6th Grade Math Checklist: What Your Child Should Know

Geometry

Your child is developing advanced spatial skills — working with 3D shapes and nets, using coordinate grids with negative numbers, calculating angles, and understanding geometric transformations like reflection and translation.

• Angles in triangles (age 11+)

  Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning

  • Calculate the area of a trapezium using A = ½(a + b) × h and explain why the formula works
  • Find the volume of a triangular prism by calculating cross-sectional area × length
  • Derive the formula for the volume of a cylinder as π × r² × h by reasoning from the prism formula

• Angle sums in triangles and polygons

  Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons

  • Calculate a missing angle in a triangle by subtracting the known angles from 180°
  • Find the sum of interior angles in a hexagon by dividing it into triangles
  • Calculate each interior and exterior angle of a regular polygon given the number of sides

• Types of angles (age 8+)

  Use and interpret standard geometric diagram conventions: mark right angles with a small square, equal lengths with single or double tick marks, and equal angles with arc marks; label angles in three-letter notation (∠ABC) and individual angles with a single letter or number; draw diagrams showing angles at a point, angles on a straight line, and angles inside polygons with these conventions; read diagrams with these marks to identify given information and find unknown values

  • Mark a right angle with a small square symbol in a diagram and explain what it means
  • Use tick marks to show equal lengths in a shape and double tick marks for a second pair of equal sides
  • Read and interpret angle notation (e.g. angle ABC) and identify the angle being referred to in a diagram

• Coordinate Transformations

  Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

  • Reflect a shape in a given mirror line (including diagonal lines) and state the coordinates of the image
  • Rotate a shape about a given centre by 90° or 180° and describe the result
  • Translate a shape by a given vector and verify that lengths and angles are preserved

• Coordinates (age 10+)

  Describe positions on the full coordinate grid (all four quadrants); use coordinates with negative values

  • Plot points with negative coordinates such as (−3, 4) and (2, −5) on a four-quadrant grid
  • Identify the quadrant in which a given point lies
  • Describe the position of a shape using coordinates in all four quadrants

• Translating and reflecting shapes

  Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes

  • Translate a triangle 3 units right and 2 units down on a coordinate grid and state the new coordinates
  • Reflect a shape in the x-axis and list the coordinates of the reflected vertices
  • Explain how translation changes coordinates (add/subtract) while reflection changes the sign of one coordinate

• Classifying shapes by properties

  Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties

  • Explain why all squares are rectangles but not all rectangles are squares
  • Place quadrilaterals in a hierarchy diagram showing subset relationships
  • Identify properties shared by all parallelograms and explain why rhombuses and rectangles are special cases

• Numbers on a number line

  Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin

  • Identify the x-axis, y-axis, and origin on a coordinate grid
  • Explain that (3, 5) means go 3 along the x-axis and 5 up the y-axis
  • Distinguish (2, 4) from (4, 2) by explaining each coordinate's meaning

• Plotting points in the first quadrant

  Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context

  • Plot the point (4, 7) accurately on a first-quadrant grid
  • Graph a set of data pairs (e.g. time vs distance) as points on the coordinate plane
  • Read coordinates of a plotted point and explain what they represent in a given scenario

• Angles in triangles (age 10+)

  Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties

  • Find a missing angle in a triangle given two angles (using angle sum = 180°)
  • Calculate a missing angle in a quadrilateral (angle sum = 360°)
  • Calculate the interior angle of a regular hexagon from the angle sum formula

• Types of angles (age 11+)

  Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons

  • Use correct notation for line segments (AB), angles (∠ABC), and parallel lines (AB ∥ CD)
  • Sketch a regular hexagon and describe its rotational and reflective symmetry
  • Identify and label perpendicular and parallel lines in a given figure using standard symbols

• Properties of triangles and quadrilaterals

  Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

  • List and verify properties of a parallelogram (opposite sides parallel/equal, opposite angles equal, diagonals bisect each other)
  • Explain why a square is a special case of both a rectangle and a rhombus
  • Derive the relationship between the radius, diameter, and circumference of a circle

• 2-D shapes (age 10+)

  Draw 2-D shapes using given dimensions and angles, using a ruler and protractor accurately

  • Draw a triangle with sides 5 cm, 7 cm and an included angle of 60°
  • Construct a rectangle with given length and width using a ruler and set square
  • Draw a regular pentagon given the side length and interior angle

• Understanding angles (age 10+)

  Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties

  • Find a missing angle at a point given the other angles (total 360°)
  • Use the straight-line property (angles sum to 180°) to find an unknown angle
  • Identify vertically opposite angles and use the property that they are equal to find unknowns

• Measuring angles (age 11+)

  Draw and measure line segments and angles accurately using ruler and protractor, and interpret scale drawings to extract real measurements

  • Draw a triangle accurately given two sides and the included angle (SAS)
  • Measure angles in a geometric figure to the nearest degree using a protractor
  • Read a scale drawing to determine actual lengths, explaining the scale used

• Understanding angles (age 11+)

  Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems

  • Find a missing angle using the fact that angles on a straight line sum to 180°
  • Use vertically opposite angles are equal to set up and solve an equation for an unknown
  • Combine multiple angle facts in a single diagram to find several missing angles step by step

• Transformations on a grid

  Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

  • Reflect a shape in a given mirror line on a grid and label the new coordinates
  • Translate a shape by a given number of squares horizontally and vertically and describe the movement
  • Rotate a shape 90° or 180° about a given centre on a grid and check the image is congruent to the original

• Nets of 3-D Shapes

  Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net

  • Draw the net of a cube, cuboid, or triangular prism and fold it mentally to identify which faces connect
  • Build a 3-D shape from its net and check that all faces, edges, and vertices match
  • Identify which of several given nets will fold into a specific 3-D shape and explain why the others won't

• 3-D shapes (age 10+)

  Recognise, describe, and build simple 3-D shapes, including making nets

  • Identify which net will fold into a given 3-D shape
  • Construct the net of a triangular prism and fold it to verify
  • Describe a 3-D shape by naming its faces, edges, and vertices

• 3-D shapes (age 11+)

  Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections

  • Count and describe the faces, edges, and vertices of a triangular prism and a square-based pyramid
  • Describe the 2-D cross-section produced by slicing a cylinder horizontally or a cone vertically
  • Use properties of 3-D shapes to determine whether a given net will fold into a specified solid

• Parts of a circle

  Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius

  • Label the radius, diameter, and circumference on a circle diagram
  • Calculate the diameter given a radius of 4.5 cm (diameter = 9 cm)
  • Explain the relationship between radius and diameter in their own words

Fractions

Your child is mastering advanced fraction operations — adding, subtracting, and multiplying fractions with different denominators, dividing with fractions, and solving real-world problems using visual models and mathematical reasoning.

• Decimals and fractions (age 10+)

  Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts

  • Convert 3/8 to 0.375 by dividing 3 ÷ 8
  • State that 1/5 = 0.2 = 20% from memory
  • Use fraction–decimal–percentage equivalences to compare 30%, 1/3, and 0.35 and put them in order

• Fractions of a whole (age 10+)

  Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers

  • Explain that 3/4 means 3 ÷ 4 and verify by showing 3/4 × 4 = 3
  • Solve: '9 people share a 50-pound sack equally — how many pounds each?' and express the answer as 5 5/9
  • Use a visual model to show that sharing 3 wholes among 4 people gives each person 3/4

• Multiplying fractions (age 11+)

  Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)

  • Calculate a fraction of a given amount by multiplying
  • Calculate a percentage of a given amount by converting to a decimal and multiplying
  • Use the operator interpretation to solve multi-step problems involving discounts, taxes, and portions

• Decimal & Percent Notation

  Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value

  • Read and write decimal numbers correctly, identifying the value of each digit (ones, tenths, hundredths)
  • Use the % symbol correctly and explain that per cent means 'out of 100'
  • Convert between simple fractions, decimals, and percentages (e.g. 1/2 = 0.5 = 50%) and explain why they are equal

• Mixed & Improper Fractions

  Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

  • Add, subtract, multiply, and divide with positive and negative integers
  • Apply formal written methods to calculations with decimals of any size
  • Perform all four operations with proper fractions, improper fractions, and mixed numbers

• Simplifying Fractions

  Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator

  • Simplify 18/24 to 3/4 by identifying the HCF of 18 and 24
  • Express 2/3 and 5/8 with a common denominator of 24
  • Explain why dividing numerator and denominator by a common factor produces an equivalent fraction

• Dividing fractions (unit fractions)

  Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result

  • Compute (1/3) ÷ 4 = 1/12 and explain using a visual model of splitting 1/3 into 4 equal parts
  • Create a story context for (1/6) ÷ 3 and solve it
  • Verify (1/3) ÷ 4 = 1/12 by showing (1/12) × 4 = 1/3

• Decimals and fractions (age 11+)

  Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms

  • Convert any terminating decimal to a fraction in simplest form
  • Convert any fraction with a denominator whose prime factors are only 2 and 5 to a terminating decimal
  • Explain why some fractions produce terminating decimals and others do not

• Area with Fractions

  Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths

  • Tile a 2/3 × 3/4 rectangle with 1/12 squares and count to find area = 6/12 = 1/2
  • Explain why the number of unit-fraction tiles equals the product of the two fractions
  • Calculate the area of a rectangle with sides 1 1/2 and 2/3 using fraction multiplication

• Dividing unit fractions and whole numbers

  Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations

  • Solve: '3 people share 1/2 lb of chocolate equally — how much each?' (1/6 lb)
  • Solve: 'How many 1/3-cup servings in 2 cups of raisins?' (6 servings)
  • Create a story context for a given unit-fraction division expression

• Multiplication as scaling

  Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1

  • Predict without calculating whether 3/4 × 7 is greater or less than 7
  • Explain why multiplying by 5/3 makes a number larger and multiplying by 2/5 makes it smaller
  • Relate multiplying a/b by n/n = 1 to the principle of fraction equivalence

