## Educators' Guide for Pedagogy and Assessment

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### Learning Area: Mathematics

# Mathematics > LEVEL 6

### 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, write and order whole numbers to one milion in figures and words.

WRITING

2] I can recognise, read and position numbers on a number line.

COGNITIVE LEARNING

3] I can recognise the place value of any digit in a whole number up to one million.

4] I can compare and order whole numbers up to one million and include symbols such as <, > or =.

5] I can identify odd and even numbers.

6] I can count forward and backwards in 1s, 2s, 10s and 100s starting from any whole number.

WRITING

7] I can count forward and backwards in steps of 3, 4, or 5 to and from any whole number.

WRITING

8] I can count forward/backwards in steps of 25 (to/from any multiple of 25) and 50 (to/from any multiple of 50).

WRITING

9] I can recall the first ten multiples of the following numbers: 7 & 9.

10] I can list the first five multiples of any whole numbers up to and including 100.

11] I can identify common multiples of two numbers.

12] I can identify the least common multiple (LCM) of two numbers.

13] I can identify factors of any two-digit number.

14] I can generate, and recall the first ten square numbers.

COGNITIVE LEARNING

WRITING

15] I can generate and recall the first five cube numbers.

COGNITIVE LEARNING

WRITING

16] I can use decimal notation for tenths and hundredths and know what each digit represents.

17] From a one-digit number I can count forward and backwards in steps of 0.1, 0.2, 0.25 and 0.5.

18] I can recognise and extend number sequences and predict the next few terms.

COGNITIVE LEARNING

WRITING

19] I can associate 0.25 with one quarter and 0.75 with three quarters.

COGNITIVE LEARNING

20] I can associate 0.1 with one tenth and 0.01 with one hundredth.

COGNITIVE LEARNING

21] I can read and use the terms ‘simple fraction’, ‘numerator’ and ‘denominator’.

22] I can recognise mixed numbers which include a whole number and a fraction and can use the term 'mixed numbers'.

23] I can recognise, use and generate equivalent fractions.

COGNITIVE LEARNING

24] I can compare and order simple fractions, mixed numbers and decimals, & position them on a number line.

COGNITIVE LEARNING

25] I can relate simple fractions which have a denominator which is a factor of 100 to decimals.

26] I can recognise the relationship between fractions and decimals.

27] I can state one number lying between two given decimal numbers.

WRITING

2] I can recognise, read and position numbers on a number line.

COGNITIVE LEARNING

3] I can recognise the place value of any digit in a whole number up to one million.

4] I can compare and order whole numbers up to one million and include symbols such as <, > or =.

5] I can identify odd and even numbers.

6] I can count forward and backwards in 1s, 2s, 10s and 100s starting from any whole number.

WRITING

7] I can count forward and backwards in steps of 3, 4, or 5 to and from any whole number.

WRITING

8] I can count forward/backwards in steps of 25 (to/from any multiple of 25) and 50 (to/from any multiple of 50).

WRITING

9] I can recall the first ten multiples of the following numbers: 7 & 9.

10] I can list the first five multiples of any whole numbers up to and including 100.

11] I can identify common multiples of two numbers.

12] I can identify the least common multiple (LCM) of two numbers.

13] I can identify factors of any two-digit number.

14] I can generate, and recall the first ten square numbers.

COGNITIVE LEARNING

WRITING

15] I can generate and recall the first five cube numbers.

COGNITIVE LEARNING

WRITING

16] I can use decimal notation for tenths and hundredths and know what each digit represents.

17] From a one-digit number I can count forward and backwards in steps of 0.1, 0.2, 0.25 and 0.5.

18] I can recognise and extend number sequences and predict the next few terms.

COGNITIVE LEARNING

WRITING

19] I can associate 0.25 with one quarter and 0.75 with three quarters.

COGNITIVE LEARNING

20] I can associate 0.1 with one tenth and 0.01 with one hundredth.

COGNITIVE LEARNING

21] I can read and use the terms ‘simple fraction’, ‘numerator’ and ‘denominator’.

