Year 7 Mathematics: Term 1
A 48-session self-study mathematics course covering the first term of UK Key Stage 3 Year 7. It builds the number, algebra, ratio, geometry and statistics foundations that every later KS3 and GCSE topic depends on. Each session gives a plain-language explanation of one idea, an original labelled SVG diagram, a fully worked example written as continuous reasoning, a common-mistake checkpoint, self-checks and graded multiple-choice practice.
📚 Course Curriculum
Lesson route. Estimated study time: 40–50 minutes. You need: notebook, pencil, ruler. !Place value chart for 4,506,213 showing millions down to units. Learning goals. By …
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Lesson route. Estimated study time: 40–50 minutes. !Number line from -10 to 10 marking five city temperatures. Learning goals. You will learn to:. place positive …
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Lesson route. Estimated study time: 45–55 minutes. !Number line showing -5+8=3 and 4-(-7)=11 as movements. Learning goals. You will learn to:. model addition and subtraction …
Open trial session →Lesson route. Estimated study time: 40–50 minutes. !Grid of sign rules for multiplying and dividing, with a pattern proof. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 45–55 minutes. !BIDMAS order of operations with a worked example. Learning goals. You will learn to:. state the BIDMAS order …
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Lesson route. Estimated study time: 40–50 minutes. !Number line rounding 3847 to the nearest hundred. Learning goals. You will learn to:. round whole numbers to …
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Lesson route. Estimated study time: 40–50 minutes. !Factor rainbow diagram showing all nine factor pairs of 36. Learning goals. By the end of this session, …
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Lesson route. Estimated study time: 45–55 minutes. !Factor tree splitting 84 down into its prime factors, 2 squared times 3 times 7. Learning goals. You …
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Lesson route. Estimated study time: 45–55 minutes. !Venn diagram of the prime factors of 36 and 48, with the shared factors giving HCF 12. Learning …
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Lesson route. Estimated study time: 45–55 minutes. !Two bus timelines meeting after 60 minutes, the LCM of 15 and 20. Learning goals. You will learn …
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Lesson route. Estimated study time: 40–50 minutes. !Bars comparing a proper fraction, an improper fraction and its mixed number form. Learning goals. By the end …
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Lesson route. Estimated study time: 40–50 minutes. !Three bars showing that one half, two quarters and four eighths are equivalent. Learning goals. You will learn …
Open trial session →Lesson route. Estimated study time: 45–55 minutes. !Bars showing 2/3 and 3/4 both converted to twelfths, then added to give 17/12. Learning goals. You will …
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Lesson route. Estimated study time: 45–55 minutes. !Area model for multiplying fractions, and a keep-flip-multiply diagram for dividing them. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 45–55 minutes. !Conversion triangle between fractions, decimals and percentages, with a common equivalences table. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 45–55 minutes. !Ten percent building blocks used to find 35 percent of 180. Learning goals. You will learn to:. find …
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Lesson route. Estimated study time: 45–55 minutes. !Bar chart comparing two jacket prices after different discounts, £48 versus £49. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 40–50 minutes. !Bar model showing a flour to sugar ratio of 3 to 2 split into five equal parts. Learning …
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Lesson route. Estimated study time: 45–55 minutes. !Bar model sharing £60 in the ratio 2 to 3, giving £24 and £36. Learning goals. You will …
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Lesson route. Estimated study time: 45–55 minutes. !Comparison of a directly proportional relationship and one that is not proportional. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 45–55 minutes. !Map scale of 1 to 25000 converting an 8 cm map distance to 2 km real distance. Learning …
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Lesson route. Estimated study time: 45–55 minutes. !Notation cards for ab, 3a, a squared and a over b, with an annotated expression showing its terms. …
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Lesson route. Estimated study time: 45–55 minutes. !Terms sorted by colour into a-terms, b-terms and constants, then collected. Learning goals. You will learn to:. identify …
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Lesson route. Estimated study time: 45–55 minutes. !Three-step substitution of a = -3 into 2a squared minus 3a, using brackets and BIDMAS. Learning goals. You …
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Lesson route. Estimated study time: 45–55 minutes. !Area model for 4 times the bracket 2x plus 5, splitting into 8x and 20. Learning goals. You …
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Lesson route. Estimated study time: 45–55 minutes. !Arrows showing that expanding 3(2x + 5) and factorising 6x + 15 are reverse processes. Learning goals. You …
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Lesson route. Estimated study time: 45–55 minutes. !Growing T-shaped dot pattern for the sequence 5, 8, 11, with the nth term derivation. Learning goals. You …
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Lesson route. Estimated study time: 40–50 minutes. !Balance scale showing x + 7 = 12 solved by subtracting 7 from both sides. Learning goals. By …
