Year 2 Maths Tutor Online | Derive, Check and Explain

In short

Year 2 maths in England is set by the statutory Year 2 programme of study from the DfE, for children aged 6 to 7. Children recall addition and subtraction facts to 20 fluently and derive related facts up to 100, use tens and ones, add and subtract two-digit numbers, check answers with the inverse, learn the 2, 5 and 10 times tables, find thirds and quarters, tell the time to five minutes and read simple charts. We teach it live online through our Elementary Maths course, in a class of 15 to 20 or 1-on-1, and the opening class costs nothing.

Courses for Year 2

Which course fits a Year 2 child?

Elementary Maths is the core Year 2 course. Mental Maths builds the quick facts that make deriving possible, and Reasoning and Readiness stretches a child who finds class work easy.

Y2 / 01

Elementary Maths

Placed by grade with a short check: place value, two-digit adding and subtracting, the first tables, fractions, measures and data.

Open the syllabus →

Y2 / 02

Mental Maths for Kids

Making ten, doubles and near doubles, the facts a Year 2 child derives everything else from. Ages 5 to 10.

Open the syllabus →

Y2 / 03

Reasoning and Readiness

Pattern, shape and number puzzles across ages 6 to 9, once class work feels easy.

Open the syllabus →

Derive and check

What is the big change in Year 2 maths?

Children move from working every answer out to building new facts from old ones, and from trusting an answer to checking it. Both are written into the Year 2 programme.

Two statutory lines carry the change. Children should "recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100". And they should "recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems". The first says: if you know 3 + 7, you also know 30 + 70. The second says: if you think 52 − 18 is 34, add 34 and 18 and see whether you get back to 52.

How three ideas grow from Year 1 to Year 3 (DfE programmes of study; our pairing)
Idea	Year 1	Year 2	Year 3
Number facts	Bonds and subtraction facts within 20	Facts to 20 fluently; related facts to 100	Facts used with three-digit numbers
Checking	Not yet named	The inverse, to check and to solve missing numbers	Estimating and using the inverse to check
Order	Not yet named	Adding can be done in any order; subtracting cannot	Used in mental methods with larger numbers
Place value	Numbers to 100, beginning to see tens	Tens and ones in every two-digit number; zero as a place holder	Hundreds, tens and ones
Written methods	Number sentences	Recording in columns to prepare for formal methods	Formal column addition and subtraction

The curriculum's notes spell out how deriving is meant to look, using a whole family of facts: 3 + 7 = 10, 10 − 7 = 3 and 7 = 10 − 3 lead to 30 + 70 = 100, 100 − 70 = 30 and 70 = 100 − 30. They also link checking to order: children add numbers in a different order to check, which "establishes commutativity and associativity of addition". Those are long words for a simple habit, one every Year 2 child can learn: try it another way and see if you get the same answer.

Why this matters more than speed

A child who only counts gets slower as numbers grow. A child who derives gets faster, because each new fact rests on one already known.

Checking with the inverse also means a child catches their own mistakes, which builds confidence far better than being told an answer is wrong.

The test question

The end of KS1 tests are optional, and the DfE suggests May 2027 for any school that chooses them. The curriculum is the same either way.

A child who derives and checks is well prepared for any test a school uses, without special drilling.

Source: DfE, Mathematics programmes of study: key stages 1 and 2, Years 1 to 3, read on 31 October 2026; DfE, Primary assessments: future dates, updated 12 October 2026. The pairing across years is ours.

The Year 2 content

What do children learn in Year 2 maths?

Eight areas, from number to statistics. This is a plain-English summary of the statutory Year 2 requirements, with one useful note from the curriculum for each.