22] I can recognise mixed numbers which include a whole number and a fraction and can use the term 'mixed numbers'.

23] I can recognise, use and generate equivalent fractions.

COGNITIVE LEARNING

24] I can compare and order simple fractions, mixed numbers and decimals, & position them on a number line.

COGNITIVE LEARNING

25] I can relate simple fractions which have a denominator which is a factor of 100 to decimals.

26] I can recognise the relationship between fractions and decimals.

27] I can state one number lying between two given decimal numbers.

### 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 and computers)*and other learning resources (*e.g. Cuisenaire rods, Unifix cubes, base 10 blocks, fraction wall)*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 add or subtract by using the nearest multiple of 10, 100 or 1000 then adjusting

COGNITIVE LEARNING

2] I can use column addition and subtraction with up to four-digit numbers.

COGNITIVE LEARNING

3] I can work through situations involving addition and subtraction with three-digit numbers.

COGNITIVE LEARNING

4] I recognise that division is the inverse of multiplication. I can also state and write a division statement corresponding to a given multiplication statement (6, 7, 8, and 9 multiplication facts), and vice versa.

COGNITIVE LEARNING

5] I can multiply and divide any integer by 10, 100, or 1000.

6] I recognise unit fractions, (one fifth, one eighth, one tenth, one hundredth)

7] I can find remainders after division and express the remainder as a fraction.

COGNITIVE LEARNING

8] I can work through simple two-step situations using addition, subtration, multiplication and/or division.

I can also give a rough estimate of the answer of such situations and I can check the reasonableness of the answer.

9] I can round any whole number to the nearest ten, hundred and thousand.

10] I can round remainders to the nearest whole number depending on the context.

11] I can write tenths and hundredths in decimal form and vice versa.

COGNITIVE LEARNING

12] I can add and subtract whole and decimal numbers up to two decimal places using informal methods.

13] I can use column addition or subtraction methods using decimal numbers up to two decimal places.

COGNITIVE LEARNING

14] I can derive quickly decimals that total 1 or 10.

15] I can use written methods for ThHTU x U ; HTU x TU ; U.t x U ; TU.t x U ; U.th x U

16] I can use written methods for TU ÷ U ; HTU ÷ U ; HTU ÷ TU ;

U.t ÷ U ; U.th ÷ U

17] I can use written method for multiplication and division by 10 and 100 including decimals.

18] I can derive doubles and halves of whole and decimal numbers.

COGNITIVE LEARNING

19] I can use brackets to order operations on positive numbers.

20] I can round a decimal number with two decimal places to the nearest tenth or to the nearest whole number.

21] I can find fractions of whole numbers.

COGNITIVE LEARNING

22] I can use simple fractions and mixed numbers.

COGNITIVE LEARNING

23] I can reduce a fraction to its simplest form.

COGNITIVE LEARNING

24] I can change an improper fraction into a mixed number and vice versa.

COGNITIVE LEARNING

25] I can read and interpret scales involving whole numbers.

READING AND UNDERSTANDING

*e.g. 14 + 8 = 14 + 10 − 2*.COGNITIVE LEARNING

2] I can use column addition and subtraction with up to four-digit numbers.

COGNITIVE LEARNING

3] I can work through situations involving addition and subtraction with three-digit numbers.

COGNITIVE LEARNING

4] I recognise that division is the inverse of multiplication. I can also state and write a division statement corresponding to a given multiplication statement (6, 7, 8, and 9 multiplication facts), and vice versa.

COGNITIVE LEARNING

5] I can multiply and divide any integer by 10, 100, or 1000.

6] I recognise unit fractions, (one fifth, one eighth, one tenth, one hundredth)

*and use them to find fractions of shapes, numbers and quantities. I can associate fractions (one fifth, one eighth, one tenth, one hundredth) and division.**e.g. How much is*^{1}/_{8 }of 32? Therefore, how much is^{5}/_{8 }of 32?7] I can find remainders after division and express the remainder as a fraction.

COGNITIVE LEARNING

8] I can work through simple two-step situations using addition, subtration, multiplication and/or division.

