Mathematics

Calculate accurately, explain place value and check whether an answer is reasonable.

1. Long division and checking remainders

   Divide a multi-digit whole number and interpret what a remainder means in context.

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2. Adding and subtracting decimals

   Use place value to align quantities and explain regrouping.

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3. Multiplying decimals

   Connect decimal multiplication to whole-number products and powers of ten.

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4. Dividing decimals

   Scale both quantities to make a divisor whole, then check by multiplication.

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5. Common factors and common multiples

   Choose a greatest common factor or least common multiple according to the problem.

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Planning references: 6.NS.B.2 · 6.NS.B.3 · 6.NS.B.4

Use equal-sized pieces and inverse multiplication to explain division, including mixed numbers.

1. Why fraction division works

   Count fractional groups and explain the reciprocal rule instead of memorising it alone.

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2. Mixed numbers and division stories

   Translate a situation into fraction division and explain any unused amount.

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Planning references: 6.NS.A.1

Connect diagrams, tables and unit rates; find a percentage, recover a whole and convert units.

1. Fractions and ratios

   Describe parts of a whole and compare quantities without confusing the two.

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2. Ratio tables and double number lines

   Scale two linked quantities together and represent their relationship.

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3. Unit rates, prices and constant speed

   Find an amount per one unit and use it to compare or predict.

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4. Percentages as parts per hundred

   Connect fractions, decimals and percentages to find a part of a whole.

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5. Finding a whole from a percentage

   Work backwards from a known part and distinguish a count from a percentage.

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6. Converting units with ratios

   Use equivalent quantities to convert length, mass, time and rates.

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Planning references: 6.RP.A.1 · 6.RP.A.2 · 6.RP.A.3

Order rational numbers, interpret absolute value and reason about locations in four quadrants.

1. Negative numbers and distance

   Use a number line to distinguish a signed change from a distance.

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2. Ordering fractions, decimals and negatives

   Compare rational numbers using a common scale and interpret inequalities.

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3. Opposites and absolute value

   Distinguish a signed position from its distance from zero.

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4. Coordinates in four quadrants

   Locate points and describe reflections using the signs of their coordinates.

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5. Distances on a coordinate grid

   Find horizontal and vertical distances, including paths crossing an axis.

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Planning references: 6.NS.C.5 · 6.NS.C.6 · 6.NS.C.7 · 6.NS.C.8

Write and evaluate expressions, then justify equivalent forms using the properties of operations.

1. Powers and order of operations

   Read an exponent as repeated multiplication and evaluate expressions in a consistent order.

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2. Writing and reading expressions

   Translate words into algebra and identify terms, factors and coefficients.

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3. Substituting into formulas

   Replace a variable with its value and carry units through the calculation.

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4. The distributive property

   Expand or factor an expression while preserving its value.

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5. Collecting like terms

   Combine repeated quantities without confusing different variables or powers.

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6. Proving expressions are equivalent

   Use structure to justify an identity and a counterexample to reject one.

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Planning references: 6.EE.A.1 · 6.EE.A.2 · 6.EE.A.3 · 6.EE.A.4

Test solutions, solve one-step equations, show inequalities and connect a rule to a table and graph.

1. Testing equation and inequality solutions

   Substitute candidates to find which values make a mathematical statement true.

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2. Solving one-step equations

   Model a situation, undo one operation and verify a rational-number solution.

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3. Inequalities on a number line

   Translate a constraint and show an entire set of possible values.

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4. Rules, tables and dependent variables

   Connect changing quantities through an equation, a table and a graph.

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Planning references: 6.EE.B.5 · 6.EE.B.6 · 6.EE.B.7 · 6.EE.B.8 · 6.EE.C.9

Draw and decompose shapes, unfold solids into nets and use fractional dimensions with correct units.

1. Area of a triangle

   Explain the half-base-times-height formula using a matching pair of triangles.

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2. Parallelograms and composite areas

   Rearrange or split shapes to calculate areas without double-counting.

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3. Area, volume and units

   Build a rectangular prism from layers and keep square and cubic units distinct.

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4. Volume with fractional edge lengths

   Count fractional cubes and connect their count with the prism formula.

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5. Prism nets and surface area

   Unfold a solid, identify all faces and total the area of its outer surface.

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6. Pyramid nets and triangular faces

   Distinguish a face's slant height from the vertical height of a solid.

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7. Polygons on a coordinate grid

   Draw vertices in order and use coordinate differences to measure sides.

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Planning references: 6.G.A.1 · 6.G.A.2 · 6.G.A.3 · 6.G.A.4

Ask questions that allow variation; display, summarise and interpret data in context.

1. Asking a statistical question

   Plan a question that anticipates variation and define the data you need.

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2. Dot plots and distribution shape

   Display each observation and describe clusters, gaps and unusual values.

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3. Mean, median and a fair share

   Calculate two measures of centre and explain what each summarises.

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4. Range, interquartile range and mean absolute deviation

   Explain why the centre alone cannot describe a distribution.

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5. Histograms and box plots

   Choose and read a display that summarises a numerical distribution.

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6. Interpreting a distribution in context

   Choose appropriate summaries and explain what the data can and cannot support.

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Planning references: 6.SP.A.1 · 6.SP.A.2 · 6.SP.A.3 · 6.SP.B.4 · 6.SP.B.5