New Jersey Mathematics Curriculum Framework - Preliminary Version
(January 1995)
© Copyright 1995 New Jersey Mathematics Coalition
STANDARD 12: MEASUREMENT
All students will develop their understanding of measurement and systems of measurement
through experiences which enable them to use a variety of techniques, tools, and units of
measurement to describe and analyze quantifiable phenomena.
|
K-2 Overview
Students in the early grades encounter measures in many situations, from their daily work with the
calendar to situations in stories that they are reading to describing how quickly they are growing. Many
opportunities for integrating the study of mathematics with other subject areas thus present themselves
in a natural way. Measures which arise in stories can provide opportunities for students to explore these
measures in the mathematics class. Hands-on science activities often require students to measure objects
or compare them directly. Daily calendar activities provide numerous opportunities not only for work
with the calendar but also with temperature and numbers.
The study of measurement also provides opportunities for students to further develop their number sense
and to practice their counting skills. Only by using measures can students recognize that numbers are
often used to describe and compare the properties of physical objects. Students in the early grades should
make estimates not only of discrete objects like marbles or seeds but also of continuous properties like
the length of a jumprope or the number of children's feet in a dinosaur's footprint.
Students need to focus on identifying the property that they wish to measure. Students need to
understand what is meant by the length of an object or its weight or its capacity. Concrete experiences
in describing the properties of objects, in sorting objects, and in comparing and contrasting objects
provide them with opportunities to develop these concepts.
Students also need experience in making direct comparisons. Which string is longer? Which child is
taller? Which rock is heavier? Which glass holds more? Making comparisons will help children better
to understand the properties which they are discussing. They also begin to make some indirect
measurements. For example, in order to compare the height of the blackboard with the height of a
window, they might measure both objects using links and then compare the number of links used for
each. Students also use thermometers to measure temperature indirectly, reading the height of the column
of mercury to determine how warm or cold it is.
In grades K-2, students should use a variety of non-standard units to measure objects. How many links
long is a desk? How many erasers high are you? How many pennies balance a Unifix cube? In each
case, students should first be asked to make an estimate and then proceed to actually measure the object.
Students should also use different units to measure the same object. They should begin to understand that
when the size of a measuring unit increases, the number of units needed to measure the object decreases.
In these grades, students also begin to use standard measurement units in an informal way. Students
explore length using inches, feet, centimeters and meters; liquid capacity using quarts, pints, cups, and
liters; mass/weight using pounds, ounces, grams, and kilograms; time using days, weeks, months, years,
seconds, minutes, and hours; and temperature using degrees Fahrenheit and Celsius.
Whether making direct comparisons, using non-standard units, or using standard measurement units,
students in the early grades should always estimate a measure first and then perform the measurement.
In this way, their estimation and number sense skills will be reinforced.
STANDARD 12: MEASUREMENT
All students will develop their understanding of measurement and systems of measurement
through experiences which enable them to use a variety of techniques, tools, and units of
measurement to describe and analyze quantifiable phenomena.
|
K-2 Expectations and Activities
The expectations for these grade levels appear below in boldface type. Each expectation is followed by
activities which illustrate how the expectation can be addressed in the classroom.
Experiences will be such that all students in grades K-2:
A. use and describe measures of length, distance, capacity, weight, area, volume, time, and
temperature.
- Students find out how many cubes long their hand is. The class might then generate a
graph showing the results.
- Using a large map, students estimate and then use links to find who goes farther to
school. This type of activity might be related to a specific story that has been read in
class.
- Students name objects big enough to hold a football or too small to hold a soccer ball.
- Students lay out a model zoo with several toy animals, using boxes of different sizes for
their cages or yards. They also cut doors of appropriate sizes in the boxes for the
animals.
- Students move thermometers to different parts of the room, watching to see how the
temperature changes. For example, it may be very hot by the radiators and very cold
next to the windows.
- Students name objects they can lift and ones that they cannot lift.
- Students estimate and then use balances to find out how many pennies balance an object.
- Students cut strips of paper to fit around a pumpkin or to make Santa's belt.
- Students fill a large bottle with water using first a juice glass and then a cup. They then
compare the measures.
- Students make their own measuring jug using an empty mayonnaise jar. They pour in
one cupful of water and mark the water level on the jar with a marker, then another and
another.
