🧠 WHY BOX — Why learn this?

Understanding this topic helps you solve real-life math problems and prepares you for the SSPA exam.

學好這個課題能幫助你解決生活數學問題,為 SSPA 考試做好準備。

📖 Story Context / 故事情境

Imagine you are shopping and need to calculate totals, discounts, or split bills. Math is everywhere in daily life!

想像你在購物時需要計算總額、折扣或分攤帳單。數學無處不在!

📋 Parent Corner / 家長專區
This topic covers key SSPA exam concepts. Encourage your child to practice the worked examples and common trap questions.
本課題涵蓋 SSPA 考試重點。請鼓勵孩子練習例題和陷阱題。
Primary 5 · 20th Lesson · Student Handout
Simulation 2 Review + Winter Vacation SSPA Special Training Plan
Semester 1 Final Lesson · Review and Reflection · 75 minutes · 1-to-3 Online Lesson
Corresponding textbooks:L19 SSPA Mock Exam (2) Review + Winter Vacation Independent Practice Plan
Core Traps:🪤 T1 Multi-digit · T2 Decimal · T3 Reverse Questions · T5 Area · T9 Score - Simulation 2 Five Major Score-Losing Areas
SSPA Related:🔴 High frequencyIntegrated diagnosis of sub-test traps, personalized weakness location
Pre-requisite knowledge:L1–L18 full semester content + L19 mock exam
Objective of this class:❶ Diagnose the reasons for losing points in the five major traps in Simulation 2 ❷ Self-assessment of personal weaknesses ❸ Develop a 15-minute daily exercise plan during winter vacation ❹ Targeted error correction exercises
Student Name: Class: Date: Time Spent:
I.Mock Exam2 SSPA five major trap disaster areas (L19 review)
Trap 1: T1 multi-digit number - "rounding" approximation trap 🔴 SSPA
① When taking approximate values, you must clearly see "which digit to take" - tens of thousands, thousands, hundreds?
② Key rules: Look at the target positionThe next digitThe number determines whether to "enter" or "round"
③ Common mistakes: when you get to the "ten thousand digits", you stop after looking at the thousands digits, without confirming the value of the tens of thousands digits
④ Another mistake: forgetting to clear all subsequent digits after placing them (for example, 345,678 rounded to the nearest ten thousand = 350,000, not 35,000)
Example questions T1-1: Similar questions to Question 5 of Simulation 2
Round 2,847,563 to the nearest hundred thousand digits.
❌ Common mistakes
2,800,000
I only looked at 4 (round) in the tens of thousands place, but the hundreds of thousands place is 8. I need to look at the next level in the millions place.
✅ Correct solution
2,800,000
The hundred thousand digit = 8, look at the ten thousand digit = 4 (<5, round down) → 2,800,000
Trap 2: T2 Decimal — Decimal Point Position Trap for Decimal Multiplication 🔴 SSPA
① Multiply decimals: first multiply the integers, then count the total number of decimal places and add the decimal point
② The most frequent error |||SEP|||: 0.3 × 0.4 = 1.2 (correct = 0.12) - Forgetting that multiplying decimals by decimals will get smaller and smaller③ The second error: the decimal point is placed in the wrong position - it should be from the far right of
|||SEP||| Start counting to the left④ Verification formula: "Multiplier < 1 → Product < Multiplicand" (0.3 × 0.4 → The answer must be < 0.3)Start counting to the left
④ Verification formula: "Multiplier < 1 → product < multiplicand" (0.3 × 0.4 → the answer must be < 0.3)
Example questions T2-1: Similar questions to Question 2 of Simulation 2
Calculate 0.25 × 0.4 = ?
❌ Common mistakes
0.25 × 0.4 = 1.00
Directly 25×4=100, I forgot to count from the right at the decimal point
✅ Correct solution
0.25 × 0.4 = 0.100 = 0.1
25×4=100, the total number of decimal places is 2+1=3 → 0.100 → the simplest 0.1
Pitfall 3: T5 Area — Trapezoidal/Polygonal Area Unit Confusion 🔴 SSPA
① Area of trapezoid = (upper base + lower base) × height ÷ 2 ——not(upper base + lower base + height) × 2
② Area of parallelogram = base × height (|||SEP||| notbase × hypotenuse)③ Area of triangle = base × height ÷ 2 —— Must divide |||SEP|||
③ Area of ​​triangle = base × height ÷ 2 —— requireddivide by 2!
④ Combined graphics: first divide into basic graphics, find the area respectively, and then add the sum
Example T5-1: Simulation 2 trapezoid area problem
The upper base of the trapezoid is 8 cm, the lower base is 12 cm, and the height is 5 cm. Area = ?
❌ Common mistakes
(8+12+5) × 2 = 50 cm²
Confusing the perimeter and area formulas - adding the height and multiplying by 2
✅ Correct solution
(8+12)×5÷2 = 50 cm²
(Upper bottom + Lower bottom)×Height÷2 = 20×5÷2 = 50 cm²
Trap 4: T9 fractions - addition and subtraction with different denominators "straight addition and straight subtraction" 🔴 SSPA
① Fractions with different denominatorscannotdirect addition and subtraction - they must be divided first
② Three steps: find LCM → expand the numerator simultaneously → add the numerators with the same denominator
③ The answer must be reduced toThe simplest fraction |||SEP|||, the improper fraction must be transformedMixed fractions④ Adding and subtracting mixed fractions: Recommended to convert to improper fractions (least error-prone)
④ Adding and subtracting mixed numbers: It is recommended to convert to improper fractions (least error-prone)
Example T9-1: Simulation 2 Fraction Questions
23 + 14 = ?
❌ Common mistakes
37
Numerator + numerator, denominator + denominator - different denominators can never be added directly!