• Dividing by Fractions

  Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend

  • Compute 4 ÷ (1/5) = 20 and explain: 'How many fifths fit in 4 wholes?'
  • Create a story context for 6 ÷ (1/4) and solve it
  • Verify 4 ÷ (1/5) = 20 by showing 20 × (1/5) = 4

• Real-world fraction multiplication

  Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations

  • Solve: 'A recipe needs 2 1/3 cups of flour; you want to make 1 1/2 batches. How much flour?'
  • Draw a fraction model to represent and solve a multiplication word problem
  • Check the reasonableness of a fraction product in context using estimation

• Dividing fractions

  Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions

  • Divide a fraction by a fraction using the reciprocal method
  • Use visual fraction models to represent and explain fraction division
  • Create story contexts for fraction division problems and solve them

• Multiplying fractions (age 10+)

  Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form

  • Compute (2/3) × (4/5) = 8/15 and show with an area model
  • Use a visual model to demonstrate (2/3) × 4 = 8/3 = 2 2/3
  • Simplify the product 3/4 × 2/3 = 6/12 = 1/2

• Adding Fractions (Unlike Denominators)

  Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator

  • Compute 2/3 + 5/4 by converting to twelfths: 8/12 + 15/12 = 23/12
  • Subtract 1 3/5 from 3 1/4 using a common denominator
  • Explain the strategy of finding a common denominator and verify using a visual model

• Fraction Word Problems

  Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness

  • Solve: 'Tara ate 2/5 of a pizza and Sam ate 1/3. How much did they eat together?'
  • Recognise that 2/5 + 1/2 ≠ 3/7 because 3/7 < 1/2 but the sum should exceed 1/2
  • Estimate a fraction sum using benchmarks (0, 1/2, 1) before computing exactly

• Comparing fractions (age 10+)

  Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks

  • Order 3/4, 7/8, 5/6, and 11/12 from smallest to largest
  • Compare 7/5 and 4/3 using common denominators
  • Place improper fractions and mixed numbers on a number line in correct order

Multiplication & Division

Your child is advancing to sophisticated multiplication and division — using formal written methods for complex calculations, working with decimals, and applying the order of operations to solve multi-step problems.

• Long multiplication (age 10+)

  Fluently multiply multi-digit whole numbers (up to 4 digits by 2 digits) using the formal written method of long multiplication

  • Correctly compute 2,463 × 37 using long multiplication
  • Explain each partial product in a long multiplication and why they are added
  • Multiply a four-digit number by a two-digit number without procedural errors

• Division with remainders (age 10+)

  Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate

  • Compute 4,752 ÷ 13 using long division and express the remainder as a fraction
  • Decide whether to round up or down a division remainder in a real-life context (e.g. buses needed)
  • Explain each step of the long division algorithm for a 4-digit ÷ 2-digit calculation

• Rounding Answers

  Solve problems which require answers to be rounded to specified degrees of accuracy

  • Compute a division and round the result to one decimal place as specified
  • Determine the appropriate degree of accuracy for a measurement context (e.g. round to nearest penny)
  • Solve a problem where an unrounded decimal answer must be interpreted in context (e.g. whole containers needed)

• Brackets in Expressions

  Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols

  • Evaluate 3 × (4 + 5) by computing inside the parentheses first
  • Evaluate {2 × [3 + (7 − 1)]} with nested grouping symbols
  • Insert parentheses into an expression to make it equal a target value

• Order of operations

  Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations

  • Explain why 8 + 2 × 5 = 18 (not 50) by referencing multiplication before addition
  • Evaluate a multi-step expression like 12 ÷ 3 + 4 × 2 correctly as 12
  • State the correct order: brackets, then orders/exponents, then multiplication/division (L→R), then addition/subtraction (L→R)

• Writing Number Sentences

  Write simple numerical expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g. recognise that 3 × (18932 + 921) is three times as large as 18932 + 921)

  • Write an expression for 'add 8 and 7, then multiply by 2' using parentheses
  • Explain what 4 × (365 − 12) represents without computing it
  • Compare two expressions and determine which is larger without evaluating

• Decimal place value

  Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)

  • Correctly compute 4.56 × 7 using a written method
  • Use place-value reasoning to explain why 3.2 × 5 = 16.0
  • Model a decimal multiplication using an area diagram or expanded form

• Division with Decimals

  Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers

  • Compute 14.76 ÷ 4 using a written method to get 3.69
  • Explain how to continue long division past the decimal point to obtain a decimal quotient
  • Solve a context problem that requires dividing a decimal amount equally (e.g. sharing £18.60 among 5 people)

• Multi-step problems: choosing operations

  Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts

  • Solve a three-step word problem involving a mix of all four operations
  • Explain why particular operations were chosen for each step of a multi-step problem
  • Identify and correct an error in a multi-step solution that used the wrong operation

• Using inverse operations

  Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations

  • Use addition and subtraction as inverse operations to check and solve problems
  • Use multiplication and division as inverse operations to check and solve problems
  • Recognise that squaring and square-rooting are inverse operations

• Multiplying and dividing (age 10+)

  Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart

  • Compute 3.456 × 100 = 345.6 correctly
  • Compute 45.2 ÷ 1000 = 0.0452 correctly
  • Explain why multiplying by 10 shifts each digit one place to the left

• Factors, multiples, and primes

  Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems

  • List all factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6)
  • State the first five multiples of 7
  • Find the common factors of 24 and 36

• Estimation to check answers to calculations

  Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

  • Estimate 487 × 23 by rounding to 500 × 20 and use this to check a calculated answer
  • Determine whether an exact answer or an estimate is more appropriate in a given context
  • Spot an unreasonable answer by comparing with a quick mental estimate

• Ratio (age 11+)

  Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions

  • Evaluate expressions involving brackets, indices, and all four operations in the correct order
  • Explain why the order of operations is necessary to avoid ambiguity
  • Use the reciprocal of a number and understand that a number multiplied by its reciprocal gives 1

• Ratio (age 10+)

  Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts

  • Mentally compute 45 × 8 by partitioning into 40 × 8 + 5 × 8
  • Use known facts to derive 6.5 × 4 mentally
  • Solve a multi-operation mental calculation such as 250 × 3 + 500 and explain the strategy used

• Dividing by two-digit numbers

  Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context

  • Use short division to compute 3,648 ÷ 16 efficiently
  • Explain when short division is more appropriate than long division
  • Interpret a remainder as a decimal or fraction in a measurement context

• Factors, multiples, and primes (age 11+)

  Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property

  • Express any integer as a product of its prime factors using index notation
  • Find the HCF and LCM of two numbers using prime factorisation
  • Apply the unique factorisation theorem to explain why every number has exactly one set of prime factors

• Sign Rules for Multiplication

  Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient

  • Apply the sign rules when multiplying two integers (positive × negative, negative × negative)
  • Apply the sign rules when dividing two integers
  • Solve multi-step real-world problems involving all four operations with positive and negative rational numbers

Algebra

Your child is beginning to work with algebra — using letters to represent unknown numbers, creating and following rules for number patterns, and translating word problems into mathematical equations.

• Numbers on a number line

  Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

  • Write an inequality from a worded constraint (e.g., 'must be at least 12' → x ≥ 12)
  • Represent the solution set of an inequality on a number line with open or closed circles
  • Solve a one-step or two-step inequality such as 3x + 1 < 10

• Coordinates (age 11+)

  Plot and read coordinates in all four quadrants of the Cartesian plane, using positive and negative x- and y-values to describe positions precisely

  • Plot points with negative coordinates accurately in all four quadrants
  • Identify the quadrant a point belongs to from its coordinate signs
  • Read coordinates from a graph including fractional and negative values

• Using Simple Formulae

  Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))

  • Substitute values into P = 2(l + w) to find the perimeter of a rectangle
  • Use the formula for area of a triangle (A = 1/2 × b × h) given base and height values
  • Interpret a formula expressed in words and use it to compute an output

• Writing Algebraic Equations

  Express missing number problems algebraically using letters for unknowns; translate word problems into equations

  • Write 'I think of a number, double it, and add 5 to get 17' as 2n + 5 = 17
  • Solve a one-step equation such as 3x = 24 and explain the reasoning
  • Express a word problem as an algebraic equation and find the unknown value

• Algebraic Notation

  Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently

  • Read and interpret expressions using standard algebraic conventions for multiplication, division, and powers
  • Write algebraic expressions from word descriptions using correct notation
  • Understand that juxtaposition means multiplication and that a/b means a divided by b

• Solving Linear Equations

  Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

  • Solve one-step and two-step linear equations in one variable
  • Solve equations requiring expansion of brackets and collection of like terms
  • Solve equations with the unknown on both sides and with fractional or negative coefficients

• Collecting Like Terms

  Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence

  • Identify like terms in an algebraic expression
  • Combine like terms involving positive and negative coefficients
  • Simplify expressions involving multiple variables and constant terms

• Expanding Single Brackets

  Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers

  • Multiply a single positive term over a bracket to expand the expression
  • Multiply a negative term over a bracket, correctly handling signs
  • Combine expanding brackets with collecting like terms to simplify fully

• Expressions & Equations Vocabulary

  Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)

  • Define and distinguish between expression, equation, and inequality
  • Identify terms, coefficients, and factors in algebraic expressions
  • Use the vocabulary of algebra precisely in mathematical discussions

• Algebraic Transformations

  Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations

  • Translate a word problem or real-world situation into an algebraic expression or formula
  • Construct a table of values from an algebraic rule
  • Plot the corresponding graph and interpret it in the context of the problem

• Substituting into Formulae

  Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations

  • Substitute positive and negative values into algebraic expressions and evaluate
  • Substitute values into formulae involving multiple operations and powers
  • Use correct order of operations when evaluating expressions after substitution

• Generating Sequences

  Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither

  • Continue a sequence given a term-to-term rule involving addition, subtraction, or multiplication
  • Generate the first five terms from a position-to-term formula such as 3n − 2
  • Classify sequences as arithmetic (constant difference), geometric (constant ratio), or other

