
4Fourth Standards
Top Mathematicians

Number, money and measure

4.NS.1.1
Estimation and rounding
• Having investigated the practical impact of inaccuracy and error, I can use my knowledge of tolerance when choosing the required degree of accuracy to make reallife calculations.
• Rounds answers to a specified significant figure.
• Demonstrates that the context of the question needs to be considered when rounding.
• Demonstrates the impact of inaccuracy and error, for example, the impact of rounding an answer before the final step in a multistep calculation.
• Uses a given tolerance to decide if there is an allowable amount of variation of a specified quantity, for example, dimensions of a machine part, 235 mm ± 1 mm. 

4.115

4.215

4.315

4.415

4.515

4.615

4.710

4.815

4.915

4.1020

4.1115

4.1210


4.NS.1.10
Patterns and relationships
• Having explored how reallife situations can be modelled by number patterns, I can establish a number sequence to represent a physical or pictorial pattern, determine a general formula to describe the sequence, then use it to make evaluations and solve related problems.
• I have discussed ways to describe the slope of a line, can interpret the definition of gradient and can use it to make relevant calculations, interpreting my answer for the context of the problem.
• Having investigated the pattern of the coordinate points lying on a horizontal or vertical line, I can describe the pattern using a simple equation.
• I can use a given formula to generate points lying on a straight line, plot them to create a graphical representation then use this to answer related questions.
• Determines a general formula for the nth term to describe a sequence and uses it to solve related problems, linear examples only.
• Calculates the gradient of lines in a coordinate diagram.
• Draws conclusions about the gradient of a line, for example, 'does the ramp meet building regulations?'.
• Communicates the gradient of vertical and horizontal lines and states the equation of these lines as x = a or y = b or equivalent.
• Uses a given formula to plot a straight line onto a Cartesian diagram. 

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4.1475

4.1485

4.14915

4.15010

4.15110

4.1525

4.1535

4.1545

4.1555

4.15610

4.1575

4.3515

4.5415

4.11615

4.11715

4.11815

4.1195

4.1205

4.12110

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4.12315

4.12410


4.NS.1.11
Expressions and equations
• Having explored the distributive law in practical contexts, I can simplify, multiply and evaluate simple algebraic terms involving a bracket.
• I can find the factors of algebraic terms, use my understanding to identify common factors and apply this to factorise expressions.
• Having discussed the benefits of using mathematics to model reallife situations, I can construct and solve inequalities and an extended range of equations.
• Expands brackets using the distributive law and simplifies.
• Solves an extended range of linear equations involving the distributive law, for example, ax ± b = cx ± d, where a, b, c and d are integers.
• Solves linear inequalities, including on simple closed intervals.
• Solves problems by expressing the given information appropriately as an equation, inequation or formula.
• Evaluates algebraic expressions involving a bracket.
• Factorises expressions with a numeric common factor. 

4.15815

4.15915

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4.16310

4.1645

4.1655

4.1665

4.1675

4.1685

4.1695

4.1715

4.1725

4.17310

4.17410

4.17510

4.1765

4.17715

4.1785

4.12410


4.NS.1.2
Number and number processes
• Having recognised similarities between new problems and problems I have solved before, I can carry out the necessary calculations to solve problems set in unfamiliar contexts.
• I have investigated how introducing brackets to an expression can change the emphasis and can demonstrate my understanding by using the correct order of operations when carrying out calculations.
• Interprets and solves multistep problems using the four operations.
• Applies the correct order of operations in all calculations, including those with brackets. 

4.1315

4.1415

4.1515

4.1620

4.1715

4.1820

4.1915

4.2020

4.215

4.2215

4.2315

4.2420

4.2515

4.2610

4.2710

4.285

4.2915

4.3015

4.3115

4.3215

4.3315

4.3415

4.3515

4.365

4.3715

4.3815

4.3910

4.4020

4.4115

4.4220

4.4315

4.4415

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4.4720

4.4810

4.495

4.505

4.5120

4.5220

4.5310

4.5415

4.555

4.5620

4.5720

4.5815

4.595


4.NS.1.3
Multiples, factors and primes
I have investigated strategies for identifying common multiples and common factors, explaining my ideas to others, and can apply my understanding to solve related problems.
I can apply my understanding of factors to investigate and identify when a number is prime. 

