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Maths Makes Sense Maths Makes Sense and Mathematics andand Mathematics and

Numeracy (Northern Ireland) Numeracy (Northern Ireland) For Maths Makes Sense 5 and 6

(Key Stage 2)

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Maths Makes Sense and Mathematics and Numeracy (Northern Ireland)

This document is intended to help you use the Maths Makes Sense resources for children aged 9 to 11 alongside Mathematics and Numeracy (the statutory requirements of the Northern Ireland Mathematics Curriculum).

This chart shows you how the Maths Makes Sense 5 and 6 end-of-block objectives correlate to the statutory requirements of Key Stage 2 Mathematics and Numeracy. The simple lay-out, provided in an editable format, will assist you with your planning so that you are able to integrate Maths Makes Sense seamlessly into your classroom.

Maths Makes Sense identifies that all learners need both informal learning and formal learning and identifies opportunities for both. The Northern Ireland Curriculum for Mathematics and Numeracy highlights the importance of presenting mathematical activities in contexts that have a real meaning for children, helping them to see the relevance of mathematics to their everyday lives. Throughout the Maths Makes Sense Learning System opportunities exist to help achieve this important aspiration of the Northern Ireland Curriculum for Mathematics and Numeracy.

The significance placed on the development of mathematical language in Maths Makes Sense mirrors its fundamental importance in the Mathematics and Numeracy Curriculum. Pupils must understand mathematical language and use the correct vocabulary to talk about their work.

The methodology of Maths Makes Sense will support the methodologies of the Mathematics and Numeracy Curriculum. The direct instruction, modelled on guided practice and partner teaching will allow teachers to help pupils to learn the key concepts identified in this curriculum. The importance of partner work as a key feature of Maths Makes Sense will support the requirement for co-operative learning.

The Northern Ireland Matching Charts identify the statements from the Northern Ireland Curriculum for Mathematics and Numeracy which sit parallel to the end-of-block objectives. These Maths Makes Sense objectives have been matched mainly to the requirements for Key Stage 2. However, as Maths Makes Sense seeks to contribute to the raising of standards, the end-of-block objectives on occasion match to elements in provision for Key Stage 3. In these instances, the relevant end-of-block objectives are matched to the Northern Ireland Levels of Progression in Using Mathematics across the curriculum for Key Stage 3 which become a statutory part of assessment in 2012/2013.

It should be noted that in Maths Makes Sense the Northern Ireland Key Stage 2 Mathematics Curriculum Processes in Mathematics are a part of virtually every mathematics lesson. Therefore it would not be helpful to include repeatedly statements such as ‘present information and results clearly’ and


‘understand mathematical language and use it to discuss their work and explain their thinking’. Processes statements are included only when they are very much the main feature of the Maths Makes Sense objectives. It should be assumed that other statements of Processes in Mathematics may also be relevant.

To find out more about Maths Makes Sense, please visit our website: www.oxfordprimary.co.uk/mms/


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Maths Makes Sense 5

Block 1

Maths Makes Sense 5 end-of-block objectives

Northern Ireland Curriculum Key Stage 2

Block 1, Arithmetic 1 Write two or three 4-digit whole

numbers vertically and calculate (with more than one tricky column) using addition and subtraction

Use the three operations + / − /÷, with vulgar fractions or mixed numbers with the same denominator

Multiply and divide vulgar fractions and mixed numbers by a whole number.

Processes in MathematicsCommunicating Mathematically present information and results clearly.

NumberUnderstanding Number and Number Notation develop an understanding of place value [to include up to two decimal

places, use this to multiply and divide numbers by 10 and 100;] understand and use vulgar fractions, [decimal fractions and

percentages and explore the relationships between them;]Operations and their Applications engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places, multiply and divide decimals by whole numbers, use these operations to solve problems.]

Block 1, Geometry Name the images of objects that

are points, line segments or polygons in a symmetrical shape

Know the line of symmetry is the perpendicular bisector in a symmetrical shape

Name two congruent shapes in a shape with an axis of symmetry.

Processes in MathematicsCommunicating Mathematically understand mathematical language and use it to discuss their work

and explain their thinking;

Shape and SpaceExploration of Shape construct a range of regular and irregular 2-D shapes, [classify these

through examination of angles and sides,] recognise line [and rotational] symmetry, reflect shapes in a line, [explore tessellations, name and describe common 2-D shapes,] begin to understand congruence in 2-D shapes;

Position, Movement and Direction develop language associated with line and angle, [recognise

properties of acute, obtuse and reflex angles, investigate angles in triangles and quadrilaterals, measure and draw angles up to 360°;]

Block 1, Data and Measure Solve word problems (involving

capacity, volume or length) by using a division Maths Story, identifying the basic Real-Life Story as a Type 1 or Type 2 division

Solve word problems (involving capacity, volume or length) by finding a percentage of a value or the result of a percentage increase or decrease

Choose the correct operations to solve one-step and multi-step word problems involving capacity, volume or length

Make a simple 3D shape by drawing, cutting out and folding a net

Recognise that a cube cut through one diagonal forms two congruent

NumberUnderstanding Number and Number Notation understand and use vulgar fractions, decimal fractions and

percentages and explore the relationships between them;

Measures [understand the relationship between units and convert one metric unit

to another,] use the four operations to solve problems; calculate [perimeter and the areas and] volumes of simple shapes;

Shape and SpaceExploration of Shape construct 3-D shapes, [investigate the number of faces, edges and

vertices on these shapes], name and describe common 3-D shapes, explore the relationship between 2-D and 3-D shapes.


triangular prisms.