• Number Pattern Relationships

  Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane

  • Generate sequences starting at 0 with rules 'add 3' and 'add 6'; observe terms in one are twice the other
  • Form ordered pairs from corresponding terms and plot them on a coordinate grid
  • Explain informally why the relationship between the two sequences holds

• Equations with Two Unknowns

  Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)

  • List all whole-number pairs (a, b) where a + b = 12 with a, b > 0
  • Find three pairs that satisfy 2x + y = 20
  • Explain systematically how to generate all integer solutions to a two-variable equation within a given range

• Systematic Listing

  Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)

  • List all possible meal combinations from 3 starters and 4 mains
  • Organise combinations into a systematic table to ensure none are missed
  • Explain why the total number of combinations equals the product of the options in each category

• Linear number sequences

  Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule

  • Continue the sequence 2.5, 4.0, 5.5, ... and state the rule as 'add 1.5'
  • Generate terms of a sequence that crosses zero (e.g. 3, 1, −1, −3, ...)
  • Describe the term-to-term rule for a given linear sequence and predict the 10th term

Ratio & Proportion

Your child is learning to compare quantities and solve problems involving ratios, proportions, percentages, and scale — essential skills for understanding relationships between numbers in real-world contexts.

• Compound Units

  Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

  • Calculate average speed given distance and time, converting between km/h and m/s if needed
  • Compare unit prices of two products sold in different quantities to find the better deal
  • Use the density formula to find mass, volume, or density given the other two values

• Scale and similar shapes (age 11+)

  Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa

  • Calculate a real-life distance from a map measurement using a given scale (e.g. 1:25,000)
  • Draw a scale diagram of a room using a chosen scale factor
  • Convert between map distance and actual distance in problems involving different units

• One Quantity as a Fraction

  Express one quantity as a fraction of another where the result may be less than 1 or greater than 1, and interpret the meaning in context

  • Express 45 minutes as a fraction of 2 hours (= 3/8)
  • Express a larger quantity as a fraction of a smaller one and explain why the result exceeds 1
  • Simplify the resulting fraction and interpret its meaning in the original context

• Calculating Percentages

  Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison

  • Calculate 15% of 360 by finding 10% and 5% and combining
  • Compare two discounts given as percentages of different original prices
  • Explain a strategy for finding any percentage of an amount using known percentage facts

• Scale and similar shapes

  Solve problems involving similar shapes where the scale factor is known or can be found

  • Find the missing side of a similar rectangle given a scale factor of 3
  • Determine the scale factor between two similar triangles from given side lengths
  • Use a scale factor to enlarge or reduce a shape and verify that all sides are in the same ratio

• Percentages as Fractions

  Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%

  • Convert fluently between percentages, fractions, and decimals
  • Express one quantity as a percentage of another
  • Calculate percentage increases and decreases and interpret percentages greater than 100%

• Unit Conversions

  Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate

  • Convert between area units such as cm² and m² using the square of the linear scale factor
  • Perform multi-step conversions (e.g. convert 2.5 hours to seconds via minutes)
  • Convert volume units such as cm³ to litres and explain the relationship

• Ratio Problems

  Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

  • If the ratio of red to blue beads is 3:5 and there are 15 blue beads, find the number of red beads
  • Use multiplication facts to find the missing value: 'For every 2 apples there are 5 oranges; if there are 20 oranges, how many apples?'
  • Explain the multiplicative relationship between two quantities in a ratio context

• Ratio Notation

  Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations

  • Write a ratio from a word problem and simplify it (e.g. 12:8 = 3:2)
  • Convert a ratio to equivalent fractions of a whole (e.g. 3:2 means 3/5 and 2/5)
  • Simplify ratios involving decimals or fractions by finding a common multiplier

• Understanding fractions

  Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

  • Share 40 sweets between two children in the ratio 3:5
  • Solve: 'Tom gets twice as many as Sam and Sam gets three times as many as Jo. If there are 30 altogether, how many does each get?'
  • Use fraction knowledge to explain why sharing in ratio 2:3 means one person gets 2/5 of the total

• Dividing Quantities by Ratio

  Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole

  • Share £60 between two people in the ratio 2:3 by finding the value of one part
  • Express the result of sharing 24 sweets as 10 and 14 in ratio form as 5:7
  • Solve problems involving three-part ratios (e.g. divide 180 in the ratio 1:2:3)

• Bar Models for Ratios

  Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer

  • Draw a bar model to represent a ratio problem — e.g. sharing £20 in the ratio 3:2 by drawing 5 equal blocks
  • Use a bar model to solve a proportion problem and explain each step
  • Compare bar models with other representations (tables, double number lines) and explain when each is most useful

• Percentages (age 9+)

  Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole)

  • Explain the difference between a 'ratio' and a 'proportion' using a concrete example like mixing paint
  • Use 'per cent' correctly and convert between fractions, decimals, and percentages in context
  • Define 'scale factor' and use it to describe how a shape has been enlarged or reduced

• Proportional Reasoning Vocabulary

  Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts

  • Distinguish between 'direct proportion' and 'inverse proportion' with real-world examples
  • Use 'rate', 'speed', and 'density' correctly and explain what units they are measured in
  • Calculate using compound measures — e.g. work out the speed of a car that travels 120 miles in 2 hours

• Proportion Graphs

  Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed

  • Plot pairs of proportional values on a coordinate grid and draw the straight line through the origin
  • Explain why a directly proportional relationship always passes through (0,0)
  • Read a proportion graph to find an unknown value — e.g. 'If 3 kg costs £6, how much does 5 kg cost?'