✅ Correct solution
1112
LCM(3,4)=12 → 812+312=1112
Trap 5: T3 inverse question - find the original number when the result is known 🔴 SSPA
① The key to the reverse question: start from the final result of|||SEP||| Auxiliary: Assume the unknown → Column → Solve the equation④ Verification: Substitute the answer back to the original question to check whether it is reasonablePush backOperation
② When working backwards, addition and subtraction are reciprocal, and multiplication and division are reciprocal: the original "addition" becomes "subtraction" when working backwards.
③ Best to useequationAuxiliary: Assume unknowns → List → Solve equations
④ Verification: Substitute the answer back to the original question to check whether it is reasonable
Example T3-1: Simulation 2 reverse question
Xiao Ming has some candy. After taking |||SEP|||, I bought 15 more pills and now I have 45 pills. How many grains were there?13Later, I bought 15 more pills, and now I have 45 pills. How many grains were there?
❌ Common mistakes
45 + 15 = 60,60 × 13 = 20
Calculate forward, not backward - you bought 15 before reaching 45, you should subtract 15 first
✅ Correct solution
(45 − 15) ÷ (1 − 13) = 30 ÷ 23 = 45
Working backward: there were 30 pills before buying 15, this is the remaining 23 after eating 13
🧠 General tips for the five major traps: "Looking at multiple digits, decimal points, memorizing area formulas, dividing fractions first, and working backwards"
II. Self-Assessment Checklist of Personal Weaknesses (Self-Assessment Checklist)
⚠️ Please honestly self-assess the following 10 items and check the ones where you often make mistakes. This is the "bullseye" for your winter vacation training!
✓Weakness descriptionTrap categorySSPA frequency
☐Q1.When approximating multiple digits, the wrong target digit is taken (for example, rounding to the thousands digit is regarded as rounding to the 10,000 digit)T1 multi-digit🔴 high
☐Q2.After approximating multiple digits, forget to clear the following digits to zero.T1 multi-digit🔴 high
☐Q3.Wrong decimal point position in decimal multiplication (especially the 0.3 × 0.4 category)T2 decimal🔴 high
☐Q4.The decimal point position of the quotient of decimal division is wrongT2 decimal🟡 medium
☐Q5.Forgot to divide the area of ​​the trapezoid by 2, or use the wrong formula (for example, add the height and then multiply)T5 area🔴 high
☐Q6.Area of ​​combined graphics: Forgot to divide or overlapping parts are calculated incorrectlyT5 area🔴 high
☐Q7.Direct addition and subtraction of fractions with different denominators (numerator + numerator, denominator + denominator)T9 score🔴 high
☐Q8.I forgot to reduce the fraction answer, or the improper fraction was not converted into a mixed number.T9 score🔴 high
☐Q9.When working backwards in the reverse problem, the direction of operation is reversed (when adding, subtracting, forgetting to change)T3 reverse🔴 high
☐Q10.Missing answer sentences for application questions/Missing units/Confusing columnsT7 Application🟡 medium
III.Winter SSPA per day 15 minutes special training plan (two weeks = 14 days)
Planning Principles 🔴 SSPA Preparation
① Only15 minutes——The focus iscontinuousrather than long-term
② Focus on1 trap |||SEP|||, practice the five major traps in turn (can be cycled twice in two weeks)Each exercise: 3 minutes to review the rules → 10 minutes to do the questions → 2 minutes to mark the answers
④ Rest on Sunday (or make up for unfinished exercises during the week)
④ Rest on Sunday (or make up for unfinished exercises during the week)
daydatefocus trapExercise content (15 minutes)✓
1Day 1T1 multi-digit5 questions on taking approximate values ​​+ 5 questions on reading and writing numbers☐
2Day 2T2 decimal5 questions on multiplication of decimals + 5 questions on division of decimals☐
3Day 3T5 area3 questions on the area of ​​a trapezoid + 3 questions on the area of ​​a triangle + 2 questions on combined figures☐
4Day 4T9 score5 questions on adding and subtracting different denominators + 5 questions on adding and subtracting mixed fractions☐
5Day 5T3 reverse5 inverse problems (with equation assistance) + 3 application problems☐
6Day 6T1+T2 mixedMulti-digit + decimal mixed exercises 10 questions (timed 12 minutes)☐
7Day 7🌿 Rest days (or make up for unfinished questions from Day 1-6)☐
8Day 8T5 area10 questions on mixed areas of all shapes (timed 12 minutes)☐
9Day 9T9 scoreFour mixed fractions 5 questions + 5 application questions☐
10Day 10T3 reverse5 questions on converse problems + 5 questions on application of equations☐
11Day 11T2 decimal10 mixed decimal questions (including approximate values)☐
12Day 12comprehensiveSelected 10 questions from the mock paper (limited to 15 minutes)☐
13Day 13Personally the weakestFor the traps with the most incorrect marks on Days 1-12, do 10 more questions.☐
14Day 14📋 Summary: Count the wrong questions in the past two weeks and make a list of "still need to improve"☐
⚠️ Key rules: After each exercise, you must "correct the answer + mark the wrong question + understand the cause of the error." Doing nothing = doing nothing.
IV.L19 Common Mistake for correctness reviewquestion (total 20 question · Focus on the five traps)
Group A — T1 morenumber of digitsapproximate value (questions 1-4)
🎫 Exam tips (SSPA must read)

