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Educators' Guide for Pedagogy and Assessment

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Learning Area: Mathematics 

Mathematics > LEVEL 7




Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

Subject Focus: Number - The number system

1] I can read and write  whole numbers to one billion in figures and words.
 WRITING
2] I can recognise the place value of any digit in a whole number up to one billion.
3] I can compare and order whole numbers up to one billion and include symbols such as <, > or =.
4] I can identify common multiples of three numbers. 
5] I can identify the least common multiple (LCM) of three numbers.
6] I can identify all factors of any two-digit number, e.g. factors of 24 are 1, 2, 3, 4, 6, 8, 12 , 24.
7] I can work out the square of a number and recall the first ten square numbers.
COGNITIVE LEARNING
8] I can deduce that squares and square roots are inverses of each other.
 COGNITIVE LEARNING
9] I can work out the cube of a number and recall the first five cube numbers.
COGNITIVE LEARNING
10] I can deduce that cubes and cube roots are inverses of each other.
COGNITIVE LEARNING
11] I can define what a prime number is and can identify prime numbers up to hundred.
COGNITIVE LEARNING
12] I can use decimal notation for tenths, hundredths and thousandths and know what each digit represents.
13] From a two-digit number I can count forward and backwards in steps of 0.1, 0.2, 0.25 and 0.5.
14] I can recognise that particular fractions have specific recurring decimal patterns, e.g. 1/3 = 0.333...
 COGNITIVE LEARNING
15] I can describe percentage as the number of parts in every hundred. Hence, I can represent 1% as a hundredth.
16] I can associate 25% with a quarter, 50% with one half and 75% with three quarters.
17] I can recognise the relationship between fractions, decimals and percentages.
18] I can relate fractions which have a denominator which is a factor of 100 to integral percentages.
19] I can state one fraction lying between two given fractions.
20] I can recognise, represent and use directed numbers in real life situations such as temperature, floor levels and debt. I can represent directed numbers on a number line. 



Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

Subject Focus: Number - The number system (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets, computers & calculators) and other learning resources (e.g. Cuisenaire rods, Unifix cubes, base 10 blocks) to learn about numbers and their properties.



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 (Whole Numbers, Decimal Numbers & Fraction Numbers - The Four Operations)

1] I can use assistive technology to add and subtract numbers that involve four or more digits.
 USE OF DIGITAL TECHNOLOGY
2] I can work through situations involving addition and subtraction with four or more digit numbers.
 COGNITIVE LEARNING
3] I recognise unit fractions and use them to find fractions of shapes, numbers and quantities. I can interpret the relationship between division and fractions e.g. 2/3 means 2 ÷ 3 and vice versa.
4] I can find remainders after division and express the remainder as a a fraction and as a decimal rounded up to two decimal places.
 COGNITIVE LEARNING
5] I can work through situations involving addition, subtraction, multiplication and/or division of integers. I can also give a rough estimate of the answer of such situations and I can check the reasonableness of the answer.
6] I can round any whole number to the nearest ten, hundred, thousand and ten thousand.
7] I can work out mentally the square root of squares up to 100 and the cube root of cubes up to 125 without a calculator and use a calculator for other values.
 COGNITIVE LEARNING
8] I can use primes to write numbers as a product of prime factors.
9] I can work out problems involving least common multiples.
10] I can use column addition or subtraction methods using decimal numbers up to three decimal places.
 COGNITIVE LEARNING
11] I can use written methods for multiplication and division of numbers  by up to two digits.
      e.g. 125 × 9 ; 256 ÷ 8 ; 54 × 36 ; 391 ÷ 23 ; 175 × 1.4 ; 18.6 × 2.7 ; 2.4 ÷ 0.6 ; 7.2 ÷ 0.16
12] I can add, subtract, multiply and divide directed numbers.
13] I can use the BIDMAS rule with both positive and negative numbers.
14] I can round any decimal number up to three decimal places.
15] I can find fractions of a number without using assistive technology.
16] I can change mixed numbers into decimals and vice versa.
17] I can read and interpret scales involving decimals.
 READING AND UNDERSTANDING
18] I can find equivalent fractions of a given fraction.
19] I can add and subtract two fractions (including mixed numbers) with different denominators using equivalent fractions.
20] I can multiply and divide two fractions including mixed numbers.
21] I can work through situations involving the addition, subtraction, multiplication and division of fractions and mixed numbers.



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 (Percentages)

1] I can convert percentages to fractions and vice versa.
2] I can convert percentages to decimals and vice versa.
3] I can find percentages of quantities.
 COGNITIVE LEARNING
4] I can express a quantity as a percentage of another.
5] I can find percentage increase and percentage decrease.



