically demonstrate reflections.

2. Graph/grid paper: to visualize translations and rotations.
   3. Cut-out cardboard shapes: for hands-on manipulation of shapes during transformations.

4. Real-life objects (e.g., books, pencils): to

demonstrate rotation, reflection, and translation clearly.