# Key stage 1: Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 78 concepts ready. In the app: https://ai.page/roadmap/uk-nc-2013-key-stage-1-mathematics

Part of: [National Curriculum in England](https://ai.page/roadmap/uk-nc-2013.md)

Goal: The national curriculum in England: Key stages 1 and 2 framework document, Key stage 1

## 1. Number - addition and subtraction

- [Addition as combining or putting together two](https://ai.page/c/addition-as-combining-or-putting-together-two/index.md): Understand addition as combining or putting together two groups to find the total
- [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
- [Reading +, −, and = symbols](https://ai.page/c/reading-and-symbols/index.md): Read, write, and interpret the symbols +, −, and = in number sentences
- [Numbers up to 10 into pairs](https://ai.page/c/numbers-up-to-10-into-pairs/index.md): Decompose numbers up to 10 into pairs in more than one way (part-part-whole)
- [Number bonds to 9](https://ai.page/c/number-bonds-to-9/index.md): Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)
- [Number bonds](https://ai.page/c/number-bonds/index.md): Recall number bonds (addition and related subtraction facts) within 20
- [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
- [Representing Addition and Subtraction](https://ai.page/c/representing-addition-and-subtraction/index.md): Represent addition and subtraction using objects, drawings, and mental images
- [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
- [Early Word Problems](https://ai.page/c/early-word-problems/index.md): Solve one-step word problems involving addition and subtraction to 20, including missing-number problems
- [Mental addition and subtraction (age 6+)](https://ai.page/c/mental-addition-and-subtraction-age-6/index.md): Add and subtract a two-digit number and ones mentally and using concrete/pictorial representations
- [Adding and subtracting tens mentally](https://ai.page/c/adding-and-subtracting-tens-mentally/index.md): Add and subtract a two-digit number and tens mentally and using concrete/pictorial representations
- [Adding two two-digit numbers](https://ai.page/c/adding-two-two-digit-numbers/index.md): Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods
- [Mental and written addition and subtraction](https://ai.page/c/mental-and-written-addition-and-subtraction/index.md): Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures
- [Fluent addition and subtraction](https://ai.page/c/fluent-addition-and-subtraction/index.md): Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- [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
- [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
- [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

## 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
- [Finding halves and quarters (age 5+)](https://ai.page/c/finding-halves-and-quarters-age-5/index.md): Recognise, find, and name a quarter as one of four 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
- [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. Geometry - position and direction

- [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
- [Turns & Directions](https://ai.page/c/turns-and-directions/index.md): Describe movement and direction, including whole, half, quarter, and three-quarter turns
- [Patterns & Sequences](https://ai.page/c/patterns-and-sequences/index.md): Order and arrange combinations of mathematical objects in patterns and sequences
- [Position, direction, and movement](https://ai.page/c/position-direction-and-movement/index.md): Use mathematical vocabulary to describe position, direction, and movement, including straight lines and distinguishing rotation as a turn in terms of right angles (quarter, half, three-quarter turns, clockwise and anti-clockwise)

## 4. Geometry - properties of shapes

- [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](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 (age 6+)](https://ai.page/c/2-d-shapes-age-6/index.md): Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line
- [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
- [2-D faces on 3-D shapes](https://ai.page/c/2-d-faces-on-3-d-shapes/index.md): Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid)
- [Sorting 2-D and 3-D shapes](https://ai.page/c/sorting-2-d-and-3-d-shapes/index.md): Compare and sort common 2-D and 3-D shapes and everyday objects by their properties

## 5. Measurement

- [Comparing Lengths & Heights](https://ai.page/c/comparing-lengths-and-heights/index.md): Compare two objects directly by length or height and describe the difference using language such as long, short, tall, longer, shorter, taller, double, half
- [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
- [Comparing durations](https://ai.page/c/comparing-durations/index.md): Use comparative language for time: quicker, slower, earlier, later
- [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
- [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
- [Measuring mass and weight (age 4+)](https://ai.page/c/measuring-mass-and-weight-age-4/index.md): Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter than
- [Comparing Capacity](https://ai.page/c/comparing-capacity/index.md): Compare and describe capacity and volume using language such as full, empty, more than, less than, half full
- [Measuring length and height (age 5+)](https://ai.page/c/measuring-length-and-height-age-5/index.md): Measure and begin to record lengths and heights using non-standard and standard units
- [Measuring mass and weight](https://ai.page/c/measuring-mass-and-weight/index.md): Measure and begin to record mass/weight using non-standard and standard units
- [Capacity and volume](https://ai.page/c/capacity-and-volume/index.md): Measure and begin to record capacity and volume using non-standard and standard units
- [Coin Values](https://ai.page/c/coin-values/index.md): Recognise and know the value of different coins and notes
- [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
- [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 =
- [Pounds & Pence Notation](https://ai.page/c/pounds-and-pence-notation/index.md): Recognise and use symbols for pounds (£) and pence (p) and combine amounts to make a particular value
- [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
- [Sequence intervals of time](https://ai.page/c/sequence-intervals-of-time/index.md): Compare and sequence intervals of time
- [Telling Time: Minutes](https://ai.page/c/telling-time-minutes/index.md): Tell and write the time to five minutes, including quarter past and quarter to, and draw clock hands to show these times
- [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