Block 1, Arithmetic 2 Complete missing number grids

and missing number sentences Complete sequences involving

square numbers Use information displayed in grids

to solve word problems Solve one- and two-step word

problems involving any of the four operations.

Processes in MathematicsMaking and Monitoring Decisions identify and obtain the information required for a task, [suggesting

appropriate sources to find the information;]

NumberPatterns, Relationships and Sequences in Number explore and predict patterns and sequences of whole numbers, [follow

and devise rules for generating sequences;] understand and use [multiples and factors and] the terms [prime,]

square [and cube, appreciate inverse operations;] understand that a letter can stand for an unknown number.Operations and their Applications engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places, multiply and divide decimals by whole numbers,] use these operations to solve problems.

Handling DataCollecting, Representing and Interpreting Data interpret a wide range of tables, [lists, graphs and diagrams, create

and interpret frequency tables, including those for grouped data;]

Block 1, Reasoning Write a.m./p.m. times using 24-

hour clock notation Write 24-hour times as a.m./p.m.

times Calculate the mean number of days

in four consecutive years Calculate the duration between two

times written using 24-hour notation.

Processes in MathematicsMathematical Reasoning recognise general patterns and relationships and make predictions

about them;

NumberPatterns, relationships and sequences with number explore and predict patterns and sequences of whole numbers; follow

and devise rules for generating sequences; Operations and their Applications engage in a range of activities to develop understanding of the four

operations of number; [appreciate the use of brackets; add and subtract with up to two decimal places; multiply and divide decimals by whole numbers;] use these operations to solve problems.

Measures recognise times on the analogue and digital clocks and understand

the relationship between the 12 and 24-hour clocks, [use timetables.]

Handling DataCollecting, Representing and Interpreting Data understand, calculate [and use] the mean [and range] of a set of

discrete data.


Block 2



Block 2, Arithmetic 1 Write two or three 4-digit decimal

numbers vertically, with up to three decimal places, and calculate with more than one tricky column, using addition and subtraction

Multiply two vulgar fractions where the denominator of one and the numerator of the other are equal.

Processes in MathematicsCommunicating Mathematically present information and results clearly.NumberUnderstanding Number and Number Notation develop an understanding of place value to include up to two decimal

places, [use this to multiply and divide numbers by 10 and 100;] understand and use vulgar fractions, [decimal fractions and

percentages and explore the relationships between them;]Operations and their Applications engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets,] add and subtract with up to two decimal places, [multiply and divide decimals by whole numbers, use these operations to solve problems.]

Block 2, Geometry Name and draw acute angles,

obtuse angles, reflex angles and right angles

Name and calculate vertically opposite angles and supplementary angles

Use a protractor to draw acute angles, obtuse angles, and right angles.


and explain their thinking; interpret situations mathematically using appropriate symbols [or

diagrams;]

Shape and SpacePosition, Movement and Direction understand the notion of angle in the context of turning, recognise

right angles, [understand clockwise and anti-clockwise, know the eight points of the compass, use Logo to understand movement and turning, be introduced to a programming language and use it to create pictures and patterns and to generate shapes;]

develop language associated with line and angle, recognise properties of acute, obtuse and reflex angles, [investigate angles in triangles and quadrilaterals,] measure and draw angles up to 360°;

use co-ordinates to plot and draw shapes in the first quadrant.

Block 2, Data and Measure Appreciate the need for standard

units Know the metric units of mass: g,

kg: length: mm, cm, m, km: and volume/capacity: ml, ℓ, cm3, m3

Know imperial units of measure, e.g. pound, ounce, inch, foot, yard, mile, pint, gallon

Interpret a reading that lies between two unnumbered divisions on a scale

Convert between metric units, e.g. kg and g to kg

Convert between imperial units, e.g. lb and oz to oz.

Measures appreciate important ideas about measurement including [the

continuous nature of measurement and] the need for appropriate accuracy;

understand the relationship between units and convert one metric unit to another, [use the four operations to solve problems;]


Block 2, Arithmetic 2 Use > / < / ≥ / ≤ with positive whole

numbers, e.g. in the form 8 < m < 10

Use a calculator to check if a number is a factor of another number

Distinguish between a factor and a proper factor.

Processes in MathematicsCommunicating Mathematically interpret situations mathematically using appropriate symbols [or

diagrams;]Mathematical Reasoning check results [and consider whether they are reasonable.]

NumberPatterns, Relationships and Sequences in Number understand and use [multiples and] factors [and the terms prime,

square and cube], appreciate inverse operations; understand that a letter can stand for an unknown number.

Block 2, Reasoning Solve algebraic equations that

have an expression which is the sum of two terms using algebraic methods, one term being solely ‘x’ and the other term a 1-digit number, e.g. x + 2 = 5

Solve algebraic equations that have an expression which consists of one term using algebraic methods, a product of ‘x’ and a 1-digit number, e.g. 2x = 6.


square and cube, appreciate inverse operations;] understand that a letter can stand for an unknown number.


Block 3



Block 3, Arithmetic 1 Use a/b and a ÷ b interchangeably,

e.g. 5/8 and 5 ÷ 8 Use the division button on a

calculator to convert vulgar fractions to finite decimal fractions (no vulgar fractions with infinite decimal equivalents)

Use the four operations (+ / − / × / ÷) with combinations of positive and negative numbers, including tricky examples (but not the product of two negative numbers).


diagrams;]

NumberUnderstanding Number and Number Notation understand and use vulgar fractions , decimal fractions [and

percentages] and explore the relationships between them; understand and use negative numbers in context.Operations and their Applications engage in a range of activities to develop understanding of the four


Block 3, Geometry Use a calculator to calculate the

circumference of a circle using C = x d

Use a calculator to calculate the area of a circle using A = x r2.