4.NS.1.4
Powers and roots
• I have developed my understanding of the relationship between powers and roots and can carry out calculations mentally or using technology to evaluate whole number powers and roots, of any appropriate number.
• Within reallife contexts, I can use scientific notation to express large or small numbers in a more efficient way and can understand and work with numbers written in this form.
• Shows understanding that square roots of whole numbers can have positive and negative values, for example, ˆš9 = ±3.
• Uses knowledge of the inverse relationship between powers and roots to evaluate whole number roots of any appropriate number, ³ˆš27 = 3.
• Uses knowledge of mathematical notation to express numbers in scientific notation. 

4.710

4.1210

4.6010

4.6115

4.6215

4.6310

4.6415

4.655

4.6610

4.6710

4.6810

4.695

4.7010

4.7110

4.7210

4.7310

4.7410


4.NS.1.5
Fractions, decimal fractions and percentages
• I can choose the most appropriate form of fractions, decimal fractions and percentages to use when making calculations mentally, in written form or using technology, then use my solutions to make comparisons, decisions and choices.
• I can solve problems involving fractions and mixed numbers in context, using addition, subtraction or multiplication.
• Using proportion, I can calculate the change in one quantity caused by a change in a related quantity and solve reallife problems.
• Chooses the most efficient form of fractions, decimal fractions or percentages when making calculations.
• Uses calculations to support comparisons, decisions and choices.
• Calculates the percentage increase or decrease of a value.
• Applies addition, subtraction and multiplication skills to solve problems involving fractions and mixed numbers.
• Uses knowledge of proportion to solve problems in reallife which involve changes in related quantities. 

4.215

4.315

4.415

4.515

4.615

4.815

4.915

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4.1620

4.1715

4.1820

4.1915

4.2020

4.215

4.2215

4.2315

4.2420

4.2515

4.2610

4.2710

4.285

4.2915

4.3015

4.3115

4.3215

4.3315

4.3415

4.3515

4.365

4.3715

4.3815

4.3910

4.4020

4.4115

4.4220

4.4315

4.4415

4.5815

4.595

4.7520

4.7615

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4.785

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4.8015

4.8115

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4.1195

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4.12315

4.12410


4.NS.1.6
Money
• I can discuss and illustrate the facts I need to consider when determining what I can afford, in order to manage credit and debt and lead a responsible lifestyle.
• I can source information on earnings and deductions and use it when making calculations to determine net income.
• I can research, compare and contrast a range of personal finance products and, after making calculations, explain my preferred choices.
• Applies understanding of credit and debit in relation to earnings and deductions.
• Uses budgeting skills to manage income effectively and justifies spending and saving choices.
• Calculates net income by selecting appropriate information.
• Compares a range of personal finance products.
• Communicates the impact of financial decisions.
• Applies knowledge of currency conversion to determine best value. 

4.915

4.3815

4.3910

4.4020

4.4115

4.4220

4.4315

4.4415

4.4515

4.4615


4.NS.1.7
Time
• I can research, compare and contrast aspects of time and time management as they impact on me.
• I can use the link between time, speed and distance to carry out related calculations.
• Demonstrates effective time management skills, for example, working with different time zones or making plans, including across midnight.
• Carries out calculations involving speed, distance and time involving decimal fraction hours.
• Calculates time durations across hours, days and months. 

4.5120

4.5220

4.5310


4.NS.1.8
Measurement
• I can apply my knowledge and understanding of measure to everyday problems and tasks and appreciate the practical importance of accuracy when making calculations.
• Through investigating reallife problems involving the surface area of simple 3D shapes, I can explore ways to make the most efficient use of materials and carry out the necessary calculations to solve related problems.
• I have explored with others the practicalities of the use of 3D objects in everyday life and can solve problems involving the volume of a prism, using a formula to make related calculations when required.
• Demonstrates understanding of the impact of truncation and premature rounding.
• Calculates the area of kites, parallelograms and trapeziums.
• Uses formulae and calculates the surface area of cylinders, cuboids and triangular prisms.
• Calculates the volume of triangular prisms and cylinders using formulae. 

4.1255

4.1265

4.1275

4.12815

4.1295

4.1305

4.1315

4.1325

4.1335

4.1345

4.1355

4.1365

4.1375


4.NS.1.9
Mathematics  its impact on the world, past, present and future
• I have discussed the importance of mathematics in the real world, investigated the mathematical skills required for different career paths and delivered, with others, a presentation on how mathematics can be applied in the workplace.
• Contributes to discussions and presentations on the role of mathematics in everyday life and in the workplace.
• Investigates the mathematical skills required for a range of careers, including those in STEM subjects. 