Number Representation & Place Value

Your child is mastering large numbers and decimals — reading, writing, and comparing numbers up to 10 million, understanding how decimal places work, and using negative numbers in real-world contexts like temperature and money.

• Place Value × 10 and ÷ 10

  Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left

  • Explain that the 4 in 0.04 is 1/10 of the 4 in 0.4
  • State that a digit moving one place left is ×10 and one place right is ÷10
  • Compare the value of the 6 in 6,000 and in 0.006

• Reading and writing numbers (age 10+)

  Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning

  • Write 347.392 in expanded form: 3×100 + 4×10 + 7×1 + 3×(1/10) + 9×(1/100) + 2×(1/1000)
  • Compare 0.372 and 0.38 using place-value reasoning
  • Write 'five and sixty-two thousandths' as 5.062

• Fractions on a number line (age 11+)

  Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations

  • Order a mixed set of positive and negative integers, decimals, and fractions
  • Use the symbols =, ≠, <, >, ≤, ≥ correctly in mathematical statements
  • Compare numbers presented in different forms such as 0.75 and 3/4

• Numbers to Ten Million

  Solve number and practical problems involving reading, writing, ordering, comparing, rounding, and negative numbers up to 10,000,000

  • A country's population is 8,274,500 — round to the nearest million for a headline
  • Order the depths of three ocean trenches given in metres including negative values
  • Estimate the total attendance at three events by rounding each to the nearest 100,000

• Reading and writing numbers to 10,000,000

  Read, write, order, and compare numbers up to 10,000,000 and determine the value of each digit

  • Write 4,302,561 in words
  • Order four seven-digit numbers from smallest to largest
  • State the value of the 7 in 7,045,200 as seven million

• Reading Decimal Places

  Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)

  • State the value of each digit in 2.635 (2 ones, 6 tenths, 3 hundredths, 5 thousandths)
  • Explain the relationship between adjacent decimal places (each place is ten times smaller)
  • Write a number given digit values (e.g. 4 ones, 0 tenths, 7 hundredths, 3 thousandths = 4.073)

• Fractions on a number line

  Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line

  • Identify the value of any digit in numbers of any size including decimals
  • Place positive and negative integers, decimals, and fractions on a number line
  • Use place value to compare and order numbers across the full number system

• Decimal place value

  Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy

  • Round 3.4567 to 2 decimal places (3.46)
  • Round 7,654,321 to the nearest 100,000 (7,700,000)
  • Use rounding to estimate 4.83 × 2.17 ≈ 5 × 2 = 10

• Decimal place value (age 11+)

  Round numbers and measures to an appropriate degree of accuracy including to a specified number of decimal places or significant figures

  • Round numbers to a given number of decimal places
  • Round numbers to a given number of significant figures
  • Choose an appropriate degree of accuracy for a given context

• Square and cube numbers

  Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations

  • Calculate squares, cubes, and higher integer powers of whole numbers
  • Find square roots and cube roots of perfect squares and perfect cubes
  • Recognise key powers (powers of 2 up to 2¹⁰, powers of 3 up to 3⁵, etc.) and distinguish exact roots from approximations

• Measuring temperature

  Use negative numbers in context (temperature, finance, sea level); calculate intervals across zero

  • The temperature falls from 3°C to −5°C — what is the drop? (8 degrees)
  • Calculate the difference between a bank balance of −£120 and £350
  • Order −7, −3, 0, 2, 5 on a number line and find the interval from −7 to 5

• Patterns with Powers of Ten

  Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)

  • Write 10⁴ = 10,000 and explain the exponent means four factors of 10
  • Explain why 3.4 × 10² = 340 by describing the decimal shift
  • Predict 2.56 × 10³ without calculating and explain the pattern

• Numbers on a number line

  Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements

  • Define absolute value as distance from zero on a number line
  • Calculate the absolute value of positive and negative rational numbers
  • Distinguish between comparing absolute values and comparing signed numbers in real-world contexts

Measurement

Your child is mastering advanced measurement skills — calculating volume and area using formulas, converting between different units of measurement, and solving real-world problems involving length, mass, and capacity.