- Students make their own ruler, marking off intervals equal to the length of one paperclip.
- Students estimate and measure the distance around an object using Unifix cubes or paper
clips.
- Students conduct experiments using timers: how many times can you bounce a ball before
all the water runs out of the can? how many times can you clap your hands before the
sand runs out of the timer? how many times can you blink your eyes in one minute?
- Students make a book describing their day at school. On each page, they stamp a clock
face and write underneath a time that the teacher has written on the board. They then
draw the hands on the face to show the time. When the actual time of day on the
classroom clock matches a time in their book, students draw a picture of what they are
doing next to the correct clock face.
- Students line up pattern blocks in different ways to measure the width of a sheet of paper.
- Students build a variety of structures using a specified number of wooden cubes.
B. compare and order objects according to some measurable attribute.
- Students compare the lengths of pencils to find out which is longest. They might also
be asked to put a set of pencils in order from longest to shortest.
- Students use water, rice, or sand to fill different objects, pouring from one object into
another to find out which object holds more and why.
- Students line up in order, from tallest to shortest.
- Children make stick drawings of a family: father, mother, school-aged child, and baby.
Which is tallest? Which is shortest?
- Students make boxes out of cardboard and arrange them from smallest to largest.
- Each group of students is given a cup and several containers of different sizes, plain
white paper, and 1 inch graph paper. They find out how many cups there are in the
container and show the number of cups on the graph paper under a picture of the
container. After completing the graph, they put the containers in order from largest to
smallest.
- Students compare pattern blocks to see which is taller.
C. recognize the need for a uniform unit of measure.
- Students measure the width of their desk using their hands and compare their results.
They discuss what would happen if the teacher measured their desks with her hand.
- Students read and discuss How Big Is a Foot? by Rolf Myllar. The king wishes to give
the queen a special bed for her birthday and measures the size using his foot. He gives
the measurements to the carpenter, who gives them to the little apprentice. The bed is
too small, but the apprentice solves the problem and everyone lives happily ever after.
They use their own feet to measure the length of the hallway and compare their results.
Finally, they measure the hallway using metersticks.
D. develop and use personal referents for standard units of measure (e.g., width or a finger is
approximately one centimeter).
- Students identify things on their body that are the same length as a unit cube from a base
tens block set (1 centimeter).
- Students make a list of things that come in quarts and things that come in liters.
- Students play with quart containers to see what they can find out about quarts. They
make a list of their findings, including some disagreements. They then proceed to
discuss what makes a quart a quart and why their findings disagree.
- Students find out that ten pennies weigh about an ounce.
- Students find that most first-graders are more than a meter tall.
E. select and use appropriate standard and non-standard units of measurement to solve real-life
problems.
- Students decide whether they should use paper clips or pennies to measure the weight of
a pencil.
- Students discuss whether they should use links or metersticks to measure the length of
the gym.
- Students write about how they might measure the distance from the cafeteria to their
classroom.
F. understand and incorporate estimation and repeated measures in measurement activities.
- Students estimate how many of their shoes will fit in a giant's footprint and write their
estimates. They trace around their shoes and cut them out. After the teacher has pasted
a few shoes onto the giant's shoe, the students revise their estimate. They then check the
accuracy of their estimates by pasting as many shoes as will fit in the giant's shoe.
- Students estimate the weight of various objects in beans and then use a balance scale to
check the accuracy of their measurements.
G. integrate measurement activities across the curriculum.
- Students read The Little Gingerbread Man and make a gingerbread village. In doing so,
they measure lengths and capacities.
- Students measure the heights of bean plants at regular intervals, making a graph of their
findings.
- An ice cube is placed on a plastic tray in five different parts of the classroom. One
group of students is assigned to each ice cube and tray. The students are asked to
estimate how long it will take each ice cube to melt. They then observe the ice cube at
five-minute intervals, recording their observations. After the ice cubes have melted, the
groups share their observations and compare the length of time it took for the ice cubes
to melt. They make a conjecture about the warmest spots in the classroom and then
measure the temperature in each location to confirm their conjecture.
New Jersey Mathematics Curriculum Framework - Preliminary Version
(January 1995)
© Copyright 1995 New Jersey Mathematics Coalition