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Four operations in context
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Foundational skills
Identify addition from context
\[ \text{Example: } \text{Total?} \rightarrow + \]
Recognise when a word problem requires addition.
Identify subtraction from context
\[ \text{Example: } \text{Left?} \rightarrow – \]
Recognise when a word problem requires subtraction.
Identify multiplication from context
\[ \text{Example: } \text{Groups?} \rightarrow \times \]
Recognise when a word problem requires multiplication.
Identify division from context
\[ \text{Example: } \text{Shared?} \rightarrow \div \]
Recognise when a word problem requires division.
Choose between all four operations
\[ \text{Context} \rightarrow +, -, \times, \div \]
Identify the correct operation from a word problem.
One-step: Addition
Addition — combining two amounts
\[ \text{Tom has 5, gets 3} \rightarrow 8 \]
Solve a one-step addition problem where two amounts are combined.
Addition — increasing an amount
\[ 150 \text{ books, } 50 \text{ more} \rightarrow 200 \]
Solve a one-step addition problem where an amount is increased.
Addition — finding a total from parts
\[ 20 \text{ boys, } 30 \text{ girls} \rightarrow 50 \]
Solve a one-step addition problem where parts are combined to find a total.
One-step: Subtraction
Subtraction — taking away
\[ \text{Had 50, gave 10} \rightarrow 40 \]
Solve a one-step subtraction problem where an amount is taken away.
Subtraction — finding the difference
\[ \text{A: 50, B: 40} \rightarrow 10 \]
Solve a one-step subtraction problem to find the difference.
Subtraction — missing part
\[ \text{Need 100, have 80} \rightarrow 20 \]
Solve a one-step subtraction problem to find a missing part.
One-step: Multiplication
Multiplication — equal groups
\[ 5 \text{ boxes of } 4 \rightarrow 20 \]
Solve a one-step multiplication problem involving equal groups.
Multiplication — scaling and cost
\[ 3 \text{ items at £5} \rightarrow \text{£15} \]
Solve a one-step multiplication problem involving cost or scaling.
Multiplication — arrays and area
\[ 4 \text{ rows of } 6 \rightarrow 24 \]
Solve a one-step multiplication problem involving rows/columns.
One-step: Division
Division — sharing equally
\[ 20 \text{ shared by } 4 \rightarrow 5 \]
Solve a one-step division problem where a total is shared equally.
Division — grouping
\[ 20 \text{ put in 5s} \rightarrow 4 \text{ groups} \]
Solve a one-step division problem where items are put into equal groups.
Division — finding a unit amount
\[ 5 \text{ cost £20} \rightarrow \text{£4 each} \]
Solve a one-step division problem to find the value of one item.
Two-step: Same operation
Two additions
\[ 10 + 5 + 8 \rightarrow 23 \]
Solve a two-step problem requiring addition twice.
Two subtractions
\[ 100 – 20 – 10 \rightarrow 70 \]
Solve a two-step problem requiring subtraction twice.
Two multiplications
\[ 3 \times 4 \times 5 \rightarrow 60 \]
Solve a two-step problem requiring multiplication twice.
Two divisions
\[ 100 \div 2 \div 5 \rightarrow 10 \]
Solve a two-step problem requiring division twice.
Two-step: Mixed operations
Addition then subtraction
\[ (10 + 5) – 3 \rightarrow 12 \]
Solve a two-step problem requiring addition then subtraction.
Subtraction then addition
\[ (20 – 5) + 8 \rightarrow 23 \]
Solve a two-step problem requiring subtraction then addition.
Multiplication then add/sub
\[ (3 \times 4) + 2 \rightarrow 14 \]
Multiply then add or subtract.
Division then add/sub
\[ (20 \div 4) + 3 \rightarrow 8 \]
Divide then add or subtract.
Add/sub then multiply
\[ (2 + 3) \times 4 \rightarrow 20 \]
Add or subtract then multiply.
Add/sub then divide
\[ (10 + 10) \div 2 \rightarrow 10 \]
Add or subtract then divide.
Multiply and divide
\[ (4 \times 10) \div 8 \rightarrow 5 \]
Solve a two-step problem requiring both multiplication and division.
Multi-step problems
Three-step mixed
\[ \text{Buy, Spend, Earn} \]
Solve a three-step problem involving mixed operations.
Three additions
\[ A + B + C + D \]
Solve a three-step problem requiring three additions.
Operation selection
\[ \text{Context decides ops} \]
Multi-step where student determines correct operations.
Implied calculation
\[ \text{Area } – \text{ Broken} \]
Multiplication needed before subtraction (implied).
Special cases
Division — round up
\[ 20 \div 6 \rightarrow 4 \text{ boxes} \]
Division with remainder where context requires rounding up.
Division — round down
\[ 20 \div 6 \rightarrow 3 \text{ full} \]
Division with remainder where context requires rounding down.
Division — remainder
\[ 20 \div 6 \rightarrow 2 \text{ left} \]
Division problem where the answer is the remainder.
Extra information
\[ \text{Ignore irrelevant data} \]
Word problem with extra info not needed for calculation.
Inverse — find start
\[ ? – 5 = 10 \rightarrow 15 \]
Find the starting amount using inverse operations.
Inverse — missing part
\[ 20 – ? = 15 \rightarrow 5 \]
Find a missing part using inverse operations.
Multi-step inverse
\[ (? \times 2) + 1 = 11 \rightarrow 5 \]
Two-step inverse problem.
Timer (Optional)
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