##
* *Reflection: Student Ownership
Time Pictures - Section 4: Time Fractions on a Number Line

Whenever possible, I allow for creativity even within the fixed parameters of a lesson such as this. In this lesson 1/4 + 1/4 + 1/4 + 1/4 = 4/4. That's it. That cannot be altered.

What **can** change is how a student represents it. The student whose number line and fraction diagrams is the lesson image clearly enjoys color and designs and as long as he is not misrepresenting the content, I see no reason not to allow him to draw out the models like this.

I can also see that he is attending to the idea of benchmark fractions having the same denominator and adding up to a whole because of the way in which he has colored the denominators and sure enough, when I asked him to explain this model to me, he was able to explain the meaning of the denominator.

I think some might perceive this paper as messy or think that he was randomly doodling but research has actually shown that some people think more productively when they are drawing little designs. The wave of color he drew across the paper in no way detracted from his accurate models of unit fractions on a number line or as part of a rectangle. In fact, in his mind, the wave probably provides some kind of delineation between different content. It seems like a small thing but I don't think it's small at all. If I forced him to write it out with just pencil, in a straight line, exactly as I modeled on the board, I think I would potentially be thwarting him in his development of a conceptual understanding.

*Allowing for Creativity*

*Student Ownership: Allowing for Creativity*

# Time Pictures

Lesson 2 of 11

## Objective: SWBAT create a model on graph paper using 5 minute increments to represent different portions of their day at school.

#### Opener

*5 min*

*"Today we're going to do something a little different. We'll create a simple design to represent the different activities we have here at school. In order to create this design, you will need graph paper and your crayons. On this graph paper, each square will represent 5 minutes. Our job is to recreate our schedule together and then color in the sections to represent our different activities, and of course create a key."*

I show them this 5 Minute Art as a representation of an imaginary school day.

#### Resources

*expand content*

I give students 1 inch graph paper. I tell them that each square inch represents a five minutes.

We are going to color blocks to represent units of time that we spend on different activities throughout the school day. Using what they know, the very familiar schedule of a school day, helps them develop their understanding of the abstraction of periods of time. 95 minutes is a very abstract idea. If I say, "the time we spend on math each day," they have a very exact sense of what that period of time feels like.

On the document camera, I model the following:

"If it took me 5 minutes to brush my teeth this morning, how many squares will I color in? (1) I'll use yellow.

If it took me 15 minutes to walk my silly, small dog, how many squares will I color in? (3) I'll use green.

Now I'll stop for a moment and add these to colors to the key at the bottom of my page. Otherwise, I will forget which color represents which activity. I'll put my key all the way at the bottom so it doesn't get in the way of my time picture. Remember, plan ahead!"

I color a square yellow and write: brush teeth

I color a square green and write: walk dog

I go through two more examples.

"It took me 10 minutes to cut up fruit for my breakfast. How many squares will I color in? (2)

I'll color them red and add that information to the key at the bottom of my page."

"It took me 35 minutes to drive to work. How many squares will I color in? Let's count by five minute increments. 5, 10... 35. I'll color those squares brown, since that's the color of my car. I'll add that information to the key at the bottom of my page."

Then we start to build time art based on our schedule. First we write up our schedule, then we calculate the elapsed time, and then we color in the first four blocks of time on the graph paper. Time Art Explanation They complete the rest of the day on their own.

#### Resources

*expand content*

For the second half of this lesson, I work with students as a whole group to make rectangular and number line models of the way in which several benchmark fractions add up to a whole. As a general rule, I try to discourage them from drawing rectangular models of fractions because they tend to be uneven and they draw their rectangles in different sizes this can lead to erroneous comparisons.

We neatly draw a square. Depending on the group of students, I might explicit to the point of having them measure down 2 or 4 lines or even having them measure it out with a ruler (2 inches by 2 inches, for example).

They divide the square into two equal pieces and label each piece 1/2.

Next to that square they draw a number line with a 0 on the left side and a 1 on the right side. Then they divide the space between the 0 and the 1 in half and label the 1/2 and under "1" write 2/2.

When creating the model of the thirds it's trickier to get even pieces. I model taking my time, and writing my dividing lines lightly before I commit to making them permanent. We divide a rectangle into 3 reasonably equal pieces and label each piece 1/3. Then we draw another number line, again starting at 0 (though I like to leave some space to the left of 0) and ending at one. We lightly mark the halfway mark and I show them how that makes it easier to mark the thirds. We label the pieces on the number line 0/3, 1/3, 2/3, 3/3.

I continue to talk through the same process and we make models of fourths and eighths.

If they are able to process it, I also encourage them to label some of these fractions as parts of an hour. I do not have them label 1/8 as part of an hour as it is 7 1/2 minutes, and a fraction shouldn't be used to label a fraction.

I've included two examples of student work.

*expand content*

#### Homework

*2 min*

For tonight's Time Homework, students will complete a more thorough version of the form they used last night. Instead of just recording what they are doing on the hour, they will record the start and end time for at least 5 activities.

I encourage them to be specific to the closest five minutes if not to the closest minute, and that I will be very suspicious if all of their activities start and end at either *o'clock* or *half past*!

I prefer that they record their activities continuously from the time they leave school to the time they go to bed, but some of them are not able to do so, so the five activity parameter gives them some flexibility.

*expand content*

Love this idea! I'm going to try it with my higher math group. Thank you for sharing!!

| one year ago | Reply

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- UNIT 1: 1st Week: Getting to Know Each Other Through Graphs
- UNIT 2: Addition and Subtraction
- UNIT 3: Multiplication
- UNIT 4: Introduction to Basic Division
- UNIT 5: Division in Context
- UNIT 6: Time
- UNIT 7: Rounding
- UNIT 8: Place Value Practice
- UNIT 9: Fractions
- UNIT 10: Math and Me: Nutrition, Health and More
- UNIT 11: Geometry in Architecture
- UNIT 12: Time Cycle 2
- UNIT 13: Patterns in Math
- UNIT 14: Area and Perimeter
- UNIT 15: Solving Mult-Step Word Problems Using the Four Operations
- UNIT 16: Musical Fractions
- UNIT 17: Volcanoes (Data Collection, Graphs, Addition & Subtraction)

- LESSON 1: It's Time We Begin
- LESSON 2: Time Pictures
- LESSON 3: Lucky Luggage Tags: Elapsed Time to the Hour
- LESSON 4: Lucky Luggage Tags: An International Challenge
- LESSON 5: Using Open Number Lines to Determine Elapsed Time
- LESSON 6: Fractional Parts of an Hour: An Investigation
- LESSON 7: Fractional Parts of an Hour (Day 1)
- LESSON 8: Fractional Parts of an Hour (Day 2)
- LESSON 9: Review of Telling Time to 5 Minutes
- LESSON 10: Time to the Minute
- LESSON 11: Time Midway Assessment