1.3 Calculator-Available vs. Non-Calculator Strategy and Item Formats

LANTITE Numeracy Item Formats

Questions in both sections appear in two core response formats. ACER's framework adds that 5 of the 65 numeracy items are unscored trial items; you cannot tell which ones, so give every question full effort:

1. Selected-Response Questions: These include simple multiple-choice items (usually four options, one correct) and complex multiple-choice items, where you choose a response for each of several statements—such as Yes/No, True/False, or True/False/Unable to determine—based on a shared chart or table.
2. Short-Answer Numeric Entry Questions: Instead of choosing from options, you type a calculated number directly into an on-screen text box. Because there are no multiple-choice options to alert you if you misplace a decimal point or misread a unit label, short-answer items require strict formatting and rounding discipline.

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Precision, Formatting, and Rounding Rules for Short-Answer Entry

1. Units Are Printed Outside the Input Box

Most numeric-entry boxes show the unit before or after the answer space—such as $, %, km, mL, hours, minutes, or students. ACER's practice-test instructions say almost all numeracy questions need a numeric response only, so type only the number (digits and, where required, a decimal point). A non-numeric entry triggers a pop-up warning and is not saved, so never type currency symbols, percentage signs, units, or words.

Always inspect the unit printed beside the box before typing your answer. A classic LANTITE trap provides stimulus dimensions in centimetres or minutes, while the label next to the answer box specifies metres or hours. Entering 150 when the box reads metres (instead of 1.5) turns a correct calculation into an incorrect response.

2. Preserve Full Precision Until the Final Step

In multi-step calculations, never round intermediate subtotals. Rounding a unit rate or intermediate decimal halfway through a four-step problem introduces cumulative rounding drift that can push your final digit outside the accepted scoring key. Keep full decimal precision on the on-screen calculator (and jot down at least 4–5 significant decimal digits on your scratch paper), then round only the final answer to the exact place value specified in the prompt:

• "to one decimal place" (tenth): Look at the second decimal digit ($24.36 \rightarrow 24.4$).
• "to two decimal places" (hundredth / nearest cent): Look at the third decimal digit ($18.426 rounds to $18.43).
• "to the nearest whole number / whole dollar": Look at the first decimal digit ($139.64 \rightarrow 140$).
• "to the nearest 5 cents": Applicable to Australian cash rounding rules ($14.32 rounds to $14.30; $14.33 rounds to $14.35).

3. Contextual Ceiling (Round Up) vs. Floor (Round Down) Constraints

When a problem asks for a physical count of people, vehicles, containers, or purchasable items, real-world constraints override standard nearest-integer ($0.5$) rounding:

• Ceiling Rounding (Always Round Up to the Next Whole Integer): Required whenever every person or item must be accommodated or supervised, or a minimum target must be reached. For example, if $148$ students are travelling on 45-seat buses, $148 \div 45 = 3.288...$ buses. Under standard rounding, $3.288$ rounds down to $3$, but $3$ buses hold only $135$ students and leave $13$ students behind. You must round up to $4$ buses. The same ceiling rule applies to mandatory adult-to-student supervision ratios and minimum paint tins needed to coat a wall.
• Floor Rounding (Always Round Down to the Completed Whole Integer): Required whenever a fixed budget, material length, or capacity cannot be exceeded. If a school department has a strict grant of $600.00 to purchase graphing calculators costing $44.00 each, $600 \div 44 = 13.636...$ calculators. Although $13.636$ is closer to $14$, buying $14$ calculators costs $616.00, which exceeds the grant. You must round down to $13$ calculators.

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Mastering the On-Screen Calculator and Two-Pass Pacing

Safe Operation of the Section 1 On-Screen Calculator

ACER designed the on-screen calculator specifically for this test, and its published guide (The on-screen calculator, 2019) documents how it behaves:

• Open and close it with the calculator icon at the top right of the screen; it closes automatically each time you move to the next question.
• It follows the order of operations: 17.50 + 19.75 × 3 = gives $76.75$, whereas (17.50 + 19.75) × 3 = gives $111.75$.
• The last result is stored in Ans for the next calculation, and the calculator icon beside an answer box copies the displayed result into that box.
• The % key converts a percentage to a decimal: 15% × 1250 = gives $187.5$, but 1250 − 15% = gives $1249.85$, because it subtracts $0.15$ rather than $15\%$ of $1250$.

