Use rulers, set squares, and compasses to construct precise 2D lines, polygons, circles, and geometric patterns.

Master fraction conversions, common denominators, and addition and subtraction of fractions and mixed numbers in applied contexts.

Master adding and subtracting fractions with like, related, and unrelated denominators using lowest common denominator strategies.

Master addition and subtraction of positive and negative integers using number lines, visual models, and algebraic rules.

Add and subtract mixed numbers with and without regrouping, and apply fraction operations to multi-step expressions and real-world scenarios.

Build mental flexibility, understand fact families, and solve combined addition and subtraction challenges within 10.

Translate real-world scenarios into equations and solve one-step, two-step, and multi-step word problems using addition and subtraction.

Explore key addition rules, use ten-frames, and master number bonds and word problems within 10.

Solve multi-step problems involving reverse percentages, mixed rational operations, comparative data analysis, and successive percentage changes.

Classify items using multiple criteria, Venn diagrams, and Carroll diagrams, and record data using tallies and drawings.

Understand angles as measures of turn, classify angle types, and estimate angle sizes in degrees using key benchmarks.

Calculate unknown interior and exterior angles across special quadrilaterals and multi-sided polygons using angle formulas and algebraic equations.

Apply angle sum rules for lines, points, triangles, and quadrilaterals to calculate missing angles and solve geometric deduction puzzles.

Identify angle notations and calculate missing angle measures using geometric rules for intersecting lines, points, and various types of triangles.

Apply trigonometric methods to solve practical, multi-step problems involving angles of elevation and depression, bearings, and combined geometric diagrams.

Explore curved nets, design functional packaging, evaluate cross-sections, and build compound 3D structures.

Apply decomposition strategies and area subtraction methods to solve practical problems in material estimation, landscaping, and room renovation.

Apply estimation techniques and contextual rounding rules to real-world scenarios, measurement data, and calculator outputs.

Solve multi-step problems involving compound 3D shapes, missing dimensions, container capacity, packing, and the distinction between volume and surface area.

Refine estimation accuracy through measurement feedback, strategic reasoning, real-world DIY scenarios, and interactive challenges.

Formulate, troubleshoot, and evaluate multi-step mathematical expressions and real-world formulas using brackets and proper precedence.

Calculate arc lengths, sector areas, and the perimeter and area of composite circular shapes in theoretical and real-world contexts.

Decompose multi-part 2D figures—including rectilinear shapes, triangles, and circular sectors—to calculate total area and perimeter.

Apply quadratic (k²) and cubic (k³) scale factors to calculate surface areas, volumes, and material costs for similar 2D and 3D shapes.

Identify term-to-term sequence rules and construct visual figurate number patterns including square, triangular, and cube numbers.

Balance two-sided equations, solve for unknown values using symbols and early variables, and apply algebraic reasoning to puzzles and real-world scenarios.

Understand bank accounts, debit vs credit cards, PIN security, cash withdrawals, and create balanced personal budgets.

Read and measure three-figure bearings, interpret map scales, and create accurate scale drawings of routes and journeys.

Draw, scale, and verify horizontal and vertical bar graphs on grid paper and using digital tools.

Calculate mean, median, mode, range, and interquartile range from raw data, ungrouped frequency tables, and grouped frequency distributions.

Calculate fractional and percentage parts of quantities using mental strategies and decimal multipliers, and determine percentage increase and decrease.

Master the core relationships and formulas linking speed, distance, and time to solve fundamental travel time and pace calculations.

Perform arithmetic with mixed metric units, read measurement scales, and solve multi-step real-world measurement problems.

Apply calendar reading skills to organize weekly routines, count down to upcoming events, track monthly patterns, and map yearly milestones.

Use perpendicular chord bisectors, radius-derived isosceles triangles, and multi-step circle theorem strategies to solve geometric proofs and real-world engineering problems.

Master tangent-radius relationships and the angle in a semicircle theorem to calculate missing angles and lengths in right-angled circle configurations.

Explore circle properties, sort 2D shapes using logical diagrams, and investigate geometric applications in nature, engineering, and the built environment.

Understand the constant pi and master calculating and rearranging formulas for the circumference and area of circles.

Formulate simple questions, collect classroom information, and represent findings using physical objects, tally marks, and pictographs.

Position, compare, and order mixed numbers and improper fractions on number lines and apply fraction conversions to real-world contexts and word problems.

Evaluate and compare expressions, order sets of numbers using inequality chains, and solve relational word problems.

Compare lengths and heights directly and measure objects using non-standard units like cubes and paperclips.

Compare sets of items and numerals using the language of more, less, fewer, and the same.

Compare, order, and measure objects by size, length, and height using descriptive vocabulary and non-standard units.

Develop an intuitive understanding of weight by hefting, using pan balances, and measuring objects with non-standard units like cubes and marbles.

Compare, order, and position large numbers on number lines, and use place value concepts to solve mental math problems and real-world scenarios.

Read number words, navigate visual number representations, and compare and order numbers up to 100.

Link compass points to angle turns, navigate routes using 8-point and 16-point compasses, use programmable technology, and calculate three-figure bearings.

Combine simpler geometric pieces to build composite figures, solve tangram puzzles, and analyze why shapes fit together.

Decompose and calculate the volume, surface area, and real-world capacity of composite, hollow, and multi-part 3D structures.

