The doubles are relatively easy to learn and can form a powerful anchor for the near-doubles and other facts. They are one of the earliest sets of facts students work on.

A key scaffold is a visual reference to the various double facts. For example, 3 + 3 is called the Bug Double. Most bugs have 3 legs on each side, and 6 in total, so it illustrates 3 + 3 = 6. These visual representations must satisfy two properties. First, the total must be evident to the student, such as a spider has eight legs.

Secondly, the representation must be innately composed of the two equal parts. A bug has 3 legs on each side, that’s just how they are. A set of two tricycles doesn’t meet this second condition – while the total is 6, tricycles don’t naturally come in groups of two.

The visual anchors we use for 7+7 and 8+8 aren’t, in my experience, as strong as the others. For these, I’ve come to prefer early work on a doubles plus 2 strategy. For instance, once students know 6+6=12, then I start to ask that fact right before asking 7+7. Most students can see that adding 2 to the 6+6 fact can let them find the answer and provide a scaffold.

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The most valuable of all talents is that of never using two words when one will do.