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* *Reflection: Flexibility
Where Would It Be? - Section 2: Measuring to a Fraction

When I presented a yardstick with all the numbers carefully covered and the stick was then divided into 3 clear parts and I asked students how I might use it to measure, the students were convinced that I could still measure in inches even though the inches were no longer visible. I wanted them to see the thirds we had just talked about in the warm up, and to me it seemed so obvious, but to the students, it was not obvious.

They guessed that I could measure in inches, or feet, or centimeters, or even kilometers. Some wanted to draw the inches on the stick. Others said maybe I could just break my tower in half or just count the blocks in my block tower. They were not seeing the three pieces on the unmarked stick.

I listened to their suggestions and then went back to the stick. I said how many lines do you see on the stick now? (2) and how many parts. Many were blank on this. I asked them to show me with fingers how many parts of the stick they saw and about 1/3 (funny that is our fraction too!) did not see the 3 pieces. I had to go back again and we all counted the pieces together, 1,2,3. Ok I said, there are 3 pieces so if my stick is the whole thing, and it is divided into 3 equal pieces, what fraction is it divided into? Again I got blank stares and those who looked away so I wouldn't call on them.

I tried again. Ok, lets think about dividing this stick into fractions. The stick is 1 whole stick. I see 3 parts so I have divided it into 3 equal parts, 1,2,3. Can I label each one as a fraction? Finally hands went up and a student said it is thirds. (OK, I thought, now we are making progress). Ok, it is divided into thirds, so if I put it next to my block tower, how many thirds long is the tower? "TWO" students called out. Yes, it is 2 parts long and what fraction is that? (2/3).

I had to keep backing up and rephrasing my questions because students did not see what to me was so obvious, that the stick was in thirds. My thought is that while I understand what a fraction is, they do not, so the division into thirds was not obvious. I had to show them exactly what to look at to identify that the stick was indeed divided into thirds.

Once they jumped this hurdle, the rest of the lesson was easy for everyone.

You just never know what students will grasp or not grasp, so you have to check often for understanding by backing up and asking questions, breaking things into even smaller increments of understanding and by listening to what they are understanding and extending that learning with questions that will carry students even further, or you may be left with just a few survivors by the end of your lesson.

*Beyond The Box*

*Flexibility: Beyond The Box*

# Where Would It Be?

Lesson 3 of 10

## Objective: SWBAT identify parts of inches, feet and centimeters as halves,and quarters as they use length to clarify fractional parts.

I ask students to take out their math suitcases and find their math fraction squares from the last lesson. I ask them to hold up quarters. How many pieces will there be if I break something into quarters? (4). I ask them to hold up halves. How many pieces will there be if I break something into halves? (2).

Now I hand them a new blank square and tell them that we are going to fold the paper into thirds. I ask how many pieces do they think will be in thirds. I take suggestions and then I demonstrate how to fold a paper into thirds. I show them that I roll the paper from one side not all the way to the other but so that my folded piece and the piece left out are about the same size, now before I crease the paper, I fold the extra over the one I just folded, and I roll it slightly until all 3 pieces look to be about the same size. Next I make good creases along the edges and I open my paper up to show 3 even sized pieces of my paper.

I ask for a volunteer to write 1/3 on the board. Next I ask students to label their thirds square. I show them how a volunteer has written 1/3 or 1 out of 3 which means one third, so they should write 1/3 on each part of the paper.

Now I ask them to put those fraction squares into their math suitcases and to come to the rug.

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#### Measuring to a Fraction

*20 min*

Today I want students to partition a rectangle (the ruler) into thirds as is described in the Common Core Standard 2GA3 for second grade. I will then extend the division by using it to measure objects. Students will need to think about how they are measuring which is also a Common Core skill as they choose the correct tool, or in this case the correct increment to measure in.

I set out a block tower measured to 2 feet and a yardstick covered with paper on one side . I review with students how many feet in a yard and show them the yardstick on one side. We review 3 feet in a yard which is also 36 inches.

