Math Heuristics for Problem Solving
Primary 3 Repeated Identity & Model Method
What is Repeated Identity in Math?
Repeated Identity is a type of math problem where students compare three or more items or people. In most cases, one of the items or people is compared to the others multiple times. Because of the nature, the Comparison model method is the best approach to solving such problems for Primary 3 children. This method involves drawing a bar model to represent the total quantity of the items being compared, and then dividing the bar into equal parts to represent the quantity of each item. The Repeated Identity concept is also sometimes referred to as Repeated Items.
How to Solve Repeated Identity Questions with Comparison Model Method?
Let's take a look at this Primary 3 word problem example:
Joseph, Ian and Mathew live in the same block of flat. He walked 6 floors up from his flat to Ian’s flat. Then he walked 11 floors down to Mathew’s flat. Mathew lives on the 13 floor. On which floor does Joseph live?
Identify the Concept
There are 3 people in the question and Ian is compared repeatedly with the others, therefore this is a Repeated Identity concept question.
Workings Explained
Find out who is the favourite identity (the identity that the other 2 are compared with). In this question, the favourite identity is Ian as “He” who is Joseph walked up from his flat to Ian’s flat, from Ian’s flat Joseph walked up to Mathew’s flat. Since Ian is the favourite identity, we will put Ian’s model in the model so that it is easier for Joseph and Mathew to compare.
- Label “J” for Joseph, “I” for Ian and “M” for Mathew. Ian’s model will be longer than Joseph’s model as Ian lives on a higher floor compare to Joseph. Cut Ian’s model into 2 parts, the 1st part will have the same length as Joseph’s model. The 2nd part of Ian’s model will be the difference, which is 6. Write “6” in the 2nd part of Ian’s model.
- Mathew’s model will be shorter than Joseph as Joseph need to pass by his own flat to go down to Mathew’s flat. Cut the 1st part of Ian’s model into 2 parts. Write “5” in the 2nd part of Ian’s model as the difference between 11 and 6 is 5. Do the same for Joseph’s model to make parts equal.
- Write “13” in Mathew’s model as he lives on the 13 floor. Write “13” in the 1st part of Joseph and Ian’s model as well.
- To find on which floor Joseph lives, we just need to add 13 to 5.
Joseph lives on the 18 floors.
Can the Comparison Model Method be used to solve other types of word problems?
The Comparison model method can be applied to solve various types of word problems. Some examples of word problem types that can be solved using the Comparison model method include,