Lesson: How long is it?

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Objective(s) and Standards (NCTM and MI):

Michigan GLCE’s -

M.PS.02.02: Compare lengths
M.UN.02.01: Measure lengths in inches approximating to the nearest whole unit.

NCTM Standards and Expectations –

Understand measurable attributes of objects and the units, systems, and processes of measurement:

select an appropriate unit and tool for the attribute being measured
understand how to measure using nonstandard and standard units

Apply appropriate techniques, tools, and formulas to determine measurements

measure with multiple copies of units of the same size
use tools to measure
use repetition of a single unit to measure something larger than the unit

Context of the lesson:

Previous Lesson

Students have measured straight lines using standard units such as centimeters and inches.

Current Lesson

Students will measure curved lines using nonstandard tools and units

Next Lesson

Students will measure area of a curved organic shape such as a lake.

Important Points:

Students should be familiar with the concept of length
Throughout the lesson, encourage the students that there are multiple ways of solving the problem

Materials:

Paper clips
Paper
worksheet
string

Lesson Plan:

Activity	Expected Student Response	Teacher Guidance
Students are asked what they know about length A drawing of two curved snakes is displayed for the class. One snake has lots of little curves while the other has one big curve. Students are asked to guess which snake is longer. They are then asked for ideas on how to prove one snake is longer than the other. Students are given the following materials: paper, ruler, string and paper clips (NO STANDARD RULER). Students come up to the drawing to offer their solutions using any of the given materials. Others are asked to agree or offer another solution. Once several methods are discussed, divide the class up into groups, each group working on a different method (one group uses paper clips, one group uses string, etc.). The worksheet [attached] has 4 drawings of snakes. Students are asked to order the snakes from longest to shortest. They then test their estimates using the method they created together. The paperclip group could have the option to work on the large snakes (since the paper clips are two big for the worksheet snakes) Groups share their answers with the rest of the class. Misconceptions are discussed.	It is measured in cm or in We use a ruler to measure it It is how long something is I think the red one is longer because it is curvier I think the black one is longer because it has that one big curve. We could make a ruler to measure the length We could line up paper clips to measure how long each one is. I made a ruler and measured that snake to be 23 centimeters Do we fill the snake head with paper clips? I made a ruler and my group member made a ruler also, but we got different answers. (Put the 1 in different positions)	Does it have to be measured in cm or inches? What about using the length of my hand? Emphasize the fact that the only way to decide which one is longer is to measure them both. Note that there are several ways this problem could be solved with the given materials. Begin to use a ruler. “What do we do with this curve? How can we measure a curve? How do you know your ruler has centimeters on it? Could you call it by a different name? Remind students what they are measuring Investigate the two rulers in a large scale on the board. Ask the rest of the class for input. Compare the made rulers to a real ruler. Allow students to discuss whether or not they think each group measured accurately.

Activity

Expected Student Response

Teacher Guidance

Students are asked what they know about length

A drawing of two curved snakes is displayed for the class. One snake has lots of little curves while the other has one big curve. Students are asked to guess which snake is longer. They are then asked for ideas on how to prove one snake is longer than the other.

Students are given the following materials: paper, ruler, string and paper clips (NO STANDARD RULER). Students come up to the drawing to offer their solutions using any of the given materials. Others are asked to agree or offer another solution.

Once several methods are discussed, divide the class up into groups, each group working on a different method (one group uses paper clips, one group uses string, etc.). The worksheet [attached] has 4 drawings of snakes. Students are asked to order the snakes from longest to shortest. They then test their estimates using the method they created together. The paperclip group could have the option to work on the large snakes (since the paper clips are two big for the worksheet snakes)

Groups share their answers with the rest of the class. Misconceptions are discussed.

It is measured in cm or in
We use a ruler to measure it
It is how long something is

I think the red one is longer because it is curvier
I think the black one is longer because it has that one big curve.

We could make a ruler to measure the length
We could line up paper clips to measure how long each one is.

I made a ruler and measured that snake to be 23 centimeters

Do we fill the snake head with paper clips?

I made a ruler and my group member made a ruler also, but we got different answers. (Put the 1 in different positions)

Does it have to be measured in cm or inches? What about using the length of my hand?

Emphasize the fact that the only way to decide which one is longer is to measure them both.

Note that there are several ways this problem could be solved with the given materials.

Begin to use a ruler. “What do we do with this curve? How can we measure a curve?

How do you know your ruler has centimeters on it? Could you call it by a different name?

Remind students what they are measuring

Investigate the two rulers in a large scale on the board. Ask the rest of the class for input. Compare the made rulers to a real ruler.
Allow students to discuss whether or not they think each group measured accurately.

Which Snake is the Longest?

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