Measures calculate [perimeter and] the areas [and volumes] of simple shapes;

Shape and SpaceExploration of Shape construct [a range of] regular [and irregular] 2-D shapes, [classify

these through examination of angles and side], recognise line and rotational symmetry, reflect shapes in a line, explore tessellations, name and describe common 2-D shapes, begin to understand congruence in 2-D shapes;]

Block 3, Data and Measure Interpret a calendar Interpret a timetable Use durations of minutes, hours,

days or months in calculations and word problems

Construct a bar chart and use it to find the mode

Understand that the mode is the most common value in a set of data.

Processes in MathematicsCommunicating Mathematically present information and results clearly.Mathematical Reasoning recognise general patterns and relationships and make predictions

about them;

NumberPatterns, relationships and sequences with number explore and predict patterns and sequences of whole numbers; follow

and devise rules for generating sequences;

Measures [recognise times on the analogue and digital clocks and] understand

the relationship between the 12 and 24-hour clocks, use timetables.

Handling DataCollecting, Representing and Interpreting Data collect, classify, record and present data drawn from a range of

meaningful situations, using graphs [tables, diagrams and ICT software;]

interpret a wide range of tables, [lists,] graphs [and diagrams,] create and interpret frequency tables, [including those for grouped data;]


Block 3, Arithmetic 2 Use divisibility tests for 2, 3, 4, 5, 6

and 10 Distinguish between factors and

proper factors.


and explain their thinking;Mathematical Reasoning recognise general patterns and relationships and make predictions

about them; understand and make general statements;


square and cube, appreciate inverse operations;]Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four


Block 3, Reasoning Solve problems involving measures

and fractions by exploring patterns and relationships in diagrams

Solve one-, two- and three-step word problems involving money.


appropriate sources to find the information;] develop a range of strategies for problem-solving, [looking for ways to

overcome difficulties.]

NumberUnderstanding Number and Number Notation understand and use vulgar fractions, [decimal fractions and

percentages and explore the relationships between them;]Money use the four operations to solve problems involving money;


to another,] use the four operations to solve problems;


Block 4



Block 4, Arithmetic 1 Use a grid for long multiplication

with up to 2-digit by 2-digit whole numbers

Use a grid for long multiplication with up to 3-digit by 2-digit decimal numbers (one or two decimal places), with answers up to three decimal places.

Processes in MathematicsCommunicating Mathematically present information and results clearly.Mathematical Reasoning check results and consider whether they are reasonable.

NumberUnderstanding Number and Number Notation develop an understanding of place value to include up to two decimal

places, use this to multiply [and divide] numbers by 10 and 100; estimate and approximate to gain an indication of the size of a solution

to a calculation [or problem;] understand and use [vulgar fractions,] decimal fractions [and

percentages and explore the relationships between them;]Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places,] multiply [and divide] decimals by whole numbers, [use these operations to solve problems.]

Block 4, Geometry Recognise corresponding angles

and know they have the same value

Recognise vertically opposite angles and know they have the same value

Recognise opposite interior angles in a parallelogram and know they have the same value.



Shape and SpacePosition, Movement and Direction understand the notion of angle in the context of turning, [recognise

right angles, understand clockwise and anti-clockwise, know the eight points of the compass, use Logo to understand movement and turning, be introduced to a programming language and use it to create pictures and patterns and to generate shapes;]

develop language associated with line and angle, [recognise properties of acute, obtuse and reflex angles,] investigate angles in triangles and] quadrilaterals, [measure and draw angles up to 360°;]

use co-ordinates to plot and draw shapes in the first quadrant.

Block 4, Data and Measure Interpret a distance-time graph Draw a distance-time graph from

given information Round measures of distance and

time.

Processes in MathematicsMaking and Monitoring Decisions take increasing responsibility for selecting and using the materials and

the mathematics required for their work;Communicating Mathematically present information and results clearly.

Measures develop skills in estimation of [length, ‘weight’, volume/capacity,] time,

[area and temperature;] appreciate important ideas about measurement including [the




meaningful situations, using graphs [tables, diagrams and ICT software;]

interpret a wide range of [tables, lists,] graphs [and diagrams, create and interpret frequency tables, including those for grouped data;]

Block 4, Arithmetic 2 Identify prime numbers from 0-100

using Eratosthenes’ sieve Write numbers as the product of

their prime factors For n as a positive whole number,

respond to a condition that describes a factor, e.g. 11 is a factor of n, and conditions that use the symbols < or ≤, e.g. 22 < n < 55, and write a value of n, i.e. 33 or 44.

Processes in MathematicsCommunicating Mathematically compare their ideas and methods of working with others; interpret situations mathematically using appropriate symbols [or

diagrams;]Mathematical Reasoning check results [and consider whether they are reasonable.]

NumberPatterns, Relationships and Sequences in Number understand and use [multiples and] factors and the terms prime,

[square and cube, appreciate inverse operations;] understand that a letter can stand for an unknown number.

Block 4, Reasoning Solve puzzles by calculating

quantities, e.g. numbers of bricks, and dimensions, e.g. lengths and heights, using pictures of 2D and 3D shapes.

