# Year 1: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 42 concepts ready. In the app: https://ai.page/roadmap/nz-moe-year-1 Part of: [New Zealand Curriculum: Mathematics](https://ai.page/roadmap/nz-moe.md) Goal: The New Zealand Curriculum (Ministry of Education): Mathematics, Year 1 ## 1. Number · Operations - [Addition in any order](https://ai.page/c/addition-in-any-order/index.md): Understand and apply the commutative property of addition: addends can be added in any order - [Subtraction as taking away or separating](https://ai.page/c/subtraction-as-taking-away-or-separating/index.md): Understand subtraction as taking away or separating from a group to find how many remain - [Adding and subtracting](https://ai.page/c/adding-and-subtracting/index.md): Add and subtract one-digit and two-digit numbers to 20, including zero - [Addition and subtraction word problems](https://ai.page/c/addition-and-subtraction-word-problems/index.md): Solve addition and subtraction word problems within 10 using objects or drawings - [Addition and subtraction within 20](https://ai.page/c/addition-and-subtraction-within-20/index.md): Add and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts - [Adding Three Small Numbers](https://ai.page/c/adding-three-small-numbers/index.md): Add three one-digit numbers using strategies including looking for pairs that make 10 - [Division as equal sharing](https://ai.page/c/division-as-equal-sharing/index.md): Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made) - [Multiplication as repeated addition](https://ai.page/c/multiplication-as-repeated-addition/index.md): Understand multiplication as repeated addition and grouping equal sets - [Arrays for multiplication](https://ai.page/c/arrays-for-multiplication/index.md): Use arrays to represent multiplication and division situations ## 2. Number · Fractions - [What Is a Half?](https://ai.page/c/what-is-a-half/index.md): Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity - [Fractions of amounts](https://ai.page/c/fractions-of-amounts/index.md): Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity - [Simple Fraction Sums](https://ai.page/c/simple-fraction-sums/index.md): Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7) - [Understanding fractions](https://ai.page/c/understanding-fractions-maths/index.md): Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2 ## 3. Number · Financial mathematics - [Adding money and giving change](https://ai.page/c/adding-money-and-giving-change/index.md): Find different combinations of coins that equal the same amount of money - [Money Addition & Subtraction](https://ai.page/c/money-addition-and-subtraction/index.md): Solve simple money problems involving addition and subtraction, including giving change ## 4. Algebra · Equations and number relationships - [Reading ×, ÷, and = Symbols](https://ai.page/c/reading-and-symbols-maths/index.md): Read, write, and interpret the symbols ×, ÷, and = in multiplication and division number sentences - [Comparing groups: more or fewer](https://ai.page/c/comparing-groups-more-or-fewer/index.md): Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies - [Inverse: addition undoes subtraction](https://ai.page/c/inverse-addition-undoes-subtraction/index.md): Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems ## 5. Algebra · Patterns - [Patterns & Sequences](https://ai.page/c/patterns-and-sequences/index.md): Order and arrange combinations of mathematical objects in patterns and sequences ## 6. Measurement · Measuring - [Choosing measurement units](https://ai.page/c/choosing-measurement-units/index.md): Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit - [Measurable Attributes of Objects](https://ai.page/c/measurable-attributes-of-objects/index.md): Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less) - [Comparing lengths by measuring](https://ai.page/c/comparing-lengths-by-measuring/index.md): Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit - [Comparing and ordering measurements](https://ai.page/c/comparing-and-ordering-measurements/index.md): Compare and order lengths, mass, and capacity and record results using >, <, and = ## 7. Measurement · Length and Area - [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes - [Measuring length (age 6+)](https://ai.page/c/measuring-length-age-6/index.md): Measure the length of an object using same-size length units laid end to end with no gaps or overlaps - [Area by Tiling](https://ai.page/c/area-by-tiling/index.md): Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths ## 8. Measurement · Time - [Telling time to the minute](https://ai.page/c/telling-time-to-the-minute/index.md): Measure and begin to record time in hours, minutes, and seconds - [Number of minutes in an hour](https://ai.page/c/number-of-minutes-in-an-hour/index.md): Know