Chapter 19Measurement

• Group Members include

• Chris

• Megan

• Tasha

• Catherine

• Shannon

Let’s Talk About MeasurementMrs. Burke's Measurement Rap

The Measurement SongBy The Rappin’ Math Teacher, Mrs. Burk  CHORUSLet’s talk about measurement,With our measure song.Let’s talk about measurement,Like how far, how wide, how long. Let’s talk about measurement,With our measure song.Let’s talk about measurement,C’mon everybody! Sing along! Meter is to measure,Like how far to get to the treasure.Liter is for liquids,Like how much does the bottle have in it?Grams is for your groceries,Whew! Man that bag is so heavy!These units are the metric system.Now I want everyone one to listen.

(Chorus)Inches, feet, yards, and miles are more units of measure.I can do measurement, just ask me it’s my pleasure.Cups, pints, quarts, and gallons are units of capacity.Like in a container how much liquid do you see?Ounces, pounds, and tons are units of mass.Like the weight of your groceries, oooh, my aching back!This song will help you with measurement you see,If you apply it to the work on the EOG.(Chorus)

Measurement •In this chapter you will learn about teaching students to develop a conceptual understanding of the measurement process and the tools that are used to do so.

Chapter 19

Topics we cover will be about nonstandard and standard units of measurement, estimation in measurement which will be helpful when looking at benchmarks and how students develop measurement ideas and formulas. P.369

Measurement

1.Measurement involved a comparison of an attribute of an item or situation with a unit that has the same attribute. Lengths are compared to units of length, areas to units of area, time to units of time and so on.

2.Meaningful measurement and estimation of measurements depend on a personal familiarity with the unit of measure being used.

3.Estimation of measures and the development of benchmarks for frequently used units of measure help students increase their familiarity with units, preventing errors and aiding in the meaningful use of measurement.

4.Measurement instruments are devices that replace the need for actual measurement units. It is important o understand how measurement instruments work.

5.Area and volume formulas provide a method of measuring these attributes by using only measure of length.

6.Area, perimeter, and volume are related. For example, as the shapes of regions or three-dimensional objects change while maintaining the same areas or volumes, there is a predictable effect on the perimeters and surface areas.

6 Big Ideas

Measurement

•Length

•Applet

•Area

•Applet

•Weight

•Time

•Angles

•Applet

We have split chapter 19 up into 5 main attributes of study; length, area, weight & volume, time and angles. We chose the approach of using the topics of study we will have in the classroom to teach about the 6 Big Ideas of the chapter.

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Click to learn about what you are interested in! Extension Lesson PowerPoint

LengthLength:

•Is usually the first form of measurement students use.

•It can be taught at the pre-k level

•It is important for students to compare the lengths of things when first learning about length

Length

•This can be an introductory lesson for pre-k students

•Have students work at stations with different objects.

•Students can sort the objects by length, from shortest to longest or longest to shortest.

Activity 19.1Longer, Shorter, Same

Have students get creative•Students can use all different objects to measure with such as,

•Feet

•Rope

•Paper clips

•Pencils

•Just about any object found in the classroom

Length

•K.3.2 Compare, sort, and order objects according to measurable (e.g., longest to shortest, lightest to heaviest) and non-measurable (e.g., color, texture) attributes.

How to Teach to Estimate•Students need to be comfortable guessing the length of various objects.

•Students can use their unit of measurement, whether it’s a ruler or a shoe to guess the length of classroom objects.

•Possible Questions:

•How many shoes long is a desk?

•How many hand prints long is the room?

How many paper clips long is this piece of paper?

Length

Activity 19.6Changing units

1. Have students use a unit of measurement such as a pencil to measure an object.

2. Then give students a new unit that is twice as long or half as long to measure with.

3. The students will then guess how many of their new unit of measurement it will take to get the length of that same object.

4. Have a class discussion on their estimation

Length

Fractions in length•Depending on age students will handle measurements that aren't whole numbers differently.

•For younger students, they may need to switch to a smaller unit of measurement to fill in the gap. Such as, the table is four books long and one eraser

•For older students, they may use fractions.

•They are able to conceptualize four feet and 6 inches, as four and a half feet.

•The understanding of fractions helps students understand the markings on a ruler

Length

The Jump to Standard UnitsActivity 19.7

•Make your own ruler

•Ask students to glue cut out paper squares to create their own ruler.