I can also give a rough estimate of the answer of such situations and I can check the reasonableness of the answer.

9] I can round any whole number to the nearest ten, hundred and thousand.

10] I can round remainders to the nearest whole number depending on the context.

11] I can write tenths and hundredths in decimal form and vice versa.

COGNITIVE LEARNING

12] I can add and subtract whole and decimal numbers up to two decimal places using informal methods.

13] I can use column addition or subtraction methods using decimal numbers up to two decimal places.

COGNITIVE LEARNING

14] I can derive quickly decimals that total 1 or 10.

15] I can use written methods for ThHTU x U ; HTU x TU ; U.t x U ; TU.t x U ; U.th x U

16] I can use written methods for TU ÷ U ; HTU ÷ U ; HTU ÷ TU ;

U.t ÷ U ; U.th ÷ U

17] I can use written method for multiplication and division by 10 and 100 including decimals.

18] I can derive doubles and halves of whole and decimal numbers.

COGNITIVE LEARNING

19] I can use brackets to order operations on positive numbers.

20] I can round a decimal number with two decimal places to the nearest tenth or to the nearest whole number.

21] I can find fractions of whole numbers.

COGNITIVE LEARNING

22] I can use simple fractions and mixed numbers.

COGNITIVE LEARNING

23] I can reduce a fraction to its simplest form.

COGNITIVE LEARNING

24] I can change an improper fraction into a mixed number and vice versa.

COGNITIVE LEARNING

25] I can read and interpret scales involving whole numbers.

READING AND UNDERSTANDING

### 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 convert euro to cent and vice versa.

2] I can work out totals of up to ten thousand euro and give the correct change.

3] I can calculate, compare and discuss special offers.

MANAGING LEARNING

2] I can work out totals of up to ten thousand euro and give the correct change.

3] I can calculate, compare and discuss special offers.

MANAGING LEARNING

### 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 simple proportion (using equivalent fractions), to solve simple problems

2] I can work through simple situations that involve direct proportion when unknown quantities are simple multiples of known quantities (

*e.g. What is the value of**□ in**1/3**= □/6*2] I can work through simple situations that involve direct proportion when unknown quantities are simple multiples of known quantities (

*e.g. A cup cakes recipe uses 2 eggs to make 10 cupcakes. How many eggs will be needed to make 25 cupcakes?*## Subject Focus: Number - Numerical calculations (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other resources (*e.g. Cuisenaire rods, Unifix cubes, base 10 blocks, fraction wall, euro coins and notes),*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 recognise and extend pictorial patterns and square number sequences.

2] I can work through an equation where there are pictures instead of numbers.

COGNITIVE LEARNING

3] I can locate position on a grid with labelled rows and columns.

2] I can work through an equation where there are pictures instead of numbers.

COGNITIVE LEARNING

3] I can locate position on a grid with labelled rows and columns.

### 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. equation balance) 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 show and label the eight compass points.

COGNITIVE LEARNING

2] I can recognise and illustrate that a whole turn is the same as 4 right angles and half a whole turn is the same as 2 right angles.

COGNITIVE LEARNING

3] I can define and illustrate that an angle is a measure of turn and can describe it.

COGNITIVE LEARNING

4] I can estimate, sort, measure and draw angles up to 180° with a protractor (margin of error: +/- 5°).

5] I can identify and distinguish between acute and obtuse angles.

COGNITIVE LEARNING

2] I can recognise and illustrate that a whole turn is the same as 4 right angles and half a whole turn is the same as 2 right angles.

COGNITIVE LEARNING

3] I can define and illustrate that an angle is a measure of turn and can describe it.

COGNITIVE LEARNING

4] I can estimate, sort, measure and draw angles up to 180° with a protractor (margin of error: +/- 5°).

5] I can identify and distinguish between acute and obtuse 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 area as the measure of the amount of surface of a flat shape.

2] I can read and write the vocabulary related to area.

WRITING

3] I know the standard metric units of area (square kilometres, square metres, square centimetres and square millimetres). I also know the abbreviation of these standard units and recognise the relationships between different units of the same measure.

