Recognise and use square numbers and cube numbers 4 - Reasoning

The exercise presented is a reasoning task involving multiplication and division with a focus on square numbers, cube numbers, and prime numbers. Students are asked to identify the values of three cards labelled P, Q, and R. The value on card P must be a square number, which is an integer that can be expressed as the square of another integer. Card Q should display a cube number, which is an integer that is the cube of another integer. Finally, card R must show a two-digit prime number, which is a prime number consisting of two digits.

To solve this puzzle, students must find a combination of a square number (P) and a cube number (Q) that, when added together, equal a two-digit prime number (R). The clues provided guide students to explore the relationships between these types of numbers and use their understanding of multiplication, division, and number properties to find valid combinations. Examples of correct answers include P: 2² = 4 and Q: 3³ = 27, which sum to R: 4 + 27 = 31, a two-digit prime number. Another valid solution is P: 3² = 9 and Q: 4³ = 64, which sum to R: 9 + 64 = 73, also a two-digit prime number. The task encourages logical thinking and application of numerical concepts to find the value of each card.