Checking whether a model's answer makes practical sense | Year 9

01 / LEARN

The idea, step by step

Substitute and estimate

After solving a financial equation, substitute the result back into the original rule. Also make a rough estimate: interest of thousands of dollars on a small principal at a few percent should trigger a check. A calculator can correctly evaluate a wrongly entered formula.

Keep the units visible. A monthly time inserted into a formula expecting years, or a percentage inserted without dividing by 100, can produce a neat but implausible result. Check whether a reported amount is interest alone or the total balance.

A practical answer needs a practical input

Counts of tickets or items are usually non-negative whole numbers. A length is positive, a supplied price must meet its domain, and a prediction beyond the modelled range needs justification. Report currency to cents at the final step unless the question asks otherwise.

Rounding each intermediate calculation can change a final comparison, so retain useful precision while working. A limitation should identify a particular assumption, such as no fees or unchanged demand. “The model might be wrong” is less useful than saying which input should be checked.

A common trap

A calculator display proves the answer fits the situation.

Instead: The model, units, allowed inputs and assumptions still need checking.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example

A calculation says 300 dollars at 4% simple interest earns 2,400 dollars in 2 years. Find and correct the likely rate-entry error.

The rate is $0.04$ , not $4$ .
$I = 300 (0.04) (2) = 24$ .
A quick estimate gives about $12$ dollars per year, supporting the correction.

Correct interest AUD 24.00

Example 2

Worked example

An item-count equation gives $n = - 8$ or $n = 5$ . The rule is $C = n^{2} + 3 n + 10$ and C=50 dollars. Interpret the result.

A count cannot be negative, so reject $- 8$ .
Check $C (5) = 25 + 15 + 10 = 50$ .
The accepted solution satisfies both the equation and the context.

n = 5

items

Check your understanding

A model permits 0 to 12 sessions. Does its formula justify a quote for 20 sessions?

Show answer

No.

Twenty lies outside the stated model domain.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A principal of 400 dollars at 5% simple interest for 2 years is said to earn 4,000 dollars. Correct it.
2 marks
For an annual interest formula, convert 9 months to years.
2 marks
Interest is 28 dollars on a 350-dollar principal. Find the final amount.
2 marks
A ticket equation gives counts 4 and 11, but only 8 places are available. Which count is feasible?
2 marks
A charge is 7.50 dollars per item. Find the total for 3 items and report it to cents.
2 marks
A model assumes no booking fee, but the venue charges one. Explain how to improve the cost model.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A principal of 400 dollars at 5% simple interest for 2 years is said to earn 4,000 dollars. Correct it.
2 marks
$I = 400 (0.05) (2) = 40$ .
AUD 40.00 interest
For an annual interest formula, convert 9 months to years.
2 marks
$9 / 12 = 0.75$ .
$0.75$ years
Interest is 28 dollars on a 350-dollar principal. Find the final amount.
2 marks
$A = P + I = 350 + 28 = 378$ .
AUD 378.00
A ticket equation gives counts 4 and 11, but only 8 places are available. Which count is feasible?
2 marks
Eleven exceeds capacity; four does not.
$4$
A charge is 7.50 dollars per item. Find the total for 3 items and report it to cents.
2 marks
$7.50 \times 3 = 22.50$ .
AUD 22.50
A model assumes no booking fee, but the venue charges one. Explain how to improve the cost model.
3 marks
The fee is paid independently of the number of people/items.
A revised form is $C = F + r n$ when fee $F$ and per-person rate $r$ are supplied.
Add the supplied booking fee as a fixed cost.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 9 financial modelling within AC9M9A05 and AC9M9M05; supplied hypothetical rates and costs, not financial advice.

Official curriculum source ↗

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