Junior Math Year 1

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Course Content

Unit 1: Place Value, Rounding, Written Methods and Number Bases

  • Lesson 1 · Place Value and Large Numbers: How Big Is a Billion?
  • Lesson 1 Exit Quiz: Place Value
  • Lesson 2 · Rounding and Estimation: Close Enough to Count
  • Lesson 2 Exit Quiz: Rounding
  • Lesson 3 · Written Multiplication: Grid, Column and a Quick Check
  • Lesson 3 Exit Quiz: Written Multiplication
  • Lesson 4 · Short and Long Division: Remainders That Make Sense
  • Lesson 4 Exit Quiz: Division
  • Lesson 5 · Number Bases: How Computers Count in Twos
  • Lesson 5 Exit Quiz: Number Bases
  • Year 1 Unit 1 Test: Place Value, Rounding, Written Methods and Number Bases (Section A)

Unit 2: Order of Operations, Factors, Primes and Powers
Unit overview By the end of this unit, students can work out calculations in the correct order, find factors and multiples quickly with divisibility tests, write any number as a product of primes, find the HCF and LCM of two numbers, and work with squares, cubes, roots and index notation. The theme is "The building blocks of numbers": how every whole number is built from primes, and how the order of a calculation decides its answer. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and diagrams for every method. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Order of operations, factors and multiples, prime numbers and prime factorisation, HCF and LCM (including word problems), squares, square roots and indices • Cambridge Lower Secondary (Stage 7): Order of operations including brackets and indices, multiples, factors, primes, squares, cubes and their roots, HCF and LCM (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): BIDMAS, prime factorisation (including product notation), HCF and LCM, squares, cubes, roots and powers; GCSE non-calculator skills • US Grade 6 (Common Core): Greatest common factor and least common multiple (6.NS.4), whole-number exponents (6.EE.1), order of operations in expressions (6.EE.2c) Students will be able to: • work out calculations using BIDMAS, and add brackets to change an answer • find all the factors of a number and use divisibility tests for 2, 3, 4, 5, 6, 9 and 10 • recognise prime numbers and write a number as a product of primes in index form • find the HCF and LCM of two numbers and choose the right one in a word problem • work out squares, cubes, square roots, cube roots and powers All questions and problems are original and written for this course. British spelling is used (US: PEMDAS, "greatest common factor" for HCF, "least common multiple" for LCM).

Unit 3: Negative Numbers, Sets and Venn Diagrams
Unit overview By the end of this unit, students can order and calculate with negative numbers (adding, subtracting, multiplying and dividing), use absolute value, describe sets with correct notation, and draw and use Venn diagrams to sort and count. The theme is "Above and below, in and out": temperatures, sea level, bank balances, clubs and surveys. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and number lines and Venn diagrams throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Integers and the four operations on directed numbers; sets, set notation, complements, and two-set Venn diagram problems (a regular Paper 2 question) • Cambridge Lower Secondary (Stage 7): Understanding integers, ordering, and adding, subtracting, multiplying and dividing integers; sorting information with Venn diagrams • UK Key Stage 3 (Year 7): Ordering and calculating with negative numbers; set notation and Venn diagrams (used again in GCSE probability) • US Grade 6–7 (Common Core): Positive and negative numbers in context (6.NS.5), the number line and absolute value (6.NS.6–7), and adding, subtracting, multiplying and dividing rational numbers (7.NS.1–2) Students will be able to: • order negative numbers and use and absolute value • add and subtract negative numbers using a number line and the two-sign rule • multiply and divide negative numbers using the sign rules, including squares and cubes • describe sets using { }, ∈, ∉, n(A), ∅, ⊂, U and A′ • draw Venn diagrams, find A ∩ B and A ∪ B, and solve counting problems All questions and problems are original and written for this course. British spelling is used (US: "integers" is common for whole negative numbers; the UK uses ξ for the universal set, shown here as U).