① Do the questions you know first, don’t get stuck on one!
② Check the unit for each question (cm vs cm² vs cm³)!
③ Geometry questions: If there is an elevation in the picture, use the height. If there is no elevation, use the formula to find it!
④ Application question: Write an answer sentence! Points will be deducted for not writing steps!
⑤ 5 minutes left: Check if the MC has been filled in and if the unit is correct!

🏆 SSPA衝刺·限時挑戰
模擬真實SSPA考試!限時作答,每題計分。答對率達80%解鎖「SSPA戰士」勳章!
⚡ 開始模擬考 →
#QuestionDifficultyWorking Space
R1Approximate 3,456,789 to the "hundredthousandth digit".🌱
R2Round 67,890,123 to the nearest million.🌿
R3Round 4,507,632 to the nearest ten thousand. And write which digit you are looking at.🌿
R4Which of the following is a correct approximation to the millionth place of 29,876,543? A. 29,000,000 B. 30,000,000 C. 29,900,000 D. 20,000,000🌳
Group B — T2 decimalcalculate (questions 5-8)
#QuestionDifficultyWorking Space
R5Calculate 0.6 × 0.3 = ?🌱
R6Calculate 0.25 × 0.8 = ?🌿
R7Calculate 0.15 × 0.4 = ? (Write the correct decimal point position after 15×4=60)🌿
R8Calculate 0.05 × 0.02 = ? (Note: How many zeros are there after the decimal point?)🌳
Group C - T5 areatrap (questions 9-12)
#QuestionDifficultyWorking Space
R9The upper base of the trapezoid is 6 cm, the lower base is 10 cm, and the height is 4 cm. Area = ?🌱
R10Triangular base 8 cm, height 5 cm. Area = ? (Careful: Did you divide by 2?)🌱
R11The parallelogram has a base of 9 cm, a height of 6 cm, and a hypotenuse of 7 cm. Area = ?🌿
R12A combined figure consists of a trapezoid and a parallelogram. Trapezoid: (4+8)×3÷2, parallelogram: 5×3. Total area = ?🌳
Group D - T9 fraction operation (questions 13-16)
#QuestionDifficultyWorking Space
R1313 + 16=? (Get points first!)🌱
R1434 − 16=? (Remember to keep it simple!)🌿
R15112 + 223=? (Tip: Convert Improper Fractions)🌳
R1623 + 14 + 16=? (Three fractions are combined)🌳
Group E — T3 reverse towardquestion (questions 17-20)
#QuestionDifficultyWorking Space
R17Add 15 to a number and then multiply it by 3. The result is 90. Find this number. (Use backwards reasoning)🌿
R18After Xiao Ming used the saved |||SEP|||, he deposited another $30, and now he has $90. How many yuan was it originally?14After you use it, you deposit another $30 and now you have $90. How many yuan was it originally?🌳
R19If you subtract 28 from a number, divide it by 4, and then add 10, the result is 25. Find the original number.🌳
R20There is some water in the bucket. After pouring out the |||SEP|||, add another 3 liters, now you have 10 liters. How many liters did it originally have?25Then, add another 3 liters and now you have 10 liters. How many liters did it originally have?🏔️
V. Additional reinforcement of practice (total 22 questions · full trap mix)
Basic layer (question 21-28 · Everyone must do)
#QuestionDifficultyWorking Space
21Round 12,345,678 to the nearest million.🌱
22Calculate 0.4 × 0.7 = ?🌱
23Triangular base 10 cm, height 6 cm. Area = ?🌱
2415 + 310 = ?🌱
25Round 5,678,900 to the nearest hundred thousand digits.🌱
