Halving and Doubling Number Towers

This interactive worksheet presents a fun and visual way to understand how numbers shrink or grow step by step through repeated halving and doubling. Students will build Number Towers, where each answer appears one below the other, forming a vertical tower of calculations.

In Halving Towers, a large number is displayed at the top. The student must successively halve it up to 10 times, entering each new result in the input boxes stacked below. For example, when the number 167936 is given, the tower will appear as:

In Doubling Towers, a smaller number appears at the top, and the student successively doubles it ten times, each result forming the next step in the tower.

All the benefits of the previous Practice Halving and Doubling the Numbers worksheet apply here — students calculate mentally from left to right using place value breakdown, not digit-by-digit computation. This left-to-right reasoning builds true number sense and mental agility. It trains students to visualize how numbers scale by powers of two.

Students can also take on extra challenges:

• Divide the second row by 4 instead of halving the first row.
• Or divide the third row by 8 to verify patterns in powers of 2.

By working vertically, students can see the pattern of growth or reduction unfold visually. Each new row represents another multiplication or division by 2, helping them grasp the exponential nature of halving and doubling. It's an engaging way to combine mental maths practice with a visual sense of numerical scaling.