# Year 5: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 57 concepts ready. In the app: https://ai.page/roadmap/nz-moe-year-5 Part of: [New Zealand Curriculum: Mathematics](https://ai.page/roadmap/nz-moe.md) Goal: The New Zealand Curriculum (Ministry of Education): Mathematics, Year 5 ## 1. Number · Number structures - [Numbers to 10,000](https://ai.page/c/numbers-to-10-000/index.md): Identify, represent, and estimate numbers up to 10,000 using different representations - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): 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 - [Rounding to 10, 100, 1000](https://ai.page/c/rounding-to-10-100-1000/index.md): Round any number to the nearest 10, 100, or 1000 - [Square and cube numbers](https://ai.page/c/square-and-cube-numbers/index.md): Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) - [Reading and writing numbers (age 9+)](https://ai.page/c/reading-and-writing-numbers-age-9/index.md): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding - [Counting forwards and backwards (age 9+)](https://ai.page/c/counting-forwards-and-backwards-age-9/index.md): Count forwards and backwards in steps of powers of 10 (10, 100, 1000, 10,000, 100,000) for any given number up to 1,000,000 - [Tenths (age 8+)](https://ai.page/c/tenths-age-8/index.md): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10 - [Negative Numbers](https://ai.page/c/negative-numbers/index.md): Count backwards through zero to include negative numbers ## 2. Number · Operations - [Adding and subtracting mixed numbers](https://ai.page/c/adding-and-subtracting-mixed-numbers/index.md): Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations - [Division with remainders (age 10+)](https://ai.page/c/division-with-remainders-age-10/index.md): 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 ## 3. Number · Rational numbers - [Decimals for Tenths & Hundredths](https://ai.page/c/decimals-for-tenths-and-hundredths/index.md): Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100) - [Simplifying Fractions](https://ai.page/c/simplifying-fractions/index.md): Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator - [Understanding Percentages](https://ai.page/c/understanding-percentages/index.md): Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal - [Division with Decimals](https://ai.page/c/division-with-decimals/index.md): Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers - [Multiplying by Tens](https://ai.page/c/multiplying-by-tens/index.md): Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations - [Comparing fractions (age 8+)](https://ai.page/c/comparing-fractions-age-8/index.md): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-maths/index.md): Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows - [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [Decimal place value (age 8+)](https://ai.page/c/decimal-place-value-age-8/index.md): Compare numbers with the same number of decimal places up to two decimal places - [Comparing Decimals](https://ai.page/c/comparing-decimals/index.md): Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, < - [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000 - [Equivalent fractions](https://ai.page/c/equivalent-fractions/index.md): Recognise and show, using diagrams, equivalent fractions with small denominators ## 4. Number · Financial mathematics - [Decimal place value](https://ai.page/c/decimal-place-value-2/index.md): Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6) - [Measurement Conversions](https://ai.page/c/measurement-conversions/index.md): Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts ## 5. Algebra · Growing patterns - [Patterns in Times Tables](https://ai.page/c/patterns-in-times-tables/index.md): Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations - [Shape patterns](https://ai.page/c/shape-patterns-maths/index.md): Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur ## 6. Algebra · Coordinate plane - [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): 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 ## 7. Measurement · Measuring - [Measuring with different units](https://ai.page/c/measuring-with-different-units/index.md): Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen - [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units ## 8. Measurement · Area and Volume - [Area of Triangles & Parallelograms](https://ai.page/c/area-of-triangles-and-parallelograms/index.md): Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles) - [Area (age 8+)](https://ai.page/c/area-age-8/index.md): Measure areas by counting unit squares (square cm, square m, square in, square ft) - [Understanding angles (age 8+)](https://ai.page/c/understanding-angles-age-8-maths/index.md): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas - [Estimating volume](https://ai.page/c/estimating-volume/index.md): Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water - [Counting Unit Cubes](https://ai.page/c/counting-unit-cubes/index.md): Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units - [Estimating answers (age 10+)](https://ai.page/c/estimating-answers-age-10/index.md): 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) ## 9. Measurement · Angles - [Degrees and turns](https://ai.page/c/degrees-and-turns/index.md): Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees - [Estimating Angles](https://ai.page/c/estimating-angles/index.md): Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size - [Measuring angles](https://ai.page/c/measuring-angles/index.md): Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure ## 10. Measurement · Time - [Comparing Time