IV. Mathematical Thinking: Developmental Overview

To understand the types of problems young children may have in mathematical thinking, it is important first to have an understanding of the developmental trajectory: at what grade level proficiency is expected for essential concepts. The content of our curriculum can be broken down into the following categories: computation, number sense, time money, patterns, geometric concepts, and problem solving. The following list is by no means exhaustive; it focuses on some of the key aspects.

    KINDERGARTEN

    By the end of Kindergarten students should have a solid understanding of the following:

    Number:

  • Know one-to-one correspondence: a particular number of objects has a set value despite the size, position, or nature of those objects.
  • Have fluent count aloud skills.
  • Group objects into sets of five, ten, etc.
  • Use ordinal numbers (e.g., first, second, third) to identify position.
  • Divide a set of 2, 4, 6, or 8 concrete items into two equal halves.

    • Geometry:

  • Recognize two dimensional shapes and explore three-dimensional solids.
  • Sort shapes by size, sides, or corners.
  • Recognize congruent shapes.

    • Time and Money:

  • Recognize and name pennies, nickels, and dimes.
  • Name days of the week.
  • Fill in numbers on a clock.
  • Sequence events in time (before/after, first/last).
    FIRST GRADE

    By the end of first grade students should have a solid understanding of the following:

    Number:

  • Estimate, count, recognize, and write numbers 0-120.
  • Understand two digit numbers and basic place value.
  • Identify basic unit fractions.
  • Understand the concepts of addition and subtraction.
  • Write and solve one-digit addition and subtraction as well as two-digit subtraction without regrouping.

    • Geometry:

  • Identify geometric shapes by appearance, name, and written word.
  • Explore three-dimensional solids.
  • Explore slides, slips, and turns.

    • Problem Solving:

  • Represent an addition or subtraction story through various means (e.g., models, patterns).
  • Explain their strategies orally or in writing--using pictures, numbers, and/or words.

    • Measurement:

  • Estimate, measure, and compare length and weight.

    • Time and Money:

  • Know the days of week and months in order.
  • Recognize and use dollar and cent signs.
  • Tell time to the half hour.
    SECOND GRADE

    By the end of first grade students should have a solid understanding of the following:

    Number:

  • Estimate, count, recognize, and write numbers 0-999.
  • Identify ordinal positions through twentieth.
  • Understand and apply the concepts of odd and even.
  • Estimate, add, and subtract two and three digit numbers, including money amounts.
  • Identify and compare fractions.
  • Understand the concepts of multiplication and division.
  • Understand apply the concepts of odd and even.

    • Geometry:

  • Identify and classify two-dimensional and three-dimensional solids.
  • Describe slides, slips, and turns.
  • Identify and create symmetrical figures.
  • Use descriptive language to identify spatial concepts.

    • Time and Money:

  • Know the days in a month.
  • Tell time to the 5 minute mark.
  • Solve problems involving elapsed time.
  • Write date using words and numbers.
  • Read and write amounts of money using dollars and cent signs and the decimal point.

    • Problem Solving:

  • Use strategies such as a chart, list, or graph.
  • Use estimation skills to solve a problem.
    THIRD GRADE

    By the end of third grade, students should have a solid understanding of the following:

    Number:

  • Solve problems involving sum and difference of whole numbers from 0-9,999 without regrouping.
  • Understand the inverse relationships between addition and subtraction and the inverse relationship between multiplication and division.
  • Know the multiplication and division facts through the nines table.
  • Use concrete materials to represent, add, and subtract fractions having like denominators of 10 or less.
  • Read, write, add, and subtract decimals expressed as tenths and hundredths.

    • Geometry:

  • Identify and draw points, lines, line segments, and angles.
  • Identify polygons and cubes.
  • Explore faces, edges, and verticies of cubes, rectangular prisms, and cylinders.
  • Investigate the use of a grid and ordered pairs to locate points.

    • Time and Money:

  • Read time to the nearest minute.
  • Find equivalent amounts of money to $10.00 and make change to $5.00.

    • Problem Solving:

  • Solve problems using a plan and articulate the thinking behind the plan.

Suggested Resources:

  • Overview
  • Teaching Tips on Using Manipulatives
  • For Parents

     

    Last updated 10.15.07

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