Part A: Numeracy
1
Number Foundations
Master whole numbers, integers, and order of operations
Learning Objectives
- Apply order of operations (BODMAS) correctly
- Work confidently with negative numbers
- Round and estimate to check answers quickly
- Understand place value in large and decimal numbers
- Solve real-world number problems in teaching contexts
Chapter Progress: 0%
1. Place Value & Number Sense
Place Value Breakdown
Understanding place value is the foundation of numeracy. Each digit in a number has a value based on its position: ones, tens, hundreds, thousands, and decimal places like tenths and hundredths.
Example 1
Ordering Decimals in Student Assessment Data
❓ Question: Arrange the four student reading fluency scores in ascending order (from smallest to largest): 3.14, 3.2, 3.015, and 3.104.
📄 Source Passage / Reference Data: Reading Fluency Scores: Student A = 3.14, Student B = 3.2, Student C = 3.015, Student D = 3.104.
📝 Step-by-Step Method:
1
List the decimal numbers vertically, aligning the decimal point.
2
Add trailing zeros so all numbers have equal decimal place length (3 decimal places).
3
Compare digits from left to right (ones digit is 3 for all; compare thousandths: 015 < 104 < 140 < 200).
🔍 Evidence Extracted: "3.015 (3.015) < 3.104 (3.104) < 3.14 (3.140) < 3.2 (3.200)"
🎯 Final Answer: 3.015, 3.104, 3.14, 3.2
💡 Why It Is Correct: Adding trailing zeros makes place value visible: 3.015 is smaller than 3.104, followed by 3.140, and 3.200 is largest.
⚡ LANTITE Exam Strategy: LANTITE Tip: Adding trailing zeros to equalise length prevents the common trap of mistaking 3.015 as larger than 3.2.
2. Operations with Whole Numbers
The Four Basic Operations
Mastering addition (+), subtraction (-), multiplication (×), and division (÷) without relying on a calculator is essential for the LANTITE exam.
Example 2
Budgeting for Classroom Art Supplies
❓ Question: A teacher needs to purchase 4 boxes of colored pencils at $12 per box and 3 reams of recycled paper at $8 per ream. What is the total cost?
📄 Source Passage / Reference Data: Classroom Requisition Request: 4 boxes of pencils at $12 each, 3 packs of paper at $8 each.
📝 Step-by-Step Method:
1
Calculate the total cost of pencils.
2
Calculate the total cost of paper.
3
Add the two sub-totals to find the overall supply cost.
🔍 Evidence Extracted: "Pencils = $48, Paper = $24, Total = $72"
🎯 Final Answer: $72 total cost
💡 Why It Is Correct: Multiplying items by unit price yields $48 for pencils and $24 for paper. Summing $48 + $24 gives $72.
⚡ LANTITE Exam Strategy: Perform sub-total calculations separately before summing total expenditures.
Keywords for Operations
| Addition (+) | Subtraction (-) | Multiplication (×) | Division (÷) |
|---|---|---|---|
| Sum, altogether | Difference, fewer | Product, times | Quotient, average |
| Combined, plus | Remaining, less than | Each, per, groups of | Share, split, per person |
3. Order of Operations (BODMAS)
What is BODMAS?
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction. It tells you the correct sequence to solve mathematical expressions.
The BODMAS Rule
B -> O -> D / M -> A / S
Example 3
Step-by-step BODMAS Calculation
❓ Question: Calculate the value of the numerical expression: 10 + 2 × 5 using the correct order of operations.
📄 Source Passage / Reference Data: BODMAS Operational Expression: 10 + 2 × 5.
📝 Step-by-Step Method:
1
Identify the operations involved: Addition (+) and Multiplication (×).
2
According to BODMAS, perform multiplication before addition.
3
Add the result to the initial number.
🔍 Evidence Extracted: "Multiplication 2 × 5 = 10 precedes Addition (+ 10)"
🎯 Final Answer: 20
💡 Why It Is Correct: Multiplication takes precedence over addition. Evaluate 2 × 5 = 10 first, then 10 + 10 = 20.
⚡ LANTITE Exam Strategy: Always evaluate multiplication and division before addition and subtraction unless brackets dictate otherwise.
Example 4
Nested Brackets Calculation
❓ Question: Evaluate the mathematical expression with nested brackets: 3 × (4 + (6 ÷ 2)).
📄 Source Passage / Reference Data: Nested Brackets Operational Expression: 3 × (4 + (6 ÷ 2)).