Durations](https://ai.page/c/comparing-time-durations/index.md): Compare durations of events and calculate the time taken by particular events or tasks - [Telling time to the minute (age 8+)](https://ai.page/c/telling-time-to-the-minute-age-8/index.md): Tell and write time to the nearest minute using analogue and digital clocks - [12-hour and 24-hour time](https://ai.page/c/12-hour-and-24-hour-time/index.md): Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks - [Converting measurement units](https://ai.page/c/converting-measurement-units/index.md): Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day) - [Telling time to the minute (age 9+)](https://ai.page/c/telling-time-to-the-minute-age-9/index.md): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days) ## 11. Geometry · Shapes - [Parallel and perpendicular lines](https://ai.page/c/parallel-and-perpendicular-lines/index.md): Identify horizontal and vertical lines and pairs of perpendicular and parallel lines - [What Is an Angle?](https://ai.page/c/what-is-an-angle/index.md): Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes - [3-D shapes (age 11+)](https://ai.page/c/3-d-shapes-age-11/index.md): 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 - [2-D shapes (age 8+)](https://ai.page/c/2-d-shapes-age-8/index.md): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry ## 12. Geometry · Spatial reasoning - [Nets of 3-D Shapes](https://ai.page/c/nets-of-3-d-shapes/index.md): 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 - [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): 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 ## 13. Statistics · Developing knowledge - [Rounding Answers](https://ai.page/c/rounding-answers/index.md): Solve problems which require answers to be rounded to specified degrees of accuracy - [Calculating the Mean](https://ai.page/c/calculating-the-mean/index.md): Calculate and interpret the mean as an average of a data set - [Reading tables](https://ai.page/c/reading-tables/index.md): Complete, read, and interpret information in tables, including timetables ## 14. Statistics · Visualisation of data - [Bar graphs](https://ai.page/c/bar-graphs/index.md): Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs ## 15. Probability · Experimental probability - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability - [The 0-to-1 Probability Scale](https://ai.page/c/the-0-to-1-probability-scale/index.md): 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 - [Calculating Simple Probability](https://ai.page/c/calculating-simple-probability/index.md): 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 - [Simple Chance Experiments](https://ai.page/c/simple-chance-experiments/index.md): Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes ## Health: 0 of 100 Of its 57 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - Numbers to 10,000 has no explanation yet - Factors, multiples, and primes has no explanation yet - Rounding to 10, 100, 1000 has no explanation yet - Square and cube numbers has no explanation yet - Reading and writing numbers (age 9+) comes before Comparing Large Numbers, which it needs - Reading and writing numbers (age 9+) has no explanation yet - Counting forwards and backwards (age 9+) has no explanation yet - Tenths (age 8+) has no explanation yet - Negative Numbers has no explanation yet - Adding and subtracting mixed numbers has no explanation yet - Division with remainders (age 10+) has no explanation yet - Decimals for Tenths & Hundredths has no explanation yet - Simplifying Fractions has no explanation yet - Understanding Percentages has no explanation yet - Division with Decimals has no explanation yet - Multiplying by Tens has no explanation yet - Comparing fractions (age 8+) has no explanation yet - Fractions on a number line has no explanation yet - Decimal place value has no explanation yet - Decimal place value (age 8+) has no explanation yet - Comparing Decimals has no explanation yet - Comparing Large Numbers has no explanation yet - Equivalent fractions has no explanation yet - Decimal place value has no explanation yet - Measurement Conversions has no explanation yet - Patterns in Times Tables has no explanation yet - Shape patterns has no explanation yet - Plotting points in the first quadrant has no explanation yet - Measuring with different units has no explanation yet - Calculating with measurements has no explanation yet - Area of Triangles & Parallelograms has no explanation yet - Area (age 8+) has no explanation yet - Understanding angles (age 8+) has no explanation yet - Estimating volume has no explanation yet - Counting Unit Cubes has no explanation yet - Estimating answers (age 10+) has no explanation yet - Degrees and turns comes before What Is an Angle?, which it needs - Degrees and turns has no explanation yet - Estimating Angles has no explanation yet - Measuring angles has no explanation yet - Comparing Time Durations has no explanation yet - Telling time to the minute (age 8+) has no explanation yet - 12-hour and 24-hour time has no explanation yet - Converting measurement units has no explanation yet - Telling time to the minute (age 9+) has no explanation yet - Parallel and perpendicular lines has no explanation yet - What Is an Angle? has no explanation yet - 3-D shapes (age 11+) has no explanation yet - 2-D shapes (age 8+) comes before Transformations on a grid, which it needs - 2-D shapes (age 8+) has no explanation yet Credit: The structure of The New Zealand Curriculum (Ministry of Education): Mathematics (https://nzcurriculum.tki.org.nz/the-nzc/learning-areas/mathematics-and-statistics); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.