## Developing Number Sense

• Relationships exist between and within numbers.
• Multiple instructional approaches are used to build student understanding of number relationships.
• Comparing, composing and decomposing, estimating, visualizing, and representing are used in connection with each other and are vital for developing number sense.

Number sense is built through developing an understanding of number relationships. Providing all students with learning opportunities to compare, compose and decompose, represent, visualize, and estimate lays the foundation for a deep understanding of relationships between and within numbers. The provincial outcomes reflect these number relationship concepts. They are critical for student achievement of outcomes throughout all math curricula.

“Through their learning of K-12 Mathematics, students should develop an understanding of the meaning of, relationships between, properties of, roles of, and representations (including symbolic) of numbers and apply this understanding to new situations and problems.” SK Curriculum Guide, Gr. 2, p. 7 Rarely are the big ideas (comparing, estimating, visualizing, representing, decomposing and composing) explored in isolation of each other. Instead, students understand mathematics through experiences that involve many of the big ideas. For example, students can estimate while using visuals. Students visualize an estimation. Students compose and decompose numbers using a visual representation.

Students that understand number relationships also understand the relationships that exist within operations. For example, the relationship between addition and subtraction, multiplication and division.

Students’ experiences with mathematics should not solely be watching the teacher and repeating procedures. This does nothing to build number sense, but instead just establishes classroom routines that are counter-productive to developing student number sense. Students are mathematicians. Teachers facilitate experiences where students are engaged in productive struggle while thinking mathematically.