The Year 2 mathematics programme of study (DfE; our summary of the statutory lines)
Area	What children learn	A note from the curriculum
Number and place value	Counting in steps of 2, 3 and 5 from zero and in tens from any number; tens and ones; comparing and ordering to 100 with <, > and =	"They count in multiples of three to support their later understanding of a third."
Addition and subtraction	Two-digit numbers and ones, two-digit numbers and tens, two two-digit numbers, and three single digits; order and the inverse	"Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers."
Multiplication and division	The 2, 5 and 10 tables with division facts; odd and even; writing × and ÷ sentences; multiplication can be done in any order, division cannot	Children "use commutativity and inverse relations to develop multiplicative reasoning"
Fractions	Thirds, quarters, two quarters and three quarters of shapes, sets and lengths; two quarters equal a half	"Pupils should count in fractions up to 10, starting from any number"
Measurement	Centimetres, metres, grams, kilograms, litres, millilitres and degrees; money; time to five minutes; minutes in an hour, hours in a day	"Comparing measures includes simple multiples such as 'half as high'; 'twice as wide'."
Properties of shapes	Sides and vertical lines of symmetry on 2-D shapes; edges, vertices and faces of 3-D shapes; flat faces on solids	Sorting shapes by their properties, using precise words
Position and direction	Patterns and sequences; turns described as right angles, clockwise and anti-clockwise	Children give each other instructions for turns
Statistics	Pictograms, tally charts, block diagrams and simple tables; questions about totals and comparisons	Pictograms may use "simple ratios 2, 5, 10", where one picture stands for more than one

Two notes are easy to overlook. Place value: Year 2 children "begin to understand zero as a place holder", the idea that the 0 in 40 is what makes it forty rather than four. And counting: the 3s appear in Year 2 counting even though the 3 times table is a Year 3 statement, because counting in threes prepares for thirds. The curriculum is quietly building the next year inside this one.

Source: DfE Year 2 programme of study, its statutory lines and their guidance notes, consulted on 31 October 2026. The middle column summarises; the right-hand column quotes or closely follows the non-statutory notes.

Maths words

Which maths words should a Year 2 child know?

More than parents expect. The curriculum wants children to talk about maths precisely, and new words arrive in nearly every area.

The Year 2 notes say that "Pupils extend their understanding of the language of addition and subtraction to include sum and difference." Shape brings sides, edges, vertices and faces; measures bring the units; position brings clockwise and anti-clockwise. A child who knows the word can follow the question, which matters even more when questions are read aloud.

Year 2 vocabulary with a home example (words from the programme of study; examples ours)
Word	What it means	Ask at home
Sum	The total when numbers are added	"What is the sum of 12 and 9?"
Difference	How much bigger one number is than another	"What is the difference between 15 and 11?"
Inverse	The operation that undoes another	"How can adding check 40 minus 13?"
Vertex, vertices	A corner where edges meet	"How many vertices does this cereal box have?"
Face, edge	A flat surface; a line where two faces meet	"How many faces does a dice have?"
Clockwise	Turning the way clock hands go	"Turn a quarter turn clockwise. What do you face?"
Tally	Marks in groups of five for counting	"Tally the red cars that pass in five minutes."

Difference is the tricky one

Many children hear "difference" and add. Line up two towers of cubes and ask how many more one has: the gap is the difference.

Counting up from the smaller number is often easier than taking away, and it gives the same answer.

Time to five minutes

Year 2 asks children to "tell and write the time to five minutes, including quarter past/to the hour". Use a real analogue clock at home; a digital display does not teach it.

Count the minute hand round in fives from the 12. It doubles as 5 times table practice.

Worked examples

Five Year 2 examples, worked through

Written by us, and each one either derives or checks. They are written for a parent beside a child, objects first where it helps.

1. A fact to 20 becomes a fact to 100

Question (ours). 60 + 40, and then 100 − 40.

Known fact. 6 + 4 = 10.

Derive. Six tens and four tens make ten tens, which is 100. So 60 + 40 = 100, and taking 40 back leaves 60.

Why it matters. This is "derive and use related facts up to 100" in action. With ten-sticks, the child can see that only the word "ten" has been added.

2. Checking a subtraction by adding

Question (ours). A child works out 81 − 26 and gets 65.

Check. Add the answer to the number taken away: 65 + 26 = 91. That is not 81, so something slipped.

