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By Grade Band


Preschool mathematicians develop the skills to look at the world through a mathematical lens. Teachers scaffold learning through thoughtful modeling, careful questioning, and intentional provocation, encouraging children to build on their innate curiosity. Children engage with mathematical concepts including patterning, numeracy, quantity, and classifying as they play and explore. This might look and sounds like:

  • Counting the number of students in their class each day, the number of items in their lunchbox, the number of pieces in a puzzle, and any number of things around them
  • Grouping items by attribute (all of the red ones over here, the blue ones over there)
  • Identifying, naming, and growing patterns
  • Engaging in oral story telling and singing that involves quantities being added or taken away (three birds in the nest, one flew away, now there are two)
  • Developing awareness of and assigning value to numerical symbols (numbers, fingers held up, dots in a group, etc)


Prekindergarten mathematicians eagerly make connections between new knowledge they are gaining and math in the world around them. Mathematical ideas are presented in real world contexts with students quickly understanding why math matters. Children deepen their connection with the number system, as well as geometric constructs and early algebraic thinking through hands-on play experiences. Whether building a block town, organizing animals in a pet shop, or counting out crackers at snack time, prekindergarten students are learning to:

  • Identify, compare, and order quantities
  • Sort items by attribute (all of the big ones over here, the small ones over there)
  • Identify, grow, and create patterns
  • Explore scenarios that involve shifting quantities (we used to have 5 but now we have 7, we got 2 more)
  • Use representation, including numbers, pictures, and words to communicate about mathematics

Kindergarten and First Grade

Mathematicians in kindergarten and first grade explore ideas, play games, and search for mathematical connections in the world around them. Students are encouraged to inquire, investigate, discuss, and construct as they explore in all mathematical areas. They participate in ongoing investigations developed within real-life contexts that encourage children to mathematize their lives. The Bridges in Mathematics curriculum provides many opportunities for students to develop mental models, to explore multiple strategies, and to communicate their thinking in clear language. Students put forth their ideas in a community of their peers and learn to justify and defend their thinking, as well as understand and appreciate peers’ ideas. Problem solving skills are developed using story problems, which allow students to visualize the actions in the problem. Kindergarten and first graders strive to move fluidly through visualization, recording, and reporting to deepen their overall understanding of the number system and other mathematical concepts. Students are encouraged to approach problems in a variety of ways, working to be accurate, fluent, and efficient in each situation. There is a focus on students developing their individual identity as a mathematician and fostering a lifelong enthusiasm for mathematics.

Second and Third Grade

Second and third graders mathematicians work to develop routines and build a mathematical community that allows them to engage in productive work and conversation about mathematical ideas, including articulating their solution strategies and understanding other’s ideas. Students solve mathematical problems that are based in real world contexts, working individually, in small groups, and with the entire class. They are given multiple opportunities to develop visual thinking, which requires both the ability to extract and use information from pictures, and the ability to put verbal or numerical information into picture form. In addition to lending depth and meaning to the basic operations, students find connectedness between mathematics and the world around them. The Bridges in Mathematics curriculum engages students in developing standards based knowledge and skills while practicing and deepening their mathematical understanding across mathematical operations and concepts.

Fourth and Fifth Grade

Fourth and Fifth grade mathematics fosters the development of visual and conceptual models of numbers and operations. The concrete manipulation of objects leads to written mathematics and the use of algorithms, helping students develop a thorough understanding of mathematical reasoning as well as greater computational fluency. Through the Bridges in Mathematics curriculum, students engage in a daily lesson, which may consist of group activities, written work, and games, as well as Number Corner, a set of activities that incorporates a calendar pattern, a number line, data collection, problem solving, and computational fluency activities. This curriculum us supplemented with a wide array of hands on enrichment and remediation activities to provide a comprehensive math experience, allowing students to grow in their breadth of standards based mathematical knowledge, computational skill, and problem solving ability.