LF-P5-S2-L24 Special project on fraction word problems—remainder + reverse

Lam Fung Academy· LF Academy

Primary 5 · Semester 2 · 24th Lesson · Student Handout

Fraction word problem special project

Unit 3 · Remaining problem ＋ Inverse towardwards reasoning · 65 minutes · 1-to-3 Online Lesson

Corresponding textbooks:"New Thinking in Primary School Mathematics (Second Edition)" Volume 5B Unit 3 Comprehensive + Modern Education 5L B Unit 13
Core traps:🪤 T3 misjudgment of fractional division word problems · T7 "What fraction is left" is mistaken for "fraction of the original number"
SSPA Related:🔴 Extremely High FrequencyPaper 1 accounts for about 20%, Paper 2 accounts for about 15%
Prerequisite knowledge:Chapter 7-8 (addition and subtraction) · Chapter 9 (multiplication) · Chapter 22 (division) · Chapter 23 (mix of four)
The goal of this class:❶ Distinguish the operation types of fraction word problems ❷ Identify the "remaining fraction" trap ❸ Multi-step reasoning ❹ Reverse reasoning (reverse the original number from the result)

Student Name: Class: Date: Time Spent:

I.Warm-Up Questions（total 4 question，5 minutes）

🍕 分數大作戰

通分、約分、四則混合！避開分母陷阱。連續答對分數翻倍！

⚡ 開始挑戰 →

#	Question	Difficulty
1	Convert "A bottle of juice has23liters, drink14liters" into a formula. (Just list the formula, no calculation required)	Basic
2	"Divide34kilograms of candy equally among 5 people" - what operation is this? Column formula.	Basic
3	"Used full-length \|\|\|SEP\|\|\|" - What fraction of the full length is the rest? (Tip: full length = 1)13"——What fraction of the total length is the rest? (Tip: full length = 1)	Basic
4	Are "remaining \|\|\|SEP\|\|\|" and "original \|\|\|SEP\|\|\|" necessarily the same? Give examples.12” and “Original12"Is it necessarily the same? Give examples.	Advanced

II.Core Knowledge ＋ Worked Examples

Knowledge Point 1: One-Step Fraction Problems—Identify Operation Types🔴 SSPA

Keywords → Operation comparison table:
① "total" "total" "total" → addition(total different parts)
② "remainder" "remaining" "difference" → subtraction(deduct a part from the total)
③ (Find the fraction of a quantity)"Equal share" "Each portion" "How much can be..." → Division
④ (distribute equally or include division)(divide equally or include division)

addition

total, total combined, total

−

Subtraction

Remaining, remaining difference, used

multiplication

Several times or parts of...

division

How much can be divided equally, each...

Example 1 - Addition Identification

Xiaomei has12boxes of chocolates, and her mother buys23boxes. How many boxes of chocolate does she have in total?

Example 2 - Subtraction Identification

A bottle of juice originally contains56liters, and drank13liters. How many liters are left?

Knowledge Point 1 Synchronized practice (circle key words → column → calculate → answer sentence)

#	Question	Difficulty
5	The cake shop sold25cakes in the morning and13cakes in the afternoon. How many cakes were sold throughout the day?	🌱
6	The original water in the water bottle is34liters, pour out15liters. How many liters are left?	🌱
7	A rope is23meters long, and the full length of12is used. How many meters were used? (Note: It means "using ½ of the full length", not "using ½ meter"!)	🌿
8	35Kilogram of sugar, divided equally into 3 small bags. How many kilograms of sugar are in each bag?	🌿

⚠️ Q7 demonstrates the key trap: "Using ½ of the full length" vs "Using ½ meter" - the former is multiplication (finding the part), the latter is subtraction (deducting the length). If the judgment is wrong, the entire question will be wrong!

Knowledge point 2: "The remaining fraction" trap 🔴 SSPA extremely high frequency killer question

This is the most common question type to get wrong in the full test!
① "Remaining a/b" ≠ "Original a/b"- You must first find the remaining amount, and then take its fraction
② Solution: First findRemaining= Original − Used/Eat/Spent
③ Find againThe remaining fraction= Remaining × Fraction
④ Never multiply directly by the original number!

