The illuminations NCTM website is a great resource for teachers who are looking for lesson ideas. There is A LOT on this website! In addition to lessons sorted by approximate grade levels, there are also interactive tools.
The activity I chose to critique is called Hopping on the Number Line. I chose this lesson because I was interested to try the activity and it fit with my current teaching topic. I felt that my students had some prior knowledge with addition facts to 18; however, had not started to look closely at the number line as a tool. Also, we have just begun exploring and discussing addition facts, so I considered this as a way to provide some extra practice and exploration. My students had not used the number line yet as a tool to show ideas during problem-based learning. Breyfogle and Williams (2009) state that, “the teacher must consider how well the task provides the opportunity for students to investigate the mathematics content in an open but structured way and how well the task connects with students’ existing knowledge while pushing them deeper (p. 277). I considered this task to provide that open but structured way to connect existing knowledge with this task.
When using the Pisa test levels, I would level this activity as a level 2 or 3. Students were using an understanding of addition and the decisions they were making were fairly sequential. This activity was engaging and provided students with practice and exploration. However, I did not consider this a problem that had my students delving into deeper learning.
The students liked the frog jumps and it was an easy “leap” (pun intended) to connect. The students also were able to use the dots on the dominoes as quick identification and they had some prior knowledge/experience with subitizing (seeing an amount under 10 quickly without counting. This blog, Teaching Math, has resources too. Check out dreambox for interactive 10 frames that could be used). This activity afforded students the ability to see numbers in addition sentences as whole parts. Students who were having more difficulty with addition sentences were challenged to leap at least the first number, rather than counting all by one, starting at one. This encouraged students to use the count-on strategy.
We also discussed the communative property. It is hoped that students who are counting by one, may be more able to grasp the idea of counting up from the larger number. They would explore and understand the communative property through play.
My more experienced students were able to add the numbers quickly and make the necessary leaps according to the domino. It was interesting to watch and listen to students who were able to leap the first number, and then break apart the second number. To record this, I adapted the activity to allow the students to show their small leaps under the larger leap that was indicated on the domino. Sharon Friesen (2010) states, “teaching practices that help students build mathematical proficiency combine concept formation with procedural fluency. In this way students gain a deep understanding of what they are doing and how to do it (p.52).” This activity and this adaptation helped my students combine concept formation with procedural fluency. Albeit, that some students are not quite proficient yet; however, I did not expect them to be after this one experience.There were some limitations to the activity. I felt that using the number line from 0-10 was a good way to begin; however, it may lead some students to think that a number line must include 0. As we delve more into addition and subtraction of larger numbers, the open number line will be used to demonstrate student thinking so that it too becomes a tool students can choose to use. In ways, this is not a limitation, but definitely something to think about when using the lesson. As for possibilities, this lesson could easily be adapted to create additional lessons to explore larger numbers, maybe by using dice (6-10sided) or cards. Another possibility could be to explore more than 2 addend addition sentences, again using the dice and rolling three leaps. Students could also be given an open number line to record on.
I enjoyed this lesson; it was easy to implement and had the students engaged using the number line. It provided me an opportunity to observe students who had challenges with the number line and possibly number concepts and understanding amount. The activity page in the picture shows a student I will be observing and listening to closely in the lessons to follow. This activity afforded formative assessment into knowledge about number lines and number concepts.
Friesen, S. (2010). Raising the floor and lifting the ceiling: Math for all. Education Canada, 48(5), 50—54.
Breyfogle, M.L, & Williams, L. (2009). Designing and Implementing Worthwhile Tasks. Teaching Children Mathematics, 15(5), 276—280.