math model

At Miller School, math lessons are designed to meet the needs of a wide variety of learners. A highly effective instructional model called Concrete, Representational, Abstract is used to help students visually and concretely model mathematics. This critical stage of learning allows students to solve math problems more efficiently and flexibly. As concepts are developed, students engage in math talks. In addition to learning math concepts (what we learn in math), students also engage in the practices of math (how we learn math).  Each lesson provides opportunities for students to think and solve like mathematicians: to engage with math concepts and practices, to express math reasoning, to explore flexible ways to think about and to solve math problems, and to look for structure and patterns in math.

Key Content Standards:

Grade 3

Understand properties of multiplication and the relationship between multiplication and division; multiply and divide within 100; use place value and properties of operations to solve multi-digit problems and to explain patterns in arithmetic; develop understanding of fractions as numbers; relate area to multiplication and to addition; work with perimeter of plane figures and distinguish between linear and area measures; describe, analyze, and compare properties of two-dimensional shapes.

Grade 4

Use place value and properties of operations to perform multi-digit arithmetic on whole numbers less than or equal to 1,000,000; gain familiarity with factors and multiples; order fractions; build fractions from unit fractions; understand decimal notation for fractions, and compare decimal fractions; understand concepts of angle and measure angles; draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Grade 5

Perform operations with multi-digit whole numbers and with decimals to hundredths; use equivalent fractions as a strategy to add and subtract fractions; multiply and divide fractions; convert like measurement units within a given measurement system; understand concepts of volume and relate volume to multiplication and to addition; classify two-dimensional figures into categories based on their properties; graph points on the coordinate plane to solve real-world and mathematical problems.

Standards for Mathematical Practice
Grades 3 to 5

  1.  Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics through word problems and real-world models.
  5.  Use appropriate tools (i.e. vocabulary terms, symbols) strategically.
  6. Attend to precision.
  7. Take advantage of technology to improve and advance learning.
  8. Look for and express regularity in repeated reasoning.

Massachusetts Curriculum Framework for Mathematics