Measurement

• Instructional programs from prekindergarten through grade 12 should enable each and every student to—

• Understand measurable attributes of objects and the units, systems, and processes of measurement
• Apply appropriate techniques, tools, and formulas to determine measurements.

### Understand measurable attributes of objects and the units, systems, and processes of measurement

Pre-K–2 Expectations: In pre-K through grade 2 each and every student should–

• recognize the attributes of length, volume, weight, area, and time;
• compare and order objects according to these attributes;
• understand how to measure using nonstandard and standard units;
• select an appropriate unit and tool for the attribute being measured.

• understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute;
• understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems;
• carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;
• understand that measurements are approximations and how differences in units affect precision;
• explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.

• understand both metric and customary systems of measurement;
• understand relationships among units and convert from one unit to another within the same system;
• understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

• make decisions about units and scales that are appropriate for problem situations involving measurement

### Apply appropriate techniques, tools, and formulas to determine measurements

Pre-K–2 Expectations: In prekindergarten through grade 2 each and every student should–

• measure with multiple copies of units of the same size, such as paper clips laid end to end;
• use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meter stick;
• use tools to measure;
• develop common referents for measures to make comparisons and estimates.

• develop strategies for estimating the perimeters, areas, and volumes of irregular shapes;
• select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles;
• select and use benchmarks to estimate measurements;
• develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms;
• develop strategies to determine the surface areas and volumes of rectangular solids.

• use common benchmarks to select appropriate methods for estimating measurements;
• select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision;
• develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes;
• develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders;
• solve problems involving scale factors, using ratio and proportion;
• solve simple problems involving rates and derived measurements for such attributes as velocity and density.