## 6. Number - multiplication and division

- [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
- [Odd and even numbers](https://ai.page/c/odd-and-even-numbers/index.md): Recognise odd and even numbers
- [Times tables](https://ai.page/c/times-tables/index.md): Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables
- [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
- [Commutative Multiplication](https://ai.page/c/commutative-multiplication/index.md): Understand and apply the commutative property of multiplication and recognise that division is not commutative
- [Multiplication as repeated addition (age 6+)](https://ai.page/c/multiplication-as-repeated-addition-age-6/index.md): Solve problems involving multiplication and division using arrays, repeated addition, mental methods, and known facts

## 7. Number - number and place value

- [Rote counting to 100](https://ai.page/c/rote-counting-to-100/index.md): Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones
- [Counting in 2s](https://ai.page/c/counting-in-2s/index.md): Count in multiples of 2, 5, and 10 (skip counting)
- [Reading and writing numbers to 20](https://ai.page/c/reading-and-writing-numbers-to-20/index.md): Read and write numerals from 0 to 20
- [Reading and writing numbers to 100](https://ai.page/c/reading-and-writing-numbers-to-100/index.md): Read and write numerals from 0 to 100
- [One More Each Time](https://ai.page/c/one-more-each-time/index.md): Each successive counting number represents a quantity that is one larger than the previous number
- [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
- [Representing numbers with objects](https://ai.page/c/representing-numbers-with-objects/index.md): Represent numbers using objects, pictorial representations, and the number line
- [Number Words to Twenty](https://ai.page/c/number-words-to-twenty/index.md): Read and write number words from one to twenty
- [Counting forwards and backwards](https://ai.page/c/counting-forwards-and-backwards/index.md): Count forwards and backwards in steps of 3 from 0
- [The two digits of a two-digit number](https://ai.page/c/the-two-digits-of-a-two-digit-number/index.md): Understand that the two digits of a two-digit number represent amounts of tens and ones
- [Counting forwards and backwards (age 6+)](https://ai.page/c/counting-forwards-and-backwards-age-6/index.md): Count forwards and backwards in tens from any number (not just multiples of 10)
- [Representing Numbers](https://ai.page/c/representing-numbers/index.md): Identify, represent, and estimate numbers using different representations including the number line
- [Comparing and ordering numbers](https://ai.page/c/comparing-and-ordering-numbers/index.md): Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding
- [Number Words to 100](https://ai.page/c/number-words-to-100/index.md): Read and write numbers to at least 100 in words
- [Place value understanding and number facts](https://ai.page/c/place-value-understanding-and-number-facts/index.md): Use place value understanding and number facts to solve problems

## 8. Statistics

- [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
- [Sorting Data into Categories](https://ai.page/c/sorting-data-into-categories/index.md): Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity
- [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

## Health: 0 of 100

Of its 78 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 as combining or putting together two has no explanation yet
- Subtraction as taking away or separating has no explanation yet
- Reading +, −, and = symbols comes before Reading and writing numbers to 20, which it needs
- Reading +, −, and = symbols has no explanation yet
- Numbers up to 10 into pairs has no explanation yet
- Number bonds to 9 has no explanation yet
- Number bonds has no explanation yet
- Adding and subtracting has no explanation yet
- Representing Addition and Subtraction has no explanation yet
- Addition and subtraction word problems has no explanation yet
- Early Word Problems has no explanation yet
- Mental addition and subtraction (age 6+) comes before The two digits of a two-digit number, which it needs
- Mental addition and subtraction (age 6+) has no explanation yet
- Adding and subtracting tens mentally comes before The two digits of a two-digit number, which it needs
- Adding and subtracting tens mentally has no explanation yet
- Adding two two-digit numbers has no explanation yet
- Mental and written addition and subtraction has no explanation yet
- Fluent addition and subtraction has no explanation yet
- Adding Three Small Numbers has no explanation yet
- Addition in any order has no explanation yet
- Inverse: addition undoes subtraction has no explanation yet
- What Is a Half? comes before Division as equal sharing, which it needs
- What Is a Half? has no explanation yet
- Finding halves and quarters (age 5+) has no explanation yet
- Fractions of amounts has no explanation yet
- Understanding fractions has no explanation yet
- Positional Language has no explanation yet
- Turns & Directions has no explanation yet
- Patterns & Sequences has no explanation yet
- Position, direction, and movement has no explanation yet
- 2-D shapes has no explanation yet
- 3-D shapes has no explanation yet
- 2-D shapes (age 6+) has no explanation yet
- Edges, vertices, and faces has no explanation yet
- 2-D faces on 3-D shapes has no explanation yet
- Sorting 2-D and 3-D shapes has no explanation yet
- Comparing Lengths & Heights has no explanation yet
- Ordering Events in Time has no explanation yet
- Days, Weeks, Months & Years has no explanation yet
- Comparing durations has no explanation yet
- Telling time to the minute has no explanation yet
- Telling Time: Hours and Half Hours comes before Reading and writing numbers to 20, which it needs
- Telling Time: Hours and Half Hours has no explanation yet
- Measuring mass and weight (age 4+) has no explanation yet
- Comparing Capacity has no explanation yet
- Measuring length and height (age 5+) has no explanation yet
- Measuring mass and weight has no explanation yet
- Capacity and volume has no explanation yet
- Coin Values comes before Reading and writing numbers to 20, which it needs
- Coin Values has no explanation yet

Credit: The structure of The national curriculum in England: Key stages 1 and 2 framework document; 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.