Growing figures

Earlier, we found the difference between the numbers in a number pattern. Today, we find how many matchsticks are added each time, and count the gaps between figures. Matchsticks make a row of joined squares. Each new figure adds one square sharing one side. Figures one, two and three are shown. How many matchsticks does figure six use? Where two shapes join, they share one matchstick, so we count it only once. Figure one has four matchsticks. Figure two has seven matchsticks. Figure three has ten matchsticks. Seven minus four is three. Ten minus seven is three. The count goes up by three each time. Figure 1 is where we start. There is no gap before it. Count the gaps from figure one. One gap. Two. Three. Four. Five. So there are five gaps. Each gap adds three matchsticks. Five times three is fifteen. Figure one has four matchsticks of its own. Four plus fifteen is nineteen. Figure six uses nineteen matchsticks.

Matchsticks make a row of joined triangles. Each new figure adds one triangle sharing one side. Figures one, two and three are shown. How many matchsticks does figure five use? Try it first. Pause if you like. The triangles share sides too. Figure one has three matchsticks. Figure two has five matchsticks. Figure three has seven matchsticks. Five minus three is two. Seven minus five is two. The count goes up by two each time. Figure 1 is where we start. There is no gap before it. Count the gaps from figure one. One gap. Two. Three. Four. So there are four gaps. Each gap adds two matchsticks. Four times two is eight. Figure one has three matchsticks of its own. Three plus eight is eleven. Figure five uses eleven matchsticks.

Matchsticks make a row of joined squares. Each new figure adds one square sharing one side. Figures one, two and three are shown. Which figure uses twenty-two matchsticks? Try it first. Pause if you like. Figure one has four matchsticks. Figure two has seven matchsticks. Figure three has ten matchsticks. Seven minus four is three. Ten minus seven is three. The count goes up by three each time. Figure 1 is where we start. There is no gap before it. Figure one uses four of the matchsticks. Twenty-two minus four is eighteen. Each gap adds three matchsticks. Eighteen divided by three is six. Count six gaps from figure one. One gap. Two. Three. Four. Five. Six. Six gaps after figure one takes us to figure seven. Figure seven uses twenty-two matchsticks. Start with figure 1, then add the same number of matchsticks for each gap after it.