5.5: Measurement
- Page ID
- 205709
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Course Competency 5. Examine strategies that teach early math skills.
CRITERIA 5.5. identify concepts of measuring and estimating.
Measurement
Figure 5.1: When measuring two cups of flour, ½ cup of salt, two tablespoons of oil to help make playdough, children use and build their mathematical knowledge.[1]
Measurement is the “assignment of a numerical value to an attribute of an object” (NCTM, 2000). Measurement is a critical concept in mathematics because of the connection to everyday life. Additionally, there are connections to other mathematics, as well as other content areas.
Supporting Measurement
The Measurement strand involves comparing, ordering, and measuring things. Included in this strand is the child’s ability to compare and order objects by length, height, weight, or capacity; to use comparison vocabulary; and to begin to measure. Young children develop an intuitive notion of measurement through natural everyday experiences. They explore and discover properties such as length, height, volume, and weight as they look for a longer block, measure who is taller, pour sand from a small bucket to a larger one, or try to pick up a heavy box and ask for help. They make comparisons to see which is longer, taller, heavier, larger, or smaller.
The information below is from the California Preschool Standards and is again provided as a reference to the age you may see these measurement related skills appear. However, remember the Wisconsin Model Early Learning Standards include the skills for measurement in order of development but do not assign a specific age to any skills as all children develop at their own rate and time. See WMELS for specific behaviors of children and strategies of adults for measurement.
At around 48 months of age |
At around 60 months of age |
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1.0 Children begin to compare and order objects. |
1.0 Children expand their understanding of comparing, ordering, and measuring objects. |
1.1 Demonstrate awareness that objects can be compared by length, weight, or capacity, by noting gross differences, using words such as bigger, longer, heavier, or taller, or by placing objects side by side to compare length. |
1.1 Compare two objects by length, weight, or capacity directly (e.g., putting objects side by side) or indirectly (e.g., using a third object). |
1.2 Order three objects by size. |
1.2 Order four or more objects by size. |
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1.3 Measure length using multiple duplicates of the same-size concrete units laid end to end. |
Teachers can support children’s development of the measurement foundations with the following:
- Provide opportunities to promote measurement concepts in the environment (things to measure and measure tools)
- Observe preschool children’s measurement concepts in everyday play and routines
- Facilitate and reinforce measurement concepts in everyday play and routines by
- Building the descriptive and comparative vocabulary
- Asking questions to bring their attention to the measurable properties of objects
- Challenging them to use measurement to solve problems
- Provide opportunities to compare and order objects
- Use literature to illustrate measurement concepts
- Provide small-group activities using standard and nonstandard measurement
- Encourage estimations of measurement
- Encourage recording and documentation of measurements[10]
As part of exploring and learning the concept of growth, the children have planted sunflower seeds in the garden. A long stick was attached to each plant, and the teacher asked that every week the children mark on the stick the height of the sunflower. Tracking the growth of sunflowers has generated comparison and measurement experiences. For example, one week the teacher pointed to one of the sunflowers and explained to the children, “Last week when we measured this sunflower, it was up to here. It was seven inches long. This week it is up to here. How many more inches do you think it grew in the past week? What is your estimate?”
Children were encouraged to make estimates and then were invited to measure the growth of this sunflower. “How can we measure how much it has grown since last time?” Children had different ideas. Some children said, “You need a ruler.” Others said, “With this” and pointed to a measuring tape. Over time, children were also comparing the sunflowers one to another. On one occasion, the teacher helped a small group of children compare the height of two flowers by using a string to represent the height of one flower and then laying the string against the second flower.
Children enjoyed tracking the sunflowers’ growth and finding out, “Which sunflower is taller?” and “Which is taller?”—the child or the sunflower.[12]
Other Forms of Measurement
Reading a Clock
Students typically don't learn to read a clock until 1st grade. Students in grades 1-3 learn to read a clock (analog and digital); in first grade, they tell time to the nearest hour and half hour, in second grade, to the nearest 5 minutes, and in third grade, to the nearest minute. In third grade, students solve problems involving elapsed time.
Time can be a difficult subject to teach because it can not be seen or manipulated. Additionally, time is difficult to comprehend for most students because the duration of time depends on what the student is waiting for. However, students in preschool can categorize and sequence time, and use language associated with time. Teachers should give students opportunities to time events in their everyday lives, such as brushing their teeth, eating lunch, riding the bus to school, etc.