Find it. Partition: 81 − 20 = 61, then 61 − 6 = 55. Check again: 55 + 26 = 81.

Why it matters. The inverse turns every subtraction into its own answer key. The child finds the mistake, not the adult.

3. Adding three numbers the easy way

Question (ours). 8 + 5 + 2.

Spot a ten. 8 and 2 make 10. The order of adding makes no difference, so add those first.

Finish. 10 + 5 = 15.

Why it matters. Year 2 asks children to add three one-digit numbers, and to know order does not matter for adding. Together they make this quick.

4. A pictogram with a key of 5

Question (ours). In a pictogram, one star stands for 5 books. Class A has 4 stars and Class B has 3 stars. How many more books did Class A read?

Read it. Count each row in fives: Class A is 5, 10, 15, 20 books; Class B is 5, 10, 15 books.

Compare. The difference is 20 − 15 = 5 books, which is also just the one extra star.

Why it matters. Pictograms with a key of 2, 5 or 10 join the times tables to data. Spotting that one extra star means 5 more is the reasoning step.

5. Counting in quarters on a number line

Task (ours). Count in quarters from 1 to 2 on a number line.

Steps. 1, 1 and a quarter, 1 and two quarters, 1 and three quarters, 2.

Notice. 1 and two quarters is the same point as 1 and a half.

Why it matters. Counting in fractions is a Year 2 expectation, and it shows that fractions are numbers on a line, not just slices.

Practice set (ours, with answers)

(1) 70 + 30. (2) 100 − 30. (3) Check 64 − 27 = 37 by adding. (4) 7 + 6 + 3. (5) Write <, > or = : 5 tens and 3 ones □ 35. (6) A key shows 1 circle = 2 children; how many children do 6 circles show? (7) How many minutes are in an hour? (8) Count in threes from 0 to 15.

Answers: (1) 100; (2) 70; (3) 37 + 27 = 64, so it is right; (4) 16; (5) 53 > 35; (6) 12; (7) 60; (8) 0, 3, 6, 9, 12, 15.

Our Year 2 classes

When is a Year 2 maths tutor worth it?

When a child still counts for facts to 20, is unsure about tens and ones, or loses confidence. Year 3 brings column methods and three new tables, and they rest on Year 2.

Free first class. The teacher asks a few derive-and-check questions and plays a place value game, to see what is secure.
A small kit. Ten-sticks or bundled straws, single counters, and a clock with hands, kept next to the screen.
Derive out loud. Children say which known fact they used. "I know 4 + 5, so 40 + 50 is 90."
Check every time. Each subtraction is checked by adding, each addition by changing the order.
Between classes. One short game and a handful of questions, plus a note for parents at the end of each block.

Group or 1-on-1 in Year 2?

Our groups of 15 to 20 work well for a Year 2 child who enjoys a lively class and is keeping up.

Pick 1-on-1 when one gap, such as tens and ones, needs closing before Year 3, or when a child works far ahead.

What we will not do

Drill a seven year old with timed papers, or promise a test score. The end of KS1 tests are optional and we teach the curriculum.

Claim a connection with your child's school or with the Department for Education. We work separately from both.

Through Year 2

Four Year 2 checkpoints

Signs that the derive-and-check habit is taking hold. Each one can be seen at the kitchen table.

Year 2 checkpoints, drawn by us from the statutory content
Checkpoint	Typical timing	What it looks like
1. Tens and ones	Autumn	Says what each digit in 47 is worth, and that the 0 in 40 matters
2. Facts to 20 without counting	Late autumn	Answers 9 + 6 and 14 − 8 quickly
3. Derived facts to 100	Spring	Uses 7 + 3 to answer 70 + 30 and 100 − 70
4. Checking by habit	Summer	Checks a subtraction by adding, unprompted

Milestone four is the prize

A child who checks their own work has become an independent learner in maths.

For the next stage, see KS2 maths tuition.

Into Year 3

The 3, 4 and 8 tables and formal columns arrive next.

