Learning About the World

Mathematics


Measurement, Classification and Data -- Measurement and Data

Goal 1: Children compare and classify objects according to their attributes, use Standard and non-Standard units of measure, tell time and work with units of money. They develop the ability to represent and interpret data, and use operations to solve problems related to measurement including geometric measurement.

By the end of each age group or grade level, most children will have met prior age group or grade level standards in this domain.

Infants Through Older Toddlers

Infants

(0-12 Months)

  1. No standards in this age group for this Element.

Young Toddlers

(9-18 Months)

  1. No standards in this age group for this Element.

Older Toddlers

(18-36 Months)

  1. No standards in this age group for this Element.
Younger Preschoolers Through Kindergartners

Younger Preschoolers

(36-48 months)

  1. No standards in this age group for this Element.

Older Preschoolers

(48-60 months)

  1. No standards in this age group for this Element.

Kindergartners

Describe and compare measurable attributes.

  1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
  2. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference.

Classify objects and count the number of objects in each category.

  1. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.
First Graders Through Third Graders

First Graders

Measure lengths indirectly and by iterating length units.

  1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.
  2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Tell and write time.

  1. Tell and write time in hours and half-hours using analog and digital clocks.

Represent and interpret data.

  1. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Second Graders

Measure and estimate lengths in Standard units.

  1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
  2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
  3. Estimate lengths using units of inches, feet, centimeters, and meters.
  4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a Standard length unit.

Relate addition and subtraction to length.

  1. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings such as drawings of rulers and equations with a symbol for the unknown number to represent the problem).
  2. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, and represent whole-number sums and differences within 100 on a number line.

Work with time and money.

  1. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
  2. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?.

Represent and interpret data.

  1. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
  2. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Third Graders

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

  1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
  2. Measure and estimate liquid volumes and masses of objects using Standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings such as a beaker with a measurement scale) to represent the problem.

Represent and interpret data.

  1. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
  2. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

  1. Recognize area as an attribute of plane figures and understand concepts of area measurement
  2. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  3. Relate area to the operations of multiplication and addition.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measurements.

  1. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Vermont Agency of Education
Secretary Daniel M. French
219 North Main Street, Suite 402
Barre, VT 05641

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