g10-05-05 · Core topics
Should the points be joined?
The same cost formula y=2x+4 describes time or item count. Which graph permits x=2.5?
1 MIN · PREDICT ON PAPER
Draw five table points. Predict whether connecting them preserves the intended inputs.
Discuss or write first. No typed answer is required to continue.
Fixed domain: [0, 4]. Learner placements: 5/5. Joining: on. The straight-line model is given.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
On the real interval [0,4], the affine model gives a line segment. On {0,1,2,3,4}, it gives five separate points. The point (2.5,9) belongs only to the time model.
Conditions: Linearity is a stated model assumption. A finite table alone does not establish a unique formula.
Mathematical justification: For each permitted x the formula gives one point. The domain decides which x occur. The rule 2x+4+x(x−1) matches two given points but is not the same rule.
1 MIN · EXIT CHECK
For 0–4 whole tickets costing 2x+4, is (2.5,9) on the graph?
Check after answering
No: 2.5 is outside the ticket-count domain.
Teacher guidance and extension
Before: Read function inputs, outputs and the stated domain; write your first prediction on paper.
Ask: Ask what half an item means before toggling the joining segments.
Watch for: All plotted data points should be connected.
Challenge: Give another formula agreeing with y=2x+4 at x=0 and 1 but differing elsewhere.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
Paper responses are enough. Drafts remain in this tab; choose local saving to include them in the existing complete backup.
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