To eliminate input errors:

1. Use Brackets and Scratch Paper as External Memory: Bracket every numerator or group that must be evaluated first, and record each intermediate subtotal on your scratch paper rather than trusting a long, unbroken chain of keystrokes.
2. Convert Percentages to Decimal Multipliers: Avoid the % key trap by typing multipliers directly: use $\times 0.15$ to find $15\%$, use $\times 1.15$ to increase a value by $15\%$, and use $\times 0.85$ to apply a $15\%$ discount (so $1250 \times 0.85 = 1062.50$).
3. Run a 5-Second Mental Order-of-Magnitude Check: Before clicking Next, approximate the calculation using rounded front-end numbers. If you are multiplying $38$ students by $24.50, mentally note that $40 \times 25 = 1{,}000$, so your exact answer ($931.00) must be just under $1,000. This immediately exposes a missed keystroke or misplaced decimal.

The Two-Pass Pacing Method

• Section 1 — Pass 1 (Minutes 0 to 75): Move methodically from Question 1 to Question 52. Complete every straightforward single-step or two-step question immediately. If a question features a dense multi-table stimulus that will take more than 2.5 minutes, write down what you have decoded, enter your best reasoned answer, note the question number on your scratch paper, and move on. This guarantees you never run out of time before seeing the final 10–15 questions of Section 1.
• Section 1 — Pass 2 (Minutes 75 to 92): Use the navigation bar at the top of the screen to return to the questions you noted and complete their calculations. Unanswered question numbers stay unshaded in the navigation bar, so check that all 52 are shaded.
• Section 2 Execution (Final 28–30 Minutes): Confirm the one-way transition into Section 2 with 25–30 minutes left on the timer. Use benchmark decomposition ($10\%, 5\%, 1\%, 25\%, 50\%$), equivalent fractions, and neat column working on your scratch paper for the 13 non-calculator questions.

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Worked Walkthroughs: Section 1 vs. Section 2

Walkthrough 1: Section 1 Multi-Step Short-Answer Problem (Calculator Available)

Scenario: A primary school plans a Year 6 excursion to a science discovery centre for $112$ students. School policy requires at least $1$ supervising adult for every $12$ students. The school hires 50-seat coaches at $640.00 per coach, and every student and supervising adult requires a coach seat. Entry to the centre costs $18.50 per student and is free for supervising adults. The school's Parents and Citizens (P&C) association contributes a flat subsidy of $550.00 toward total excursion costs. If the remaining cost is split equally among the $112$ students, what is the cost per student, rounded to the nearest whole dollar?

1. Minimum supervising adults (Ceiling Rounding):

$$112 \div 12 = 9.333... \implies 10\text{ adults required}$$

1. Total passengers and coaches required (Ceiling Rounding):

$$\text{Total passengers} = 112 + 10 = 122\text{ people}$$ $$122 \div 50 = 2.44 \implies 3\text{ coaches required}$$

1. Total coach and entry expenses:

$$\text{Coach hire} = 3 \times 640 = 1{,}920\text{ dollars}$$ $$\text{Student entry} = 112 \times 18.50 = 2{,}072\text{ dollars}$$ $$\text{Gross total} = 1{,}920 + 2{,}072 = 3{,}992\text{ dollars}$$

1. Subtract P&C subsidy and divide by $112$ students (Full Precision):

$$\text{Net cost} = 3{,}992 - 550 = 3{,}442\text{ dollars}$$ $$\text{Cost per student} = 3{,}442 \div 112 = 30.7321...\text{ dollars}$$

1. Final rounding and numeric entry: Rounded to the nearest whole dollar, $30.7321... becomes $31. Because the dollar sign is printed outside the box, type 31.

Walkthrough 2: Section 2 Non-Calculator Mental-Strategy Problem

Scenario (No Calculator): A school uniform shop buys sports jackets for $40.00 each and applies a $35\%$ markup to set the regular retail price. During an end-of-term sale, the shop offers a $15\%$ discount off the regular retail price. What is the final sale price of the jacket?

1. Decompose the $35\%$ markup on $40.00 mentally:
   • $10\%$ of $40.00 is $4.00
   • $30\%$ of $40.00 is $3 \times 4.00 = 12.00$ ($12.00)
   • $5\%$ of $40.00 is half of $4.00, which is $2.00
   • Total $35\%$ markup is $12.00 + 2.00 = 14.00$ ($14.00)
   • Regular retail price is $40.00 + 14.00 = 54.00$ ($54.00)
2. Decompose the $15\%$ discount off the new base of $54.00:
   • $10\%$ of $54.00 is $5.40
   • $5\%$ of $54.00 is half of $5.40, which is $2.70
   • Total $15\%$ discount is $5.40 + 2.70 = 8.10$ ($8.10)
3. Subtract discount from regular retail price:

$$54.00 - 8.10 = 45.90$$

The final sale price is $45.90 (notice that a $35\%$ markup followed by a $15\%$ discount is not a $20\%$ net markup on $40.00, which would falsely give $48.00, because the $15\%$ discount applies to the higher $54.00 retail price).