Processes in MathematicsMaking and Monitoring Decisions develop a range of strategies for problem-solving, [looking for ways to

overcome difficulties.]Mathematical Reasoning recognise general patterns and relationships and make predictions

about them;

NumberPatterns, Relationships and Sequences in Number understand and use [multiples and factors and] the terms [prime,

square and] cube, [appreciate inverse operations;] understand that a letter can stand for an unknown number.


to another,] use the four operations to solve problems;

Shape and Space Exploration of Shape [construct a range of regular and irregular 2-D shapes; classify these

through examination of angles and sides; recognise line and rotational symmetry; reflect shapes in a line; explore tessellations;] name and describe common 2-D shapes; [begin to understand congruence in 2-D shapes;]


Block 5



Block 5, Arithmetic 1 Use a grid for long division

including numbers with up to 3-digits divided by 1-digit whole numbers.



places, use this to [multiply and] divide numbers by 10 and 100;Patterns, Relationships and Sequences in Number understand and use [multiples and] factors [and the terms prime,

square and cube,] appreciate inverse operations;Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four


Block 5, Geometry Draw a convex polygon Draw and mark the exterior angles

for a convex polygon Show that the sum of the exterior

angles of a polygon is 360°.


through examination of angles and side, recognise line and rotational symmetry, reflect shapes in a line, explore tessellations, name and describe common 2-D shapes, begin to understand congruence in 2-D shapes;]

Position, Movement and Direction understand the notion of angle in the context of turning, [recognise

right angles, understand clockwise and anti-clockwise, know the eight points of the compass, use Logo to understand movement and turning, be introduced to a programming language and use it to create pictures and patterns and to generate shapes;]

develop language associated with [line and] angle, [recognise properties of acute, obtuse and reflex angles,] investigate angles in triangles and quadrilaterals, [measure and draw angles up to 360°;]

Block 5, Data and Measure Use ratio to convert between metric

units of measure Use ratio to convert between metric

and imperial units of measure Estimate the area of a shape in

cm2.

Measures develop skills in estimation of [length, weight, volume/capacity, time,]

area [and temperature;] understand the relationship between units and convert one metric unit

to another, use the four operations to solve problems;

Block 5, Arithmetic 2 Evaluate terms in an expression

with brackets, e.g. (2 x 3) + (1 x 2) = 6 + 2

Evaluate products in an expression with brackets, e.g. 2 x (4 + 1 x 3) = 2 x (4 + 3) = 2 x 7.

NumberOperations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four

operations of number, appreciate the use of brackets, [add and subtract with up to two decimal places, multiply and divide decimals by whole numbers, use these operations to solve problems.]


Block 5, Reasoning Carry out investigations involving

shapes, numbers and real-life situations using the ‘What if Not’ approach.

Processes in MathematicsMaking and Monitoring Decisions plan and organise their work, learning to work systematically; develop a range of strategies for problem-solving, looking for ways to

overcome difficulties.Mathematical Reasoning recognise general patterns and relationships and make predictions

about them; ask and respond to open-ended questions and explain their thinking; understand and make general statements;

NumberPatterns, Relationships and Sequences in Number explore and predict patterns and sequences of whole numbers, follow

and devise rules for generating sequences; interpret, generalise and use simple relationships expressed in

numerical, spatial and practical situations, [understand and use simple function machines;]

Measures calculate perimeter and the areas [and volumes] of simple shapes;

Shape and SpaceExploration of Shape [construct a range of regular and irregular 2-D shapes, classify these

through examination of angles and side, recognise line and rotational symmetry, reflect shapes in a line, explore tessellations, name and describe common 2-D shapes,] begin to understand congruence in 2-D shapes;


Block 6



Block 6, Arithmetic 1 Multiply decimals numbers with up

to three decimal places by multiples of powers of 10 (product no more than three decimal places), using the ‘logic of the language’

Divide decimal numbers by multiples of powers of 10 (no numbers with more than three decimal places), using the ‘logic of the language’

Use derived products to calculate multiplication and division.

Processes in MathematicsMathematical Reasoning recognise general patterns and relationships [and make predictions

about them;]


places, use this to multiply and divide numbers by 10 and 100;Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places,] multiply and divide decimals by whole numbers, [use these operations to solve problems.]

Block 6, Geometry Recognise, name and sketch

polygons (decagon, heptagon, hexagon, nonagon, octagon, pentagon, quadrilateral, triangle)

Recognise, name and sketch an equilateral triangle, isosceles triangle, right-angled triangle, scalene triangle

Recognise, name and sketch a parallelogram, rectangle, rhombus, square, trapezium

Recognise the various special triangles and quadrilaterals, use the special name and recognise them as the more general polygons.



Shape and SpaceExploration of Shape construct a range of regular and irregular 2-D shapes, classify these

through examination of angles and side, [recognise line and rotational symmetry, reflect shapes in a line, explore tessellations,] name and describe common 2-D shapes, [begin to understand congruence in 2-D shapes;]

Position, Movement and Direction develop language associated with line and angle; [recognise

properties of acute, obtuse and reflex angles;] investigate angles in triangles and quadrilaterals; [measure and draw angles up to 360°;]

Block 6, Data and Measure Calculate durations for times

specified as a.m./p.m. times and 24-hour clock times

Draw and use a double number line showing distance and time to solve word problems involving speed, distance and time

Use calculations to solve word problems involving speed, distance and time.

Processes in MathematicsCommunicating Mathematically compare their ideas and methods of working with others;

Measures understand the relationship between units [and convert one metric unit

to another], use the four operations to solve problems; recognise times on the analogue and digital clocks and understand

the relationship between the 12 and 24-hour clocks, [use timetables.]