• Area of Triangles & Parallelograms

  Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)

  • Calculate the area of a parallelogram with base 8 cm and height 5 cm
  • Calculate the area of a triangle with base 12 cm and height 7 cm
  • Explain why the area of a triangle is half the area of a related parallelogram

• Miles & Kilometres

  Convert between miles and kilometres using the approximate relationship (5 miles ≈ 8 km)

  • Convert 40 miles to approximately 64 km
  • Explain why the conversion factor between miles and km is approximately 1.6
  • Use the miles↔km relationship to compare a 10 km race with a 6-mile run

• Volume as additive

  Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms

  • Decompose an L-shaped solid into two cuboids and calculate total volume
  • Solve a real-world problem requiring the volume of a composite figure (e.g. a step-shaped structure)
  • Explain why splitting a composite solid into rectangular prisms allows calculation of total volume

• Decimal place value

  Convert among different-sized standard measurement units within a given system (e.g. 5 cm to 0.05 m) using decimal notation to up to three decimal places; convert between smaller and larger units of length, mass, volume, and time

  • Convert 3,250 g to 3.25 kg using decimal notation
  • Convert 0.45 km to 450 m
  • Explain the relationship between mm, cm, m, and km using powers of 10

• Measurement Conversions

  Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts

  • Solve: 'A recipe uses 0.75 kg of flour. How many grams are needed for 3 batches?'
  • Compare 2.5 litres and 2,450 ml by converting to the same unit
  • Solve a multi-step problem involving time, distance, and unit conversion

• Estimating answers (age 10+)

  Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)

  • Use V = l × w × h to find the volume of a cuboid 4 cm × 3 cm × 5 cm = 60 cm³
  • Explain why packing a prism with unit cubes gives the same result as multiplying edge lengths
  • Compare volumes of two cuboids and identify which has greater capacity

• Perimeter (age 10+)

  Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically

  • Draw two rectangles with area 24 cm² but different perimeters
  • Find two shapes with perimeter 20 cm but different areas
  • Explain why a long thin rectangle and a square can have the same area but different perimeters

• Counting Unit Cubes

  Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units

  • Count unit cubes in a 3D diagram to determine volume in cm³
  • Measure the volume of a small container by filling it with centimetre cubes
  • Express a measured volume using the correct cubic unit notation

• Measuring length (age 10+)

  Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units

  • Explain what 'volume' means for a 3D shape and how it differs from area
  • Identify a unit cube and explain that it represents one cubic unit of volume
  • Determine the volume of a small solid by counting the unit cubes that fill it

Mathematical Thinking

Your child is developing advanced mathematical reasoning skills — learning to construct logical arguments, make connections between different mathematical concepts, and solve complex real-world problems involving fractions, algebra, and ratio.

• Advanced Multi-Step Problems

  Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations

  • Break down a three-step ratio problem into sub-problems and plan a solution pathway
  • Identify which quantities are known/unknown in an algebraic word problem and set up equations
  • Use estimation to check whether a decimal division answer is reasonable before finalising

• Understanding fractions (age 10+)

  Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations

  • Translate a word problem into an algebraic equation and also represent it on a bar model
  • Plot data from a table onto a coordinate grid and interpret the relationship
  • Explain how a pie chart, a fraction, and a percentage all represent the same proportion

• Real-World Mathematical Modelling

  Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations

  • Choose a bar model or double number line to represent a ratio problem and solve it
  • Model a volume problem with a labelled diagram, apply the formula, and interpret the result in context
  • Determine whether a measurement answer should be rounded and to what degree of accuracy

• Advanced Maths Vocabulary

  Communicate with mathematical precision: use correct vocabulary for ratio, proportion, algebra, volume, coordinate geometry, and circle parts; specify units including cm³, m³, and miles/km; use notation for algebraic expressions and order of operations accurately

  • Use 'radius', 'diameter', and 'circumference' correctly when describing a circle
  • Distinguish between an expression, an equation, and a formula in mathematical writing
  • Specify units correctly when presenting volume calculations (e.g. 60 cm³ not just 60)

• Constructing mathematical arguments

  Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches

  • Prove that a given angle must be 60° by chaining angle facts in a logical sequence
  • Find and explain the error in a peer's fraction division calculation
  • Construct a counter-example to disprove a false conjecture (e.g. 'multiplying always makes bigger')

• Choosing Maths Tools

  Select and use tools and representations strategically: choose between mental methods, formal written methods, algebraic approaches, coordinate grids, and technology based on the demands of the problem

  • Explain why long division is more appropriate than mental methods for 4,752 ÷ 13
  • Choose a coordinate grid approach to verify a translation rather than computing from a description alone
  • Select a formula-based approach rather than counting cubes to find volume efficiently

• Order of operations (age 10+)

  Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently

  • Use the property that all rectangles are parallelograms to deduce missing angle facts
  • Recognise that 3 × (n + 5) = 3n + 15 by applying distributive structure
  • Use the equivalence 1/8 = 0.125 = 12.5% flexibly to solve a comparison problem

• Generalising with repeated reasoning

  Recognise and use repeated reasoning to generalise: describe algebraic rules for nth terms, use properties of operations to simplify, and verify generalisations with specific cases

  • Explain that the interior angle sum of an n-sided polygon is (n−2) × 180° based on the pattern for triangles, quadrilaterals, pentagons
  • Predict the 20th term of a linear sequence by identifying and applying the general rule
  • Generalise that dividing by n always gives a denominator of n in the fraction, for any whole numbers

