Starting in kindergarten and moving through the first grade, students of early math begin to develop a mental fluency with numbers and the relationships between them known as "number sense." Number relationships—or math strategies—are comprised of several crucial functions:

**Complete Operations**over places (i.e. from tens to hundreds, or thousands to hundreds)**Composing and Decomposing Numbers**: Decomposing numbers means breaking them down into their component parts. In Common Core, kindergarten students learn to decompose numbers in two ways: decomposing into tens and ones with a focus on numbers 11-19; showing how any number between 1 and 10 can be created using different addends.**Equations**: Mathematical problems that show that the values of two mathematical expressions are equal (as indicated by the sign =)

Manipulatives (physical objects used to facilitate a better understanding of numerical concepts) and visual aids—including ten frames—are important teaching tools that can be used to help students get a better grasp of number sense.

### Making a Ten Frame

When you make ten frame cards, printing them on durable card stock and laminating them will help them last longer. Round counters (the ones pictured are two-sided, red and yellow) are standard, however, pretty much anything that fits inside the frames—miniature Teddy bears or dinosaurs, lima beans, or poker chips—will work as a counter.

### Common Core Objectives

Math educators have increasingly acknowledged the importance of “subitizing”—the ability to instantly know "how many” on sight—which is now part of the Common Core Curriculum. Ten frames are a highly effective way to teach the skills required to recognize and understand number patterns that are essential for operational fluency in math tasks including the ability to add and subtract mentally, to see relationships between numbers, and to see patterns.

“Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).”

—From CCSS Math Standard 1.OA.6

### Building Number Sense

Emerging math students require plenty of time to explore number concepts. Here are some ideas to get them started working with a ten frame:

- What numbers don't fill one row? (numbers less than 5)
- What numbers fill more than the first row? (numbers greater than 5)
- Look at numbers as sums including 5: Have students make the numbers to 10 and write them as composites of 5 and another number: i.e. 8 = 5 + 3.
- Look at other numbers in the context of the number 10. For example, how many do you need to add to 6 to make 10? This will later help students decompose addition greater than 10: i.e. 8 plus 8 is 8 plus 2 plus 6, or 16.

### Manipulatives & Visual Aids for Special Needs Students

Children with learning disabilities will likely need extra time to learn number sense and may require additional manipulative tools in order to achieve success. They should also be discouraged from using their fingers when counting as it may later become a crutch when they reach the second and third grade and move on to more advanced levels of addition and subtraction.