Unit 4: Fractions: Equivalence and the Four Operations
Unit overview By the end of this unit, students can find equivalent fractions and simplify, compare and order fractions, convert between mixed numbers and improper fractions, and add, subtract, multiply and divide fractions, including mixed numbers and word problems. The theme is "Sharing fairly": pizzas, recipes, ribbons, budgets and water tanks. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and fraction walls, bar models and pie diagrams throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Fractions: equivalence, ordering, the four operations with fractions and mixed numbers, and fraction word problems (shares of money, quantities and time) • Cambridge Lower Secondary (Stage 7): Equivalent fractions, ordering, adding and subtracting fractions and mixed numbers, multiplying and dividing fractions by whole numbers and by fractions (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Equivalent fractions, simplifying, ordering, the four operations with fractions and mixed numbers; GCSE non-calculator fraction skills • US Grade 6 (Common Core): Dividing fractions by fractions and interpreting quotients (6.NS.1); building on adding, subtracting and multiplying fractions (5.NF.1–7) Students will be able to: • find equivalent fractions and write fractions in simplest form • compare and order fractions, and convert between improper fractions and mixed numbers • add and subtract fractions and mixed numbers using a common denominator • find fractions of amounts and multiply fractions and mixed numbers • divide by fractions using reciprocals, and solve fraction word problems All questions and problems are original and written for this course. British spelling is used (US: "improper fraction" and "mixed number" are the same terms).

Unit 5: Decimals, Percentages and Money
Unit overview By the end of this unit, students can read, order and round decimals, add, subtract, multiply and divide decimals without a calculator, move between fractions, decimals and percentages, find percentages of amounts, and work out profit, loss and discounts. The theme is "Shopping and money": prices, bills, sales, sports results and budgets, in dollars, euros and pounds. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and place-value charts, hundred grids and bar models throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Decimals and approximation, fractions, decimals and percentages, percentage of a quantity, profit and loss percentages, and discount (regular Paper 1 and Paper 2 questions) • Cambridge Lower Secondary (Stage 7): Place value and rounding of decimals, the four operations with decimals, equivalence of fractions, decimals and percentages, and percentages of quantities (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Ordering and rounding decimals, written calculation with decimals, interchanging fractions, decimals and percentages, percentages of amounts, and simple financial maths; GCSE non-calculator percentage skills • US Grade 6 (Common Core): Fluent operations with multi-digit decimals (6.NS.3), percent as a rate per 100 and finding a percent of a quantity (6.RP.3c), and solving unit-rate and money problems (6.RP.3) Students will be able to: • read, compare, order and round decimals, and multiply and divide them by 10, 100 and 1,000 • add, subtract, multiply and divide decimals using written methods • convert between fractions, decimals and percentages, and order mixed amounts • find percentages of amounts and write one number as a percentage of another • work out profit, loss, profit and loss percentages, discounts and price increases All questions and problems are original and written for this course. Prices use dollars, euros and pounds. British spelling is used (US: "percent" is often written as one word).

Unit 6: Ratio, Rates and Proportion
Unit overview By the end of this unit, students can write and simplify ratios, share amounts in a ratio, compare prices using unit rates, scale recipes and use direct proportion, and calculate speed, distance and time. The theme is "Fair shares and best buys": paint, prizes, recipes, shopping and journeys. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and bar models, tables and graphs throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Ratio and proportion, sharing in a given ratio, rates (including speed, distance and time), and simple exchange-rate problems • Cambridge Lower Secondary (Stage 7): Using ratio notation, simplifying ratios, dividing a quantity in a ratio, direct proportion and the unitary method (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Ratio notation, reduction to simplest form, dividing in a ratio, the unitary method, best buys and compound units such as speed • US Grade 6 (Common Core): Ratio concepts and language (6.RP.1), unit rates (6.RP.2), equivalent-ratio tables and graphs, unit pricing and constant speed (6.RP.3a–b, 6.RP.3d) Students will be able to: • write a ratio in the correct order and in its simplest form, including ratios with units • share an amount in a ratio of two or three parts, including from one share or the difference • find unit rates and use them to decide which buy is better value • solve direct-proportion problems with the unitary method, including recipes and currency • calculate speed, distance and time, and read a distance–time graph All questions and problems are original and written for this course. Prices use dollars, euros and pounds; exchange rates are examples, not real rates. British spelling is used.

