Use Negative Numbers in Context and Calculate Intervals Across Zero 8 - Reasoning

In this mathematical reasoning task, students are challenged to apply their understanding of negative numbers and intervals to find the missing numbers in a sequence. The sequence presented is "-18, __, __, 30," and the condition is that the difference between consecutive numbers must remain constant. To solve this, students must first calculate the interval that exists between the given numbers, which are -18 and 30. The difference between these two numbers is 48, and since there are three intervals to cover this difference, each interval must be 16 units apart.

With the interval determined, students can then work out the missing numbers. Starting from -18 and adding 16 gives the first missing number as -2. Adding another 16 to -2 gives the second missing number as 14. The complete sequence is therefore "-18, -2, 14, 30," satisfying the condition that the difference between consecutive numbers is the same. This exercise not only reinforces the concept of negative numbers but also helps students to understand how to calculate evenly spaced intervals across zero, a foundational skill in understanding number lines and place value.