# Measurement & Data

The examples and guidance below are typically suited to the 3rd grade level. Further resources will be added in due course to meet the needs of students at other grade levels. Worksheets are provided from within the relevant example pages but you can also find them all listed here on the measurement and data worksheets page.

## What is in the Measurement & Data section? ##### Worksheets

Practice with printable measurement worksheets. ##### Bar and Picture Graphs

Create and Interpret Bar and Picture Graphs. ##### Measurements & Line Plots

Measure to fractions of inches and record on a Line Plot. ##### Introduction to Area

Measure area with unit squares. ##### Square Inches and Centimetes

Find area in square inches and centimeters. ##### Calculating Area

Calculate area of rectangles and compound shapes. ##### Finding Perimeter

Determine perimeter and unknown side lengths ##### Weight

Measure weight in kilograms and in grams ##### Volume

Measure volumes of liquids using liters and milliliters ##### Weight & Volume

Identify issues common to weight and volume e.g. conservation

Credit: Adapted and summarized from Common Core Standards Writing Team. (2019) Progressions for the Common Core State Standards for Mathematics (draft February 7, 2019). Tucson, AZ: Institute for Mathematics and Education, University of Arizona

### Measurement and Data

Students working with data in Kindergarten to 5th grade are preparing for their studies of statistics and probability which is typically started in 6th grade. Their studies involve both categorical data and measurement data.

• Categorical – sorting objects into groups e.g. organizing number cards into piles of odd and even.
• Measurement – taking measurements (typically starting with lengths) and recording these to form sets of data that are used to create line plots (also known as dot plots).

### Geometric Measurement

Geometric measurement connects geometry and number - the two most important domains in early mathematics. It is the assignment of a number to a magnitude of some attribute of an object or event that can be compared with other objects of events. Comparison using Geometric measurement is different to comparisons your children will have encountered in earlier grade where the number of objects were counted exactly and compared. For example, with length, the measurement can always be sub-divided into smaller lengths and more precise length can be recorded. This is quite different from counting a number of objects or events. e.g. 5 apples are always going to be 5 apples.

To measure attributes your children must be able to identify and distinguish them from other attributes. For example, starting with direct comparisons they can use terms such as "taller" and "tallest" when observing two people standing back-to-back before moving on to indirect comparisons where, if they know student A is taller than student B and that student B is taller than student C, they know student A is taller than student C without seeing them back-to-back.

Measurement allows indirect comparisons of objects and events by assigning numbers to attributes. These numbers are based on the units of measurement. Your children should develop their understanding of units in particular how units can be made up of smaller units. e.g. 1 meter is equivalent to 100 centimeters.

Using units to measure length requires two steps: selecting a unit that gives the required precision and then subdividing the object being measured by placing units, end-to-end, from the start point to the endpoint.

Area is measured using two-dimensional units - usually square - and positioning these side-by-side with no overlaps or gaps and covering the whole area to be measured. Understanding how a two-dimensional region is structured is an important progression for students.

Volume introduces a third dimension and further challenges students understanding of the spatial structuring of three-dimensional regions. The volume of cubes and rectangular prisms can be measured using three-dimensional unit objects - usually cubes - and packing them with no spaces or gaps to completely fill the region being measured.