Thomas Young WAITSFIELD ELEMENTARY SCHOOL, WAITSFIELD, VT
1st Grade Math : Unit #8 - Non Standard Measuring : Lesson #7

Using Different Units to Measure Day 2

Objective: SWBAT compare lengths to see which is longer. SWBAT express that measuring an object using different length units will result in different measurements.
Standards: 1.MD.A.2 1.MD.B.3 2.MD.A.2 MP5 MP6
Subject(s): Math
60 minutes
1 Warm Up - 5 minutes

I start with everyone sitting in a circle and I draw a rectangular box on the whiteboard.  I have the student clocks out on the carpet and they know that we are going to talk about time before I even start to speak.  This year's group is really excited about and intrigued with clocks.  So the mere presence of them immediately gets their attention.  

"The other day I introduced you to the concepts of analog and digital clocks and telling time to the hour or the "o'clock time."  

When we write with digital annotation, what separates the hours and minutes."  Once someone has indicated a colon (either with the term or a description of one), I draw the colon in the middle of the rectangular box.  

"I would like you to look at my clock (I have set a demonstration clock to 3:00)  Who can come up and write this time with digital notation?"  

I call on someone to come up.  

"While "Timmy" is writing the time, I would like the rest of you to whisper to someone next to you the time that this clock says."  

I repeat this a few more times.

"Who can come up and write 8:00 with digital notation.  Once someone has written it, I ask the students to show me 8:00 with their analog clocks." There is a video in the resource section of this part of the activity.

The Core Standards expect that 1st graders can "tell and write time in hours and half-hours using analog and digital clocks (CCSS.Math.Content.1.MD.B.3)."  I repeat this several more times.

The students are using clocks to read times and placing hour and minute hands to represent set times. The core expects that "mathematically proficient students to consider the available tools when solving a mathematical problem and that they are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful (CCSS.Math.Practice.MP5)"

I am focusing on the hour times now. Once I introduce our fractions unit, I will focus on the concept of half hour times.  It is logical to wait on the half hour times till then.  The concept of half is still not clear for most first graders. 

I am using this time to continue to expose students to the time concepts presented.  I will spend a week at the end of the year, firming up these concepts with a more specific unit on telling time.

2 Continuation of Measurement Activity - 20 minutes

Advanced Preparation:  You will need to use the floor strips that were laid out in a previous lesson. Look under the Measuring with Craft Sticks, Playing Cards, and Index Cards section.  

"Today you continue measuring some of the floor strips that you used yesterday.  You will use the three units from yesterday.  You can choose from craft sticks, index cards, or paying cards.  Who could remind us how to measure the appropriate way with the craft sticks?" I then call on a student to do so. "Mathematically proficient need to communicate precisely to others. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context (CCSS.Math.Practice.MP6)."

"You will continue to use this recording sheet (display one of the copies that you made) to record your results."  The recording sheet can be found in the above linked lesson.

As students are working, you will want to observe:

*Are students using appropriate measurement techniques (there are a few pictures and videos int he resource section that model these techniques).

*How are they handling 1/2 measurements?

This activity is allowing students to "express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps (CCSS.Math.Content.1.MD.A.2)."

*There is a video of two students measuring, using playing cards, in the section resources.

Measuring with Partial Units
Developing a Conceptual Understanding

While students are learning to measure and record there are several ideas that they must understand.  One idea is the use of a partial unit.  Although it may have taken 5 tiles to cover a strip, the count can be identified as 4 1/2 or a little more than 4.  Students have a hard time understanding why the 5 tile is not part of the whole number count.  

3 Looking at Data - 20 minutes

To begin this section, you will need to collect the posters (Floor Strips 1-8) that the students were using the record their results on.  

"You are going to work in groups and make a report to the class on some of the measurements that you all just collected.  I will put you in teams of two and each team will get one of the posters with all of the measurements that people wrote on it.  You will need to use the chart to answer the questions on this sheet."

I then show them the recording sheet (see section resource) and go over the questions.

"I will give each of you each 8 minutes to look at the results and then record your answers.  You should work as a team and discuss each answer before you write it down.  When you are finished, I want you to meet me on the carpet."  There is a video of two students working on this in the section resource.

As students are working, you will want to listen in on the discussions and see how students are doing with:

  • the concept of the smallest unit needing the most number of units and the largest unit needing the least number of units.
  • if there are two different measurements for the same strip (using the same units), do they understand that one of the measurements must be incorrect.  
4 Lesson Wrap Up - 10 minutes

Gather the students back on the carpet for a discussion about their findings.  The idea of this conversation is that measuring an object using different-length units will result in different measurements.

Each group should tell the class what floor strip they measured and what they found.  

"I have noticed that many of you have said that the playing cards needed the most number of units and that the index cards needed the least.  Why do you think this is?"

Although this is an idea that the students will have to master in 2nd grade     (CCSS.Math.Content.2.MD.A.2), I still want to have a discussion about it.  First graders need to understand that "units of the same size result in the same count when measuring the same distance." Students need to be able "express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps (CCSS.Math.Content.1.MD.A.2)."

5 Continued Practice - 5 minutes

I will end this lesson with another story problem. This one will involve an addition situation.  I will call the students back to the carpet and go over the problem as a class.  I ask them to visualize the action in the story as I read it aloud.  "Who can tell me what is going on in this story?"  I call on a couple of students.  I now want you to go and work on this problem on your own. Make sure that you represent your thinking and write an equation."

I continue to work on problem like this to keep the students skills "sharp," as we continue to work on this unit on measurement.

In this particular problem, I want to see how many people solve the problem 9+8 by suing a doubles fact and then adding one more.  Although we have just started working on this concept, I wan tho see if anyone is using it in a real world situation.

The problem is in the resource section.