Recognise and use square numbers and cube numbers 3 - Reasoning

In an exercise focused on understanding square and cube numbers, Malachi encounters a common misconception. He attempts to calculate cube numbers but mistakenly multiplies the base number by three instead of raising it to the power of three. For example, he incorrectly states that 4 cubed (4³) equals 81 by multiplying four by three times, rather than multiplying 4 by itself three times. The correct calculation for cube numbers involves taking a base number and multiplying it by itself twice more. For instance, 3 cubed (3³) should be calculated as 3 x 3 x 3, which equals 27, not by simply multiplying 3 by 3.

Upon reviewing Malachi's work, it is clear that he is incorrect. The correct method for finding cube numbers is demonstrated as follows: 3 cubed is 3 x 3 x 3, resulting in 27; 4 cubed is 4 x 4 x 4, resulting in 64; and 5 cubed is 5 x 5 x 5, resulting in 125. Malachi's repeated error shows a misunderstanding of the concept of cubing a number. Instead of multiplying the base by itself three times, he has multiplied the number three by itself, proportional to the base number, leading to incorrect results like stating that 5 cubed (5³) is 243 instead of the correct value of 125.