🧠 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
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!)🌱
R143416=? (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.
Print Ctrl+P PDF | 6 pages · 50 questions | LF-P5-S1-L20 v6 EN
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