4.NS.1.1

Shape, position and movement

4.GMD.1.1
Properties of 2D shapes and 3D objects
• I have explored the relationships that exist between the sides, or sides and angles, in rightangled triangles and can select and use an appropriate strategy to solve related problems, interpreting my answer for the context.
• Having investigated the relationships between the radius, diameter, circumference and area of a circle, I can apply my knowledge to solve related problems.
• Calculates the length of any side of a rightangled triangle using the Theorem of Pythagoras.
• Calculates the size of an angle in a rightangled triangle using trigonometry.
• Calculates the length of a side in a rightangled triangle using trigonometry.
• Uses the formula C = π D or C = 2π r to calculate the circumference of a circle.
• Uses the formula A = πr2 to calculate the area of a circle.
• Calculates diameter and radius of a circle when given the area or circumference. 

4.1315

4.1325

4.1335

4.17915

4.18010

4.1815


4.GMD.1.2
Angle, symmetry and transformation
• Having investigated the relationship between a radius and a tangent and explored the size of the angle in a semicircle, I can use the facts I have established to solve related problems.
• I can apply my understanding of the properties of similar figures to solve problems involving length and area.
• I can plot and describe the position of a point on a 4quadrant coordinate grid.
• I can apply my understanding of the 4quadrant coordinate system to move, and describe the transformation of, a point or shape on a grid.
• Having investigated patterns in the environment, I can use appropriate mathematical vocabulary to discuss the rotational properties of shapes, pictures and patterns and can apply my understanding when completing or creating designs.
• Describes rotational properties of shapes, pictures and patterns, including the order of rotation.
• Uses knowledge of rotational symmetry to complete designs.
• Uses a fourquadrant Cartesian grid to read and plot coordinates.
• Applies understanding of translation to reflect or translate an object on a fourquadrant grid.
• Uses similarity to find unknown lengths of 2D shapes.
• Applies knowledge of the relationship between the tangent and radius to calculate sizes of missing angles.
• Applies knowledge of triangles, angles and circles, including semicircles, to solve problems.
• Identifies transformation by reflection or translation of a point or shape on a grid. 

4.1315

4.1325

4.1335

4.1825

4.1835

4.1845

4.1855

4.1865

4.1875

4.18810

4.18910

4.1905

4.1915

4.19210

4.1935

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4.19510

4.19610

4.1975

4.1985

4.1995


4.GMD.1.1

Information handling

4.ID.1.1
Data and analysis
• I can evaluate and interpret raw and graphical data using a variety of methods, comment on relationships I observe within the data and communicate my findings to others.
• In order to compare numerical information in reallife contexts, I can find the mean, median, mode and range of sets of numbers, decide which type of average is most appropriate to use and discuss how using an alternative type of average could be misleading.
• I can select appropriately from a wide range of tables, charts, diagrams and graphs when displaying discrete, continuous or grouped data, clearly communicating the significant features of the data.
• Interprets raw and graphical data.
• Uses statistical language, for example, correlations, to describe identified relationships.
• Calculates the mean, median, mode and range of a data set.
• Selects the most appropriate statistical diagram to display a given data set, for example, stem and leaf.
• Justifies the most appropriate statistical diagram to display a given data set.
• Uses different types of charts to display discrete, continuous and grouped data appropriately. 

4.20010

4.2015

4.2025

4.2035

4.20410

4.2055

4.2065

4.2075

4.20810

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4.2135

4.2145

4.2155

4.2165

4.2175

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4.22010

4.22110

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4.2235

4.2245

4.2255

4.2265

4.2275

4.2285

4.2295

4.2305

4.2315

4.2325

4.1555


4.ID.1.2
Ideas of chance and uncertainty
• By applying my understanding of probability, I can determine how many times I expect an event to occur, and use this information to make predictions, risk assessment, informed choices and decisions.
• Calculates the probability and determines the expected occurrence of an event.
• Applies knowledge and skills in calculating probability to make predictions. 

4.2335

4.2345

4.2355

4.23615

4.2375

4.2385

4.2395

4.2405


4.ID.1.1