##
* *Reflection: Vertical Alignment
Fractional Parts of an Hour (Day 1) - Section 2: Guided Practice

There is no such term as "double abstraction" and it's actually a silly phrase, but it's how I think of tasks such as what is being asked of students in this lesson. Not only is time a very abstract and complete intangible concept, but in this lesson it's being used as an overlay for the beginning of our exploration of fractions. Why attempt something with a double layer of complexity?

I made the choice to do this because what third graders need to understand about time is vertically aligned to what they need to know about fractions. All of our expressions about time involve chunking the given quantity of time into an implied, if not explicit, fraction. So while it may be initially difficult for students to move from the concepts of 1 minute as a 60th of an hour through the intervals of 5, 10, 15 and 20 to the idea of 30 minutes as 1/2 of an hour, they have heard people talk about time enough, and have worked with it sufficiently in class at this point, for there to be a framework into which the content of this lesson can nestle itself.

Any time there is a multi-layered task such as this, there are bound to be not only student questions (a given) but also student ideas and approaches that aren't something I considered in the planning of this lesson. For that reason, it's important to be flexible, and move with the students where they need to go. If the study guide (formerly know as a, gasp, worksheet) isn't completed, nothing is lost. It's an old paradigm that says that all the paperwork must be completed for learning to occur. Everything I put on the study guide is meaningful, but don't be afraid to leave it by the wayside if your students' line of inquiry leads elsewhere. While the content of this lesson is foundation, that can always be returned to at a later date. The primary goal is that students begin to see the different ways in which different size parts can add up to the same whole.

*Double Abstraction*

*Vertical Alignment: Double Abstraction*

# Fractional Parts of an Hour (Day 1)

Lesson 7 of 11

## Objective: SWBAT manipulate fraction pieces that represent different parts of an hour to create combinations that equal 1 hour in all.

#### Opener - Homework Review

*5 min*

I review student homework prior to teaching a lesson if it contains concepts necessary for the current day's lessons. Upon review of student work, I saw few mistakes so I abbreviated the amount of time I might have usually dedicated to the review. I expected it would take more than 8 minutes. The students had to identify which part of an hour was shaded on a sheet on which clocks were divided into 1, 5, 10, 15, 20 and 30 minute increments. This was based on their work in yesterday's lesson "Fractional Parts of an Hour: An Investigation".

This was their homework page: HW Time as Fractions

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#### Guided Practice

*20 min*

We open with an Entrance Ticket prompt:

**Write down 3 reasons that it's important to tell time, based on your own life and discussions we have had about telling time over the past week.**

After students have had time to think, and write, I show the students the fractional pieces that they will be working today and they identify the number of minutes represented by each piece.

I have pieces cut out to represent 1 minute (1/60), 5 minutes (1/12), 10 minutes (1/6), 15 minutes (1/4), 20 minutes (1/3) and 30 minutes (/2).

I model how different increments of time/fractions can be added together to make one whole hour (MP4 - Model with mathematics).

I emphasize that for today, they are to look for pieces that fit together to make an hour (by building on the hour template) and record the equation (MP7 - Look for and make use of structure). I point out that we are not actually adding the numerators and denominators, we are just representing all the pieces that when combined make an hour. To add the pieces we would, of course, need a common denominator.

For today, the purpose is that they see that there are many combinations that can make 1 whole hour. They understand time increments because of our prior work so they don't reject the idea that 1/2 + 1/6 + 1/6 + 1/6 can equal one. Given that equation on paper, my experience has been that students do not think that can make one whole because, w/out knowledge of common denominators, they come up with all sorts of predictable errors, such as thinking the answer to the problem above would be 4/20.

I model several problems and have students write the equations because this is complex enough that I want to briefly take some of the cognitive load off by removing the demand of immediate verbal processing and allowing for think time, which is especially important for my ELL students who have a 3rd tier of complexity - learning new words in English that they probably do not have in their home language.

#### Resources

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#### Independent Practice

*20 min*

I pass out ziploc bags with pre-cut paper pieces in different colors and representative sizes for 1 min. (1/60), 5 min (1/20), 10 min. (1/6), 15 min (1/4), 20 min (1/3) and 30 min (1/2) .

Students work independently or collaboratively to come up with as many different ways to design an hour as they can using the Time Fraction Pieces (B&W) I copied them on colored paper. (If you have a color copier, here they are in color: Time Fraction Pieces (Color)). The students record the equation for each model they build.

Circulate and ask students to explain their thinking. Some examples of questions for students:

**Extra support:**

How many minutes are there in (1/60, 1/30, 1/20, 1/15, 1/10, 1/5) of an hour? What made you decide to use _______?

**On Level:**

What fraction of an hour is representative of (1 min., 5 min., 10 min., 20 min., 30 min., 60 min.)?

How is this model different from __________? (a second model they have made, a neighbor's model)

Explain one of your equations for the parts that equal an hour.

What are two/three different ways to represent (1 hour, 30 minutes, 20 minutes, 15 minutes, 10 minutes, 10 minutes?)

**Enrich:**

Which fractional part of an hour is most commonly used? (Opinion) Why? Which one do you use the most? Do we use most at school? Are there any other ways in which it might be helpful to partition an hour? In what circumstances?

Here is an example of student work: Fractional Parts of Hour Student Work

*expand content*

#### Wrap-Up

*8 min*

I ask students to share a favorite example from their work. They read the hour off as fractions or as pieces of time. Expressing out loud the minutes that add up to an hour, or the fraction pieces that add up to one whole hour, give the students additional practice and provide support for auditory learners.

I am constantly asking them, "Why," and the boy who answers in this video explains his reasoning for selecting the example of 10 minute increments without prompting.

#### Resources

*expand content*

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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