Response to investigate
Move the six and change the sign.
Practical disciplinary literacy
Maths: disciplinary literacy in practice
Read an equation as a relationship and justify operations that preserve equality.
The task students are answering
Material to use
Give the equation 2x + 6 = 18 and two solutions. A: subtract 6 from both sides to get 2x = 12; divide both sides by 2 to get x = 6. B: subtract 6 only from the left side to get 2x = 18; divide by 2 to get x = 9.
Ask students
Which solution preserves equality? Identify the first invalid step in the other solution and explain why it is invalid.
Expected response
An annotated solution, one explanation of the invalid step and a substitution check in the original equation.
What to look for
- Identifies solution A as valid.
- Explains that the same operation must be applied to both sides.
- Checks that x = 6 satisfies the original equation; x = 9 does not.
How a response can develop
The model and sample responses below address the question above. Reveal the teaching interpretation after discussing what is clearer in the improved response.
Represent
2x + 6 = 18 represents two equal quantities.
Transform
Subtract 6 from both sides: 2x = 12. Divide both sides by 2: x = 6.
Verify
Substitute: 2 × 6 + 6 = 18. The original equality holds.
More precise response
Subtract six from both sides to preserve equality. Then divide both sides by two. Substituting x = 6 gives 18 on each side.
Reveal the teaching interpretation
The shorthand may conceal understanding. Ask for a balance sketch or oral justification before deciding whether the difficulty is conceptual or linguistic.
These are invented teaching samples. One response alone does not establish proficiency, attainment or a learning difficulty.
Teacher preparation and teaching sequence
Prepare the material described in Visual model. Read the exact student question aloud and show the expected response before modelling. For Music and PE, supply the recording or demonstration first.
- Read or observe: introduce the task: Explain and check a solution to 2x + 6 = 18.
- Model: think aloud through the three-part model, connecting each decision to the evidence.
- Notice: compare the two sample responses. Identify one meaning difference, not just a difference in length.
- Rehearse: Pairs compare a valid solution with one that subtracts from only one side. Annotate the first invalid step.
- Transfer: Solve 3x + 5 = 20 and explain why each operation is valid. Verify by substitution.
Useful language to notice
Subtract six from both sides to preserve equality. Then divide both sides by two. Substituting x = 6 gives 18 on each side.
Highlight words that connect evidence, explanation and qualification. Choose a small useful phrase set rather than asking learners to memorise the entire model.
Use the task with your class
Student instructions
Which solution preserves equality? Identify the first invalid step in the other solution and explain why it is invalid.
Produce: An annotated solution, one explanation of the invalid step and a substitution check in the original equation.
Independent follow-up
Solve 3x + 5 = 20. Explain each operation and verify your answer by substitution.
Use the fresh task after practice. Record what the learner achieves and which supports remain necessary.
Adapt and keep your resource
Edit these fields for your class or department. Drafts stay in this browser; use anonymised evidence. Download an editable text copy to keep it elsewhere.
Model the decisions, then invite a response
“What did you do to both sides, and why does that preserve equality?”
“What evidence supports that connection?”
“Which condition, exception or limitation matters here?”
Respond to the sample
The shorthand may conceal understanding. Ask for a balance sketch or oral justification before deciding whether the difficulty is conceptual or linguistic.
First establish the learner’s subject meaning through talk, a sketch or a familiar-language response. Then address one English choice that helps communicate that meaning.
Access, independence and department use
Access: introduce essential terms with a representation; allow bilingual notes, partner rehearsal and a brief sentence frame. Keep the subject reasoning.
Independence: use fresh content and remove the full model. Retain required access arrangements and record any prompts.
Department pilot: use this routine in one unit. Collect a small anonymised sample before and after teaching, note the support provided and review with an EAL colleague.
Plan a manageable pilotMaths: disciplinary literacy in practice
Everyday communication and academic language
BICS is a useful shorthand for interpersonal communication; CALP draws attention to the language demands of academic learning. They are not two learner categories or a direct WIDA/CEFR conversion. Familiar conversation can conceal difficulty with a dense text or an unfamiliar subject explanation. Look at the task, context, support and individual language domains.
Plan from what learners can do
WIDA’s Key Uses provide a useful way to identify the communicative purpose: recount, explain, argue or discuss. Use the grade-band descriptors with the learner’s domain-specific evidence and choose support that keeps the subject thinking intact.
- Recount: Describe the sequence used to solve a ratio problem.
- Explain: Explain why two fractions are equivalent using a representation.
- Argue: Decide whether a worked solution is valid and justify your judgement with a counterexample or calculation.
- Discuss: Compare two methods and agree when each is useful.
Open the subject language planner
Original teaching examples informed by WIDA Can Do Descriptors. They are not official descriptors or predicted assessment outcomes.