COGNITIVE LEARNING

4] I can estimate, measure and compare areas.

COGNITIVE LEARNING

5] I can use the decimal notation to express metric measures of area.

6] I can define perimeter as the edge of a shape.

COGNITIVE LEARNING

7] I can identify the perimeters of regular and irregular polygons and can measure and calculate their lengths.

8] I can work out the areas of squares and rectangles by counting squares on a grid.

COGNITIVE LEARNING

9] I can work out the area of squares and rectangles by using the fomula: length x breadth.

COGNITIVE LEARNING

10] I can work out the area of a right-angled triangle by considering it as half a rectangle.

11] I can work out the area of compound shapes that are made up of squares and rectangles.

2] I can read and write the vocabulary related to area.

WRITING

3] I know the standard metric units of area (square kilometres, square metres, square centimetres and square millimetres). I also know the abbreviation of these standard units and recognise the relationships between different units of the same measure.

COGNITIVE LEARNING

4] I can estimate, measure and compare areas.

COGNITIVE LEARNING

5] I can use the decimal notation to express metric measures of area.

6] I can define perimeter as the edge of a shape.

COGNITIVE LEARNING

7] I can identify the perimeters of regular and irregular polygons and can measure and calculate their lengths.

8] I can work out the areas of squares and rectangles by counting squares on a grid.

COGNITIVE LEARNING

9] I can work out the area of squares and rectangles by using the fomula: length x breadth.

COGNITIVE LEARNING

10] I can work out the area of a right-angled triangle by considering it as half a rectangle.

11] I can work out the area of compound shapes that are made up of squares and rectangles.

### 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 convert and use larger to smaller standard units of time (hours, minutes and seconds) and vice versa.

2] I can read and write time to the hour/half hour/quarter hour using terms 'o'clock', 'half past', 'quarter past'

and 'quarter to'.

3] I can read, write and use the 12-hour clock (analogue and digital) to one minute also using terms 'past' and 'to'.

4] I can read and use the 24-hour clock (analogue and digital).

5] I can read and use a timetable and a timeline.

READING AND UNDERSTANDING

6] I can work out the duration of a time interval, the starting time and the finishing time.

7] I can estimate and measure time using seconds, minutes and hours. COGNITIVE LEARNING

8] I can solve word problems involving addition and subtraction of time given in hours and minutes.

2] I can read and write time to the hour/half hour/quarter hour using terms 'o'clock', 'half past', 'quarter past'

and 'quarter to'.

3] I can read, write and use the 12-hour clock (analogue and digital) to one minute also using terms 'past' and 'to'.

4] I can read and use the 24-hour clock (analogue and digital).

5] I can read and use a timetable and a timeline.

READING AND UNDERSTANDING

6] I can work out the duration of a time interval, the starting time and the finishing time.

7] I can estimate and measure time using seconds, minutes and hours. COGNITIVE LEARNING

8] I can solve word problems involving addition and subtraction of time given in hours and minutes.

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

1] I can use assistive technology (

*e.g. tablets and computers)*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 horizontal and vertical lines.

COGNITIVE LEARNING

2] I can recognise and draw examples of parallel and perpendicular lines. I can draw such lines on a square grid.

COGNITIVE LEARNING

2] I can recognise and draw examples of parallel and perpendicular lines. I can draw such lines on a square grid.

### 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 deduce that the angles on a straight line add up to 180°. I can also work out the size of missing angles in diagrams showing angles on a straight line.

COGNITIVE LEARNING

2] I can deduce that the angles around a point add up to 360°. I can also work out the size of missing angles in diagrams showing angles at a point.

COGNITIVE LEARNING

COGNITIVE LEARNING

2] I can deduce that the angles around a point add up to 360°. I can also work out the size of missing angles in diagrams showing angles at a point.

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 (Triangles)

1] I can classify triangles according to the length of their sides and the size of their angles (scalene, isosceles, equilateral and right-angled triangles).

