Basic Numeracy Review
Back to Numbers
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Back to Numbers
Open with a calm, welcoming tone. This lesson is a mixed-age review, so keep examples familiar and low-stakes.
Our learning goal
I can use number facts, place value, and simple operations to solve basic number problems.
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What number words or maths ideas do you already know?
Use this as a calm activation. Accept words like add, take away, bigger, tens, ones, number line, counting, equal, total.
Reading and writing numbers
Numbers can be shown in digits and in words
We read numbers from left to right
Each digit has a place in the number
Example: 245 means 2 hundreds, 4 tens and 5 ones
For younger or less confident pupils, stay within 2- or 3-digit numbers first, then extend if needed.
Comparing numbers
A number can be greater than, less than, or equal to another number
Compare the biggest place value first
Example: 318 > 281 because 3 hundreds is more than 2 hundreds
The symbols are >, < and **=
Students may reverse the symbols. Reinforce the meaning with concrete language such as 'more than' and 'less than'.
Ordering numbers
When we order numbers, we put them in a sequence from smallest to largest or largest to smallest.
Example: 14, 29, 31, 45
We look carefully at the tens first, then the ones if needed.
Use a number line if learners need visual support. Mixed-age groups may order 2-digit, 3-digit or 4-digit numbers.
Using a number line
A number line shows numbers in order
Numbers get bigger as we move right
Numbers get smaller as we move left
It helps us compare, count on and count back
This slide links number sense to later addition and subtraction. Emphasise direction and spacing.
Place value
A digit's value depends on its place
In 472, the 4 means 4 hundreds
The 7 means 7 tens
The 2 means 2 ones
If appropriate, extend to thousands for older pupils, but keep the core language the same for all learners.
Making numbers in parts
A number can be split into parts.
472 = 400 + 70 + 2
This is called partitioning. It helps us understand what each digit is worth.
Partitioning is a key bridge to mental maths and written methods.
Ten more, ten less
Adding 10 changes the tens digit
Subtracting 10 changes the tens digit
Example: 53 → 63 is ten more
Example: 53 → 43 is ten less
The ones digit stays the same
Some pupils may also be ready for 100 more and 100 less; mention only if it supports the group.
Counting patterns
We can count in 1s, 2s, 5s and 10s
Counting in patterns helps us work quickly
Skip counting helps with repeated addition
It also helps with multiplication later
Keep this rooted in numeracy review rather than moving deeply into multiplication.
Addition means combining
Addition joins numbers together
We can add by counting on
We can use number facts we already know
Example: 7 + 5 = 12
Model several routes: objects, number line, and mental counting on. Different learners may rely on different supports.
Finding sums step by step
A larger addition can be broken into parts.
23 + 14 = 23 + 10 + 4
23 + 10 = 33
33 + 4 = 37
This shows decomposition without overloading formal written methods.
Number bonds and facts
Number bonds are pairs that make a total
Important bonds include numbers that make 10 and 20
Knowing facts quickly helps with harder questions
Example: 6 + 4 = 10
Useful review point for mixed attainment. You can vary totals while keeping the structure the same.
Checking addition
We can check if an answer is reasonable
We can add in a different order
We can use subtraction to check
Example: if 9 + 8 = 17, then 17 - 8 = 9
This is a good place to emphasise accuracy without making the lesson feel like a test.
Which number bond makes 10?
6 and 5
7 and 2
6 and 4
8 and 3
Checks number bonds from slide 12. Distractors are near-miss totals.
Complete the addition paragraph
Addition means numbers together. We can count on to add. In 23 + 14, we can split 14 into 10 and 4. Then 23 + 10 = 33 and 33 + 4 = 37. We can also use subtraction to check an addition answer.
Uses taught addition language only: combining, count on, 37, check.
What helps you solve an addition question?
Expected elements: students may say number bonds, counting on, splitting into parts, or using subtraction to check. Invite more than one valid method.
Subtraction means taking away
Subtraction finds how many are left
It can also find the difference between numbers
We can count back or count up
Example: 15 - 6 = 9
Be explicit that subtraction has more than one meaning: take away and difference.
Counting back and counting up
For some questions, counting back is helpful
For others, counting up is easier
Example: from 18 to 20 is 2, then to 25 is 5 more
So the difference between 18 and 25 is 7
This supports flexible thinking. Some pupils find counting up easier than take-away subtraction.
Breaking subtraction into parts
We can split a number to make subtraction easier.
34 - 12 = 34 - 10 - 2
34 - 10 = 24
24 - 2 = 22
Keep the worked example simple and visible. This mirrors the addition decomposition strategy.
Checking subtraction
Addition can check subtraction
Example: if 13 - 5 = 8, then 8 + 5 = 13
This helps us spot mistakes
The numbers should fit the story of the question
Link back to inverse operations in simple language: addition and subtraction undo each other.
Words that help us choose
Some maths words give us clues.
Add, total, altogether often link to addition.
Take away, left, difference often link to subtraction.
We still need to think carefully about what the problem means.
Avoid teaching keywords as rigid rules; the final sentence matters because some word problems are trickier.
Choosing a good method
Use objects when you need something concrete
Use a number line to count on or back
Use place value to split numbers into parts
Use known number facts to work mentally
This is especially important for a special education setting: validate different successful methods.
An example problem
Sam has 27 stickers and gets 5 more.
We can count on from 27, or add 3 and then 2.
27 + 5 = 32
Walk through more than one method aloud so pupils see that maths can be flexible.
What good number sense looks like
Reading numbers correctly
Knowing which number is bigger or smaller
Using place value to understand numbers
Choosing sensible ways to add or subtract
Checking if an answer makes sense
This lands the lesson by tying together the full review into one picture of basic numeracy.
Which word often tells us to subtract?
altogether
difference
total
sum
Checks understanding of clue words from slide 18 without treating keywords as rigid rules.
Complete the subtraction ideas
Subtraction can mean taking away or finding the between numbers. We can count up from 18 to 25 to find 7. We can also split 12 into 10 and 2, so 34 - 12 = 34 - 10 - 2. Addition can check subtraction answers.
Anchors the key subtraction ideas from slides 14-17: difference, count up, subtract 10, check.
Which method helps you most with number problems?
Objects
Number line
Place value
Number facts
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What is one thing you learned today?
Reflection only. Encourage simple answers such as place value, number bonds, counting on, or checking answers.
What helped you understand maths best today?
Reflection only. Students might mention number lines, counters, worked examples, or splitting numbers into parts.
How did you feel about today's number work?
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Glossary
digit - one symbol used to write a number, such as 3 or 7
place value - the value of a digit because of its place in a number
ones - the first place in a whole number
tens - the place that means groups of ten
hundreds - the place that means groups of one hundred
partitioning - splitting a number into parts to show its value
number line - a line that shows numbers in order
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Glossary
addition - combining numbers to find a total
subtraction - taking away or finding the difference
sum - the answer to an addition question
difference - how much bigger one number is than another
number bond - a pair of numbers that makes a known total
equal to - having the same value as
reasonable - likely to be correct and make sense
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