Fact Families

Fact families involve three numbers that are related. They work together to make a set of four facts - two addition and two subtraction facts. Fact families "allow children to think about part-whole relationships while also helping them realize that subtraction and addition are opposites of one another" (Cobb, 1987; Sun & Zhang, 2001; Zhou & Peverly, 2005, as cited in Kurz, Yanik and Garcia, 2009, p. 353). In its simplest form it involves rearranging parts of the equation using the set three numbers hence the chosen objective to "represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts" (ACMNA015, ACARA, 2016).
The mind mapping portion of this case study provided a clear path for learning as it forced me to start with the end in mind - the learning

“Children’s thinking follows natural developmental paths in learning maths. When teachers understand this they can build learning environments that are developmentally appropriate and effective” (Sarama and Clement, 2009, p.63). The diagnostic task, delivered through the Online Mathematics Interview, helped to reveal such thinking and the depth of understanding the focus child has about subtraction and addition. The findings indicate that the focus child is aware of the relationship between addition and subtraction but assumes that they behave in the same way, when they do not. Given the individual nature of this case study, the limitations must be acknowledged. The mental math strategies used by the focus child and the rationale for why a certain strategy was used over the next cannot be generalised to other students her age or even in her class. Nevertheless, the case study does show the value in conducting diagnostic tasks, such as the Mathematics Online Interview, to determine the individual learning points for each