Block 6, Arithmetic 2 Evaluate terms in an expression

that includes brackets, e.g. recognise 5 + 4 + 2 × 5 as an expression with three terms, evaluate 5 + 4 + 10 and recognise 5 + (4 + 2) × 5 as an expression with two terms and evaluate 5 + 30

Insert brackets in an expression so it has a specified value, e.g. calculate and write ‘2 × 5 + 1 + 2 = 13 and 2 x (5 + 1) + 2 = 14’ and also insert brackets for 2 × 5 + 1 + 2 to have the value 16.

NumberPatterns, Relationships and Sequences in Number understand and use [multiples and] factors and the terms prime,

[square and cube; appreciate inverse operations]; Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four


Block 6, Reasoning Calculate durations of shop

opening times from information in a grid

Use information in a grid about duration of tracks on a CD to calculate differences between durations, total durations and mean durations

Calculate equivalences and fractions of periods of time using years, days, hours, minutes and seconds.


percentages and explore the relationships between them;]

Measures understand the relationship between units [and convert one metric unit

to another], use the four operations to solve problems; recognise times on the analogue [and digital] clocks and understand

the relationship between the 12 and 24-hour clocks, use timetables.

Handling DataCollecting, Representing and Interpreting Data interpret a wide range of tables, [lists, graphs and diagrams; create

and interpret frequency tables, including those for grouped data;] understand, calculate [and use] the mean [and range] of a set of

discrete data.


For coverage of the following Key Stage 3 Levels of Progression in Using Mathematics objectives please see Maths Makes Sense 5 as

detailed below:

Expansion of the Levels of Progression in Using Mathematics across the Curriculum: Key Stage 3 (Levels 1–7)

Maths Makes Sense 5 Main teaching

Level 6Number and Algebra [add, subtract,] multiply and divide decimals;

Block 4, Arithmetic 1 Block 6, Arithmetic 1

Level 6Number and Algebra understand and use order of precedence in

numerical calculations, including the use of brackets;


Level 6Number and Algebra understand, use and calculate ratio [and

proportion;]

Block 2, Data and Measure Block 5, Data and Measure Block 6, Reasoning

Level 6Number and Algebra use equivalences between fractions, decimals

and percentages to solve problems;

Block 1, Data and Measure

Level 6Number and Algebra use conventional notation in algebra;

Block 2, Reasoning

Level 6Shape, Space and Measures use, convert and calculate measures involving

metric and, where appropriate, imperial units;

Block 2, Data and Measure Block 3, Data and Measure

Level 6Shape, Space and Measures calculate the circumference and area of circles;

Block 3, Geometry

Level 6Shape, Space and Measures understand and use compound measures;


Level 6Shape, Space and Measures use co-ordinates in all four quadrants;

Block 1, Geometry

Level 6Handling Data : work out [and use] the [median and] mode;

Block 3, Data and Measure Block 5, Data and Measure

Level 7Number and Algebra use the four operations with fractions;

Block 2, Arithmetic 1


Maths Makes Sense 6

Block 1



Block 1, Arithmetic 1 Use a grid for long multiplication of

HTU by TU, e.g. 324 × 23 = 7452 Estimate the value of products by

rounding each factor Use the product of a 3-digit whole

number and a 2-digit whole number and, using approximation, work out a related product of decimal numbers



places, use this to multiply [and divide] numbers by 10 and 100; estimate and approximate to gain an indication of the size of a solution

to a calculation [or problem;]Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places], multiply [and divide] decimals by whole numbers, [use these operations to solve problems.]

Block 1, Geometry Find the sum of the exterior angles

of a polygon Find the sum of the interior angles

of a polygon





Position, Movement and Direction understand the notion of angle in the context of turning, [recognise

right angles, understand clockwise and anti-clockwise, know the eight points of the compass, use Logo to understand movement and turning, be introduced to a programming language and use it to create pictures and patterns and to generate shapes];

develop language associated with [line and] angle, [recognise properties of acute, obtuse and reflex angles,] investigate angles in triangles and quadrilaterals, [measure and draw angles up to 360°;]

Block 1, Data and Measure Solve distance word problems

using kilometres Solve volume word problems using

millilitres and litres Solve mass word problems using

grams and kilograms

NumberUnderstanding Number and Number Notation estimate and approximate to gain an indication of the size of a solution

to a calculation or problem;Operations and their Applications develop strategies to add and subtract mentally; engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places, multiply and divide decimals by whole numbers,] use these operations to solve problems.

Measures


understand the relationship between units and convert one metric unit to another, use the four operations to solve problems;

Block 1, Arithmetic 2 Use a short method for

multiplication of up to 3-digit by 2-digit whole numbers, e.g. 712 × 39 = 27768

Use a short method for division of up to 3-digit by 2-digit whole numbers, including remainders, e.g. 474 ÷ 13 = 36 r 6


NumberUnderstanding Number and Number Notation estimate and approximate to gain an indication of the size of a solution

to a calculation or problem;Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four


Block 1, Reasoning Calculate the mean, median, mode

and range of a sample



NumberPatterns, Relationships and Sequences in Number understand that a letter can stand for an unknown number.Understanding Number and Number Notation [count, read, write and] order whole numbers;

Handling DataCollecting, Representing and Interpreting Data understand, calculate [and use] the mean and range of a set of

discrete data.


