Architecture
Mathematics may be an essential tool to model real-life structures consisting of complex shapes and forms.
Les critères MYP selon lesquels cette unité est évaluée.
- Connaissances et compréhension
- Étude de configurations
- Communication
- Application des mathématiques dans des contextes réels
Ce que couvre cette unité
Les sous-thèmes enseignés, dans l'ordre suivi par le département.
- Surds
- Pythagoras
- Significant figures
- 3D Trigonometry
- 3D Shapes: Volume, Surface Area
Objectifs d'apprentissage
What students should be able to do by the end of this unit.
Surds
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- Differentiate between rational and irrational numbers.
- Understand the concept of surds and their approximate values.
- Simplify surds by extracting the largest square factor.
- Multiply and divide surds, and add/subtract like surds.
- Rationalise a denominator of the form 1/√a.
Pythagoras' Theorem
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- Apply Pythagoras' theorem to find a missing side in a right-angled triangle.
- Use the converse of Pythagoras' theorem to test whether a triangle is right-angled.
- Use Pythagoras' theorem to find distances between two points in 2D.
- Use Pythagoras' theorem to find lengths in 3D solids (space diagonals, slant heights).
- Give Pythagoras answers in surd form where appropriate.
- Apply Pythagoras' theorem to practical problems (ladders, ziplines, triangles in real contexts).
Mensuration
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- Use vocabulary for 3D shapes: vertex, edge, face.
- Classify 3D shapes and identify their properties.
- Draw and interpret nets of 3D solids.
- Calculate the volume of prisms (including cylinders).
- Calculate the volume of pyramids and cones (V = ⅓ × base area × height).
- Calculate the volume of a sphere (V = ⁴⁄₃ π r³).
- Calculate the surface area of prisms and cylinders.
- Calculate the surface area of a sphere (SA = 4πr²).
- Convert between units of capacity, area and volume.
- Substitute values into mensuration formulae.
- Rearrange mensuration formulae to make a different variable the subject.
Trigonometric Ratios
Cochez pour suivre vos progrès sur cet appareil. Enregistré ici uniquement — l'enseignant ne le voit pas.
- Identify and name the sides of a right-angled triangle (opposite, adjacent, hypotenuse).
- Define the sine, cosine and tangent ratios (SOH CAH TOA).
- Use trigonometric ratios to find a missing side in a right-angled triangle.
- Use inverse trigonometric ratios to find a missing angle in a right-angled triangle.
- Use exact values of sin, cos and tan at 30°, 45° and 60°.
- Apply right-angle trigonometry to angles of elevation and depression.
- Apply right-angle trigonometry to problems set inside 3D solids.
Matériel de révision sélectionné, à télécharger.
Un pack de révision pour cette unité est en préparation.
Cadrage MYP
- ATL ciblées
- Communication – I. Communication skills
- Thinking – VIII. Critical thinking skills
- Concepts clés
- Form is the shape and underlying structure of an entity or piece of work, including its organization, essential nature and external appearance.
- Contexte mondial
- Scientific and technical innovation