Earlier this summer, a group of us met for a few days to build a series of assessments (for kindergarten through grade 2) for our district. We spent a quite a bit of time discussing, debating, and deciding on what mathematical concepts the grade level assessments should focus on: what information do we need to know about kids’ levels of understanding, what information do we want available for our PLC conversations, what information is important to share with parents, and what information might the district need for compliance for funding? We also want to connect the assessments to the district grade level days, where we can spend some time on the ideas and the role of formative assessment in our daily work.
One of the tasks we included in the assessment plan for grade 2 is entitled Hitting the Target and comes from Illustrative Mathematics. It is designed to “help students develop flexible strategies for adding and subtracting within 20” (from the Commentary section of the task).
We selected this task for a number of reasons:
- The task is in a game format. We like having a game format available to support kids’ learning of really important ideas.
- Hitting the Target offers so many instructional uses: a game that can be shared with the entire class, an activity that pairs of kids can play throughout the year, a formative assessment task that can be used across the school year to monitor students’ development of number sense (and fluency).
- The task supports the development of flexible strategies—as noted above. That is a really important aspect of Hitting the Target. It also connects to other routines and opportunities that are being woven into classrooms in our district: Number Talks and Counting Circles.
- Formative assessment is an inherent component and attribute of the task. We can learn so much about students’ ideas and mindsets about math as they play Hitting the Target.
SUMMARY of Hitting the Target
Play the game as a whole class. This allows all kids to understand the technical aspects of the game, as well as, provides opportunity for them to see the range of ideas and strategies that can be used.
- You need a set of number cards from 1 to 10. (pdf provided by Illustrative Mathematics)
- Ask a student to select 5 number cards from the set of 1 to 10.
- Have another student select a target number between 10 and 20.
- Students must add and/or subtract 2 or more of the 5 number cards to get the target number.
- Ask students to share the number combinations and explain the strategies they used to hit the target number. Record the expressions.
- As the strategies are shared, provide labels/names for them: making 5s, making 10s, using known facts.
- Once students are comfortable with the game and understand how it works, they can play in pairs.
VARIATIONS and Suggestions
- Use a regular deck of cards: aces through 10. Aces have a value of 1. We like this modification because the possibility for doubles is available.
- Use dice. You can use dice that range 0 – 5, or 5 – 10, or make your own dice using blank cubes or blank dice.
- You can use a deck of ten frame cards. (www.52pickup.me)
- Give kids a record sheet so that they can keep track of their work.
- Kids can keep track of their work on big white boards (http://www.whiteboardsusa.com). They can also use chart paper/construction paper and markers.
Regardless of the materials and the target number, the task is designed to support learning opportunities for kids to build computational fluency (and confidence). “Computational fluency refers to having efficient, accurate, generalizable methods (algorithms) for computing numbers that are based on well-understood properties and number relationships.” (From NCTM—Principles and Standards for school mathematics, as quoted in the Commentary section of the task.) The idea of computational fluency is one that is the focal point of lots of conversations; teachers are talking about the depth and range of fluency in mathematics, what fluency looks like in classrooms, and how this is the same and/or different from the previous set of state standards. Lots of opportunities for professional dialogue.
We really liked all of the possibilities this task offers kids and their teachers. It provides kids with multiple opportunities, over time, to build number sense. Using Hitting the Target in many settings and situations within their classrooms provides teachers with a range of data and information about their kids and how their students’ thinking and strategies are being developed. The options to vary and modify Hitting the Target means that it is accessible to all kids – everyone has an entry point into the mathematics conversation – and that is so important.