Block 2



Block 2, Arithmetic 1 Use a grid for long division of

ThHTU by U, e.g. 6342 ÷ 6 = 1057 Estimate the value of quotients by

rounding Use the quotient of a 4-digit whole

number and a 1-digit whole number and, using approximation, work out a related quotient of decimal numbers, e.g. 63.42 ÷ .6 = 105.7

Processes in MathematicsCommunicating Mathematically present information and results clearly.Mathematical Reasoning recognise general patterns and relationships [and make predictions

about them;] check results and consider whether they are reasonable.


places, use this to multiply and divide numbers by 10 and 100; estimate and approximate to gain an indication of the size of a solution

to a calculation [or problem;]Operations and their Applications know the multiplication facts up to 10 x 10; engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets, add and subtract with up to two decimal places, multiply and] divide decimals by whole numbers, [use these operations to solve problems.]

Block 2, Geometry Recognise reflection, translation,

enlargement and rotation as transformations

For an object and its image, recognise and name the transformation



through examination of angles and sides; recognise line and rotational symmetry]; reflect shapes in a line; [explore tessellations; name and describe common 2-D shapes]; begin to understand congruence in 2-D shapes;

Position, Movement and Direction understand the notion of angle in the context of turning; recognise

right angles; understand clockwise and anti-clockwise; [know the eight points of the compass; use logo to understand movement and turning; be introduced to a programming language and use it to create pictures and patterns and to generate shapes;]

Block 2, Data and Measure Draw a pie chart from data

presented in a frequency table

Processes in MathematicsMaking and Monitoring Decisions take increasing responsibility for selecting and using [the materials

and] the mathematics required for their work; Communicating Mathematically interpret situations mathematically using appropriate [symbols or]

diagrams; present information and results clearly.

Handling DataCollecting, Representing and Interpreting Data interpret a wide range of tables, lists, graphs and diagrams, create

and interpret frequency tables, [including those for grouped data;]


Shape and SpacePosition, Movement and Direction [develop language associated with line and angle, recognise

properties of acute, obtuse and reflex angles, investigate angles in triangles and quadrilaterals, measure and] draw angles up to 360°;

Block 2, Arithmetic 2 Convert a vulgar fraction to a

percentage Convert a percentage to a decimal

fraction Convert a decimal fraction to a

percentage


percentages and explore the relationships between them;Patterns, Relationships and Sequences in Number understand that a letter can stand for an unknown number.

Block 2, Reasoning Measure the probability of events,

e.g. the probability of rolling a 3 on a fair dice numbered 1-6 is 1/6

Handling DataIntroduction to Probability become familiar with and use the language of probability; understand possible outcomes of simple random events, understand

that there is a degree of uncertainty about the outcome of some events while others are certain or impossible;


Block 3



Block 3, Arithmetic 1 Use equivalent fractions in

calculations using each of the four operations

NumberUnderstanding Number and Number Notationunderstand and use vulgar fractions, [decimal fractions and percentages and explore the relationships between them;]

Block 3, Geometry Use a protractor to measure the

size of an angle, in degrees, and a ruler to measure the length of a line, in millimetres

Draw the image of a polygon in a mirror line

Complete the drawing of a named, partially-drawn shape on a pair of axes

Calculate the size of the two equal angles in an isosceles triangle

Sort quadrilaterals according to their properties

Complete the co-ordinates of the corners of a named shape using knowledge of its properties

Find the angle of rotation for an object and image polygon


and explain their thinking; present information and results clearly.

Measures appreciate important ideas about measurement including [the


Shape and SpaceExploration of Shape construct a range of regular and irregular 2-D shapes, classify these

through examination of angles and side, recognise line [and rotational] symmetry, reflect shapes in a line, [explore tessellations,] name and describe common 2-D shapes, [begin to understand congruence in 2-D shapes;]

Position, Movement and Direction develop language associated with line and angle, recognise properties

of acute, obtuse [and reflex angles], investigate angles in triangles and quadrilaterals, measure [and draw] angles up to 360°;

Block 3, Data and Measure Solve problems involving ratio and

proportion by scaling up or scaling down

Interpret and read a scale to measure mass

Compare the usefulness of different weighing scales for measuring mass


mathematics required for their work;Patterns, Relationships and Sequences in Number understand that a letter can stand for an unknown number.

Measures develop skills in estimation of [length,] weight, [volume/capacity, time,

area and temperature;] appreciate important ideas about measurement including the

continuous nature of measurement and the need for appropriate accuracy;

understand the relationship between units and convert one metric unit to another, use the four operations to solve problems;

Block 3, Arithmetic 2 Write the ratio of one quantity to

another Write a quantity as a fraction or

percentage of the total quantity Solve word problems by calculating

a quantity following a percentage increase or decrease

Processes in MathematicsMaking and Monitoring Decisions develop a range of strategies for problem-solving, looking for ways to

overcome difficulties.



Handling Data Collecting, Representing and Interpreting Data


interpret a wide range of tables,[ lists, graphs and diagrams; create and interpret frequency tables, including those for grouped data;]

Block 3, Reasoning Interpret a distance-time graph for

distance travelled and time taken Interpret a distance-time graph for

faster and slower (speed) Interpret a temperature-time graph

for rise, fall and difference in temperature



Handling DataCollecting, Representing and Interpreting Data explain their work orally and/or through writing and draw conclusions; interpret a wide range of [tables, lists,] graphs [and diagrams, create

and interpret frequency tables, including those for grouped data;]


Block 4



Block 4, Arithmetic 1 Calculate with negative numbers

using the four operations (using 1 + -1 = 0 with tricky examples)

Calculate with vulgar fractions using the four operations (using equivalent fractions and improper fractions with tricky examples)


percentages and explore the relationships between them] understand and use negative numbers [in context.]

