Students will decode positional logic to generate and analyze number sequences.
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Visual of children of varying heights.
The number each child calls out represents the count of taller children standing in front of them.
Introduce the rule of counting taller children in front.
Imagine you are standing in a line of children. Instead of saying your name, you have to call out a specific number based on a hidden rule. Let's uncover how this rule works!
Step-by-step example of applying the positional rule.
Problem. A line of 7 children facing left calls out a sequence of numbers based on the rule: count the taller children standing in front of you. Determine why the children call out the sequence 0, 0, 1, 0, 3, 0, 3.
Faded example for arranging a new sequence.
We want to arrange heights so the sequence reads 0, 1, 1, 2, 4, 1, 5. To solve this, we must build the line from left to right based on the rule. The first child always calls out because there is no one in front of them to count. The last child in this sequence calls out , which means exactly five children in front of them are taller. If a child calls out a 0, it means they are the person among everyone standing in front of them. This does not necessarily mean they are the tallest in the entire line. For example, a medium-height person could call out 0 if only shorter people are in front of them. Always remember to only count the people of the person, never behind.
Conceptual questions on positional logic.
If a person is the tallest in the entire group, what number will they ALWAYS call out?