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 (Money & Consumer Mathematics)

1] I can use published exchange rates to convert from one currency to another.
2] I can work through simple situations involving directed numbers, personal and household finance (e.g. pocket money invested in a bank account, finding out how much it will cost to prepare a meal, calculating which item is the best buy when items come in various sizes e.g. oil in one litre bottles vs oil in two litre bottles).



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 write ratios in their simplest form, (including decimal numbers and numbers with different units).
 COGNITIVE LEARNING
2] I can find one quantity of a ratio given the other and divide a quantity in a given ratio.
3] I can use ratio to solve problems.
4] I can use simple map ratios.
5] I can use simple proportion (using ratio notation) to solve simple problems. e.g. What is the value of □ in 1:3 = □:6?
6] I can work through simple situations that involve direct proportion using the unitary method, (including price, distance, time, mass and capacity).



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, (e.g. Cuisenaire rods, Unifix cubes, base 10 blocks), 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 write a sequence given the first term and the rule. I can recognise and extend pictorial patterns and number sequences. I can tabulate the terms corresponding to the first few stages of a pictorial pattern and determine the terms in the next stages.
2] I can use algebraic notation to represent two or more unknown values in  expressions involving +, −, x and ÷.
 WRITING
3] I can derive a formula from a situation involving two or more unknown values with positive and negative inputs.
4] I can simplify linear algebraic expressions by collecting like terms.
5] I can simplify algebraic expressions by multiplying linear terms, e.g. -4 × 5b, -2a × -3b and x × (-3x) and can multiply a single term over a bracket,
     e.g. -2(a + 3), 3(x + 4) + 2(x - 1), 2(1 - x) - 3(x + 2).
6] I can evaluate linear expressions by substituting directed numbers .
7] I can change the subject of a formula that uses one or two operations. 
8] I can write down and solve an equation using the balancing method involving unknown and whole numbers on both sides.
9] I can use and solve simple linear equations involving brackets, e.g. solve for x: 4(x - 1) = 2x + 6 
10] I can work through situations leading to solution of linear equations in one unknown, e.g. mystery numbers, geometric shapes, etc.
11] I can plot points and read coordinates from a grid in all four quadrants.
 READING AND UNDERSTANDING
12] I can write the coordinates of a set of points for equations of the form: y = ±mx ± c
 WRITING
13] I can construct tables of values for linear functions.
14] I can plot the graph of a linear function from a table of values.
15] I can explain what the gradient of a line represents.
16] I know that parallel lines have equal gradients.
17] I can explain what the y-intercept represents.
18] I can indicate that for the equation y = mx + c the value of m determines the gradient of the graph and the value of c determines the y-intercept.
19] I can write the equation of a straight line  given the gradient and the y-intercept.
20] I can verify whether a line passes through a point.
21] I can use straight line graphs to find the value of one coordinate given the other.
22] I can interpret straight line graphs in real life situations, e.g. conversion graphs, distance-time graphs, etc.
23] I can work out the input/output of number (function) machines involving up to two operations and can find the rule for a number machine involving up to two operations given a set of input and output values. I can build and use number machines from real life situations.
 LEARNING TO DO 



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 estimate, measure and draw angles up to 360° with a protractor.
 COGNITIVE LEARNING
2] I can identify and distinguish between right, acute, obtuse and reflex angles.



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 define the volume of a solid shape as the measure of the amount of material that makes up that shape.
2] I can convert larger to smaller standard metric units of mass (kg, g),  length (km, m, cm, mm) and capacity (l, ml) and vice versa.
3] I can work out the areas of irregular and regular shapes by counting squares on a grid.
 COGNITIVE LEARNING
4] I can derive and use formulae to find the area of a square and a rectangle. 
5] I can derive and use formulae to find the area of a parallelogram, a triangle and a trapezium.
6] I can calculate the area of compound shapes that include right-angled triangles, parallelograms and trapezia.
7] I can define the notion of pi as the ratio of the circumference to the diameter.
8] I can use formulae to find the circumference and area of a circle.
9] I can define the surface area of a solid shape as the total amount of surface of the shape.
10] I can calculate the surface area of cubes and cuboids. I can use formulae to calculate the volume of cubes and cuboids, including compound shapes made up of cubes and cuboids.



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

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

1] I can read and write vocabulary related to time.
 WRITING
2] I can convert and use larger to smaller standard units of time (days, hours, minutes and seconds) and vice versa. e.g. 2.4 hours = 144 minutes.
3] I can read and use the 12-hour and the 24-hour digital and analogue clock.
WRITING
4] I can read and use a calendar, a timetable and a timeline.
 READING AND UNDERSTANDING
5] I can determine time intervals in days, hours and minutes.