Block 4, Geometry Draw the lines of symmetry of a

polygon Write the number of lines of

symmetry for any polygon Identify and write the order of

rotational symmetry for any polygon

Shape and SpaceExploration of Shape [construct a range of regular and irregular 2-D shapes, classify these

through examination of angles and side,] recognise line and rotational symmetry, reflect shapes in a line, [explore tessellations,] name and describe common 2-D shapes, begin to understand congruence in 2-D shapes;

Block 4, Data and Measure Collect, select, process and

present data, making use of ICT Interpret data to answer questions

and solve problems Construct and interpret frequency

tables, bar charts and pie charts, making use of ICT

Plan and carry out a survey, suggesting and developing lines of enquiry, to collect discrete or discrete grouped data


appropriate sources to find the information;] plan and organise their work, learning to work systematically;Mathematical Reasoning ask and respond to open-ended questions and explain their thinking;


meaningful situations, using graphs, tables, diagrams and ICT software;

explain their work orally and/or through writing and draw conclusions; interpret a wide range of tables, [lists,] graphs and diagrams, create

and interpret frequency tables, including those for grouped data; design and use a data collection sheet, interpret the results, [enter

information in a database or spreadsheet, and interrogate and interpret the results;]

Block 4, Arithmetic 2 Solve word problems involving

money using addition, subtraction, multiplication or division

Add and subtract ‘squares’ and ‘cubes’ of numbers, e.g. find the sum of 102 and 8.73

Calculate the product of a given number closest to a specified number, e.g. find the product of 28 that is closest to 298

Processes in MathematicsMaking and Monitoring Decisions take increasing responsibility for selecting and using the [materials

and] mathematics required for their work;

NumberPatterns, Relationships and Sequences in Number understand and use multiples and factors and the terms [prime]

square and cube, [appreciate inverse operations;]Operations and their Applications engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets], add and subtract with up to two decimal places, multiply and divide decimals by whole numbers, use these operations to solve problems.

Money use the four operations to solve problems involving money;


Block 4, Reasoning Identify terms and products in

expressions Evaluate expressions with and

without brackets, e.g. 3 + 2 × 3 = 9, (3 + 2) × 3 = 15

Insert brackets in an expression for it to take a specified value, e.g. insert brackets so that the expression 3 + 2 × 3 has the value 15

NumberOperations and their Applications engage in a range of activities to develop understanding of the four



Block 5



Block 5, Arithmetic 1 Use the formulae for diameter,

circumference and area of a circle Use the formula for the area of a

triangle Use the formula for the volume of a

cuboid and a cylinder

NumberPatterns, Relationships and Sequences in Number understand that a letter can stand for an unknown number.

Measures calculate [perimeter and] the areas and volumes of simple shapes;


through examination of angles and sides; recognise line and rotational symmetry; reflect shapes in a line; explore tessellations]; name and describe common 2-D shapes; [begin to understand congruence in 2-D shapes;]

[construct 3-D shapes; investigate the number of faces, edges and vertices on these shapes]; name and describe common 3-D shapes; [explore the relationship between 2-D and 3-D shapes.]

Block 5, Geometry Calculate an exterior angle of a

regular polygon Calculate an interior angle of a

regular polygon Calculate the third angle in a

triangle

Processes in Mathematics Communicating Mathematically present information and results clearly.


operations of number; [appreciate the use of brackets; add and subtract with up to two decimal places; multiply and divide decimals by whole numbers; use these operations to solve problems.]

Shape and SpacePosition, Movement and Direction develop language associated with [line and] angle, [recognise

properties of acute, obtuse and reflex angles], investigate angles in triangles and quadrilaterals, [measure and draw angles up to 360°;]

Block 5, Data and Measure Convert between yards and metres Calculate the perimeter and the

area of compound shapes Calculate surface area and volume

of cuboids Solve problems involving

dimensions and volume of cuboids


mathematics required for their work; develop a range of strategies for problem-solving, looking for ways to

overcome difficulties.


operations of number; [appreciate the use of brackets; add and subtract with up to two decimal places; multiply and divide decimals by whole numbers; use these operations to solve problems.]

Measures calculate perimeter and the areas and volumes of simple shapes;


Block 5, Arithmetic 2 Use inequalities to identify a range

of possible values for a number, e.g. find the value of m, where 15 < m < 20 and m is a whole number

Use algebraic notation for the sum, difference, product and quotient of two numbers, e.g. m + n, m – n, mn, m/n

Find the greatest or smallest sums, differences, products and quotients of two numbers with a range of possible values

Calculate the product of a given number closest to a specified number, e.g. calculate the product of 34 closest to 241


and explain their thinking; interpret situations mathematically using appropriate symbols [or

diagrams;]

NumberPatterns, Relationships and Sequences in Number understand that a letter can stand for an unknown number.Operations and their Applications engage in a range of activities to develop understanding of the four

operations of number, [appreciate the use of brackets; add and subtract with up to two decimal places, multiply and divide decimals by whole numbers, use these operations to solve problems.]

Block 5, Reasoning Solve linear equations that involve

one operation with whole and decimal numbers

NumberPatterns, Relationships and Sequences in Number [understand and use multiples and factors and the terms prime square

and cube], appreciate inverse operations; understand that a letter can stand for an unknown number.


