## Learning Center 1: Addition and Subtraction

K-3 mathematics standard: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

In this learning center, students can learn to subtract and add by playing with small objects. Cards showing a number and the corresponding amount of dots or objects, as well as the plus, minus, and equals signs, provide a compact and visual guide; whereas linking plastic blocks offer a more kinetic approach and help develop fine motor skills. A board can be used to arrange the cards or blocks to represent examples (e.g. “2+3=5”) or tasks by leaving blanks.

### Handout

This learning center’s number cards can be replaced with regular playing cards, if necessary. Moreover, any small objects that can be handled safely by the students can be used as additional learning aids, especially if they can link together, like building blocks or legos. To guide students in this activity center, offer simple addition and subtraction tasks, asking them how many things one can take away or add a number to make another number. Ensure to provide ample visual tips: cards, blocks, or any other objects from the environment can help. Cooperative activities can be offered to multiple students: asking each to find a number that together add up to a chosen sum, or asking them to come up with multiple combinations that add up to the same number. After the activity, students’ understanding of counting can be assessed by asking to apply their addition and subtraction skills in practice, such as asking to bring a different number of things for two students, then clarifying what the total would be.

## Learning Center 2: Place Value

K-3 mathematics standard: Work with numbers 11-19 to gain foundations for place value.

In this learning center, students can learn to count past ten and place value. Plastic blocks similar to those from Learning Center 1 are used in this learning center. However, a long “base” piece that can hold up to ten regular pieces is added. Students can group pieces together to gain a visual and kinetic understanding of the concept of two-digit numbers.

### Handout

This learning center aims at teaching children to count from 11 to 19. It is critical to explain that in large groups of objects (11-19 for this age category), we count tens separately from ones: eleven is “ten and one”. Focus on ensuring that the students understand this concept; it may be tempting to try and explain that the same principle is used for counting past 20, but that may be difficult for them to grasp. It is particularly important to provide context for why ten is such a central number: ten fingers on both hands is a common example. Show examples of numbers between 11 and 19, ask how many ones are in each, and engage students in learning the names of these numbers. After the activity, students should be able to name the numbers 11-19 and clearly indicate that these numbers consist of ten and a different number, and explain the relationship between the two digits in them.

## Learning Center 3: Grouping and Counting

K-3 mathematics standard: Classify objects and count the number of objects in each category.

This learning center can use a tablet or phone application to teach students grouping and counting objects. A simple application can display a series of objects, chosen randomly, and placed at random on the screen. The objects are selected from multiple groups based on an attribute: color, shape, or size. The student’s tasks are, first, identify the characteristics present by tapping on one of the objects shown and choosing an icon representing the property; once all properties are chosen, the student has to correctly count the objects corresponding to each group and tap the appropriate number on the screen.

### Handout

This learning center teaches students to find key similarities in groups of objects and count them according to these similarities. It makes use of a tablet with an appropriate application installed. However, any physical objects that the students can safely hold can be used as additional materials. To guide students in this activity, explain the rules to them and, if necessary, help them in identifying the groups of objects. The possible groups in the applications are: “short,” “long,” “round,” “rectangular,” “oval,” as well as colors: green, red, and blue. You can suggest groupings to the students by pointing to two objects and asking what they think they have in common. If multiple students approach the center, you can guide them to collaborate by suggesting each counts a different group so the task can be completed faster, or suggest that they discuss what groups they can see. At the end of the activity, their progress can be estimated by asking them to count objects in the environment based on a property.

## Rationale

Students can enter kindergarten with a diverse range of mathematical proficiency. However, they are generally expected to have only basic understanding of mathematical concepts and can only apply them in situations where they relate to a specific, object-bound measurements (Papadakis, et al., 2016). As they learn, they can start detaching their calculations from physical objects, instead using “physical or mental representations of objects (Papadakis, et al., 2016, p. 371). Because of this, the learning centers make heavy use of physical objects and images of specific objects without introducing pure enumeration.

Developing early number sense is a critical outcome of kindergarten. This is a practical skill, which can be learned through demonstrations, practice and, especially for English learners, mathematics verbalizations (Doabler, et al., 2018). As such, the proposed learning centers offer opportunities to practice in guided and unguided scenarios, as well as opportunities for collaborative and group activities encouraging verbalizations and discussion between students.

The use of technology in education, regardless of a student’s age, is a growing point of interest. The use of tablets, specifically, has been found to have a significant beneficial effect on kindergarten students’ mathematical outcomes compared to traditional methods (Zaranis & Valla, 2018). These findings suggest that developing learning centers that make use of such devices is beneficial, provided the teaching materials are designed appropriately for the child’s abilities. Thus, the application for the tablet is intended to be used with volunteer guidance while presenting the mathematical and logical tasks as a game.

## References

Doabler, C. T., Clarke, B., Kosty, D., Smolkowski, K., Kurtz-Nelson, E., Fien, H., & Baker, S. K. (2018). Building number sense among English learners: A multisite randomized controlled trial of a Tier 2 kindergarten mathematics intervention. *Early Childhood Research Quarterly, 47*, 432-444. Web.

Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2016). Improving mathematics teaching in kindergarten with realistic mathematical education. *Early Childhood Education Journal, 45*(3), 369-378. Web.

Zaranis, N., & Valla, V. (2018). Tablets in learning mathematics for kindergarten students. In L. Daniela (Ed.), *Didactics of smart pedagogy* (pp. 267–284). Springer International Publishing. Web.