Unit 7: Expressions, Formulae and Equations
Unit overview By the end of this unit, students can write expressions from words, simplify them by collecting like terms, substitute numbers into expressions and formulae, expand and factorise single brackets, and solve linear equations, including those with brackets and letters on both sides. The theme is "Letters that work for us": number tricks, phone plans, taxi fares and balance scales. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and area models and balance diagrams throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Algebraic expressions, simplification, substitution, expansion of brackets, factorisation by common factor, and linear equations in one variable (a regular Paper 1 and Paper 2 topic) • Cambridge Lower Secondary (Stage 7): Using letters to represent unknowns, simplifying and constructing expressions, substituting into formulae, expanding a single bracket and solving simple linear equations (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Algebraic notation, simplifying and manipulating expressions by collecting like terms and multiplying a single term over a bracket, substitution into formulae, and solving linear equations; GCSE Foundation algebra • US Grade 6 and 7 (Common Core): Writing and evaluating expressions (6.EE.1–2), equivalent expressions and the distributive property (6.EE.3–4, 7.EE.1), and solving one-step and two-step equations (6.EE.7, 7.EE.4a) Students will be able to: • write expressions from words, using correct algebraic notation • simplify expressions by collecting like terms, and multiply simple terms • substitute positive and negative numbers into expressions and formulae • expand a single bracket, expand and simplify, and factorise using a common factor • solve one-step, two-step and bracket equations, and equations with letters on both sides All questions and problems are original and written for this course. British spelling is used (US: "factor" for "factorise").

Unit 8: Sequences, Functions, Coordinates and Graphs
Unit overview By the end of this unit, students can continue sequences and find their nth term, use function machines forwards and backwards, find rules from tables, plot and read coordinates in all four quadrants, draw straight-line graphs from tables of values, and read real-life graphs. The theme is "Patterns and pictures": matchstick patterns, secret machines, treasure maps and graphs that tell a story. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and term cards, function machines, coordinate grids and graphs throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Number patterns and sequences, mappings and relations, the Cartesian plane and plotting points, tables of values and straight-line graphs, and reading travel and conversion graphs • Cambridge Lower Secondary (Stage 7): Term-to-term and position-to-term rules, function machines, coordinates in four quadrants, tables of values and graphs of linear functions, and interpreting real-life graphs (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Generating terms of a sequence and finding the nth term of a linear sequence, coordinates in all four quadrants, plotting linear functions and interpreting real-life graphs; GCSE Foundation sequences and graphs • US Grade 6 to 8 (Common Core): Plotting points in all four quadrants (6.NS.6–8), dependent and independent variables in tables and graphs (6.EE.9), and functions and linear graphs (8.F.1–5) Students will be able to: • continue sequences, describe term-to-term rules and recognise special sequences • generate terms from an nth term and find the nth term of a linear sequence • use function machines forwards and backwards and find rules from tables • read, plot and reflect points in all four quadrants and find midpoints • draw straight-line graphs from tables and read and interpret real-life graphs All questions and problems are original and written for this course. British spelling is used.

Unit 9: Angles, Shapes, Symmetry and Constructions
Unit overview By the end of this unit, students can measure, draw and name angles, use angle facts on lines, around points and where lines cross, find missing angles in triangles and quadrilaterals, recognise line and rotational symmetry, reflect shapes, and carry out ruler-and-compass constructions. The theme is "Shapes all around us": skateboard turns, scissors, roofs, logos and parks. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and protractor, angle, symmetry and construction diagrams throughout. No calculator is used; students need a ruler, a protractor and compasses. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Angles and their measurement, angles at a point and on a line, angles in triangles and quadrilaterals, line symmetry and reflection, and ruler-and-compass constructions of perpendicular bisectors, angle bisectors and 60° angles • Cambridge Lower Secondary (Stage 7): Classifying and measuring angles, angle properties of lines, triangles and quadrilaterals, line and rotational symmetry, reflection, and constructing triangles and bisectors (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Angle facts with reasons, angle sums of triangles and quadrilaterals, symmetry and reflection, and standard ruler-and-compass constructions; GCSE Foundation geometry • US Grade 7 (Common Core): Foundations for supplementary, vertical and adjacent angles (7.G.5) and for constructing triangles from given conditions (7.G.2) Students will be able to: • name, estimate, measure and draw angles, including reflex angles • use angle facts on a straight line, around a point and for vertically opposite angles, with reasons • find missing angles in triangles (including isosceles and equilateral) and quadrilaterals, and use the exterior angle • recognise lines of symmetry and rotational symmetry, and reflect shapes in a mirror line • construct perpendicular bisectors, angle bisectors, 60° angles and triangles from three sides All questions and problems are original and written for this course. British spelling is used (US: "trapezoid" for "trapezium").

