Elementary Measurement - Lesson 1

BACK TO ES Mathematics UDL Instructional Unit

Objectives

• Students will be able to choose the appropriate tool to measure various lengths.
• Students will be able to correctly measure various objects using inches and feet.
• Students will be able to explain why using standardized units is important and how measuring is practical in real life situations.

Essential Questions

• What are standard units of measure?
• Why is it important to use appropriate standard units of measure?
• How are standard units of measure important to our everyday lives?

Vocabulary

Centimeter - a standard unit of length in the metric system equal to 1/100 of a meter (may be mentioned in Lesson 1 but not defined until Lesson 3)

Distance - the amount of space between two things, places, or people

Foot - a standard unit of length in the US Customary system equal to 12 inches

Height - the vertical (up and down) distance from the top of an object or figure to its base

Inch - a standard unit of length in the US Customary system equal to 1/12 of a foot

Length - a measurement of the distance from one point to another

Measure - to determine a quantity/amount

Measurement - a determined quantity/amount

Meter - a standard unit of length in the metric system equal to 100 centimeters (may be mentioned in Lesson 1 but not defined until Lesson 3)

Nonstandard - not the same (e.g., the width of your thumb versus the width of my thumb) or not marked (e.g., a piece of string used to measure length)

Ruler - a wooden or plastic tool used to measure lengths up to 12 inches

Standardized - the same

Tape Measure - a tool consisting of a flexible ribbon of cloth or metal used to measure lengths up to several feet

Unit - a set amount used to consistently determine quantities

US Customary System of Measurement - a system of measurement that includes units such as inches, feet, yards and miles (for length); also referred to as imperial units or English units; this system is not commonly used outside of the United States

Width - measurement of the distance from one side or edge to the opposite side or edge

Yard Stick - a usually wooden tool used to measure lengths up to 3 feet (1 yard)

Materials

• Masking tape or painter's tape
• Math journals
• Chart paper
• How Big is a Foot? storybook
• A piece of blank paper (just to demonstrate how to measure using a ruler)
• Rulers (enough for each student)
• Tape measure (ideally, at least one for each pair of students and one for each of the 8 stations in the Practice section)
• Yard sticks (ideally, at least one for each pair of students and one for each of the 8 stations in the Practice section)
• Classroom supplies/features
  • Stapler
  • Bookshelf
  • Doorway
  • Window
  • Filing cabinet
  • Computer screen
  • Hardcover book
  • Picture frame
• One blank sheet of paper (or could use grid paper)

Introduction

Activate Previous Knowledge

1. Using masking or painter's tape, tape a 5- to 10- foot line on the floor, depending on the amount of floor space you have. (This could be done in the gym or other room if you want a longer length than you have room for in your classroom. This same line will be used again in Lesson 3.)
2. Ask students to take turns "measuring" the taped line using just their feet (heel-toe-heel-toe-heel-toe). As each student takes his/her turn, the other students should help count and record each "measurement" in their math journals, or each student can record his/her "measurements" on chart paper displayed in the classroom.
3. After all students have measured the line with their feet, you, the teacher, should do the activity as well and have the student(s) record your measurement.
4. Have the students look at and compare all of the "measurements".

– Guiding questions should include:

• "Are all of the measurements the same?"
• "Why aren't all of the measurements the same?"
• "How could the line be measured so that no matter who measures it, the same measurement will be determined?"

5. Ask the students to verbally list the kinds of tools they have used to measure things (e.g., string, rulers, and tape measures). Have them add this list to their math journals or to a new piece of chart paper displayed in the classroom.

Additional Considerations for Emerging Readers and Emerging Communicators

1. Attach a tactile support alongside the tape, such as a rope or stick.

Place corresponding tape (with or without the additional tactile support) on the wall. (This does not take the place of the tape on the floor, which will be used by most students and allows easier access for students whose gross motor skills do not allow them to access the floor measurement activity.)

2. As the student walks the tape:
• Have a partner place a dot (removable) or other marker for each step along the tape, which the student can then count at the end.
• Have the student or peer place a cube, token, or other manipulative for each step in a container.
• Have the student place a tick mark or tally or write the numeral for each step in his/her math journal.
• Have the student enter each step into a calculator using the "+1" function.

If the student cannot access the floor tape, trace his/her foot and use any of the above suggestions as he/she "walks" his/her foot outline along the tape on the wall.

On the chart paper or in the journal (these could have the "measurers'" pictures as well as the names) for his/her own measurement, peers' measurements, and the teacher's measurement, the student can:

i. writes his/her measurement;

ii. trace the numeral (if the student is working on fine motor skills);

iii. attach a sticky note on which the numeral is written (if the student is working on number recognition, he/she can select the correct number from two or more options); and/or

iv. access and work in a digital journal using assistive technology.