🪤 Trap detonation example 3 (the most important demonstration in this class!)

A ribbon is34meters long. After using13meters, use the remaining12to wrap gifts. How much rice did it take to wrap the gift?

❌ Fatal errors (80% of students)

34 × 12 = 38rice

Just calculate the "remaining ½" as "½ of the original ribbon"!

✅ Correct solution

remaining =34 − 13 = 512→ Wrapping gifts =512 × 12 = 524rice

You must first find the remainder, and then take the remaining ½ (not ½ of the original ribbon!)

🧠 Tip: "When you see "remainder", first subtract and then multiply - first subtract the remainder and then multiply the fraction. Circle the three words "remainder" and be careful not to multiply the original number directly!"

Example 4 - Multiplicative "What fraction is left"

Xiao Ming has pocket money |||SEP|||. After spending |||SEP|||, he saves the remaining |||SEP|||. How much have you saved? (Answer with mixed fractions)35,it took15Finally, put the remaining23Savings. How much have you saved? (Answer with mixed fractions)

Knowledge Point 2 Synchronous practice (circle "the remaining" → first find the remaining → again take fraction → answer sentence)

#	Question	Difficulty
9	A bottle of orange juice78liters, drank14liters. The remaining13is used to make jelly. How many liters are used to make jelly?	🌿
10	A bag of sugar weighs45kilograms. After using15kilograms, the remaining12is used to make cakes. How many kilograms were used to make the cake?	🌿
11	A rope is56meters long. Cut off13meters first, and use the remaining25to make knots. How many meters did it take to make the knot?	🌳
12	A box of juice34liters, drank12liters. Then divide the remainder equally among 3 friends. How many liters does each person receive?	🌳
13	The sister had a box of chocolate \|\|\|SEP\|\|\|. After eating the58box, the remaining14was given to her brother. How many boxes does the brother get? (Note: There are two traps in the question - subtract first and then multiply!)34Gave it to my brother. How many boxes does the brother get? (Note: There are two traps in the question - subtract first and then multiply!)	🌳

⚠️ The second biggest trap: "divide the remainder equally" = first subtract (find the remainder), then divide (divide equally). Not divide first and then subtract! In the wrong order, the answer is completely different.

Knowledge point 3: Multi-step reasoning text questions 🔴 SSPA advanced must test

A question contains two or more operational steps, which need to be executed in the correct order:
① Circle all key data(quantity, fraction, relational words)
② Draw process arrow |||SEP|||: original → first step (+−×÷) → intermediate result → second step (+−×÷) → answer|||SEP||| (Add parentheses when necessary)
③ Calculatestep by step, check whether it is reasonable at each step (for example, the remaining value cannot be greater than the original)
④ Calculate step by step, check whether each step is reasonable (for example, the remainder cannot be greater than the original)

Example 5 – Addition, Subtraction and Mixing

The original water in the bucket is56liters. After using13liters, add12liters. How many liters of water are there now? (need to subtract first and then add)

Example 6 - Mixed multiplication and division

A rope is23meters long. After using the full length of |||SEP|||, divide the remaining length into 3 equal parts. How many meters long is each section?14Finally, divide the remaining pieces into 3 equal parts. How many meters long is each section?

Knowledge Point 3 Synchronous practice (draw process → column → step by step calculation → answer sentence)

#	Question	Difficulty
14	A bottle of juice34liters, drank14liters in the morning, and added12liters in the afternoon. How many liters are there in total now?	🌿
15	A box of cakes weighs58kg. After cutting off14kilograms, divide the remainder equally among 3 people. How many kilograms does each person get?	🌳
16	Xiaohua has a35premium, and Xiao Ming has132 times the premium. How many liters of water do they have in total?	🌳
17	A rope is 112meter long. After using the full length of \|\|\|SEP\|\|\|, use the remaining25for decoration. How much rice was used to make the decoration?13Used for decoration. How much rice was used to make the decoration?	🌳

Knowledge Point 4: Reverse Reasoning Word Questions 🔴 SSPA Killer Questions

Infer the original quantity from the result - present the score question of Paper 2!
① Identification |||SEP|||: The question gives the "final result" and asks you to find "how many there are"Strategy |||SEP|||: From the final result
② Reverse operation(addition, subtraction, subtraction, addition, multiplication, transformation, division, division, transformation and multiplication)Formula: Forward sequence formula, solve the problem in reverse direction - reverse each step in the forward direction
③ Check calculation: Use the calculated original number, calculate it once in the forward direction, it should be equal to the result given in the question
④ Check calculation: Use the calculated original number and calculate it once, it should be equal to the result given in the question.