Lessons can pause over school holidays.

Catalogue

Nine courses for six and seven year olds

Core maths, faster facts and thinking courses for the end of Key Stage 1.

I

Core maths

Years 2 and 3

UK / Y21 / 01

Elementary Maths

Year 2 content, objects first, then numbers.

Open the syllabus

UK / Y21 / 02

Mental Maths

Making ten and doubles, for quick facts.

Open the syllabus

UK / Y21 / 03

Early Maths Foundations

For a child who needs numbers to 20 made firm.

Open the syllabus

II

Stretch

For keen thinkers

UK / Y22 / 01

Reasoning and Readiness

Pattern, shape and number reasoning, ages 6 to 9.

Open the syllabus

UK / Y22 / 02

Abacus maths

Place value you can push with a finger.

Open the syllabus

UK / Y22 / 03

Problem solving

Logic and word problems, from age 7.

Open the syllabus

III

Making

From age 6

UK / Y23 / 01

Coding for kids

Block programs with turns in right angles.

Open the syllabus

UK / Y23 / 02

Scratch games

Short games once reading is steady.

Open the syllabus

UK / Y23 / 03

Minecraft coding

For a Year 2 child turning seven.

Open the syllabus

Lessons

Inside a Year 2 class

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. All our teachers are based in India and all class times are listed in UK time.

After school

Short and lively, before tea.

Early evening

After clubs and activities.

Weekend morning

For calm, focused work.

Derive, do not count

Every new fact is linked to one already known.

Check by inverse

Children check their own answers every lesson.

Words matter

Sum, difference, vertex and clockwise used precisely.

Real clocks

Analogue clocks for time to five minutes.

Free first class

A friendly trial with a few derive-and-check games, free.

Group or 1-on-1

A group of 15 to 20, or one child with a teacher.

Student work

Projects from our classes

A small selection of student work from regular lessons, none of it marked. Student labs holds the rest.

AI and ML

NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · Open it

AI and ML

Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · Open it

AI and ML

GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · Open it

Web app

SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

Fees for Year 2 maths classes

No charge for the first class. Then one monthly fee, smaller for a group place than 1-on-1, which starts only after a course and a weekly time are settled. You can stop whenever you choose.

Free first class

USD 0

no card required

A friendly first class
A check of place value and facts to 20
Booking needs only a phone number

Book it

Group batch

USD 100

a month, billed in US dollars

15 to 20 Year 2 children
One teacher all year
Derive-and-check games at home
An update after each block

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One to one

USD 150

a month, billed in US dollars

One teacher, one child
Built around a specific gap
Room to stretch an able child

Enquire

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Year 2 questions

What parents of Year 2 children ask

What should my child be able to do in maths by July of Year 2?

Facts to 20 recalled fluently and related facts to 100, tens and ones, adding and subtracting two-digit numbers, checking with the inverse, the 2, 5 and 10 times tables, thirds and quarters, time to five minutes and simple charts.

What does derive related facts up to 100 mean?

Using a known fact to find a bigger one. If a child knows 3 + 7 = 10, they can derive 30 + 70 = 100 and 100 minus 70 = 30 without counting.

What is the inverse in Year 2 maths?

Adding and subtracting undo each other, so a child can check 52 minus 18 = 34 by adding 34 and 18. The Year 2 curriculum asks children to use this to check calculations and solve missing number problems.

Which times tables are in Year 2?

The 2, 5 and 10 times tables, with their division facts. Children also count in threes from zero, which prepares for the 3 times table in Year 3.

Is Year 2 maths harder than Year 1?

It moves faster. Numbers go to 100 in calculations, written methods start, and children are expected to explain and check. A secure Year 1 makes it much easier.

Are Year 2 maths worksheets enough practice?

They help with written calculation, but many Year 2 skills are spoken or practical: deriving facts aloud, checking by adding, reading a real clock and measuring. Mix worksheets with short games.

Does my Year 2 child have to sit SATs?

