In this curriculum, multiple activities are used to teach each learning goal for the purpose of keeping students engaged and to ideally reach as many students as possible since every student learns in a different way. However, in terms of assessment, the format does not often change very much from day-to-day, as required by the curriculum at this stage in the kindergarten school year. Students are observed in small group activities by the teacher and adult assistants (we have Americorps members who also lead small groups and observe) and notes are taken on their progress and checklists are completed. During formative observations, questioning is used to clarify student ideas and reasoning behind choices and notes are made. Students during this time are engaged with varieties of manipulatives, depending on the activity, and are engaged with discussion with one another. Once they have determined an answer, depending on the goal of the activity, students have different recording sheets to record their work to be collected and graded. These recording sheets are authentic because each one is a written or visual representation of what they did with their manipulatives. For example, during the activity Inventory Bags, students remove manipulatives (for example, pattern blocks) from a bag, count them, and then record their results by writing the number they counted, representing that same number with the same number of tally marks, and then representing the number with pictures (if the number was 5 pattern blocks, they might draw five circles). They have to record their results in three different ways, to show that they can count objects and understand that the numbers represent a specific value. By successfully completing this activity and recording their work, students show they are mastering the first learning goal which states that students will be able to accurately count, identify, and record numbers up to 12. 
Formative assessments for learning goal 2 work in much the same way. Students learn by engaging with manipulatives, such as building towers of connecting cubes and comparing the length of the towers to other objects. They learn about the concepts of longer and shorter by physically comparing objects and discovering for themselves. They then record their findings on recording sheets that are specifically designed for the activity. While they are engaged with activities and recording their findings, they are observed and notes are taken for the purpose of understanding individual student approaches to their work and determining where the root of problems are, whenever applicable. These notes help guide review sessions and help decide whether activities need to be brought back for more days than originally planned. 
Formative assessments for learning goal 3, again, involve students recording their data after they work with manipulatives to complete the purpose of the activity. For example, during the activity Ordering Cards, students are instructed to flip over four cards at a time that have a number from 0-10 written on each one, and then put those four cards in order from least to greatest. After they have ordered the cards, they make a physical record of their work so that their understanding of the position of numbers and the concept of ordering from least to greatest can be graded. So again, students are engaging with physical materials and recording their findings, which is the same general form of assessment that has been used throughout the unit. Students are also observed while they work and notes are taken, and questions are asked to understand choices students make.  Students are also informally assessed based on their answers during the whole group instruction part of the lesson, which applies to lessons under each learning goal. For example, students might be asked to remind us what different ways we use to record our work during Inventory Bags, and they will be informally assessed based on their answer. We also count as a whole group when modeling activities like counting connecting cubes, and I watch and listen to see who is struggling with counting or who is counting too fast or too slow which can indicate an issue with one-to-one correspondence. There are also many lessons which involve engaging with the Smartboard for guided practice before sending students to their small group centers. Ordering Cards is one of those lessons, where students have to flip electronic versions of the cards over and order them from least-to-greatest. Student success with this and student responses to whether or not the answers are correct will guide whether additional practice is necessary prior to centers. 