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. plastic money, cardboard clocks, 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 (Lines & Lines Segments)

1] I can recognise and draw examples of parallel lines and transversals.  
2] I can recognise vertically opposite angles, alternate angles, corresponding angles and interior angles within sets of parallel lines and transversals.



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 (Angles)

1] I can work out the size of missing angles in situations involving vertically opposite angles, alternate angles, corresponding and interior angles within sets of parallel lines and transversals.



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 follow a proof that the angle sum of a triangle is 180˚. I can apply and follow a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices.
2] I can use the properties of triangles (equilateral, isosceles, scalene and right-angled triangle) in order to solve problems involving missing 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 (Quadrilaterals)

1] I can classify quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium and kite) according to the length of their sides and the size of their angles. 
COGNITIVE LEARNING
2] I can deduce that the sum of the angles of a quadrilateral is 360°. I can also work out the size of missing angles in quadrilaterals.
 COGNITIVE LEARNING
3] I can use the properties of quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium and kite) in order to solve problems involving missing 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 (3D Shapes)

1] I can identify nets that are possible or not possible for a cube, a cuboid, a triangular prism and a square- based right pyramid.



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 (Circles)

1] I can identify the centre, radius, chord, diameter and circumference of a circle.



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 (Constructions)

1] I can construct 60° and 90° angles using a straight edge and compasses only, and using a dynamic geometry software package.
2] I can construct triangles given the length of one side and two angles; the length of two sides and the included angle using ruler and protractor. I can construct triangles given three sides using ruler and compasses only. I can construct triangles (involving 60° and 90° angles) using ruler and compasses only. I can construct triangles using a dynamic geometry software package.
3] I can construct regular hexagons using ruler and compasses.



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 (Coordinate Geometry)

1] I can use positive and negative coordinates to plot points and draw shapes.
2] I can find the coordinates of a missing vertex of a shape.



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 (Assistive Technology & Other Resources)

1] I can use simple LOGO commands such as PU, PD, FD, BK, RT, LT and REPEAT.
2] 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 and draw lines of symmetry in 2D shapes and pictures (e.g. flags and dominoes).
2] I can classify quadrilaterals (square, rectangle, parallelogram, trapezium, rhombus and kite) using reflective symmetry.
3] I can draw and describe reflections in the x axis ; y axis ; y = ±c ; x = ±c ; y = ±x.
MANAGING LEARNING



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

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

1] I can identify the order of rotational symmetry of a regular polygon.
2] I can identify one or multi-coloured 2D shapes having rotational symmetry and find their order of rotational symmetry.
3] I can draw and describe rotations of a simple shape about a vertex or about the origin using angles of 90° and 180°.
 MANAGING LEARNING



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

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

1] I can draw and describe translations using a column translation vector.
MANAGING LEARNING



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 construct a frequency table with grouped or ungrouped discrete data.
 PRACTICAL
2] I can construct a bar chart using grouped or ungrouped discrete data from a frequency table.
 PRACTICAL
3] I can interpret data from frequency tables and bar charts.
4] I can interpret pie charts.
5] I can construct pie charts.
6] I can construct and interpret a carroll diagram.
7] I can find the mean of a set of ungrouped data.
8] I can differentiate between the mean, median, mode and range of a set of ungrouped data. I can work through problems involving the mean, mode, median and range; and decide when best to use each type of average using words like "outlier".
9] I can find the median of a set of ungrouped data.
10] I can find the mode of a set of ungrouped data.
11] I can find the range of a set of ungrouped data.



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.



Learning Area Outcome: I understand ideas of chance and uncertainty.

Subject Focus: Data handling & chance – Probability

1] I can mention events that are certain to happen, and others that will not.
 COGNITIVE
2] I can describe events as certain, very likely, likely, evens, unlikely, very unlikely or impossible.
 COGNITIVE
3] I can estimate a probability by experiment.
 LEARNING TO DO
4] I can work out the probability of an event. e.g. the probability of getting 4 when throwing a die.
5] I can distinguish between experimental and theoretical probability.
6] I can deduce that the probability of a certain event is 1 and the probability of an impossible event is 0.
7] I can mark the probability on a probability scale.
8] I can identify the set of all possible outcomes of a single event.
9] I can deduce that the probability of all mutually exclusive outcomes of an experiment add up to 1.
10] I can construct a possibility space of two events and use it to work out the probability of an outcome.
 COGNITIVE LEARNING



Learning Area Outcome: I understand ideas of chance and uncertainty.

Subject Focus: Data handling & chance – Probability (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets, computers and calculators) and other learning resources to learn about probability.




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