→

Thinking in the direction

original → subtraction → remainder → × fraction

←

reverse operation

Infer from the result that ÷ becomes ×, + becomes −

✓

Check calculation

Use the original number to calculate and confirm

⚠

trap

Pay attention to unit and fraction types

Example 7 - Reverse Reasoning (Subtraction Reverse)

Xiao Ming had some chocolates. After eating14boxes, there were12boxes left. How many boxes of chocolate were there?

Example 8 - Reverse Reasoning (Hybrid Reverse)

From a rope, first cut off13meters, and then use the remaining12for handicrafts. For handicrafts,14meters are used. How many meters long was the rope?

Knowledge Point Four Synchronization Practice

#	Question	Difficulty
18	A bottle of juice, after drinking13liters, there will be14liters left. How many liters did it originally have?	🌿
19	Some candies are divided equally among 4 people, and each person gets16kilograms. How many kilograms of candy were there?	🌿
20	A box of cakes, eaten12boxes, and then eaten13boxes, leaving16boxes. How many boxes of cakes were there?	🌳

🧠 Tip (reverse reasoning): "Calculate backwards from end to beginning, add, subtract, multiply, and divide, subtract, add, divide, multiply, and remember to check it after you finish the calculation."

III. Lesson Layered Synchronization Practice

Basic layer (total 5 questions, all must do, all text questions)

#	Question	Difficulty
21	Xiaomei has23meters of ribbon, and Xiaohua has14meters. How many meters of ribbon do they have in common?	🌱
22	A bottle of water has35liters and uses110liters. How many liters are left?	🌱
23	The13of the cake is chocolate flavor, and the rest is strawberry flavor. What percentage of the cake is strawberry flavor?	🌱
24	34Kilograms of flour, make one cake per18kg. How many cakes can be made?	🌱
25	A rope is45meters long. After using15meters, the remaining12How many meters have been left?	🌿

Advanced layer (total 4 questions, 🚶🚀 choose do)

#	Question	Difficulty
26	A bottle of juice56liters. After pouring12liters, divide the remaining juice equally among 4 people. How many liters does each person get?	🌿
27	A bag of rice weighs78kg.14kilograms were used to cook rice, and the remaining23were used to cook porridge. How many kilograms were used to cook the porridge?	🌿
28	My brother used13of his pocket money to buy books, and then used the remaining12to buy stationery. He spent101yuan to buy stationery. How many yuan was it originally?	🌳
29	There are35liters of juice in the bottle. After pouring14liters of water, pour out13of the mixture. How many liters were poured out?	🌳

🌳 challenge layer (total 2 questions, 🚀 choose do, SSPAKiller Questions)

#	Question	Difficulty	Working Space
30	For a rope, first cut off \|\|\|SEP\|\|\|, then cut off the remaining \|\|\|SEP\|\|\|, and finally there will be 3 meters left. How many meters long was the rope? (First find what fraction of the original amount is left after the second cut, and then work in reverse)13, and then cut off the rest12, and finally 3 meters remain. How many meters long was the rope? (First find what fraction of the original amount is left after the second cut, and then work in reverse)	🏔️
31	Xiao Ming spent25of his pocket money to buy snacks, and then spent the remaining13to buy stationery, and finally he was left with41yuan. How much is the original pocket money?	🏔️

IV.🏔️ The ultimate challenge — SSPAPaper 2 practical question

#	Question	Difficulty	Working Space
🏔️1	\|\|\|SEP\|\|\| on the bookshelf is for Chinese books,14is for English books, and the remaining13is for math books. If mathematics books occupy \|\|\|SEP\|\|\|, what fraction of the total space on the bookshelf is occupied by books? (Check: Chinese + English + Mathematics = total number of books)12Put the math book. If math books took up bookshelf524, what fraction of the total space on the bookshelf is occupied by books? (Check: Chinese + English + Mathematics = total number of books)	🏔️
🏔️2	A barrel of oil contains56liters. The first time I used14liters, the second time I used the remaining \|\|\|SEP\|\|\|, and the third time I used the remaining23of the second time. How many liters are left at the end?12. How many liters are left at the end?	🏔️