📝 Step-by-Step Method:
1
Start with the innermost set of brackets: (6 ÷ 2).
2
Substitute back and resolve the outer set of brackets: (4 + 3).
3
Perform the final multiplication outside the brackets.
🔍 Evidence Extracted: "Innermost (6 ÷ 2 = 3) → Outer (4 + 3 = 7) → Final (3 × 7 = 21)"
🎯 Final Answer: 21
💡 Why It Is Correct: Innermost brackets (6 ÷ 2 = 3) are solved first, then outer brackets (4 + 3 = 7), and finally 3 × 7 = 21.
⚡ LANTITE Exam Strategy: Work from the inside out when dealing with nested brackets.
4. Negative Numbers & Integers
Understanding Integers
Integers include all whole positive and negative numbers, including zero. Think of them visually on a number line to help with addition and subtraction.
Example 5
Adding and Subtracting Negative Numbers
❓ Question: Evaluate the following two integer expressions: (a) -5 + 8 and (b) -4 - 6.
📄 Source Passage / Reference Data: Canberra Weather Station Temperature Log: Overnight base = -5°C with +8°C rise; Cold front drop = -4°C with 6°C further drop.
📝 Step-by-Step Method:
1
For (a) -5 + 8: Start at -5 on the number line and move 8 units to the right.
2
For (b) -4 - 6: Start at -4 on the number line and move 6 units further to the left.
🔍 Evidence Extracted: "-5 + 8 = 3 and -4 - 6 = -10"
🎯 Final Answer: (a) 3, (b) -10
💡 Why It Is Correct: Adding positive 8 to -5 moves right past zero to +3. Subtracting 6 from -4 moves further left to -10.
⚡ LANTITE Exam Strategy: Adding a positive number moves right on the number line; subtracting a positive number moves left.
5. Rounding & Estimation
Rounding Rules
Look at the digit immediately to the right of your target place value. If it is 5 or above, round up. If it is 4 or below, keep the target digit the same (round down).
Example 6
Rounding Whole Numbers and Decimals
❓ Question: Round the whole number 4,562 to the nearest 10, 100, and 1000, and round the decimal 3.14159 to 2 decimal places.
📄 Source Passage / Reference Data: School Enrolment & Measurement Records: Student population count = 4,562; Circle ratio pi = 3.14159.
📝 Step-by-Step Method:
1
Round 4,562 to the nearest 10: check ones digit (2 < 5).
2
Round 4,562 to the nearest 100: check tens digit (6 ≥ 5).
3
Round 4,562 to the nearest 1000: check hundreds digit (5 ≥ 5).
4
Round 3.14159 to 2 decimal places: check 3rd decimal place (1 < 5).
🔍 Evidence Extracted: "4,562 (ones=2, tens=6, hundred=5) & 3.14159 (3rd d.p.=1)"
🎯 Final Answer: Nearest 10: 4,560 | Nearest 100: 4,600 | Nearest 1000: 5,000 | 2 d.p.: 3.14
💡 Why It Is Correct: Digits 5 or greater round up; digits less than 5 round down.
⚡ LANTITE Exam Strategy: Always look at the single digit immediately to the right of the rounding position.
6. Solving Word Problems
Word Problem Strategy
Tackle word problems step-by-step: Read carefully, Identify the key information, Plan your approach (choose operation), Solve, and Check if the answer makes sense in context.
Example 7
Excursion Budget Calculation
❓ Question: A primary school plans a museum excursion. Bus hire costs $450 in total, and entry tickets cost $12 per student. What is the total cost for a class of 30 students?
📄 Source Passage / Reference Data: School Excursion Cost Breakdown: Bus Hire = $450 fixed rate; Admission = $12 per student for 30 attending students.
📝 Step-by-Step Method:
1
Identify the fixed cost and variable entry cost per student.
2
Calculate the total entry ticket cost for 30 students.
3
Add the ticket sub-total to the fixed bus hire cost.
🔍 Evidence Extracted: "$450 fixed bus + 30 × $12 ($360) admission = $810 total cost"
🎯 Final Answer: $810 total cost
💡 Why It Is Correct: Total cost equals bus hire ($450) plus student ticket total (30 × $12 = $360), giving $810.
⚡ LANTITE Exam Strategy: Perform sub-total calculations separately before summing total expenditures.
Question 1 of 10
What is 48 ÷ 6 + 3 × 2?