Here are some key aspects of the math curriculum for geometry and measures for students aged 13 to 14:

Triangles: Students explore properties and theorems related to triangles, including the Triangle Inequality Theorem, the Pythagorean Theorem, and the various types of triangles (scalene, isosceles, equilateral). They apply these concepts to solve problems involving triangle congruence and similarity.

Polygons: Students study properties of polygons in more depth. They explore regular polygons, irregular polygons, and convex and concave polygons. They learn about the sum of interior and exterior angles of polygons and apply these concepts to solve problems.

Circles: Students learn about the properties of circles, including central angles, inscribed angles, arc lengths, and chords. They explore relationships between angles and arcs in circles and solve problems involving circle geometry.

Three-Dimensional Figures: Students study three-dimensional figures such as prisms, pyramids, cylinders, cones, and spheres. They learn to calculate surface area and volume for these shapes, including composite figures. They apply these concepts to solve problems involving real-world scenarios and three-dimensional modeling.

Transformations: Students further explore transformations, including translations, reflections, rotations, and dilations. They deepen their understanding of how these transformations affect the position, orientation, and size of geometric figures. They apply transformations to solve problems involving symmetry, congruence, and similarity.

Similarity and Congruence: Students deepen their understanding of similarity and congruence. They explore similarity transformations, such as dilation, and use them to establish similarity between figures. They apply congruence criteria to prove congruence between triangles and other shapes.

Trigonometry: Students are introduced to basic trigonometric concepts. They learn about sine, cosine, and tangent ratios in right triangles and apply them to solve problems involving angles and side lengths. They explore the applications of trigonometry in real-world situations, such as navigation and measuring heights.

Geometric Proofs: Students engage in more formal geometric proof activities. They learn different proof techniques, including direct proofs, indirect proofs, and proofs involving congruent triangles and parallel lines. They apply logical reasoning and deductive arguments to prove geometric theorems.

Geometric Constructions: Students further develop their skills in geometric constructions. They learn advanced constructions, such as constructing tangents to circles, dividing lines into equal parts, and constructing regular polygons. They explore the properties and applications of these constructions.

Coordinate Geometry: Students deepen their understanding of coordinate geometry. They explore concepts such as the distance formula, midpoint formula, and equations of lines. They use coordinate geometry to investigate geometric relationships and solve problems involving geometric figures on the coordinate plane.

Throughout the curriculum, students engage in problem-solving activities, mathematical modeling, and real-world applications to reinforce their understanding of geometry and measurement. They develop their skills in critical thinking, logical reasoning, spatial visualization, and mathematical communication.

- Circle
- Measures of 2D shapes
- Measures of 3D shapes
- Measures of angles
- Triangles
- Pythagoras
- Trigonometry
- Quadrilaterals
- Polygons
- Transformations
- Similar shapes

Parts of the circle 2

Identify parts of the circle: arc, chord, sector, segment and tangent

Circumference of circles

Using the formula C = 2πr calculate the circumference of circles to 2 decimal places

Circumference of semicircles

Use C = πr + 2r to calculate the circumference of the given semicircles to 2 d.p.

Area of compound shapes

Calculate the area of compound shapes constructed from parallelograms to 2 d.p.

Area of circles

Using the formula A = πr² calculate the area of the given circles to 2 decimal places

Calculate surface area of cubes

Use multiplication or the formula SA = 6H² to calculate the surface area of cubes

Calculate surface area of cuboids

Calculate the surface area of cuboids using the formula SA =2(LW+LH+HW)

Surface area of triangular prisms

Using a net or otherwise calculate the surface area of triangular prisms to 2 d.p.

Calculate volume of cubes

Use the standard formula L³ (length cubed) to calculate the volume of cubes

Volume of prisms

Calculate the volume of prisms using the formula area of cross-section x length to 2 d.p.

Calculate the volume of cylinders

Calculate the volume of cylinders using the formula area of cross-section x length to 2 d.p.

Describe the bearing

In each instance identify if the type of bearing is acute, obtuse or reflex

Estimate the bearing

Choose the most appropriate three figure bearing from the given options

Angles around parallel lines

Use parallel line rules to find alternate, corresponding and allied angles

Parallel lines and shapes

Use parallel line rules to find the missing angle in each of the given shapes

Vertically opposite angles

In each instance use vertically opposite angles to find the missing angle

Identify congruent, similar triangles

Identify triangles which are congruent, similar or neither

Labels for sides, angles

Identify the standard conventions for labeling the angles and sides of different types of triangles

Calculate the hypotenuse

Use Pythagoras' theorem to calculate the hypotenuse for these right-angle triangles to 2 d.p.

Find the missing length

Use Pythagoras' theorem to calculate the length of a side that is not the hypotenuse to 2 d.p.

Identify names of sides

Identify whether the marked sides of right angle triangles are the hypotenuse, adjacent or opposite

Rotational symmetry: quadrilaterals

Identify the order of rotational symmetry for each of the given quadrilaterals

Identify polygons from properties

Use the given properties to identify the polygon

Lines of symmetry: polygons

Identify the number of lines of symmetry possessed by each of the given polygons

Rotational symmetry: polygons

Identify the order of rotational symmetry for each of the given polygons

Exterior angles of regular polygons

Use the number of sides to calculate the exterior angles for each regular polygon

Number of sides from exterior angle

Use the exterior angle to calculate the number of sides for each regular polygon

Interior angle from exterior angle

Use the exterior angle for each regular polygon to calculate the interior angle

Sum of interior angles

Calculate the sum of the interior angles for each of the given polygons

Column vectors

Identify the correct shape on the graph for the given column vector

Describe translations

In each instance identify the correct column vector for the given translation

Identify reflections

Identify the correct shape for the described reflection

Describe reflections

Identify the line of symmetry (also called the mirror line) for each of the reflections

Describe rotation

In each instance identify the correct description for the given rotation

Rotation

Identify the correct shape on the grid for the described rotation

Positive integer scale factors

Identify the correct shape for the given positive integer scale factor enlargement

Negative scale factors

Identify the correct shape on the graph for the given negative scale factor enlargement

Identify similar shapes

Identify the pairs of shapes which are similar

Triangles: scale factors

In each instance find the scale factor between the two similar triangles

Triangles: length from scale factors

Use scale factor ratios to work out lengths on the smaller or larger triangles

Other shapes: length from scale factor

Use the scale factor to work out lengths on similar shapes that are not triangles

Number * Algebra * Ratio proportion rate * Geometry & measures * Probability * Statistics *

Secondary math home | Math topics | Math lessons | Math games | Math tests

Preschool math | Elementary math | Secondary math

Site home page | Privacy policy | FAQ | Contact | Acknowledgements | Blog

Select your view:

Copyright 2024 ic language ltd - all rights reserved

Speech synthesis support:

Site Version: 16_5_0