Block 6



Block 6, Arithmetic 1 Write a vulgar fraction as a decimal

fraction to three decimal places, using a calculator for division, e.g. 7/11 = .636

Convert decimal fractions to vulgar fractions using tenths, hundredths and thousandths, e.g. .625 = 625/1000

Write recurring infinite decimals as abbreviations using the conventional of ‘dots’ above one or two digits, e.g. write .83333333 as .83


diagrams;]Mathematical Reasoning recognise general patterns [and relationships and make predictions

about them;]

NumberUnderstanding Number and Number Notation understand and use vulgar fractions, decimal fractions [and

percentages] and explore the relationships between them;

Block 6, Geometry Draw the perpendicular bisector of

a line segment Draw the bisector of an angle Draw the circum-circle of a triangle Draw the in-circle of a triangle





Position, Movement and Direction develop language associated with line and angle, [recognise

properties of acute, obtuse and reflex angles, investigate angles in triangles and quadrilaterals], measure [and draw angles] up to 360°;


.

Block 6, Data and Measure Understand the ‘golden ratio’ Φ

(phi), is a constant with an approximate value of 1.618

Calculate ratios, and use ratios to calculate lengths and construct shapes

Plan and develop lines of enquiry to research a topic, interpret and evaluate findings

Collect, organise, select and present information using appropriate methods, including the use of ICT

Work effectively in a group


mathematics required for their work; identify and obtain the information required for a task, suggesting

appropriate sources to find the information; plan and organise their work, learning to work systematically; develop a range of strategies for problem-solving, looking for ways to

overcome difficulties.Communicating Mathematically understand mathematical language and use it to discuss their work

and explain their thinking; compare their ideas and methods of working with others; present information and results clearly.Mathematical Reasoning recognise general patterns and relationships and make predictions

about them; ask and respond to open-ended questions and explain their thinking;

Number Patterns, Relationships and Sequences in Number understand that a letter can stand for an unknown number.

Measures appreciate important ideas about measurement, including the

continuous nature of measurement and the need for appropriate accuracy;

Block 6, Arithmetic 2 Solve number puzzles involving

algebraic terms, use flow diagrams to identify inverse operations

Recognise algebraic representations of odd and even numbers

Identify two factors of a number, including numbers represented algebraically, and divide it by each factor, e.g. for 3k, 3k ÷ 3 = k, 3k ÷ k = 3


diagrams;]


square and cube,] appreciate inverse operations; [interpret, generalise and use simple relationships expressed in

numerical, spatial and practical situations,] understand and use simple function machines;

understand that a letter can stand for an unknown number.

Block 6, Reasoning Express vulgar fractions as

percentages

NumberUnderstanding Number and Number Notation understand and use vulgar fractions, [decimal fractions] and



For coverage of the following Key Stage 3 Range objectives, please see Maths Makes Sense 6 as

detailed below:

Expansion of the Levels of Progression in Using Mathematics across the Curriculum: Key Stage 3 (Levels 1–7)

Maths Makes Sense 6 Main Teaching and Daily Practices

Level 6Number and Algebra [add, subtract,] multiply [and divide] decimals;

Block 1, Arithmetic Block 2, Arithmetic 1

Level 6Number and Algebra round to a given number of decimal places;

Block 4, Arithmetic 2 Block 5, Arithmetic 2 Block 5, Reasoning Block 6, Arithmetic 1 Block 6, Reasoning

Level 6Number and Algebraunderstand and use precedence in numerical calculations, including the use of brackets;

Block 4, Reasoning

Level 6Number and Algebra understand, use [and calculate] ratio and proportion;

Block 2, Arithmetic 2 Block 2, Reasoning Block 3, Arithmetic 1 Block 3, Data and Measure Block 3, Arithmetic 2 Block 6, Data and Measure

Level 6Number and Algebra add and subtract fractions, including mixed numbers;


Level 6Number and Algebra use equivalences between fractions, decimals and

percentages to solve problems;

Block 3, Arithmetic 2 Block 6, Reasoning

Level 6Number and Algebra use appropriate formulae;


Level 6Number and Algebra use conventional notation in algebra;

Block 5, Arithmetic Block 5, Arithmetic 2 Block 5, Reasoning Block 6, Arithmetic 2

Level 6Shape, Space and Measure use, convert and calculate measures involving metric,

and where appropriate, imperial measures;


Level 6Shape, Space and Measure calculate perimeters and areas of composite shapes

involving squares, rectangles [and triangles];



Level 6 Shape, Space and Measure calculate surface areas and [composite] volumes of

cubes and cuboids;


Level 6Shape, Space and Measure calculate the circumference and area of circles;


Level 6Shape, Space and Measures understand and use compound measures;

Block 3, Reasoning

Level 6Number and Algebra use co-ordinates in all four quadrants;

Block 2, Geometry Block 3, Geometry

Level 6Handling Data [construct and] interpret a variety of [diagrams and]

graphs for discrete and continuous data;

Block 2, Data and Measure Block 3, Reasoning

Level 6Handling data work out [and use] the median and mode

Block 1, Reasoning

Level 7Number and Algebra use the four operations with fractions;


Level 7Number and Algebra manipulate simple algebraic [expressions,] equations

[and formulae];

Block 5, Reasoning Block 6, Arithmetic 2

Level 7Shape, Space and Measure enlarge a 2-D shape by a given scale factor;

Block 2, Geometry

Level 7Handling Data apply their knowledge of the rules of probability to

calculate an outcome or combination of outcomes;

Block 2, Reasoning


Documents

Maths Makes Sense 1 end-of-block objectivesassets.oxfordowl.co.uk/2014/10/02/09/41/59/650/mms_ni… · Web viewSolve word problems (involving capacity, volume