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Lesson route. Estimated study time: 45–55 minutes. !Three-step flow solving 3x + 5 = 20 by undoing operations in reverse order. Learning goals. You will …
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Lesson route. Estimated study time: 45–55 minutes. !Four-step flow solving 3(x + 4) = 21 by expanding the bracket first. Learning goals. You will learn …
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Lesson route. Estimated study time: 45–55 minutes. !Three-step flow solving 5x + 3 = 2x + 18 by collecting x terms onto one side. Learning …
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Lesson route. Estimated study time: 45–55 minutes. !Four-step translation of a rectangle perimeter word problem into an equation. Learning goals. You will learn to:. define …
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Lesson route. Estimated study time: 40–50 minutes. !Number lines showing x less than 5 with an open circle and x greater than or equal to …
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Lesson route. Estimated study time: 40–50 minutes. !Angles on a straight line, angles around a point, and vertically opposite angles. Learning goals. By the end …
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Lesson route. Estimated study time: 40–50 minutes. !Triangle angles rearranged along a straight line to show they sum to 180 degrees, and an isosceles triangle …
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Lesson route. Estimated study time: 45–55 minutes. !A quadrilateral, pentagon and hexagon each split into triangles from one vertex. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 45–55 minutes. !Corresponding, alternate and co-interior angles formed by a transversal crossing two parallel lines. Learning goals. You will learn …
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Lesson route. Estimated study time: 40–50 minutes. !Nested hierarchy of the quadrilateral family showing squares, rectangles, rhombuses, trapeziums and kites. Learning goals. You will learn …
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Lesson route. Estimated study time: 45–55 minutes. !A triangle reflected in the y-axis, and a point rotated 180 degrees about the origin. Learning goals. You …
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Lesson route. Estimated study time: 40–50 minutes. !L-shaped composite figure with missing edges found by subtraction. Learning goals. By the end of this session, you …
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Lesson route. Estimated study time: 40–50 minutes. !Rectangle area on a grid, and a triangle shown as exactly half of a rectangle. Learning goals. You …
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Lesson route. Estimated study time: 45–55 minutes. !A parallelogram rearranged into a rectangle, and two trapeziums forming a parallelogram. Learning goals. You will learn to:. …
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Lesson route. Estimated study time: 40–50 minutes. !A cube, triangular prism and square-based pyramid labelled with faces, edges and vertices, satisfying Euler's formula. Learning goals. …
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Lesson route. Estimated study time: 40–50 minutes. !A cuboid built from four stacked layers of unit cubes, showing volume as length times width times height. …
Open trial session →Lesson route. Estimated study time: 40–50 minutes. !Types of data, and a tally chart converting shoe-size data into a frequency table. Learning goals. By the …
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Lesson route. Estimated study time: 45–55 minutes. !Mean, median, mode and range calculated for the data set 4, 7, 7, 9, 12, 15. Learning goals. …
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Lesson route. Estimated study time: 45–55 minutes. !A sports survey shown as a pie chart with calculated angles, and a books-read pictogram with a half-symbol …
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Lesson route. Estimated study time: 50–60 minutes. !A roadmap of all ten Term 1 units, with two worked examples combining skills across units. Learning goals. …
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Course Syllabus
Term 1 is organised into ten units. Unit A (sessions 1-6) builds number foundations: place value, negative numbers, and the order of operations. Unit B (7-10) covers factors, multiples and primes, including HCF and LCM. Unit C (11-17) develops fractions, decimals and percentages and the links between them. Unit D (18-21) introduces ratio, proportion and scale. Unit E (22-27) opens algebra: notation, simplifying, substituting, expanding, factorising and sequences. Unit F (28-33) solves equations and inequalities, including forming equations from word problems. Unit G (34-39) covers angle facts, polygon properties and transformations. Unit H (40-44) covers perimeter, area and an introduction to 3D shapes and volume. Unit I (45-47) covers data handling: collecting data, averages, and charts. Unit J (48) is a cumulative review and assessment session.
Course Outcomes
By the end of Term 1, a student can: read, write, compare and order positive and negative integers and decimals, and round numbers to a given accuracy; apply the order of operations correctly; find factors, multiples and prime factorisations, and use them to find the HCF and LCM; convert fluently between fractions, decimals and percentages; calculate percentages of amounts; simplify and use ratios and solve direct proportion problems; use correct algebraic notation, simplify, substitute, expand and factorise expressions; generate sequences and find a term-to-term or nth-term rule; solve linear equations and simple inequalities, including forming an equation from a worded problem; use angle facts in triangles, quadrilaterals and parallel lines; calculate perimeter, area and the volume of cuboids; and collect, represent and summarise data using averages and charts.
📝 Practice Questions
240 interactive questions with instant feedback and explanations.
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