When in full sprint towards your goal, you receive the ball, take a step and a half without dribbling in order to make a layup, is this traveling. You see this all the time in the college and NBA. This is considered traveling in high school. In the rule book, it does not say, you must dribble before you take your step and half to make a layup?
As you say, the receiving player makes a step and a half, which I assume you mean one hard step and a second step taken to jump for the layup. Consider referring the rules outlined in the Wikipedia article for traveling in basketball.
From the rules for the NBA (emphasis mine)
b. A player who receives the ball while he is progressing or upon completion of a dribble, may take two steps in coming to a stop, passing or shooting the ball. A player who receives the ball while he is progressing must release the ball to start his dribble before his second step.
A second step is considered a traveling foul if the player proceeds to dribble the ball afterwards. However, if he is progressing to shoot, the second step is the last permitted legal step for the player.
From the rules for the NFHS (not taken from Wikipedia as it claims to be the same as NCAA, so a different source has been provided.)
Art. 2. A player, who catches the ball while moving or dribbling, may stop, and establish a pivot foot as follows:
a. When both feet are off the playing court and the player lands:
- On one foot followed by the other, the first foot to touch shall be the pivot foot;
b. When one foot is on the playing court:
- That foot shall be the pivot foot when the other foot touches in a step;
Art. 3. After coming to a stop and establishing the pivot foot:
a. The pivot foot may be lifted, but not returned to the playing court, before the ball is released on a pass or try for goal.
Going by the combination of these lines, it appears that your interpretation is correct and a second step (i.e return of the pivot foot to the court) would result in a traveling violation. I am not a basketball coach, just an enthusiast, and the way the rules read, it appears there is a discrepancy in the rules for high school basketball and NBA. Perhaps someone who has coached or worked in high school basketball or NCAA can shed more light on this discrepancy.
However, the NCAA rules read much like the NFHS rules, yet a second step is permitted. This might be due to the refs and coaches not following this rule to the line and going by the rules of the NBA, where most of the NCAA players aspire to play anyway.
That rule must be from the old NBA rule book. They allow one step, a hop, and then two steps.– Coach-DDec 2, 2016 at 5:26