Not necessarily. The end of KS1 tests are optional, and the recommended window for schools that choose them is May 2027. Ask your child's teacher what the school plans.

How can I tell if my child needs extra help in Year 2?

Watch for counting on fingers for facts within 20, confusion over what each digit in a two-digit number is worth, or worry about maths. Any of these is worth a word with the teacher.

When are classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Times are shown in UK time.

Are you connected with my child's school?

No. We run our classes entirely separately from schools, local authorities and the Department for Education.

Primary maths

Pages for families at the end of Key Stage 1

What comes next, and other ways to keep a keen child busy.

KS2 maths tuition

The step after Year 2, through to Year 6.

The Year 4 tables check

Where the 2, 5 and 10 tables lead, two years on.

First grade maths (US)

US grade 1, for comparison across systems.

Primary Maths Challenge

Puzzles for confident primary children.

KS2 coding lessons

Coding from Year 3, for young problem solvers.

Coding classes in the UK

Our UK index of maths and coding pages.

Related pages in this guide

Part of the guide: UK maths year by year, Reception to Year 11

Primary, Reception to Year 6

Secondary, Year 7 to Year 11

Scotland

More guides: UK maths exam boards and specification codes · UK selective school maths tests: 7+, 11+, 13+ and 16+ · UK university admissions: maths tests and computing applications · UK maths enrichment, competitions and able pupils

Start here

Try a free Year 2 maths class

Add a phone number and a teacher will ring you back at a UK time of your choosing. The first class uses a few derive-and-check questions to find your child's starting point.

Want more detail first? Look at the Elementary Maths course week by week, or read how we teach.

WhatsApp us · +91 91233 66161 · connect@modernagecoders.com

The quickest route is WhatsApp, which is free from a UK mobile. Someone from our team in India will reply from a +91 number.

Want a class sooner? Book a priority demo

A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.

Book a priority demo

Which course fits a Year 2 child?

Elementary Maths

Mental Maths for Kids

Reasoning and Readiness

What is the big change in Year 2 maths?

Why this matters more than speed

The test question

What do children learn in Year 2 maths?

Which maths words should a Year 2 child know?

Difference is the tricky one

Time to five minutes

Five Year 2 examples, worked through

1. A fact to 20 becomes a fact to 100

2. Checking a subtraction by adding

3. Adding three numbers the easy way

4. A pictogram with a key of 5

5. Counting in quarters on a number line

Practice set (ours, with answers)

When is a Year 2 maths tutor worth it?

Group or 1-on-1 in Year 2?

What we will not do

Four Year 2 checkpoints

Milestone four is the prize

Into Year 3

Nine courses for six and seven year olds

Core maths

Elementary Maths

Mental Maths

Early Maths Foundations

Stretch

Reasoning and Readiness

Abacus maths

Problem solving

Making

Coding for kids

Scratch games

Minecraft coding

Inside a Year 2 class

Derive, do not count

Check by inverse

Words matter

Real clocks

Free first class

Group or 1-on-1

Projects from our classes

NutriLife

Misti

GuardianX

SkyCast

Fees for Year 2 maths classes

Rated 4.9 across 547 Google reviews

What parents of Year 2 children ask

What should my child be able to do in maths by July of Year 2?

What does derive related facts up to 100 mean?

What is the inverse in Year 2 maths?

Which times tables are in Year 2?

Is Year 2 maths harder than Year 1?

Are Year 2 maths worksheets enough practice?

Does my Year 2 child have to sit SATs?

How can I tell if my child needs extra help in Year 2?

When are classes?

Are you connected with my child's school?

Pages for families at the end of Key Stage 1

KS2 maths tuition

The Year 4 tables check

First grade maths (US)

Primary Maths Challenge

KS2 coding lessons

Coding classes in the UK

Related pages in this guide

Primary, Reception to Year 6

Secondary, Year 7 to Year 11

Scotland

Try a free Year 2 maths class

Want a class sooner? Book a priority demo

Keep exploring Modern Age Coders

More maths tuition

Learn more

From the blog

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