Primary 3 Unchanged Identity & Model Method

Math Heuristics for Problem Solving

Primary 3 Unchanged Identity & Model Method

What is Unchanged Identity in Math?

Unchanged Identity refers to a type of math problem where the quantity of one of the items, or identities, in the problem remains the same throughout the given scenario. The Change model method is the best approach to solving such problems for Primary 3 children. This method involves drawing a model and identifying the changes in quantities for the other item, or identity, while keeping the unchanged identity constant. Unchanged Identity is also known as Unchanged Item or One Item Unchanged.

How to Solve Unchanged Identity Questions with Change Model Method?

Let's take a look at this Primary 3 word problem example:

Detailed solution for Primary 3 Unchanged Identity concept example

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Pauline had 57 stamps. After she was given some more stamps, she found that the total number of stamps she had was 24 fewer than the number of stamps Grace had. How many stamps were given to Pauline if Grace had 99 stamps?

Identify the Concept

… sentence tell us this is Unchanged Identity concept question as…

Workings Explained

Grace is the Unchanged Identity – The number of stamps Grace had will not change. This is also “Before-After” question as something happened – Pauline was given more stamps. Therefore we must draw 2 models.

  1. 2nd sentence tell us that even after Pauline was given more stamps, she still had fewer stamps than Grace. There Grace’s model will be longer than Pauline’s model. Since Grace had more stamps, we can cut Grace’s model into 2 parts.

    • The 1st part of the model will have the same amount as Pauline (this is known as making parts equal).

    • The 2nd part of the model will be the difference between both Grace and Pauline. We know Grace had 42 more stamps than Pauline (99-57=42), write “42” in the difference box.

    • Label this as “Before” or “At First” model and label “G” for Grace’s model and “P” for Pauline’s model.
  2. Bring the model down and label this model as “End” or “After” model. We will make the changes in the “After” model. Use dotted lines to draw a box for Pauline as Pauline was given more stamps. Cut Grace’s difference box into 2 parts (that means Grace has 3 parts in total in her model). 1 part will have the same amount as what was given to Pauline, the 2nd part will be the new difference between them, which is 24.

  3. We can find the amount given to Pauline by taking the difference between them at first minus the difference between them in the end (42-24=18).

Pauline was given 18 stamps.

Identify the Concept

2nd sentence tell us this is Unchanged Identity concept question as only Pauline was given more stamps but not Grace.

Workings Explained

Grace is the Unchanged Identity – The number of stamps Grace had will not change. This is also “Before-After” question as something happened – Pauline was given more stamps. Therefore we must draw 2 models.

  1. 2nd sentence tell us that even after Pauline was given more stamps, she still had fewer stamps than Grace. There Grace’s model will be longer than Pauline’s model. Since Grace had more stamps, we can cut Grace’s model into 2 parts.

    • The 1st part of the model will have the same amount as Pauline (this is known as making parts equal).

    • The 2nd part of the model will be the difference between both Grace and Pauline. We know Grace had 42 more stamps than Pauline (99-57=42), write “42” in the difference box.

    • Label this as “Before” or “At First” model and label “G” for Grace’s model and “P” for Pauline’s model.
  2. Bring the model down and label this model as “End” or “After” model. We will make the changes in the “After” model. Use dotted lines to draw a box for Pauline as Pauline was given more stamps. Cut Grace’s difference box into 2 parts (that means Grace has 3 parts in total in her model). 1 part will have the same amount as what was given to Pauline, the 2nd part will be the new difference between them, which is 24.

  3. We can find the amount given to Pauline by taking the difference between them at first minus the difference between them in the end (42-24=18).

Pauline was given 18 stamps.

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,

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