I now turn the yardstick over to the covered side. I ask how we might divide this side into 3 even parts? (I take suggestions and then have 2 volunteers work together to mark the yardstick into 3 feet. How many pieces is my yardstick divided into? (3) What do we call it when three pieces make a whole (thirds).

Today I am going to pretend that I only have this side of my yardstick. I have divided it into thirds and I need to measure things with this. Can I do that? Why or why not? We talk about whether we can measure to the fraction of a yard.

Next I show students my tower and ask if anyone can measure it with my blank yardstick. I let a volunteer come up and measure it and I ask them to write on an individual white board beside the tower how long they think it is. (2/3 of a yard). If the student writes 2 I bring out a second yardstick and say here is one (point to one) here is two (lay it end to end with the first). Hmm, my block tower doesn't seem to be 2 yardsticks long. Can anyone help me figure this out? I take suggestions for why 2 doesn't describe the size of the block tower. We work together to realize that the tower is less than 1 yardstick long so it must be a fraction of the yardstick. What fraction could it be?

When we have discovered that the tower is 2/3 of a yard, we do the same with several other objects that are either 1/3, 2/3 or 3/3 of a yardstick long.

I give different students a chance to practice measuring and writing the fractions. I ask for a thumbs up for those who think they could do this on their own?

When most students are feeling confident, I ask students to return to their seats.

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#### Independent Practice

*15 min*

I give each student a paper strip marked into thirds. The strip is one foot long and I have students compare it to a ruler so they realize that now they are measuring in thirds of a foot rather than thirds of a yard. We review that there are 12 inches in a foot. You may want to ask if anyone can figure out how many inches in 1/3 of a foot? Students can measure to determine that there are 4 inches in a third of a foot if you want to bring in this analogy. (I realized afterwards that this made things more confusing so I would recommend leaving this question out unless a student raises it.)

Today, I tell students, you will be measuring things to the nearest 1/3 of a foot. You will use this paper ruler to measure the things listed on your paper and you will record the measurements in fractions.

On each table I place 5 objects that are either 1/3, 2/3 or 3/3 of a foot long. (I place the same 5 objects on each table so we can share our results later.) I ask students to take turns measuring each object. When they have measured all objects they should write the names of the objects from smallest to largest on the bottom of the page. (This will help them to compare fractional sizes and begin to visualize that 1/3 is smaller than 2/3 etc.)

I give students about 15 minutes to complete this part of the lesson.

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#### Sharing Out

*10 min*

I ring the bell and bring students back together as a group. I collect the objects and bring them to the front of the room. I have a 1/3, 2/3 and 3/3 sign on the table so students can see them. I ask students to volunteer to come up and place an object in the correct pile. We sort all the objects in this manner.

I ask for a thumbs up to make sure students agree with where objects have been placed. We may have some disagreement if students measured objects in different directions and we talk about this and come to an agreement as to where objects should be placed.

Now I ask hold up a 1/3 object and a 3/3 object and ask which is bigger 1/3 of a foot or 3/3 of a foot? How do you know?

I repeat this several more times.

I ask if I have something that is 3/3 of a foot, is there another way to say that? (It is 1 foot). I help students to see that 3/3 parts is the same as 1 foot or 1 ruler by holding the ruler up to the object that is 3/3 foot long. You can see that this object is the same as 1 ruler or 1 foot, and also 3/3 parts of the ruler long.

I ask students to tell me when they have a fraction with the same bottom (denominator) and a different top (numerator), how will I know which one is more? (the top number will be bigger because it means more pieces).

This is a concept that I introduce here but will build upon in the next lesson.

*expand content*

##### Similar Lessons

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Fractions Can Be Fun
- LESSON 2: Fractions of Time and Money
- LESSON 3: Where Would It Be?
- LESSON 4: Numerators and Denominators
- LESSON 5: North of the Dungeon
- LESSON 6: A Whole and Its Parts
- LESSON 7: More Than One Name for a Fraction
- LESSON 8: Eating Fractions
- LESSON 9: Equivalent Fractions
- LESSON 10: Fraction Assessment