Mastering whole number word problems is crucial for primary school students as these problems form the foundation for advanced mathematics. Here, we will explore six common Types of Whole Numbers Problem sums that every student must learn to solve efficiently. By understanding these methods, students can build confidence in whole number problem solving and improve their problem-solving skills.
Table of Contents:
1.1 Comparison Model
1.6 Grouping Method
Common Types of Whole Numbers Problem Sums
1. Comparison Model
The Comparison Model is used when comparing two or more quantities. It helps students visualise differences between values and find relationships between them.
Example:
Andrew, Pat, and Bernard shared a total of 221 toy cars. Andrew received 25 toy cars fewer than Pat and 35 toy cars more than Bernard. How many toy cars did Bernard receive?
Solution:
2. Simultaneous Concept
The Simultaneous Concept involves solving equations where two conditions must be satisfied at the same time.
Example:
The total cost of 3 hairclips and 5 hairbands was $31. The total cost of 5 hairclips and 2 hairbands was $20. How much did each hairclip cost?
Solution:
By solving the two equations simultaneously, we find:
Each hairclip cost $2.
3. Systematic Listing
Systematic Listing is useful for problems requiring logical arrangements or pattern identification.
Example:
Ken has some pens and he wants to pack them into boxes. If he packs them into boxes of 7, there will be 3 pens left. If he packs them into boxes of 6, he will be short of 3 pens. What is the smallest whole number of pens Ken has?
4. Excess and Shortage
The Excess and Shortage method is useful for distribution problems.
Example:
A group of boys share a packet of erasers. If each boy gets 7 erasers, they need 6 more. If each gets 4 erasers, 3 are left. How many erasers are there?
5. Assumption Method
The Assumption Method helps solve problems where total values are known but individual quantities are unknown.
Example:
AGrader bought 26 tables and chairs. A table costs $120 and a chair costs $80. The total cost was $2600. How many chairs were bought?
6. Grouping Method
The Grouping Method helps in problems involving sets and common multiples.
Example: Judy bought an equal number of muffins and tarts. She paid $201 in total. How many did she buy?
Key Mathematical Concepts
Understanding the properties of whole numbers is essential for solving whole numbers word problems with answers efficiently.
Closure Property: Whole numbers remain whole under addition subtraction multiplication but not division.
Commutative Property: The product of two whole numbers remains the same regardless of the order (e.g., 3 x 4 = 4 x 3).
Distributive Property: Helps simplify expressions involving subtraction multiplication and division.
Understanding Whole Numbers
Positive integers: Numbers greater than zero.
Negative integers: Numbers less than zero.
Numbers are 0: Zero is the smallest whole number but not a negative number.
Set of whole numbers: Includes number and natural numbers but excludes fractions or decimals.
Mastering these whole number word problems will significantly improve students’ whole number problem solving abilities. Practising different types of whole number problems ensures students can confidently find the answer in any exam or real-life scenario. Keep practising, and soon, solving whole numbers word problems with answers will become second nature!
Give your child a strong foundation in math with AGrader’s Primary Math Programme, where every weekly lesson is carefully designed to stay ahead of the latest MOE syllabus. Our structured approach ensures that students learn concepts before they are covered in school, giving them a confidence boost in class. With high-quality in-house curated worksheets and experienced teachers guiding them every step of the way, students from P1 to P6 receive the best support to master problem sums and tricky concepts. Plus, they get exclusive access to Everloop System and extra after-class learning resources—completely free! A P6 student can even revise P5, P4, and P3 materials to strengthen their fundamentals and bridge any gaps. Give your child the advantage they deserve—enrol in AGrader’s Primary Math Programme today!
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