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By using real object representations, young children are capable of masterful algebraic thinking. The first-graders here are using simple scales and six film canisters with varying amounts of sand inside. Two canisters are filled completely (A=Alex and A=Angela); two are filled halfway (B=Burt and B=Balinda); and two have only a few grains of sand (C=Cory and C=Caitlin).

After several experiences with comparing and ordering the film canisters by weight, the children are invited to participate in a performance task related to the notion of algebraic equality. The teacher sets up the performance task with the following vignette.

There are six children in the Can family (each represented by a film canister). At the park, all six children want to ride the super seesaw at the same time. To help the Can family decide who should ride together, place the Cans on the scale to show balance. Draw a picture of what you find out.

The children discover that balance must be created by placing the cans on the scale in the following equation: A + C + B = C + A + B. Then the teacher asks, “What if Alex wants to get off the seesaw?” Josh describes the needed sequence of events: “If Alex wants to get off the seesaw, then Angela has to get off too, because she is the one who weighs the same.” In first-grade language,

Josh describes the algebraic notion of maintaining equality within an expression (that is, B + C – A = C + B – A). Without being prompted by further questions, Pfeifer adds, “And if Caitlin wants to get off the seesaw, Cory has to get off because they are the same.” Many other children see the connections and note that Burt and Balinda are also the “same” and would have to be removed together to keep the balance or maintain equality.

In this activity, young children can see in concrete terms what maintaining balanced equations encompasses. Ebony includes a precise illustration and declares, “The scale is balanced” (see Figure 7). Josh writes, “We made it balance by putting three on each side of the scale. And we know that ABC and ABC are right because we see it” (see Figure 8). Josh’s illustration impressively includes the amount of sand in each canister. Pfeifer explains, “It does not work if you use the wrong cans. It has to be ABC and ABC. We know because we tried it” (see Figure 9). Her illustration depicts this important part of the learning process.