Students will learn how to multiply whole numbers, and decimal numbers, by powers of 10. They'll also learn how to describe how the decimal point moves. For example, in \(2.8 \cdot 10^{-3},\) the decimal moves \(3\) places to the left.

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Next, give your students these challenges:

- Red Express Train by NRICH

5 on the Clock by NRICH: Note the solution provided by NRICH is wrong. Here's the solution: The hour will read 5 for 60 mins. Likewise, the hour will read 15 for 60 mins. We've got 22 hours left to account for. There will be a 5 in the 10 minute column for 10 minutes per hour. Over the 22 hours we've left to account for, that's 10 * 22 = 220 times. Now we've got 22 hours left to account for, and 50 of those minutes to account for per hour. A 5 occurs in the 1 minute column once per 10 minutes. Thus, over 50 minutes, a 5 will occur in the 1 minute column 5 times. Over 22 hours, that's 5 * 22 = 110 times. We've considered when a 5 appears in the 1 hour column, the 10 minute column, and the 1 minute column, so we must be done. Adding everything up, we have 60 + 60 + 220 + 110 = 450 times. So over 24 hours, at least one 5 will be present 450 times. The answer is the same for a 12 hour clock. On a 12 hour clock you will have 5 AM and 5 PM instead of 5 and 15, which doesn't affect our count. Here's a small Python program you can use to verify my answer is correct:

```
h, m = 0, 0
n = 0
while h < 24:
if '5' in str(h) + ':' + str(m):
n += 1
if m < 59:
m += 1
else:
m = 0
h += 1
print(n)
```

Conclude by leading this investigation:

Integral Centrifuge II (multiplication of negatives)

by MathPickle