26Calculate 0.8 × 0.05 = ?🌿
27The upper base of the trapezoid is 5 cm, the lower base is 7 cm, and the height is 6 cm. Area = ?🌱
2823 + 19 = ?🌱
Advanced layer (question 29-36 · 🚶🚀 Select do)
#QuestionDifficultyWorking Space
29Take 67,543,210 to the nearest tens of millions and write the Chinese pronunciation.🌿
30Calculate 0.35 × 0.6 = ? (Multiply the integers first, then count the decimal places)🌿
31The parallelogram has a base of 12 cm and a height of 5 cm. Area = ? (Don’t use a bevel!)🌿
3235 + 23 = ?(LCM(5,3)=?)🌿
33Three times a number plus 12 equals 48. Find a certain number. (Backward calculation: 48−12=36, 36÷3=?)🌿
34Calculate 0.45 ÷ 0.5 = ? (Hint: divide by 0.5 = multiply by 2)🌿
35The upper base of the trapezoid is 3 cm, the lower base is 9 cm, and the height is 8 cm. Area = ?🌿
36213 + 114=? (convert improper fractions first)🌳
🌳 challenge layer (question 37-42 · 🚀 choose do)
#QuestionDifficultyWorking Space
37If you multiply a number by 0.5 and then add 8, the result is 23. Find the original number.🌳
38A rectangle is 15 cm long and 8 cm wide. Cut out a triangle from it (base 8 cm, height 5 cm). Remaining area = ?🌳
3958 + 34 + 12=? (Three numbers can be divided into three numbers, LCM(8,4,2)=?)🌳
40For a barrel of oil,14was used on the first day, and the remaining13was used on the second day, leaving 12 liters. How many liters did it originally have? (Double reverse!)🏔️
41Round 99,876,543 to the nearest million. And explain: why not 100,000,000?🌳
42Calculate 0.125 × 0.8 = ? Write out the complete process of "first multiply integers → count decimal places → point decimal points".🌳
VI. The Lessoncorecommon errorsummary
🎯 Review of Learning Objectives - After completing this lesson you should be able to:
☐ Identify all trap types in our hall ☐ Solve 🌱basic questions independently (100% correct) ☐ Challenge🌿Advanced questions (80%+ correct) ☐ Explain the lesson formula to classmates
#common errorCorrect Approach
1Take approximations to see misalignmentCircle the target position first → look at the next digit → ≥5 and <5 will be rounded → clear the rest
2Wrong decimal point when multiplying decimalsAfter multiplying the integers → count the total number of decimal places → click from right to left
3The area of ​​the trapezoid is forgotten ÷2Remember the formula: (upper base + lower base) × height ÷ 2, not multiplied by 2
4Parallelogram uses hypotenuseArea = base × height (height is the vertical distance, not the hypotenuse)
5Direct addition of fractions with different denominatorsLCM must be found first through the denominator → the numerator is expanded simultaneously → the denominator remains unchanged
6The answer is not reducedFinal step: Check if the numerator and denominator have common factors
7Reverse question inferenceWork backwards from the final result: addition, subtraction, multiplication, division, order reversal
Lam Fung Academy · LF Academy · We don't teach math. We teach trap avoidance.
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