Thinking in Tens: Why 3 Tens Plus 4 Tens Works Like 3 Plus 4

Look for this idea outside of your lessons. Counting units is how measuring works. Three feet plus four feet is seven feet by the same reasoning. This is worth learning because understanding the reason means you never have to memorize the shortcut.

Watch for it today, and when you spot it, tell someone what you noticed and how you knew. Ask yourself where else the same idea might be hiding, then go and look.

Let us look at this together. Here is the reason behind the shortcut. A ten is one unit, just a bigger one. Three of anything plus four of the same thing is seven of them: three apples plus four apples, three rods plus four rods, three tens plus four tens.

The unit changes but the counting does not. That is why every small addition fact you know becomes a tens fact for free. You learned it once and get it twice.

Try it with a different unit to prove the point. Three baskets plus four baskets is seven baskets. Three hundreds plus four hundreds is seven hundreds. The unit changes, the counting does not, and that idea will carry you for years. Say it out loud once, and then try it with real objects.