Comprehensive reasoning question (🚀Choose do, Paper 2 points question)

#	Question	Difficulty	Working Space
R1	For a bottle of water, I used14on the first day, used the remaining13on the second day, and ended up with12liters left. How many liters of water was there? (Hint: The remaining ⅓ of the first day was used on the second day, that is, ⅓ of the "original ¾" was used on the second day = the original ¼)	🏔️
R2	A, B, and C share candies. A ate \|\|\|SEP\|\|\|, B ate the remaining \|\|\|SEP\|\|\|, and C ate the last remaining box (\|\|\|SEP\|\|\| box). How many boxes of candy were there?13, B ate the rest12, B ate all that was left (14box). How many boxes of candy were there?	🏔️

V. Class afterhomework

Basic must-do questions (total 6 questions, all text questions, must write answer sentences)

#	Question	Difficulty
H1	A bottle of orange juice34liters, my brother drank14liters, and my sister drank13liters. How many liters did they drink in total?	🌱
H2	A rope is45meters long, cut off110meters. How many meters are left?	🌱
H3	23Kg of sweets, one pack per16kilogram. How many bags can be packed?	🌱
H4	A pancake, the sister ate13and the brother ate \|\|\|SEP\|\|\|. How much of the pancake is left?14. How much of the pancake is left?	🌱
H5	A bag of sugar weighs58kilograms. After using14kilograms, the remaining12is used to make desserts. How many kilograms were used to make the dessert?	🌿
H6	A ribbon is35meters long, and the full length of13is used. How many meters were used?	🌿

For advanced, choose doquestion (total 2 questions, 🚀 choose do)

#	Question	Difficulty	Working Space
H7	A rope is 112meter long. After using12meters, the remaining14is used to make knots. How many meters did it take to make the knot?	🌳
H8	Xiao Ming had pocket money, so he spent13to buy stationery, and then spent the remaining12to buy snacks, and finally he was left with \|\|\|SEP\|\|\|. How much is the original pocket money? (Expressed as a fraction, assuming original pocket money = 1)13. How much is the original pocket money? (Expressed as a fraction, assuming original pocket money = 1)	🏔️

VI. The Lessoncorecommon errorsummary

✅ Self-examination in this hall (tick after completion)

☐ I know the pitfalls of solving each knowledge point ☐ I can complete 🌱basic questions independently ☐ I can challenge 🌿advanced questions ☐ I remember the formula

🎯 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 error	Correct Approach
1	"Used ½" vs "Used ½ meter" confusion \|\|\|SEP\|\|\|: The former is a multiple (multiplication), the latter is a quantity (subtraction): The former is a multiple (multiplication), the latter is a quantity (subtraction)	See clearly whether it is "a fraction of the total length" or "how many meters". "" is mostly multiplication.
2	"Remaining a/b" is calculated as "original a/b"	You must first find the remaining quantity, and then take the remaining a/b! This is the most important lesson in the whole class.
3	Direct addition and subtraction of fractions of the remaining amount \|\|\|SEP\|\|\|: The remaining ½ and the remaining ⅓ are directly added: The remaining ½ and the remaining ⅓ are added directly	The "remainder" is based on a different basis each time, and must be calculated individually and then added together.
4	The order of multi-step questions is wrong(Add first and then multiply as multiplication first and then add)	Circle keywords and draw process arrows to confirm the calculation order.
5	Inverse questions will not be "operated backwards"	Forward continuation, solve the problem in reverse: + changes to −, − changes to +, × changes to ÷, ÷ changes to ×
6	Missing sentences/missing units	Text questions must write "Answer:..." + complete unit, otherwise step points will be deducted
7	The fraction result is unreduced	The final step must check reduction (HCF) and improper fractions → mixed numbers

Lam Fung Academy · LF Academy · We don't teach math. We teach trap avoidance.