3. As the teacher measures using his/her own foot, the student can use any of the methods in step 2) above to count and record the teacher's measurement.
4. Allow the student to answer the teacher's questions by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc. Options may be presented as text, symbols, pictures, tactile representations, concrete objects, etc., or any combination of those. (Pre-teach concepts such as "same" that may not be consistently demonstrated using systematic instructional techniques, such as time delay, shaping, prompt hierarchy, etc.)
5. Allow the student to answer the teacher's questions by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc. Options may be presented as text, symbols, pictures, tactile representations, etc., or any combination of those. Provide a premade list for students of tools and what each tool measures as headings; have students participate by selecting the appropriate tool and what the tool measures when asked/prompted.

The student can record these measuring tools in his/her journal by:

i. writing, tracing (if the student is working on fine motor skills), or keyboarding;

ii. drawing;

iii. cutting and/or pasting pictures, symbols, icons, text, or any combination of those;

iv. selecting pictures, symbols, icons, text, tactile representations, concrete objects or any combination of those which a partner scribes; and

v. saving symbols, icons, pictures, etc. into a digital journal using assistive technology.

Establish Goals/Objectives for the Lesson

1. Share with the students that in this lesson they will learn about why "standardized" units of measure are important. Verbally define "standardized units" for the students. For each "tool" listed on the chart made in step 5 of part a, have the students decide if it uses standardized units or if it is "nonstandardized."
2. Share with the students that they will be asked to measure a variety of things throughout this unit of study and that they will be using various tools, such as the ones they listed in Step 5 of part a.

Additional Considerations for Emerging Readers and Emerging Communicators

1. In the journal, have the student categorize the measurement tools from the list collected in the previous activity, into standardized vs. non-standardized (e.g., concrete objects may be placed into "standardized" or "non-standardized" containers, such as boxes, baskets, etc.). Pre-teach these concepts as necessary.
2. No accommodations

Body

1. Read aloud to the students the story- How big is a foot? Question the students about the issue related to the story. – Guiding questions should include:

• How did the lack of a standard unit of measure impact the main character?
• What tools would have been better for measurement? (Refer back to the list of tools created in the introduction of this lesson.)

2. Model for the students how to measure the length of a piece of paper with your thumb (nonstandard) and then with a ruler (standardized, in inches). Then model how to measure the distance from a desk to the doorway with a tape measure and a yardstick (in inches and feet). Be sure to point out the units of measure and the reasons for using a ruler vs. a yardstick. Be sure to point out the unit named on the tool, especially if using a ruler that has metric as well as US Customary units, and for now, specify that they should use the US Customary units. Also, for now, stick to whole number measurements.
3. Lead the students in a discussion about what tools would be necessary to measure the length of various objects (e.g., a pencil vs. the line on the floor used in the Introduction). In fact, demonstrate how to use a ruler to measure the length of a pencil, but do not demonstrate measuring the line on the floor because the students will do that later in the lesson. Remind students that the US Customary System uses inches and feet. Ask students to name all of the units of which they may have heard or used pertaining to length/distance (US Customary and/or metric). Using chart paper, make a list of all of the tools used, referring back to the list devised in the Introduction, adding to it if necessary (e.g., ruler, yardstick, tape measure, odometer, etc.) and then a list of all of the units named (e.g., inches, feet, yards, miles, centimeters, meters, kilometers). (It is OK if the students do not name them all. This is just to get an idea of what tools and units with which they are already familiar.)

Additional Considerations for Emerging Readers and Emerging Communicators

1. Provide a personal copy of the book for the student to follow as the teacher reads aloud. Options include:

• text supplemented with symbols;
• text with sentences or words affixed with hook-and-loop tape so the student can manipulate the text as the teacher reads;
• text (or supplement) with Braille and/or tactile representations \[resources such as Standard Tactile Symbol List available from the Texas School for the Blind http://www.tsbvi.edu/tactile-symbols may be useful in determining representations; some representations may need to be pre-taught (Rowland, 2012), but use of the same representations/symbols (or the system) during this and other lessons will reduce the need for pre-teaching\]; or
• illustrations in the text with -
  • hook-and-loop tape so the student can manipulate the illustrations
  • tactile qualities added such as outlining with glue, puffy paint, yarn, etc.

Allow the student to answer the teacher's questions by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc. Options may be presented as text, symbols, pictures, tactile representations, concrete objects, etc., or any combination of those.