•They then use their ruler and measure items listed by the teacher

•The class can then have a discussion on how their rulers gave them all the same answer

•This helps students make the connection as to why we have standard units of measurement

Length

Extension of Activity 19.7•Using the rulers, have students mark individual squares from 1-12

•This will help students use standard rulers

•By counting the squares and not the ruler lines, students will learn to correctly measure using a ruler.

•An effective way to introduce students to counting squares is to measure items shorter then the ruler.

1 2 3 4 5 6 7 8

Length

For more examples on Length visit hereTable of Contents

Area

Comparison activities• Important to distinguish

between size, shape, length, other dimensions

• Must develop a sense of the conservation of area.

• Activities where the area of the same shape is rearranged into different shapes are recommended

• Tangrams are an easy way to demonstrate this while providing an interactive activity for the children.

Area

Units of Area

• Important for students to develop the idea of the units that represent area.

• Students can start with non-traditional counters such as beans. It is not so important that the entire shape be covered as it is that students understand the concept of units.

• When students have a firm understanding of the units, they can graduate to tiles or to pieces of paper that are cut to a specific size. This helps students understand the concepts of square area.

• Use of grids and arrays helpful and will lead to integration of multiplication, perimeter, and area.

Area

Area/perimeter relationships• This can be confusing since it is

two different measurement measuring the same object. It is important for the separation of attributes to be clearly delineated.

• While it is important to separate the two as concepts, it is equally important to integrate the two as being interrelated and influencing each other.

• Using arrays and grid paper to work back and forth between perimeter and area can be very effective when correlating the two concepts.

Volume and CapacityCapacity: Measures amount a 3-D object

would hold.

Volume: Measures capacity but can also refer to solid objects.

• Should start with activities that develop a sense of conservation of capacity.

• Students can use non-traditional measuring units (beans, etc.) to measure the capacity of various shapes.

• Shapes with the same capacity but drastically different shapes will help children build the concept that different shapes can have the same capacity.

• Using shapes with different surface areas but the same capacity help students realize that surface area does not dictate capacity.

Volume and CapacityUnits of Volume

• Can use cubes of a given size. Useful to start with non-traditional units, the cubes can segue into standard cubic units.

Containers

• Containers that can be filled and emptied repeatedly allow for greater use in exploration.

• Non-square containers give students a sense of conservation of capacity as well as the relationship between surface area and volume.

• Solid shapes can be introduced when concepts of capacity are cemented and students have begun measuring surface area to help with volume.

For more examples on Area & Perimeter, Volume & Capacity visit here

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Weight & Mass

•Weight is

•A measure of the pull or force of gravity on an object

•Mass is

•the amount of matter in an object and a measure of the force needed to accelerate it

•For our purposes, weight and mass are interchangeable

Comparison Activities

•Conceptual:

•Holding an object in each hand and identifying which is heavier.

•Two types of scales-

•Balances (weight) and Spring Scales(mass)

•Tasks like estimating, sorting and ordering objects are helpful and possible when using scales to teach weight and mass.

Weight & MassHow To Teach Weight & Mass:

Units of Weight or Mass•Objects of the same mass can be used as weight units.

•Light Objects:

•Paperclips, blocks, cubes

•Heavier Objects:

•Metal Washers

•Standard weights used to measure the weight of heavier things

•Kilogram or more

Weight & Mass

What would this look like?Activities to do with your students when learning concepts of weight & mass.

1.Have children place objects, of differing weights and ask them to decide which is heavier or lighter.

2.Have children place different weights in the pans of a balance scale to have them “see” the difference.

3.Have children put different objects on the spring scale and watch the weight pull/push down on the spring.

4.Prior to all activities, have them estimate the objects weight or sort the items by size (weight)

Weight & Mass

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Time...is a virtue

Although time can not be seen nor held, the concept comes with daily life. It is taught through...

Duration Clock Reading Elapsed Time

Time is not your typical measurement attribute, but it is important to address.

Time...is a virtue

*All attributes of time can and should be introduced in early elementary. In the NCTM standards duration and clock reading are a requirement in 1st and 2nd grade, and elapsed time in 3rd grade. *

Time

Duration: length of an event from its beginning to its end.

Non-Standard units: ex. The steady drip of water into an empty container. The level of water is marked at the end of a period. Once the container is emptied and used to time a second duration, the two markings can be compared.

