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Measurement

Use This Simple Idea to Help Students Understand Fractions of an Inch

Because rulers have so many small lines, they are difficult for students to understand and differentiate.  Because of this struggle,  I took a flat ruler and placed it on the copy machine and blew it up until an inch section was about as large as the page like below.

 

Then I cut off the centimeter section and the marks after the one inch mark.

 

Because linear measurement is more difficult for students to conceptualize, I relate it to parts of a whole by using this enlarged ruler.  Now that I have trimmed all of the sections off, students can see it as 1 WHOLE rectangular section as opposed to the daunting linear ruler.  I have students fold the ruler section into half along the half inch line.  When we study parts of a whole, we fold colored paper in half.  This make the ruler like parts of a whole instead of a linear model, so the ruler marks are easier for students to understand.

 

Next, students label the half point on the ruler where the paper folded.

 

Then students fold the halves into half to make fourths and label the fourths.  After labeling fourths, students begin to see equivalent fractions.

 

You could fold the fourths an additional time to make eighths also, but elementary students aren’t required to know eighths yet.

 

An additional fold would make sixteenths, but this is not really needed since all of the marks denote sixteenths.  Now you and your students can pull this ruler out anytime you need to refer to the fractional measurements.  The only thing to beware of is that students recognize this  fractional pattern repeats for every inch.  You will have to repeat the pattern for each number for students to recognize this.  Another error that can occur is that students leave the whole number off of their measurement and only think that the fractional marks stand for fractions alone.  Measuring to fractional inches greater than 1 and writing fractions greater than 1 need  to be modeled.  I hope this tidbit helps you and your students!

Edited 1/25/14:  I just found this great free ruler picture that would be great to use for the above activity.  You can see it  here.

 

 

 

Heads Up! Linear Measurement Misconception!

While working with 5th graders today, I was reminded  about the misconceptions they have when measuring with a ruler.  Normally students are asked to measure to the nearest half or fourth of an inch.  First of all, what does nearest really mean?  We assume that 10 and 11 year old children know what nearest means…but do they?  Our number one mistake as educators–especially new educators is that we assume students know the meaning of things they often do not…only as a reflective experienced teacher do we figure this out. (had to take that rabbit trail!)  Back to measurement–once students are taught that nearest means closest we think we are in the clear, but, NOPE, we still have another problem.  When you as the teacher say, “measure to the nearest half.”  Students think that the only halves are the numbers that have halves written in them.  For example, students think that the answer has to be 1/2, 1 1/2, 2 1/2, 3 1/2 and so on.  They fail to bring their fraction understanding of wholes being two halves with them.  Students can understand that measuring to the nearest half could mean the measurement  might be a whole number (which is made up of halves) when they compare a linear ruler to wholes of a fraction like 2/2.  This same misconception occurs when students are asked to measure to the nearest 1/4.  Students think you are literally asking them to measure to only the nearest one-fourth.  Even if a measurement is 2 inches, students will say that the measurement is 2 1/4 because they hear the phrase literally.

In the example below, students who have misconceptions measuring to the nearest 1/4 will, for example, say that this marker measures to be 5 1/4 because they are looking for the number 1/4 instead of the nearest 1/4 increment.  In actuality, the marker measures to be 5 1/2 in., and students will only understand that this is the same as 2/4 through work with equivalent fractions.  Please excuse the insurance advertisement on the ruler :/.   This was the only ruler I had available at the time.

 

I will be posting more soon about teaching linear measurement :).  Come back soon!

Have You Ever Thought to Use These in Preparation for Coin Counting?

Do you know how they have those clearance buggies near the checkout at Wal-mart?  Well, I just happened across these poker chips yesterday, and I got them for…get this…50 cents!  YAY!  When I saw them, they immediately reminded me of the money activities I created, and how I prepare students to count coin values first before adding real coins.  Look how similar they look to the money sheet from my unit below.  The only thing is that there aren’t chips that would resemble pennies, but I am still going to use these next time for their manipulative factor.  Students can practice adding on 5’s and 10’s to 25’s.  If you would like a free sample of the page below from my money activities, just click the download preview button on TPT!

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