2. Provide the same materials that the teacher is using:

• adapted materials such as a ruler with tactile qualities;
• a piece of paper laminated on card stock; and/or
• other rulers that accommodate the student more effectively such as digital rulers, bendable/foldable rulers, tactile rulers, transparent/translucent rulers, simplified rulers with only inches marked) This may allow the student to mirror what the teacher is demonstrating. Provide adaptations, such as hook-and-loop tape or a "handle" to the ruler if the student's fine motor skills do not allow him/her to manipulate the tool(s); provide decreasing physical assistance to help the student manipulate the materials and mirror the skill. Allow student to move closer to the teacher during modeling or have a nearby classmate model with the student by measuring a piece of paper using your thumb and then using a ruler. Pre-teach concepts and skills the teacher is modeling (include systematic instruction techniques, such as task analysis, prompting, shaping, time delay, etc.).

3. Preplan by finding out what tools and objects will be used as examples; then provide those tools and objects for the student to interact with during the discussion (make adaptations to the materials such as those described in 2) above so the student can meaningfully interact with them). The student should participate in the discussion by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device).

• Student might contribute to the discussion by using touch, eye-gaze, assistive technology, etc.
• Options may be presented as text, symbols, pictures, tactile representations, concrete objects, etc., or any combination of those.
• Preplan at least one contribution for the student to make to the classroom discussion, at least one measurement tool, and at least one unit of measure.

Practice

1. Have students work in pairs to find the actual measurement of the tape on the floor used in the Introduction. Each student pair should first select a tool to use then measure the length of the tape and record their measurement in their math journals. Instruct the student pairs not to share their measurement with anyone else. As each pair selects a tool and measures the line, the other students should observe but not try to direct or interrupt the pair.
2. Once all pairs have taken their turn measuring the line, record each pair's measurement on chart paper. Discuss any differences.
• Guiding questions should include:

• Are any of the measurements different this time? • Why might they be different? (e.g., different tools used, different units, an error in measuring, etc.) • How did you decide which tool to use? • Why would it be helpful to use one tool over another? • Why would it be helpful to use one kind of unit over another?

3. Divide the class into two groups. The first group will take turns at 8 stations where they will choose from a selection of tools and then measure a given object at each station:
• Station 1 – the length of a stapler
• Station 2 – the height and/or width of a bookshelf
• Station 3 – the height of a doorway
• Station 4 – the width of a window
• Station 5 – the height and/or width of a filing cabinet
• Station 6 – the height and/or width of a computer screen
• Station 7 – the length of the spine of a book
• Station 8 – the length and/or width of a picture frame)

Note: Since we are still working with whole number measurements at this point, have the students round to the nearest whole number measurement if the objects do not measure right at the whole number mark. In their math journals, the remaining students should brainstorm and list 5 instances in which they might need to measure things in real life as well as identify the tool they would need to measure each thing named. When everyone in the first group has been to each of the 8 stations, they should switch places and activities with the second group.

4. Once all students have visited each station, as a class, go over each station and the correct measurement of each object. Model how to correctly measure each object. Using chart paper, chart the students' answers concerning real life situations in which measuring objects would be useful.

Additional Considerations for Emerging Readers and Emerging Communicators

1. Allow the student to participate in the tool selection within his/her pair by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc.

When the measurement activity occurs, one student could do the actual measurement by moving the selected measurement tool along the tape while the other student records each measurement through:

a) moving the tool – adapt the tool with hook-and-loop tape, a "handle", etc. so the student can more effectively and independently maneuvers the tool;

b) recording the measurement -

• place a dot (removable) or other marker for each measurement along the tape or on a note card, which the students can then count at the end;
• place a tick mark or tally or write the numeral for each measurement on a note card;
• enter each measurement into a calculator using the "+1" function;
• place a manipulative (cube, token, etc.) in a container so they can be counted for the final measurement;
• write the final measurement;
• trace the numeral;
• paste on a sticky note with the numeral on it; and
• access and work in a digital journal using assistive technology.

c) Paste card with tick marks and total counted by student into math journal or paste picture of tool used and circle correct measurement in math journal.

2. Allow the student to answer the teacher's questions by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc.

   Preplan at least one answer to one of the guiding questions.

3. Stations: Allow student to select, using his/her preferred mode of communication (eye-gaze, verbal, touch, sign, written, speech generating device, assistive technology, etc.), a measuring tool at each station. Depending on the student's skill at selecting an appropriate tool, the number of tools offered could vary:

• two tools for a student who has difficulty with selection;
• several tools for a student who can make a selection; or
• the "appropriateness" could vary from widely discrepant (e.g., Station 3 – six inch ruler vs. yardstick) to more discreet differences (e.g., Station 6 – six inch ruler vs. 12-inch ruler).

Use the station activities as opportunities to instruct and practice performance. Provide effective accommodations to the materials such as those found in Lesson 1 – Body, 2), adapted materials:

• a ruler with tactile qualities or a piece of paper;
• digital rulers;
• bendable/foldable rulers;
• tactile rulers;
• transparent/translucent rulers;
• simplified rulers with only inches marked; and
• rulers adapted with hook-and-loop tape or a "handle".