As with all mathematical attributes, they should make comparisons of events that have different durations, that are applicable to their lives.

How to Teach Duration1.Take note of short and

long events during the day.

2.Timing small events. (no longer than 2 minutes.)

Duration isn't an easy attribute to assign specific strategies for teaching. The best way is to practice everyday. A good foundation for learning duration would be to know about seconds, minutes, and hours to be able to have a concept of how long these units are.

Time

Simple activities that help to teach duration:Stacking ten blocks one at a time and then removing them one at a timePrinting the alphabetWalking slowly around a designated pathMaking a bar of 15 connecting cubes

Time

Clock Reading: the most common instrument for measuring time.

To read a clock is based on the knowledge that there are 60 minutes in an hour. What happens after the #:59?

Time

1. Being with one-handed clock.

2. Discuss what happens to the big hand as the little hand foes from one hour to the next.

3. Use two real clocks, one with only an hour hand and one with two hands.

4. Teach time after the house in 5-minute intervals.

5. Predict the reading on a digital clock when shown an analog clock, and vice versa; set an analog clock when shown a digital clock.

How to Teach Clock ReadingActivity 19.18One-Handed Clocks

Prepare a page of clock faces. On each clock draw an hour hand. Include placements that are approximately a quarter past the hour, a quarter till the hour, half past the hour. For each clock face, the students' task is to write the digital time and draw a minute hand on the clock where they think it would be.

Time

Elapsed Time: figuring the time from a point in time to another.

This is a mental process of counting for multiples of 5 minutes.

Time

1.Counting in intervals (normally of 5.)

2.Find a beginning and an end time.

Proposing a singular method or algorithm is not helpful for students.

TimeHow to Teach Elapsed Time

Simple Activity to Help Teach Elapsed Time:Use a time line to keep track of time

a) School began late today at 10:45 A.M. If you get out at 3:30, how much time will you be in school today?

Four hours from 11 to 3. Then 15 minutes in front and 30 minutes at the end—45 minutes. Three hours 45 minutes in all.

11 12 noon 3

10:45 3:30

For more examples on Time visit here

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Angles, Angles, Angles

• Challenged for two reasons:

• The attribute of angle size is often misunderstood

• Protractors are introduced and used without understanding how they really work

Angles

• What makes an angle you may ask?

• Two rays that are infinite in length with a common vertex

• And what does that mean?

• Two rays are just two different lines, infinite means they can be any length, and a common vertex means they have to meet at one point to form that angle

Difference in their size is how widely or narrowly the two rays are spread apart

Angles

• As soon as students can tell the difference between a large angle and a small angle they are ready for measuring them.

WE GOT IT!

Large Angle

Small Angle

Angles• Protractors: (why so confusing)

• Are good tools to use to measure angles but because they aren’t taught how to use very well some kids struggle learning how to use them properly.

• Students need an approximate mental image of angle size

• Can be done using two paper plates, one of color and one white, and see different sizes of angles

• When students have a strong grasp of the approximate size of angles, that will present them with the background they need to move to using and understanding a protractor

Angles

Activities to do:

1. Show students pictures of art and have them find the angles.

- This website lets the students look at different views of angles and then they get to identify what the object really is

http://kids.nationalgeographic.com/Games/PuzzlesQuizzes/Whatintheworldangles

2. Memory matching game with the words of angles on them the kids can learn

http://www.vectorkids.com/vkgeomatching.htm

For more examples on Angles visit here

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Measurement

• Ratio of an igloo’s circumference to its diameter: Eskimo Pi

• 365.25 day of drinking low-calorie beer because its less filling: 1 lite year

• Shortest distance between two jokes: A straight line

• 1000 grams of wet socks: 1 literhosen

Fun Non-Standard Units of Measurement

•½ a lavatory: 1 demijohn•1 kilogram of falling figs: 1 Fid Newton•8 nickels: 2 paradigms

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Follow Up Reflections

1. What it means to measure something. Does your explanation work equally well for length, area, weight, volume and time?

2. What are some of the reasons why we offer non-standard and standard units to our students? What are the benefits of each?

3. Do you think that we should teach specific formulas first for finding the area and perimeter of squares and rectangles? What are the benefits and what are the drawbacks?

Take a few moments to ponder…

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