Unit 10: Measures
Unit overview By the end of this unit, students can convert between metric units, find the perimeter and area of rectangles and compound shapes, find the area of triangles, parallelograms and trapeziums, describe 3D shapes and their nets, and calculate surface area and volume. The theme is "Measuring our world": recipes, gardens, walls, signs, presents, fish tanks and sandpits. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and shape, net and cuboid diagrams throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Units of measurement and conversion, perimeter and area of plane shapes (including triangles, parallelograms and trapeziums), nets, surface area and volume of cuboids, and capacity • Cambridge Lower Secondary (Stage 7): Converting metric units, area of rectangles, triangles, parallelograms and trapeziums, compound shapes, surface area from nets and the volume of cuboids (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Metric conversion, perimeter and area formulae, compound shapes, properties of 3D shapes, surface area and volume of cuboids; GCSE Foundation measures • US Grade 6 (Common Core): Area of triangles, quadrilaterals and polygons by composing and decomposing (6.G.1), volume of right rectangular prisms (6.G.2), nets and surface area (6.G.4), and unit conversion (6.RP.3d) Students will be able to: • convert between metric units of length, mass and capacity, and choose sensible units • find the perimeter and area of rectangles and compound shapes, including missing sides • find the area of triangles, parallelograms and trapeziums using the perpendicular height • describe 3D shapes by faces, edges and vertices, and use nets to find surface area • find the volume of cuboids and cubes, and convert between cm³ and litres All questions and problems are original and written for this course. British spelling is used (US: "trapezoid" for "trapezium", "liter" for "litre").

Unit 11: Statistics and Probability
Unit overview By the end of this unit, students can collect and organise data in tally charts, frequency tables and two-way tables, draw and read bar charts, pictograms and pie charts, find the mean, median, mode and range, compare two sets of data, and work out simple probabilities. The theme is "What the numbers say": pets, sports, libraries, pocket money, basketball and spinners. The unit has five lessons of 10–15 minutes, a unit test with three worked problems, and tables, charts and probability scales throughout. No calculator is used. These skills appear in every lower-secondary maths course and exam: • BECE Mathematics (WAEC): Collecting and organising data, frequency tables, bar charts and pie charts, mean, median and mode, and the probability of simple events (a regular Paper 2 question) • Cambridge Lower Secondary (Stage 7): Data collection, tally charts, two-way tables, bar charts, pictograms and pie charts, mode, median, mean and range, comparing distributions, and the probability scale (Checkpoint Paper 1, no calculator) • UK Key Stage 3 (Year 7): Interpreting and constructing tables and charts, the averages and range, comparing distributions, and the probability of single events; GCSE Foundation statistics and probability • US Grade 6 and 7 (Common Core): Statistical questions and distributions (6.SP.1–3), displaying and summarising data (6.SP.4–5), and the probability of chance events (7.SP.5–7) Students will be able to: • identify types of data and organise data in tally charts, frequency tables and two-way tables • draw and read bar charts, pictograms and pie charts, and choose a suitable chart • find the mean, median, mode and range, and a missing value from the mean • compare two sets of data using an average and the range, and spot outliers • use the probability scale, find probabilities as fractions, P(not), experimental probability and expected results All questions and problems are original and written for this course. British spelling is used (US: "die" is often used for one dice).

Unit 12: Review and End-of-Year Exam
Unit overview This unit brings the whole of Year 1 Maths together. Four review lessons revisit number, algebra, geometry and measures, and data and problem solving, with the common mistakes that cost the most marks and a four-step plan for word problems. The unit ends with a full end-of-year exam: Paper 1 is 40 multiple-choice questions (45 minutes, no calculator, marked automatically) and Paper 2 is six structured problems (30 marks, Part 1 without and Part 2 with a calculator), with model solutions and a marking scheme. The exam is modelled on the papers students will meet later: • BECE Mathematics (WAEC): Paper 1 objective questions across number, algebra, geometry, mensuration and statistics; Paper 2 structured questions with working (the BECE allows a calculator in neither paper, so Paper 2 Part 1 is good BECE practice) • Cambridge Lower Secondary (Stage 7): Checkpoint-style Paper 1 (no calculator) and Paper 2 (calculator) covering number, algebra, geometry and measures, and statistics and probability • UK Key Stage 3 (Year 7): End-of-year assessment of the Year 7 programme of study, with non-calculator and calculator sections in the style of GCSE Foundation papers • US Grade 6 (Common Core): Coverage of the Grade 6 domains (ratio, number system, expressions and equations, geometry, statistics) in a mixed review Students will be able to: • avoid the ten most common number mistakes and check answers by estimating • connect expressions, equations, sequences, function machines and graphs • use angle facts with reasons and choose the right formula for area, surface area and volume • solve multi-step problems with charts, averages, probability and money using Read, Plan, Solve, Check • complete a full end-of-year exam and use the results to plan revision All questions and problems are original and written for this course. British spelling is used.