Probability

• Complementary events

  Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

  • Verify that probabilities of all outcomes listed for a spinner sum to 1
  • Calculate the probability of NOT rolling a 6 as 1 − 1/6 = 5/6
  • Identify an error in a probability distribution where the values do not sum to 1

• The Probability Scale

  Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible

  • Place everyday events on a 0-to-1 probability scale with justification
  • Explain why a fair six-sided die gives each number a probability of 1/6
  • Distinguish between equally likely outcomes (fair coin) and unequally likely outcomes (biased spinner)

• Experimental probability

  Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

  • Conduct a coin-toss experiment, record results in a frequency table, and calculate relative frequencies
  • Compare experimental results with theoretical probability and explain discrepancies
  • Predict that relative frequency approaches theoretical probability as the number of trials increases

• Calculating Simple Probability

  Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations

  • Calculate the probability of drawing a blue marble from a bag of 3 blue and 7 red as 3/10
  • Use the formula P(event) = favourable outcomes ÷ total outcomes to solve at least three different problems
  • Explain why increasing the number of favourable outcomes increases the probability

• The 0-to-1 Probability Scale

  Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages

  • Place events on a number line from 0 (impossible) to 1 (certain), expressing positions as fractions or decimals
  • Explain that a probability of 0.5 means 'even chance' and connect this to the informal word 'likely'
  • Convert between informal language ('very unlikely') and a numerical position on the 0-to-1 scale

• Probabilities Sum to One

  Understand that when all possible outcomes of a trial are listed, their probabilities must add up to 1; use this to find the probability of an event NOT happening: P(not A) = 1 − P(A); apply this shortcut to avoid counting all unfavourable outcomes directly

  • List all outcomes of spinning a 4-colour spinner and verify their probabilities add up to 1
  • Calculate P(not rolling a 3) as 1 − 1/6 = 5/6 using the complement rule
  • Spot an error in a probability table where the values don't sum to 1 and explain what's wrong

• Experimental vs Theoretical

  Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results

  • Roll a die 60 times and compare experimental frequencies with the expected 10 per number
  • Explain why experimental results don't exactly match theoretical predictions but get closer with more trials
  • Predict what would happen if the experiment were repeated 600 times instead of 60

Data & Statistics

Your child is learning to interpret and create different types of graphs and charts, and beginning to calculate averages to understand what data tells us about real-world situations.

• Comparing measurements

  Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

  • Calculate mean, median, and mode for a data set and explain when each is most appropriate
  • Find the range of a data set and explain how an outlier affects the mean versus the median
  • Compare two data sets using their averages and ranges to draw conclusions

• Pictograms and tally charts (age 11+)

  Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type

  • Construct a grouped frequency table from raw continuous data, choosing appropriate class intervals
  • Draw a pie chart by calculating the angle for each category
  • Interpret a bar chart comparing two data sets and draw a conclusion about the difference

• Line graphs (age 10+)

  Interpret and construct pie charts and line graphs; use these to solve problems

  • Read values from a line graph showing temperature over a day and identify trends
  • Construct a pie chart from given data by calculating sector angles
  • Use a pie chart to determine the actual quantity represented by each sector given the total

• Calculating the Mean

  Calculate and interpret the mean as an average of a data set

  • Calculate the mean of five test scores: 72, 85, 90, 68, 95
  • Explain what the mean represents and how it differs from individual data values
  • Find a missing data value given the mean and all other values

• Understanding fractions

  Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally)

  • Create a line plot showing lengths measured to the nearest 1/8 inch
  • Use the line plot to find the total of all measurements by adding fractions
  • Solve: 'If the total liquid were redistributed equally among all beakers, how much would each have?'

• Statistical Analysis Vocabulary

  Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes

  • Correctly define and calculate the mean, median, mode, and range of a small data set
  • Use 'outlier' correctly to identify a value that doesn't fit the pattern, and explain its effect on the mean
  • Use 'correlation' correctly when describing the relationship shown in a scatter graph

Addition & Subtraction

Your child is mastering complex addition and subtraction — solving multi-step problems with large numbers and decimals, and choosing the best strategies to work out challenging calculations.

• Adding and subtracting (age 10+)

  Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals

  • Solve a two-step word problem involving addition and subtraction of numbers beyond 1,000,000
  • Choose between mental, written, and calculator methods for a multi-step problem and justify the choice
  • Interpret a real-life context to identify which addition/subtraction operations are needed across multiple steps

• Addition and subtraction strategies (age 10+)

  Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning

  • Correctly compute 3.45 + 2.78 and explain regrouping across decimal places
  • Use a number line or base-ten blocks to model 5.03 − 2.67
  • Explain why the standard algorithm works for decimal addition by connecting to place-value understanding

• Positive and Negative Numbers

  Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances

  • Represent positive and negative numbers on a number line and explain what zero means in context
  • Add a positive or negative number to any integer using number line reasoning
  • Subtract a positive or negative number from any integer, understanding that subtracting a negative is equivalent to adding