- Know and understand the measurable attributes of objects (time, temperature, length, perimeter, area, volume, capacity, weight, and angle measure).
- Know and understand the units of measurement, customary and metric systems of measurement, and the measuring process; understand aspects of size, be able to compare units and select the appropriate unit for the attribute being measured, and understand that measurements are approximations.14
- Know how to use non-standard, customary, and metric units of measurement and be able to convert and operate within each system.
- Develop formulas for measuring area, surface area, and volume for two- and three-dimensional geometric shapes and explore the independence of perimeter and area, and surface area and volume.
- Use strategies for estimating (using referents, chunking, unitizing) linear measurement, area, and volume, and verify those estimates by use of non-standard and standard units.
- Understand and use appropriate measurement instruments (rulers, scales, thermometers, clocks, calendars, beakers, cups, etc.).
- Know and understand the development of measurement in an historical context.

- Understand measurable attributes of objects and the units, systems, and processes of measurement.15
- Recognize attributes of objects and use a variety of ways for measuring those attributes (time, temperature, length, area, volume, capacity, weight, perimeter, and angle measure).
- Measure objects using non-standard and standard units (customary and metric).
- Use the appropriate unit for the attribute being measured.
- Compare attributes of different objects and different attributes of a given object.

- Apply appropriate techniques, tools, and formulas to determine measurements.16
- Recognize, name, and use appropriate tools for measuring objects.
- Find the perimeter, area, or volume of objects using concrete objects (string, square tiles, or cubes); then use non-standard and standard measures.
- Estimate measures by using common referents to make comparisons, and then verify values.

- Maintain and expand on concepts introduced in primary grades.
- Understand measurable attributes of objects and the units, systems, and processes of measurement.17
- Understand attributes introduced in primary grades and select the appropriate unit for measuring each.
- Identify, compare, and use customary and metric units of measure appropriately.
- Convert measurements within the same system (inches to feet or centimeters to meters) and convert different measures to the same unit.
- Investigate what happens to the attributes of a geometric shape when the shape is changed, such as what happens to perimeter or area when a two-dimensional shape is changed in some way.

- Apply appropriate techniques, tools, and formulas to determine measurements.18
- Develop strategies for measuring irregular geometric shapes.
- Use appropriate tools for measuring attributes.
- Select and use referents for estimating measurements.
- Develop, understand, and use formulas for area of two-dimensional geometric shapes such as rectangles, squares, triangles, and parallelograms and for surface area and volume of rectangular solids.

See Appendix A for a list of sample state standards for mathematics.

The brief activities and lesson plans listed here (by grade level) are described more extensively in Instructional Activities and Lesson Plans, where they are listed alphabetically.

Activity | Description |

Inching Alonggrades K-2 |
Have students measure objects using non-standard units, such as "inchworm" packing peanuts. |

Comparing Lengths of Arms with Linksgrades K-3 |
Have students use commercially available links or large paper clips to make chains as long as their arms. Have students compare their arm-chains and use them to measure objects. |

Is My Hand Bigger or Smaller Than Yours?grades K-3 |
Have students trace their hands and use their tracings to compare the areas of their hands. |

Measuring Desktops with Handsgrades 1-3 |
Have students trace their hands and use the tracings to measure the desktop. Emphasize area as the covering of a region with the same shape. |

Determining the Appropriate Unit of Measuregrades 1-3 |
Have students use different measuring tools to measure various objects around the classroom. Discuss with students which tools and units were easier to use for measuring the different objects. |

Finding Perimeter with a Non-Standard Unitgrades 3-4 |
Have students use pattern blocks to explore perimeter and record their work on triangle grid paper or isometric dot paper. To extend this activity, have students make different shapes with the pattern blocks, draw them on the dot or grid paper, and then identify the perimeter of the shape. |

Centimeter by Centimeter or Inch by Inchgrades 3-5 |
Have students make a meter stick (or one-foot ruler) and use it to measure objects in the classroom. For fourth and fifth grade students, specify appropriate degrees of accuracy. |

Fixed Perimetergrades 3-5 |
Have students use a piece of ribbon that measures about 10 yards to make different shapes and explore what happens to the area of shapes if the perimeter is held constant. The activity includes possible extensions. |

Finding Area with a Non-Standard Unitgrades 3-5 |
Have students use pattern blocks to explore area and record their work on triangle grid paper or isometric dot paper. Assuming that the green triangle has an area of one square unit, have students find the area of the other shapes and then build other shapes with the pattern blocks and find the area. |

Bubble Maniagrades 3-5 |
Have students create soap bubble prints to explore the concepts of diameter, circumference, and area of a circle. |

Paper-Penny Boxesgrades 3-5 |
Have students explore the concept of volume by building a paper box that will hold 100 pennies. |

Area and Perimetergrades 4-5 |
Have students construct various two-dimensional shapes with straws and gumdrops or K'NEX™ rods and connectors, and then calculate perimeter and area. |

Lighting the Perimetergrades 4-5 |
Have students use their knowledge of perimeter to determine how long a string of lights is needed to decorate the outside of a building or other structure. |

How Many Square Feet in a Square Yard?grades 4-5 |
Have students use one-foot linoleum squares to demonstrate that nine square feet are equal to one square yard. |

Tree Measurementgrades 4-5 (p. 72) |
Teach students a method for measuring the height of a tree that is too tall to measure directly. |

Creative Writing Activitygrades 4-5 |
Have students read books such as Sir Cumference and the First Round Table and then write their own stories using geometry vocabulary words. |

Creating Netsgrades 4-5 |
Have students build shapes with wooden cubes and then create nets to wrap the shapes. Use the nets to discuss surface area. |

Pumpkin Pigrade 5 |
Have students use small pumpkins to explore circumference and diameter and the relationship between these two ideas and pi. |

Pi Daygrade 5 |
Celebrate Pi Day, March 14 (also the birthday of Albert Einstein and Waclaw Sierpinski). Suggestions for celebrating include connection to children's literature, a Pi day contest, a trivia game, a visit to an online museum, and Web resources. |

Mini-Metric Olympicsgrade 5 |
Help students to become familiar with metric units by having them estimate and measure in a "Metric Olympic" setting that includes six activities. |

Lesson Plans | Description |

Can You Build It?grade 3 |
Students explore shapes and area using pattern blocks. |

Rep Tilesgrade 3 |
Students develop a deeper understanding of similarity and how perimeter changes as a result of an increase in size. They create "rep tiles" using four pattern blocks ("rep-4 tiles"). |

Visualizing Multiplicationgrades 3-5 |
Students use an area model to do multiplication. |

Rep Tilesgrades 4-5 |
Similar to the grade 3 lesson above, with added element of how area changes as a result of an increase in size. |

How Close Is Our Estimate?grade 5 |
Students explore area as the covering of a region and develop an understanding of measuring area in square units. |

The Sum of the Interior Angles of a Polygongrades 4-5 |
Students use the Geometer's Sketchpad® to find a formula for the sum of the interior angles of a polygon. |

- National Council of Teachers of Mathematics,
*Principles and Standards for School Mathematics*, p. 81. - National Council of Teachers of Mathematics,
*Principles and Standards for School Mathematics*, p. 398. - Ibid.
- Ibid.
- Ibid.

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