Solve real-world problems involving compound units (speed, density, pressure) and apply linear, area, and volume scale factors.

Use friendly numbers to estimate sums and differences, solve word problems, and evaluate whether calculated answers are plausible.

Classify data types and construct accurate stem-and-leaf diagrams, pie charts, and comparative bar charts to represent discrete and categorical distributions.

Analyze and compare subscription plans, service contracts, and consumer pricing options to make cost-effective purchasing decisions.

Construct frequency polygons and box plots for continuous data, leverage spreadsheet charting tools, and critically evaluate statistical displays.

Master the base-10 structure of the metric system and convert fluently between millimeters, centimeters, meters, and kilometers using whole numbers and decimals.

Convert accurately between metric units of mass (g, kg, t) and capacity (mL, cL, L) using decimal notation and place value.

Develop fluency with number sequences up to 10 by counting forwards and backwards, finding relative positions, and ordering numerals.

Develop core counting skills, instant quantity recognition, and numeral writing for numbers 0 through 5.

Define, construct, and evaluate formulas derived from written descriptions, tables of values, geometric diagrams, and scientific contexts.

Collect and organize data using concrete manipulatives, tally marks, and labeled pictographs with one-to-one correspondence.

Apply understanding of symmetry to complete drawings, craft paper cutouts, and build balanced patterns using blocks and art materials.

Apply time concepts to daily routines using a.m./p.m., classroom schedules, introductory 24-hour time, and word problems.

Design unbiased surveys, select representative samples, and analyze how sample size affects precision and fair conclusions.

Add, subtract, multiply, and divide decimal numbers and apply these operations to solve everyday metric and money problems.

Build an intuitive understanding of seconds and minutes by comparing fast and slow activities and using sand timers.

Analyze, calculate, and graph directly and inversely proportional relationships across financial, practical, and algebraic contexts.

Understand, graph, and solve direct and inverse proportion problems across real-world scaling, rates, and inverse relationships.

Choose appropriate scales, construct an extended range of statistical graphs, and produce clear data displays using digital tools.

Interpret and plot distance-time graphs and solve multi-step journey problems including meeting points, multi-stage travel, and arrival planning.

Construct accurate bar charts, comparative bar graphs, pictograms, and single and dual line graphs with appropriate vertical axis scales on grid paper.

Discover how early humans counted with body parts, tallies, and clay tokens, and explore ancient numeral systems created by the Egyptians, Romans, and Mayans.

Perform enlargements with positive, fractional, and negative scale factors, and analyze composite transformations and invariant properties.

Apply profit and loss calculations to real-world enterprise scenarios, including production costs, budgeting stalls, product margins, and financial statements.

Solve equations involving powers and roots and apply these concepts to geometric area, volume, and practical modeling problems.

Build an intuitive mental library of everyday reference objects and body benchmarks to estimate length, mass, liquid capacity, and surface area.

Round whole numbers and decimals to estimate calculation results and verify reasonableness.

Evaluate algebraic expressions by substituting positive and negative numbers and diagnose common algebraic mistakes.

Interpret broadcast and event listings, design structured itineraries, and solve complex scheduling and delay-management problems.

Calculate discounts, sales taxes, unit prices, and net take-home earnings from wages and deductions.

Apply expected value calculations, risk matrices, and probability models to evaluate financial choices, assess real-world hazards, and make informed decisions under uncertainty.

Design probability experiments, construct sample space diagrams, analyze trial accuracy and game fairness, and apply probability to everyday decisions.

Understand container capacity, compare amounts using direct pouring, and measure using non-standard units like scoops and cups.

Introduce line symmetry and reflective balance, helping learners identify vertical, horizontal, and multiple lines of symmetry in shapes and the real world.

Demonstrate understanding of simple equivalent fractions through practical activities, diagrams, and number lines.

Order numbers 0 to 5, count abstract events, find one more/less, and decompose numbers into parts.

Compare and measure the weight and capacity of everyday objects and containers using hands-on tools and non-standard units.

Understand hundreds, use zero as a multi-digit placeholder, and apply place value concepts to solve number puzzles.

Identify factors, factor pairs, and multiples, apply divisibility tests, and determine greatest common factors and least common multiples using listing methods.

Identify factors, multiples, prime numbers, square numbers, and apply divisibility rules to solve problems.

Investigate iconic sequences such as Fibonacci numbers and Pascal's Triangle, and master two-step and position-to-term rules for solving complex sequence puzzles.

Formulate algebraic nth term rules for linear and special sequences and apply them to analyze patterns, test membership, and solve real-world problems.

Identify operational rules in number sequences, extend and complete increasing and decreasing patterns, spot errors, and explore growing visual patterns.

Find fractions of groups and quantities by connecting equal sharing to division.

Use number line models, inverse relationships, and self-checking techniques to calculate and verify addition and subtraction efficiently.

Build an understanding of addition as combining groups, learn to use addition symbols, and practice counting on and finding number bonds within 5.

Build an understanding of multiplication through equal groups, arrays, skip counting, and basic word problems.

Understand linear perimeter and surface area concepts, apply standard formulas to squares and rectangles, and determine missing side lengths.

Understand chance vocabulary, express probabilities numerically on a 0 to 1 scale, calculate theoretical probabilities, and conduct introductory coin and dice experiments.

Understand cost price, selling price, and break-even points, and calculate basic profit and loss across single and multiple transactions.