Select a number less than 20.

Skip count with it to 1000.

How many numbers can you find that will hit no hundreds through to 1000.

This problem explores the idea that large numbers are made up of smaller numbers. It also helps students form a more accurate idea of the value of a 1000. The students develop their understanding of multiples by skip counting with a calculator, using the repeat function. For example, skip count by sevens by pressing: 7 + = = = etc. The calculator allows the students to work with large number problems. In this problem the calculator allows them to look for patterns in the multiples of numbers.

### The Problem

Select a number less than 20. Skip count with it to 1000. How many numbers can you find that will hit no hundreds through to 1000.

### Teaching sequence

- Introduce the problem by using the calculators to skip count in 8's.
- Record the multiples of 8 as they are found up to 200.
- Ask the students to predict which other hundreds they think would be "hit" (multiples of 8). Give them time to find the hits (200, 400, 600, 800)
- Discuss the pattern found.
- Read the problem for the students to work on in pairs.
- Visit with the pairs as they work asking:
*What are the next hundreds you will hit exactly? How do you know?*

Which number will you pick next? Will that number hit a hundreds number? Which one?

Can you pick a number that will hit every hundred through to 1000? Are there others? - Encourage the students to organise their findings into a list and use the list to look for patterns.
- Share lists and patterns.

#### Extension to the problem

What numbers will hit every hundred through 1000?

### Solution

11, 13, 17, 19

Solution to the Extension

1, 2, 4, 5, 10