Meredith solves a number story in which there are 3 cupcakes and then 4 more cupcakes. She mentally solves the problem and says there are 7 cupcakes. When asked how she figured it out, she says, “I don’t know.” She then is prompted to use bears to show how she solved it.

Lulu is asked to determine the sum of 8 plus 3. She explains that since she knows that 8 plus 2 is 10, 8 plus 3 is 11. Her strategy is to use a known fact that adds to 10 to find another sum that is one more.

Tasha is shown the written problem 3 + 1 =. She says it equals 2. When asked what the + sign is, she shrugs. When told it means plus, she still insists that 3 plus 1 equals 2.  Does she think that + indicates subtraction?

Chandra is asked to solve the written problem 5 – 3. She uses her fingers and writes 2. When asked how she found the answer, she says she used her fingers. However, she struggles to explain how she used her fingers. It is often challenging for young children to explain how they found answers, which is one reason to engage them in math thinking conversations. Over time, they will find it easier to explain their thinking.

Chandra is asked what the = sign means in 2 + 4 = 6. She says it means “equals,” but when asked what equals means, she says it means “plus.” Chandra is thinking of the equal sign as meaning  do what the sign says, not as equivalence.

Chandra correctly explains that 1 + 2 = 3 is correct. When shown 3 = 1 + 2, she says that sentence is not okay because “it’s backwards.” This is further evidence that Chandra is not thinking of the equal sign as meaning equivalence.

Angelo is shown the problem 12 - 8 = 16 and says it is not correct. He is asked to think about what a child might have done to get this answer. He recognizes that the child swapped 2 and 8 and subtracted 8 – 2 instead. He explains that it’s not right because “that’s not how subtraction works.”

Lulu is shown the problem 8 + 3 = 83. Her first reaction is shock. When asked why a child might write that, she says the child might think that 8 + 3 means putting together 8 and 3. When asked if it’s equal to 83, she says no because “that would be way more.” Lulu used her knowledge of magnitude to explain that 83 is not a reasonable sum.