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Emerging |
Developing |
Securing |
Mastering |
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Ordering Numbers |
The student is working towards developing understanding this topic. |
Understanding how to use the number line to order positive and negative integers. |
Order decimals on a number line. |
Order fractions. |
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Using equality and inequality symbols |
The student is working towards developing understanding this topic. |
Understanding what the symbols = < > mean |
Use the symbol ≠ |
Use the symbols ≤ ≥ |
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Comparing with percentages |
The student is working towards developing understanding this topic. |
Understanding that percentage means ‘number of parts out of 100’ |
Compare two quantities where one is a decimal, one is a percentage |
Compare two quantities where one is a fraction, one is a percentage |
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Factors and multiples |
The student is working towards developing understanding this topic. |
Understanding the difference between a factor and a multiple |
Use the concepts of Highest Common Factor & Lowest Common Multiple |
Use the concepts and vocabulary of HCF & LCM |
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Powers and roots |
The student is working towards developing understanding this topic. |
Understanding what a power and a root is |
Use integer powers & associated real roots (square & cube) |
Distinguish between exact representations of roots and their decimal approximations. |
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Negative arithmetic |
The student is working towards developing understanding this topic. |
Understanding that to apply the four operations to calculations involving negatives requires knowledge of how the presence of negative values affects the answer |
Use one of the four operations with negatives |
Use more than one of the four operations with negatives |
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Fraction arithmetic |
The student is working towards developing understanding this topic. |
Understanding that the four operations with fractions require knowledge of different methods to the four operations with integers |
Use one of the four operations with fractions |
Use more than one of the four operations with fractions |
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Order of operations |
The student is working towards developing understanding this topic. |
Understanding why it is important to have a priority of operations |
Calculate a value using the order of operations (brackets and the four operations) |
Calculate a value using the order of operations including powers and roots |
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Rounding to decimal places |
The student is working towards developing understanding this topic. |
Understand that rounding to given decimal places is the same mathematical process as rounding to 10,100,1000 etc |
Round a number to 1 decimal place |
Round measures to 2 or more decimal places |
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Ratio in its simplest form |
The student is working towards developing understanding this topic. |
Understanding what ratio notation means |
Reduce a ratio to its simplest form |
Reduce a ratio to its simplest form when conversion between units is required first |
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Dividing into a ratio |
The student is working towards developing understanding this topic. |
Understanding that an amount can be divided into a ratio |
Divide a given quantity into two parts and give the amount of one part. |
Express division into two parts as a ratio. |
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Expressing a quantity as a fraction of another |
The student is working towards developing understanding this topic. |
Understanding that one quantity can be expressed as a fraction of another |
Express one quantity as fraction/percentage of another where fraction is < 1 |
Express one quantity as fraction/percentage of another where fraction is > 1 |
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Using algebraic notation |
The student is working towards developing understanding this topic. |
Understanding why some algebraic expressions can be simplified using standard notation and others cannot |
Interpret algebraic notation: ab(axb), 3y(y+y+y), a2 axa), a3( axaxa), a/b (a÷b) |
Simplifying perimeter of shapes by writing them as algebraic expressions. |
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Language of algebra |
The student is working towards developing understanding this topic. |
Understanding that there are different words to describe different combinations of variables, constants and symbols |
Know the difference between an expression, an equation and a term |
Identify a coefficient, a variable and a constant in an algebraic expression |
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Expanding brackets |
The student is working towards developing understanding this topic. |
Understanding that a number directly before a bracket represents multiplying everything in the bracket by that number |
Multiply a single term over a bracket |
Simplify by collecting like terms after expanding two pairs of single brackets |
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Substituting into expressions |
The student is working towards developing understanding this topic. |
Understanding that substituting numbers into an algebraic expression will result in a value |
Substitute positive numerical values into an algebraic expression |
Substitute numerical values (positive & negative) into scientific formulae. |
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Equations of lines parallel to axes |
The student is working towards developing understanding this topic. |
Understanding that by looking at commonalities of the coordinates of a straight line parallel to the axes, you can write the equation of that line |
Recognise graphs of linear functions parallel to the axes |
Sketch graphs of linear functions parallel to the axes |
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Equations of y=x & y=-x |
The student is working towards developing understanding this topic. |
Understanding that by looking at commonalities of the coordinates of a straight line y=x or y=-x, you can write the equation of that line |
Recognise y=x or y=-x |
Sketch y=x or y=-x |
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Solving linear equations |
The student is working towards developing understanding this topic. |
