Math Heuristics for Problem Solving
Primary 3 Constant Difference & Model Method
What is Constant Difference in Math?
Constant Difference means that the difference between two values remains the same even after a change. This concept is often used in word problems related to age. As time passes, the age difference between two people remains constant because they both age at the same rate. For example, if today Lucas is 12-years old and Kai Kai is 4-years old, their age difference will always be 8 years no matter how old they are.
How to Solve Constant Difference Questions with Change Model Method?
Let's take a look at this Primary 3 word problem example:
Mr Lam is 36 years old. He is 4 times as old as his daughter. How old was Mr Lam when his daughter was 3 years old?
Identify the Concept
2nd sentence tells us this is a Constant Difference concept question as they are comparing the age between Mr Lam and his daughter.
Workings Explained
1st sentence “Mr Lam is 36 years old” tell us this year Mr Lam is 36 years old.
We need to draw 2 models, 1 for present/now, the other for past (the question ask for Mr Lam when his daughter was 3 years old)
- Draw the model for present/now. Label the model – “L” for Mr Lam, “D” for his daughter.
- Mr Lam is 4 times as old as his daughter this year. That means his daughter is only a quarter of his age, which is 9 years old (36 ÷ 4 = 9).
- Make parts equal in the model. Cut Mr Lam’s model into 2 parts. The 1st part of Mr Lam’s model will have the same amount as his daughter. The 2nd part of Mr Lam’s model will be the age difference between him and his daughter, which is 27 years.
- Mr Lam was 27 years older than his daughter in the past, he is 27 years older than his daughter this year and he will be 27 years older than his daughter in the future.
- Copy the model and label the model as “Past”. To find Mr Lam’s age in the past, we need to minus as he was younger in the past. Whatever number of years we take away for Mr Lam, we must take away the same number of years for his daughter.
- Mr Lam’s daughter is 9 years old this year. We know it was 6 years ago his daughter was 3 years old. Subtract 6 for Mr Lam and his daughter in the model. To find Mr Lam’s age in the past, we just need to take his present age which is 36 – 6 as it is 6 years ago. That will give us 30.
Mr Lam was 30 years old when his daughter was 3 years old.
Can the Change Model Method be used to solve other types of word problems?
The Change model method can be applied to solve various types of word problems. Some examples of word problem types that can be solved using the Change model method include,