the number of minutes in an hour and the number of hours in a day - [Time Units and Calendar Facts](https://ai.page/c/time-units-and-calendar-facts/index.md): Know the number of seconds in a minute and the number of days in each month, year, and leap year - [Ordering Events in Time](https://ai.page/c/ordering-events-in-time/index.md): Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, evening - [Days, Weeks, Months & Years](https://ai.page/c/days-weeks-months-and-years/index.md): Recognise and use language relating to dates, including days of the week, weeks, months, and years - [Telling Time: Hours and Half Hours](https://ai.page/c/telling-time-hours-and-half-hours/index.md): Tell the time to the hour and half past the hour, and draw clock hands to show these times ## 9. Measurement · Geometry - [Turns & Directions](https://ai.page/c/turns-and-directions/index.md): Describe movement and direction, including whole, half, quarter, and three-quarter turns ## 10. Geometry · Shapes - [3-D shapes](https://ai.page/c/3-d-shapes/index.md): Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones) - [2-D shapes](https://ai.page/c/2-d-shapes/index.md): Recognise and name common 2-D shapes (circles, triangles, rectangles including squares) - [3-D shapes (age 5+)](https://ai.page/c/3-d-shapes-age-5/index.md): Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes - [Edges, vertices, and faces](https://ai.page/c/edges-vertices-and-faces/index.md): Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces ## 11. Geometry · Spatial reasoning - [Shape patterns](https://ai.page/c/shape-patterns/index.md): Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently ## 12. Geometry · Pathways - [Positional Language](https://ai.page/c/positional-language/index.md): Describe the position of objects using terms such as above, below, beside, in front of, behind, next to ## 13. Statistics · Developing knowledge from data - [Sorting into categories (age 6+)](https://ai.page/c/sorting-into-categories-age-6/index.md): Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another - [Pictograms and tally charts (age 6+)](https://ai.page/c/pictograms-and-tally-charts-age-6/index.md): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data ## 14. Statistics · Visualisation of data representations (including picture graphs) - [Pictograms and tally charts](https://ai.page/c/pictograms-and-tally-charts/index.md): Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables ## Health: 0 of 100 Of its 42 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): - Addition in any order has no explanation yet - Subtraction as taking away or separating has no explanation yet - Adding and subtracting has no explanation yet - Addition and subtraction word problems has no explanation yet - Addition and subtraction within 20 has no explanation yet - Adding Three Small Numbers has no explanation yet - Division as equal sharing has no explanation yet - Multiplication as repeated addition has no explanation yet - Arrays for multiplication has no explanation yet - What Is a Half? has no explanation yet - Fractions of amounts has no explanation yet - Simple Fraction Sums has no explanation yet - Understanding fractions has no explanation yet - Adding money and giving change has no explanation yet - Money Addition & Subtraction has no explanation yet - Reading ×, ÷, and = Symbols has no explanation yet - Comparing groups: more or fewer has no explanation yet - Inverse: addition undoes subtraction has no explanation yet - Patterns & Sequences has no explanation yet - Choosing measurement units has no explanation yet - Measurable Attributes of Objects has no explanation yet - Comparing lengths by measuring has no explanation yet - Comparing and ordering measurements has no explanation yet - Measuring Perimeters has no explanation yet - Measuring length (age 6+) has no explanation yet - Area by Tiling has no explanation yet - Telling time to the minute has no explanation yet - Number of minutes in an hour has no explanation yet - Time Units and Calendar Facts has no explanation yet - Ordering Events in Time has no explanation yet - Days, Weeks, Months & Years has no explanation yet - Telling Time: Hours and Half Hours has no explanation yet - Turns & Directions comes before Positional Language, which it needs - Turns & Directions has no explanation yet - 3-D shapes has no explanation yet - 2-D shapes has no explanation yet - 3-D shapes (age 5+) has no explanation yet - Edges, vertices, and faces has no explanation yet - Shape patterns has no explanation yet - Positional Language has no explanation yet - Sorting into categories (age 6+) has no explanation yet - Pictograms and tally charts (age 6+) has no explanation yet - Pictograms and tally charts 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.