On his website peterliljedahl.com, Peter shares rich problem solving activities that he calls numeracy tasks. Many of them were co-constructed and piloted with teachers from Port Coquitlam, Prince George and Kelowna. He says that they provide a context within which you can invite learners to discuss mathematics and they create opportunities to support students’ numeracy proficiencies.
Our Alberta math Program of Studies states, “Learning through problem solving should be the focus of mathematics at all grade levels.” These numeracy tasks provide excellent opportunities for students to experience problem solving in engaging and collaborative ways. In addition, these numeracy tasks integrate the seven mathematical processes that are, “intended to permeate teaching and learning“: communication, connections, mental math and estimation, problem solving, reasoning, technology and visualization.
The numeracy tasks are posted individually so you can download the Word documents and personalize them for your classroom context and particular group of students. He has divided the tasks into grade bands: K-3, 4-6, 7-9 and 10-12. Based on field testing these tasks with students, Peter says that the tasks are upwardly applicable. In other words, a task that is listed in the K-3 section could be used for students in higher grades with alterations to the context. Click here to see this list.
Peter has discovered that the numeracy tasks fall into four main categories: fair sharing, planning, estimating across a large number of variables and modelling. He is currently exploring a new category, subjective probability, and I am looking forward to seeing some tasks in this area. At this point I have only tried the fair sharing tasks and they are great! Teachers and students are engaged immediately by the challenge of determining what is ‘fair’. There is an entry level for every student and it’s very interesting when students share and justify their conclusions. This is authentic learning at its best!
He also describes the qualities of good numeracy tasks. He includes these characteristics: low floor, high ceiling, huge degrees of freedom, fixed constraints and inherent ambiguity. If you’d like more details about these characteristics click here.
Finally, Peter shares the protocol that he and his colleagues used to create these numeracy tasks. They began with an engaging context and then determined how the situation could be problematic. They finalized the pilot task and field tested it with students. They observed students’ levels of mathematical thinking, discussion and written output. They refined the task based on this feedback. They do not believe that these tasks are perfect but that they are ‘a work in progress’ and will continue to be developed and refined over time.
I am excited to share these numeracy tasks with you and am thankful that Peter and his colleagues are sharing them with us.