Money
Students will begin working with money in second grade and solve word problems involving dollars or cents. Second graders have not been introduced to decimals; therefore, ask students to solve problems involving dollars or cents, but not a combination of the two. They will learn about dollars that include $1, $5, $10, $20, $100 bills, and coins that include quarters, dimes, nickels, and pennies. In addition, they should learn to use the $ and ¢ symbols.
Learning the value of each coin can be confusing for young students because the size of the coin doesn’t represent the value. For example, think of a dime and a nickel. The dime’s value is 10¢ whereas the nickel’s value is 5¢, but the nickel is a bigger coin. Therefore, students need to learn the value of each coin by being told, just as they learn the names of other physical objects.
Preschool students can learn about money through these behaviors stated in the Wisconsin Model Early Learning Standards:
• Child examines both sides of coins using a magnifying glass.
• Child matches and sorts coins by size or denomination.
• Child identifies penny and nickel.
• Child identifies penny and nickel, recognizing that coins have different values by matching five pennies to one nickel.
• Child knows that a nickel is worth more than a penny.
• Child uses coins to give change when playing in the play store or play post office.
• Child pays for an item at the store by counting his/ her money and giving correct amount of change.
Length
There is a recommended sequence for teaching measurement. This begins in preschool and kindergarten by asking students to make comparisons of measurable attributes, such as longer, shorter, taller, heavier, lighter, etc. This is a critical step in the development of measurement. Give students many opportunities to compare directly so the attribute becomes the focus. Additionally, ask students to discuss and justify their answers to questions such as, “Which box will hold the most?” “Which box will hold the least?” “Will they hold the same amount?” “How could you find out?” Provide students with many items to choose from in order to support their thinking, such as dried beans.
Students then continue by using models of measuring units that produce a number called a measure. In preschool and kindergarten, start with nonstandard units. For example, ask students, “How many snap cubes tall is the can?” or “How many footprints is the length of this room?” A part of the developmental process in the understanding of measurement is the opportunity to measure.
Students should be given opportunities to make or use their own measuring tools, such as paperclips, or a handprint. After students become proficient in making comparisons and measuring with nonstandard units, you can introduce common measuring tools, such as a ruler.
When students make direct comparisons for length, they must notice the starting point of each object and be aware that the objects must be matched up at the end of the object. A developmental milestone for kindergarten students is conservation of length which refers to the recognition that moving an object does not change the length.
In first grade, students indirectly measure the length of two objects by using a third object, such as a measuring tool. This is transitivity and is connected to conservation. Be sure to use the language taller, shorter, longer, and higher. If students use the words bigger and smaller, ask them to explain what they mean.
When students are measuring an object, they are deciding how many units are needed to fill, cover, or match the object being measured. Ask students to first predict the measurement, then find the measurement, and then discuss the estimates. Additionally, ask students to measure objects that are longer than their measuring tool. This will lead to some good discussions and collaborations among students.
When you ask students to use multiple copies of one object to measure a larger object, this is called iteration. Through careful questioning from the teacher, students will recognize the importance of no gaps and overlaps to get a correct measurement.
As students transition from using nonstandard units to standard units to measure, they must be taught to use a ruler correctly when measuring the length of an object. It is critical that students locate the starting point on the ruler. Notice on the ruler below that zero is not at the end.
You can ask students questions such as, “Do you start at the end of the ruler, or at zero?” and “Why do we start at zero?” and “Are we looking at the spaces or the tic marks?” Students need to understand that the spaces indicate the length of the object; the tic marks indicate the end of the space.
Students also need multiple experiences with measuring in inches, feet, centimeters, and meters. Students should measure a length twice and compare the two measurements. For example, the length of the desk is 36 inches or 3 feet; or the length of a paperclip is 3 centimeters or 30 millimeters.
Students should also be expected to estimate lengths using whole units before they measure. Additionally, students should find their own personal benchmark measurements, such as the width of one of their fingers is a centimeter, or the length between their elbow and wrist is a foot.
Mass and Volume
Beginning in third grade, students will reason about mass and volume. Students first measure and estimate the liquid volume and masses of objects using grams, kilograms, and liters. Students need multiple opportunities to weigh objects so they have a basic understanding of the size of weight of a liter, gram, and kilogram. Additionally, students need time to weigh objects and fill containers in order to develop a conceptual understanding of size and weight.
Preschool children can explore measuring mass and volume as they play with balance scales or different-size containers in the sensory table. Providing these play opportunities in preschool helps children to start developing early measurement concepts they will use later in their K-12 math education. of measurements[10]