**Instructional programs from prekindergarten through grade 12 should enable
all students to—**

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

**Pre-K–2 Expectations: **In pre-K through grade 2 all
students 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 all students
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 all students
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 all students
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 all students 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 meterstick;
- use tools to measure;
- develop common referents for measures to make
comparisons and estimates.

**Grades 3–5 Expectations:** In grades 3–5 all students 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 all students 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 all students 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.