**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.

**Grades 3–5 Expectations: **In grades 3–5 each and every student should–

- 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.

**Grades 6–8 Expectations: **In grades 6–8 each and every student should–

- 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.

**Grades 9–12 Expectations: **In grades 9–12 each and every student should–

- 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.

**Grades 3–5 Expectations:** In grades 3–5 each and every student should–

- 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.

**Grades 6–8 Expectations: **In grades 6–8 each and every student should–

- 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.

**Grades 9–12 Expectations: **In grades 9–12 each and every student should–

- analyze precision, accuracy, and approximate error in measurement situations;
- understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders;
- apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations;
- use unit analysis to check measurement computations.