Other effective adaptations include laminated card. He/she should be allowed to manipulate the tool(s) with the provision of decreasing physical assistance and to mirror the skill (similar to those found in Lesson 1 – Introduction a. 2 -place a manipulative in a container every time the tool moves, place a tick/tally mark on paper every time the tool moves, etc.)

Journals:

The student can record instances where he/she might need to measure and corresponding measuring tools selected in his/her journal using his/her preferred mode of communication (verbal, sign, written, speech generating device to select (by touch, eye-gaze, assistive technology, etc.) from multiple options (presented by text, symbols, pictures, tactile representations, concrete objects, or any combination of these, etc.)\].

The student can record these measuring tools in his/her journal by:

• writing,
• tracing (if the student is working on fine motor skills),
• keyboarding (in a digital journal),
• drawing, cutting and/or pasting pictures, symbols, icons, text, or any combination of those.

The student selects pictures, symbols, icons, text, tactile representations, concrete objects, or any combination of these which a partner scribes, saving symbols, icons, pictures, etc. into a digital journal using assistive technology.

Be consistent in the supports the student uses for journaling; refer back to the accommodations the student used in Lesson 1 – Introduction a. 5).

4. As the teacher models correctly measuring the objects at each station, quietly remind the student how he/she measured them. (Because the station activity was instructional practice, the student should have received guidance, possibly through errorless learning techniques, at each station resulting in correctly measuring each object.) Allow the student to participate in the math journal discussion by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc. Preplan at least one contribution to the discussion.

Closure

a. Revisit/Review Lesson and Objectives –

1. Ask the students to, as a class, verbally explain what "standardized unit" means and why using standardized units is important/helpful. Remind the students one of the goals of this lesson was to learn about how and why standardized units of measure are used.
2. Ask students to brainstorm and suggest alternative ways to measure that would still be standardized (i.e., if you were creating your own standardized system of measurement, what would you use?)
3. Share with students a bit of the history behind the development of the United States Customary System, also called empirical units or the English System of Measurement (i.e., barleycorns, digits, fingers, hands, inches, nails, palms, shaftments, links, spans, feet, cubits, yards, etc. – The purpose of this is just to show the students that this system of measure was devised to help people, particularly farmers, measure/judge lengths and distances and that it was, at first, nonstandardized. They do not need to add these words to their working vocabulary.) Share with students that there are, indeed, other systems of measurement, such as the metric system, which they will be learning about later in the unit.

Additional Considerations for Emerging Readers and Emerging Communicators:

1. Allow the student to participate in the class discussion by using his/her preferred mode of communication (e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc. Preplan at least one contribution to the discussion.
2. Allow the student to participate in the brainstorming using his/her preferred mode of communication e.g., verbal, sign, written, speech generating device). Student might select from multiple options by using touch, eye-gaze, assistive technology, etc. Preplan at least one contribution to the brainstorming.
3. Provide engagement supports as necessary, which may include pictures of key concepts being presented, concrete objects to manipulate, and/or positive behavioral supports.

Exit Assessment

1. Have each student draw one line of any length on a piece of blank paper using a ruler (could use grid paper). Tell the students to use their rulers to measure the line they drew but not to write the measurement down.
2. Group the students in threes. Each trio should take turns measuring each group mate's line. Each trio should compare their measurements to make sure they came up with the same measurement. They should resolve any inconsistencies by re-measuring the lines together.

Additional Considerations for Emerging Readers and Emerging Communicators:

1. The student could draw his/her line digitally using assistive technology, choosing a straw, pipe cleaner, etc. to measure, or placing two dots on the paper and have someone draw the line. Allow the student to use (if necessary) any of the adapted materials he/she used in Lesson 1 – Body 2, such as a ruler with tactile qualities, low vision ruler, audio measuring tape, or a piece of paper laminated on card stock which support student needs. Other rulers may accommodate the student more effectively, such as digital rulers, bendable/foldable rulers, tactile rulers, transparent/translucent rulers, simplified rulers with only inches marked or a ruler adapted with hook-and-loop tape or a "handle" if the student's fine motor skills do not allow him/her to manipulate the tool(s).
2. Allow the student to use (if necessary) any of the adapted materials he/she used in Lesson 1 – Body 2. These include rulers which may accommodate the student needs more effectively such as:

• rulers with tactile qualities;
• digital rulers;
• bendable/foldable rulers;
• transparent/translucent rulers;
• simplified rulers with only inches marked; and
• a ruler adapted with hook-and-loop tape or a "handle" if the student's fine motor skills do not allow him/her to manipulate the tool(s).

As this is now assessment as opposed to all previous activities in this lesson, the student's first independent attempt at measuring the three lines should be observed and recorded for accuracy.

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