COGNITIVE LEARNING

2] I can deduce that the sum of the angles of a triangle is 180°. I can also work out the size of missing angles in triangles.

COGNITIVE LEARNING

COGNITIVE LEARNING

2] I can deduce that the sum of the angles of a triangle is 180°. I can also work out the size of missing angles in triangles.

COGNITIVE LEARNING

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

1] I can draw squares and rectangles given the lengths of the sides.

COGNITIVE LEARNING

COGNITIVE LEARNING

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

1] I can sort, name and classify polygons using properties such as the number of sides and the size of the interior angles.

COGNITIVE LEARNING

2] I can identify 'regular' and 'irregular polygons'.

READING AND UNDERSTANDING

COGNITIVE LEARNING

2] I can identify 'regular' and 'irregular polygons'.

READING AND UNDERSTANDING

## Subject Focus: Shape, space and measures – Euclidean geometry (3D Shapes)

1] I can recognise and name the simple 3D shapes: the cylinder, cone, triangular prism and square-based pyramid.

COGNITIVE LEARNING

2] I can visualise the simple 3D shapes from 2D drawings.

COGNITIVE LEARNING

3] I can identify and count faces, vertices and edges of simple 3D shapes.

4] I can identify possible and impossible nets for a closed and an open cube.

COGNITIVE LEARNING

COGNITIVE LEARNING

2] I can visualise the simple 3D shapes from 2D drawings.

COGNITIVE LEARNING

3] I can identify and count faces, vertices and edges of simple 3D shapes.

4] I can identify possible and impossible nets for a closed and an open cube.

COGNITIVE LEARNING

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

1] I can recognise, name and draw the simple 2D shape: the circle.

COGNITIVE LEARNING

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 recognise reflective symmetry in regular polygons.

COGNITIVE LEARNING

2] I can identify and draw lines of symmetry in triangles and quadrilaterals.

3] I can classify triangles using reflective symmetry.

4] I can complete symmetrical patterns given one and two lines of symmetry at right angles.

COGNITIVE LEARNING

COGNITIVE LEARNING

2] I can identify and draw lines of symmetry in triangles and quadrilaterals.

3] I can classify triangles using reflective symmetry.

4] I can complete symmetrical patterns given one and two lines of symmetry at right angles.

COGNITIVE 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 describe half-right angle rotations.

2] I can describe 90° and 180° rotations both clockwise and anticlockwise. I can also describe 45°, 135°, 225°, 270° and 315° rotations both clockwise and anticlockwise.

COGNITIVE LEARNING

2] I can describe 90° and 180° rotations both clockwise and anticlockwise. I can also describe 45°, 135°, 225°, 270° and 315° rotations both clockwise and anticlockwise.

COGNITIVE 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 using a tally column.

2] I can read and interpret a bar chart and a bar-line graph.

COGNITIVE LEARNING

3] I can construct a bar chart and a bar-line graph.

PRACTICAL

4] I can work through a situation by representing and interpreting data in tables, graphs, charts and diagrams.

COGNITIVE LEARNING

5] I can read and interpret a pictograph where the symbol represents a number of units.

COGNITIVE LEARNING

6] I can draw a pictograph where the symbol represents a number of units.

PRACTICAL

7] I can complete a given Carroll diagram.

PRACTICAL

8] I can interpret the mean as the total amount divided by the number of items. I can work out the mean (number or quantity) and can work out the total amount given the mean and the number of items.

2] I can read and interpret a bar chart and a bar-line graph.

COGNITIVE LEARNING

3] I can construct a bar chart and a bar-line graph.

PRACTICAL

4] I can work through a situation by representing and interpreting data in tables, graphs, charts and diagrams.

COGNITIVE LEARNING

5] I can read and interpret a pictograph where the symbol represents a number of units.

COGNITIVE LEARNING

6] I can draw a pictograph where the symbol represents a number of units.

PRACTICAL

7] I can complete a given Carroll diagram.

PRACTICAL

8] I can interpret the mean as the total amount divided by the number of items. I can work out the mean (number or quantity) and can work out the total amount given the mean and the number of items.

### 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.