## Educators' Guide for Pedagogy and Assessment

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### Learning Area: Mathematics

# Mathematics > LEVEL 9

### Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

## Subject Focus: Number - Numerical calculations (Ratio & Proportion)

1] I can use scale drawings to find actual distances and areas.

2] I can work through situations that involve direct and inverse proportion.

3] I can use index notation and the rules for working with positive and negative fractional powers.

2] I can work through situations that involve direct and inverse proportion.

3] I can use index notation and the rules for working with positive and negative fractional powers.

### Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

## Subject Focus: Number - Numerical calculations (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets, computers and calculators)*and other resources appropriate to this level to calculate and to learn about numerical calculations.### Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

## Subject Focus: Algebra – Fundamentals of Algebra

1] I can add and subtract algebraic fractions with linear and quadratic algebraic denominators.

2] I can solve algebraically two simultaneous equations, one linear and one quadratic.

3] I can solve equations involving algebraic fractions with quadratic denominators.

4] I can solve simple equations using indices when

5] I can construct tables of values for cubic and reciprocal functions.

6] I can plot the graph of a cubic function and a reciprocal function from a table of values.

7] I can solve graphically two simultaneous equations: one linear and one cubic; or, one linear and one reciprocal.

8] I can derive and use the inverse function notation, e.g.

9] I can work through situations that use direct and inverse variation (y α x

LEARNING TO DO

10] I can interpret rates of change in linear graphs.

2] I can solve algebraically two simultaneous equations, one linear and one quadratic.

3] I can solve equations involving algebraic fractions with quadratic denominators.

4] I can solve simple equations using indices when

*x*is a power.5] I can construct tables of values for cubic and reciprocal functions.

6] I can plot the graph of a cubic function and a reciprocal function from a table of values.

7] I can solve graphically two simultaneous equations: one linear and one cubic; or, one linear and one reciprocal.

8] I can derive and use the inverse function notation, e.g.

*f*(x) = 5x - 3 then*f*^{-}^{1}(x) =^{(x + 3)}/_{5}9] I can work through situations that use direct and inverse variation (y α x

^{n}for*n*= ±1, ±2, ±3, ±^{1}/_{2}, ±^{1}/_{3})LEARNING TO DO

10] I can interpret rates of change in linear graphs.

*E.g. speed, distance and time*.### Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

## Subject Focus: Algebra – Fundamentals of Algebra (Assistive Technology & Other Resources)

1] I can use assistive technology, (

*e.g. tablets and computers)*and other resources, (e.g. algebra blocks) appropriate to this level to learn about the fundamentals of algebra.### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Angles)

1] I can use trigonometric ratios to work through situations involving angles in bearings and in 3D.

2] I can use the Sine and Cosine rules to solve any triangle.

2] I can use the Sine and Cosine rules to solve any triangle.

### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Length, Area, Volume, Mass & Capacity)

1] I can convert larger to smaller standard metric units of area and volume and vice versa.

2] I can find the area of acute and obtuse angled triangles using A = ½ ab sin C.

3] I can calculate the area of compound shapes that include non right-angled triangles.

4] I can calculate the area of a segment of a circle.

5] I can calculate the area of compound shapes that include segments of circles.

6] I can use the relationship between length, area and volume of similar shapes.

7] I can give appropriate upper and lower bounds for measurement data given to a specified accuracy (

8] I can obtain appropriate upper and lower bounds to solutions of simple calculations.

2] I can find the area of acute and obtuse angled triangles using A = ½ ab sin C.

3] I can calculate the area of compound shapes that include non right-angled triangles.

4] I can calculate the area of a segment of a circle.

5] I can calculate the area of compound shapes that include segments of circles.

6] I can use the relationship between length, area and volume of similar shapes.

7] I can give appropriate upper and lower bounds for measurement data given to a specified accuracy (

*e.g. measured lengths and measured weights)*8] I can obtain appropriate upper and lower bounds to solutions of simple calculations.

### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets computers and calculators)*and other resources (*e.g. 2D and 3D plastic shapes, measuring instruments)*appropriate to this level to learn about measures..### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, space and measures – Euclidean geometry (Triangles)

1] I can use Pythagoras’ Theorem in 3D shapes.

### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, space and measures – Euclidean geometry (Congruency & Similarity)

1] I can explain the concept of similarity. I can identify similar shapes.

2] I can prove two triangles are similar using either one of the following properties:

(i) The angles of one are respectively equal to the angles of the other (AAA).

(ii) The ratio of the three sides of the first triangle is equal to the ratio of the corresponding sides of the other.

(iii) One angle of one triangle is equal to one angle of the other triangle and the sides about these equal angles are in the same ratio.

3] I can use the fact that two triangles are similar in order to find the lengths of missing sides and angles.

COGNITIVE LEARNING

2] I can prove two triangles are similar using either one of the following properties:

(i) The angles of one are respectively equal to the angles of the other (AAA).

(ii) The ratio of the three sides of the first triangle is equal to the ratio of the corresponding sides of the other.

(iii) One angle of one triangle is equal to one angle of the other triangle and the sides about these equal angles are in the same ratio.

3] I can use the fact that two triangles are similar in order to find the lengths of missing sides and angles.

COGNITIVE LEARNING

### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, space and measures – Euclidean geometry (Loci)

1] I can describe what a locus of a point is.

2] I can use ruler and compasses only to construct the locus of a point which is:

(i) At a fixed distance from a given point.

(ii) Equidistant from a straight line.

(iii) Equidistant from two given points.

(iv) Equidistant from two intersecting straight lines.

3] I can solve problems using the above constructions involving intersecting loci and regions.

COGNITIVE LEARNING

2] I can use ruler and compasses only to construct the locus of a point which is:

(i) At a fixed distance from a given point.

(ii) Equidistant from a straight line.

(iii) Equidistant from two given points.

(iv) Equidistant from two intersecting straight lines.

3] I can solve problems using the above constructions involving intersecting loci and regions.

COGNITIVE LEARNING

## Subject Focus: Shape, space and measures – Euclidean geometry (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other resources (*e.g. 2D and 3D plastic shapes)*appropriate to this level to learn about properties of shapes.### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Reflections)

1] I can identify planes of symmetry.

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other resources*(e.g. 2D and 3D plastic shapes)*appropriate to this level to learn about transformation geometry.### Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

## Subject Focus: Data handling and chance – Statistics

1] I can read and interpret a cumulative frequency table and a cumulative frequency graph.

2] I can construct a cumulative frequency table and use it to draw a cumulative frequency graph.

3] I can interpret a histogram with unequal class intervals.

4] I can construct a histogram with unequal class intervals.

PRACTICAL

5] I can explain what the modal class, quartiles and inter-quartile range of a set of data represent.

6] I can find the class interval in which the median of a set of data lies from a grouped frequency table.

7] I can identify the modal class from a grouped frequency table.

8] I can find the range of a set of data from a grouped frequency table.

9] I can use cumulative frequency graphs to estimate the median, the quartiles and the inter-quartile range.

COGNITIVE LEARNING

10] I can interpret box-and-whisker plots.

COGNITIVE LEARNING

11] I can construct box-and-whisker plots.

PRACTICAL

2] I can construct a cumulative frequency table and use it to draw a cumulative frequency graph.

3] I can interpret a histogram with unequal class intervals.

4] I can construct a histogram with unequal class intervals.

PRACTICAL

5] I can explain what the modal class, quartiles and inter-quartile range of a set of data represent.

6] I can find the class interval in which the median of a set of data lies from a grouped frequency table.

7] I can identify the modal class from a grouped frequency table.

8] I can find the range of a set of data from a grouped frequency table.

9] I can use cumulative frequency graphs to estimate the median, the quartiles and the inter-quartile range.

COGNITIVE LEARNING

10] I can interpret box-and-whisker plots.

COGNITIVE LEARNING

11] I can construct box-and-whisker plots.

PRACTICAL

### Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

## Subject Focus: Data handling and chance – Statistics (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other learning resources to learn about statistics.