Understanding that solving equations means working out what the value of the unknown variable is |
Use a process to solve a 1 step linear equation |
Use a process to solve a 2 step linear equation |
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Term to term rule |
The student is working towards developing understanding this topic. |
Understanding that a sequence can be generated from a term to term rule and a starting number |
Generate terms of a sequence from a term to term rule. |
Identify if a sequence is arithmetic or geometric |
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Fibonacci sequences |
The student is working towards developing understanding this topic. |
Understanding how a Fibonacci sequence works |
Recognise the Fibonacci sequence |
Generate the terms of a Fibonacci sequence |
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Pie Charts |
The student is working towards developing understanding this topic. |
Understanding that to construct or interpret a pie chart accurately, you need to know the size of the angle that 1 person represents |
Interpret a pie chart by working out the size of the angle that 1 person represents |
Construct a pie chart by working out the size of the angle that 1 person represents |
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Mean & Mode |
The student is working towards developing understanding this topic. |
Understanding that mean and mode are ways to describe the average of a set of data |
Calculate the mean or mode of a list of integers |
Calculate the mean or mode from a table of ungrouped data |
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Median & range |
The student is working towards developing understanding this topic. |
Understanding why working out the range and median require ordering the data first |
Calculate the median or range of a list of integers |
Calculate the median or range from a table of ungrouped data |
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Properties of quadrilaterals |
The student is working towards developing understanding this topic. |
Understanding what makes a shape be a quadrilateral |
Illustrate quadrilaterals based on given properties including side lengths and pairs of parallel lines, number of right angles |
Illustrate quadrilaterals based on given properties including information about their diagonals |
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Properties of polygons |
The student is working towards developing understanding this topic. |
Understanding the word polygon |
Know the difference between regular polygons and irregular polygons |
Illustrate polygons (excluding quadrilaterals) based on given properties including name of shape, side lengths and number of sides |
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Congruent transformations |
The student is working towards developing understanding this topic. |
Understanding that a shape on a grid can be transformed to a congruent shape |
Construct single transformations of shapes using translation, rotation & reflection |
Identify and describe single transformations of shapes using translation, rotation & reflection |
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Labelling shapes with mathematical notation |
The student is working towards developing understanding this topic. |
Understanding the importance of labelling parts of shapes with correct mathematical notation |
Know how to describe using mathematical notation: lines (eg ab), parallel, perpendicular lines, right angles. |
Use standard conventions for labelling the sides & angles of triangle ABCabc |
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Plans and elevations |
The student is working towards developing understanding this topic. |
Understanding why a 3D shape needs front, side and plan view to show it in 2D |
Interpret plans & elevations of 3D shapes |
Construct plans & elevations of 3D shapes |
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Area of a trapezium |
The student is working towards developing understanding this topic. |
Understanding how to label the parts of a trapezium correctly to use in the formula 1/2(a+b)h |
Calculate the area of a trapezium |
Solve problems involving area of trapeziums. |
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Properties of 3D shapes |
The student is working towards developing understanding this topic. |
Understanding the definitions of face, edge, vertex (& vertices) |
Identify properties from a transparent diagram (faces, surfaces, edges vertices) of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres |
List the properties when no diagram is given (faces, surfaces, edges vertices) of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres |
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Volume of a cuboid |
The student is working towards developing understanding this topic. |
Understanding why calculating the volume of a cuboid requires the knowledge of height, length, width |
Calculate the volume of a cuboid |
Solve problems involving volumes of cuboids. |
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Angles in parallel lines |
The student is working towards developing understanding this topic. |
Understanding why a transversal intersecting parallel lines will always create the same set of 4 angles on all parallel lines |
Use the relationship between parallel lines and a transversal to calculate a missing angle |
Correctly use the definition of alternate or corresponding angles in a problem involving a missing angle |
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Language of probability |
The student is working towards developing understanding this topic. |
Understanding that situations can be described using a probability word |
Use appropriate language to describe unequally likely outcomes. |
Explaining why "it either does happen or it doesn't" should not be described as even chance (or 50/50) |
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Using a probability scale |
The student is working towards developing understanding this topic. |
Understanding that the likelihood of any situtation can be shown on a 0-1 probability scale |
Record a situtation on a 0-1 probability scale |
Record the frequency of outcomes on the 0-1 probability scale |
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Constructing Venn diagrams |
The student is working towards developing understanding this topic. |
Understanding why an item can always be placed into exactly one section of a Venn diagram |
Enter items correctly into a Venn diagram |
Using correct Venn notation, describe the elements in a given section of a Venn diagram |