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Problem Solving - Explaining methods and reasoning

Grade 3IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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RUCSAC Method: Read, Underline, Choose, Solve, Answer, Check.

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Mathematical Vocabulary: Using words like 'altogether', 'difference', 'product', and 'share' to identify operations.

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Logical Reasoning: Explaining 'how' you arrived at an answer using 'because' or 'therefore'.

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Visual Modeling: Using bar models or number lines to represent the problem visually.

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Inverse Operations: Checking your answer by performing the opposite operation (e.g., using addition to check subtraction).

📐Formulae

Part+Part=Whole\text{Part} + \text{Part} = \text{Whole}

Whole−Part=Other Part\text{Whole} - \text{Part} = \text{Other Part}

Number of Groups×Size of Group=Total\text{Number of Groups} \times \text{Size of Group} = \text{Total}

Inverse Check:If a−b=c, then c+b=a\text{Inverse Check}: \text{If } a - b = c, \text{ then } c + b = a

💡Examples

Problem 1:

Sarah has 45 stickers. She gives 18 stickers to her brother. How many stickers does she have left? Explain your method.

Solution:

45−18=2745 - 18 = 27 stickers.

Explanation:

I used subtraction because the word 'left' indicates finding the difference. I decomposed 18 into 10 and 8. First, 45−10=3545 - 10 = 35, then 35−8=2735 - 8 = 27. I checked my answer by adding 27+1827 + 18, which equals 45.

Problem 2:

There are 4 boxes of cupcakes. Each box contains 6 cupcakes. How many cupcakes are there in total? Use a model to explain.

Solution:

4×6=244 \times 6 = 24 cupcakes.

Explanation:

I used multiplication because there are equal groups. I drew a bar model with 4 blocks, each labeled '6'. To find the total, I calculated 6+6+6+66 + 6 + 6 + 6 or 4×64 \times 6, which gives 24.

Problem 3:

Leo says that 15+15+1515 + 15 + 15 is the same as 3×153 \times 15. Is he correct? Explain your reasoning.

Solution:

Yes, Leo is correct.

Explanation:

Multiplication is repeated addition. Adding 15 three times (15+15+15=4515 + 15 + 15 = 45) is the same as having 3 groups of 15 (3×15=453 \times 15 = 45). Therefore, the values are identical.