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Primary 3 Equal Amount (At First) & Model Method

Math Heuristics for Problem Solving

Primary 3 Equal Amount (At First) & Model Method

What is Equal Amount (At First) in Math?

Equal Amount (At First) is a math problem type where the amount of the items or people is the same before any change occurs. When solving word problems involving Equal Amount (At First), model drawing can be helpful for primary 3 children to visualize and simplify the problem. The Change model method is a good approach to use in this situation.

Equal Stage (Before), Equal Stage (Beginning), Equal Scenario (Before), Equal Scenario (At First), and Equal Scenario (Beginning) are all different names that may be used to refer to this concept.

How to Solve Equal Amount (At First) Questions with Change Model Method?

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

Detailed solution for Primary 3 Equal Amount (At First) concept example
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Anna made as many bracelets as Flora. They made a total of 140 bracelets. Anna gave 31 bracelets to her friends and Flora made more bracelets. In the end, Flora had thrice as many bracelets as Anna. How many more bracelets did Flora make than Anna?

Identify the Concept

… sentence tell us this is an Equal Amount (At First) concept question as…

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Workings Explained

  1. Label the first model “Before” or “At First”. Draw equal parts for both Anna and Flora. Label “A” for Anna’s model and “F’ for Flora’s model. We know they made 70 bracelets each as they made a total of 140 bracelets (140 ÷ 2 = 70). Write “70” in both Anna and Flora’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. “Anna gave 31 bracelets to her friends…”, cut Anna’s model into 2 parts, write “31” in the 2nd part of her model and shade as we are subtracting 31 from Anna. Cut the same for Flora’s model but do not shade as we are only making parts equal. Use dotted lines to draw a box for Flora as she made more bracelets.

  3. Whatever number of bracelets Anna was left with, Flora will have 3 groups of that amount (“Flora had thrice as many bracelets as Anna.”) Write “1u” (1 unit) in Anna’s 1st part of the model, write the same for Flora’s 1st part of the model as well. All 3 parts of Flora’s model will add up to 3 units. The 2nd part and the 3rd part of Flora’s model will add up to 2 units.

  4. Anna had 39 bracelets in the end (70 – 31 = 39). 1 unit = 39, 3 units will be 117 (3 × 39 = 117). Flora had 117 bracelets in the end. To find how many more bracelets Flora made than Anna, we just have to take the number of bracelets Flora had in the end minus what Anna made (117 – 70 = 47).

Flora made 47 more bracelets than Anna.

Identify the Concept

1st sentence tell us this is an Equal Amount (At First) concept question as Anna made the same number of bracelets as Flora. We will start from “At First” as they had the number of bracelets at first.

Workings Explained

  1. Label the first model “Before” or “At First”. Draw equal parts for both Anna and Flora. Label “A” for Anna’s model and “F’ for Flora’s model. We know they made 70 bracelets each as they made a total of 140 bracelets (140 ÷ 2 = 70). Write “70” in both Anna and Flora’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. “Anna gave 31 bracelets to her friends…”, cut Anna’s model into 2 parts, write “31” in the 2nd part of her model and shade as we are subtracting 31 from Anna. Cut the same for Flora’s model but do not shade as we are only making parts equal. Use dotted lines to draw a box for Flora as she made more bracelets.

  3. Whatever number of bracelets Anna was left with, Flora will have 3 groups of that amount (“Flora had thrice as many bracelets as Anna.”) Write “1u” (1 unit) in Anna’s 1st part of the model, write the same for Flora’s 1st part of the model as well. All 3 parts of Flora’s model will add up to 3 units. The 2nd part and the 3rd part of Flora’s model will add up to 2 units.

  4. Anna had 39 bracelets in the end (70 – 31 = 39). 1 unit = 39, 3 units will be 117 (3 × 39 = 117). Flora had 117 bracelets in the end. To find how many more bracelets Flora made than Anna, we just have to take the number of bracelets Flora had in the end minus what Anna made (117 – 70 = 47).

Flora made 47 more bracelets than Anna.

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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What's Problem Sum?

Problem Sum is a term commonly used in the context of math education, particularly in regions that follow the Singapore Math curriculum. It refers to a type of math problem that typically involves multiple steps and requires students to apply various mathematical concepts and strategies to find the solution. These problems are often word problems that describe a real-world scenario, requiring students to read, comprehend, and analyze the situation before applying the appropriate math operations to solve it.

In essence, a Problem Sum combines elements of arithmetic and logical reasoning, challenging students to think critically and use their problem-solving skills. It is a key component in developing a deeper understanding of math concepts and enhancing analytical abilities in students.