Investigating Fractions with Smarties

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Objective

SWBAT identify equivalent fractions.

Big Idea

Students will find equivalent fractions using Smarties candy rolls.

Opening

30 minutes

Today's Number Talk

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using a number line model. For each task today, students shared their strategies with peers (sometimes within their group, sometimes with someone across the room). It was great to see students inspiring others to try new methods and it was equally as great to see students examining each other work for possible mistakes!

Getting Started

Prior to the lesson, I placed magnetic money and fractions on the board to help students conceptualize our number talk today. 

I invited students to get a Student Number Line and Hundred Grids. I then drew a Number Line on the Board and marked 0, 1, and 2 on the line. I asked students to do the same on their own number lines.

Task #1: Compare 4/8 to 8/4

To begin, I asked students to compare 4/8 and 8/4 on their number lines and hundreds grids. During this time, some students chose to work alone while others worked with a partner in their math groups. I took this time to conference with students.

Next, some students volunteered to come up to the board to show their thinking. One student thought that 4/8 was located at 1/2 while another student thought 4/8 was located at 1 whole. Here's the conversation that followed: Where is 4:8?. Next, a student explained how to locate Where is 8:4?. I loved how she drew an area model to show 8/4 as well. 

Others watched carefully, checking their own number lines and hundreds grids to make sure they agreed with the students demonstrating their thinking. Here are a few examples of student work during this time:

Then, a student asked, "How much is 1/8 of a dollar?" As a side note, I took the time to explain how to divide 100 by 8 to get 12.5: How much is 1:8 of a dollar?. Then I related 1/4 to 1/8: If 1/4 = 25 cents, then doesn't it make sense that 1/8 = 12.5 cents?  

Task #2: Compare 13/10 to 3/2

Next, we moved on to comparing 13/10 and 3/2. Most students showed: 13/10 is equal to $1.30 and 3/2 is equal to $1.50 so 13/10 is less than 3/2.

Here is an example of student number line and hundreds grid: 

Again, a few students explained their thinking on the board. Here's the end result of today's number talk: Completed Number Line. 

Teacher Demonstration

40 minutes

Lesson Introduction & Goal

To begin the lesson, I shared today's goal: I can identify equivalent fractions using Smarties! Students couldn't wait! I explained: During the past few lessons, we've been learning about equivalent fractions. Today, I want you to see how equivalent fractions can be applied to every day life!


I knew that today's lesson would be particularly important as students to be able to model with mathematics (Math Practice 4). 

Smarties Investigation

To begin with, I passed out a roll of Smarties and a copy of the the following Smarties Activity found at Teachers Pay Teachers to each student.

Students went right to work, drawing their Smarties, identifying the fraction of each color, ordering their fractions, and comparing the fractions of each color. It didn't take students longer than 20 minutes to complete the page and discuss their results with their group members. However, the goal of this activity was to help students become familiar with their Smarties prior to moving on to the more complex part of the lesson, finding equivalent fractions!

In particular, I liked watching students stack their candies by color to visually see that that 1/15 white is less than 3/15 purple. 

Conferencing with Students

During this time, I conferenced with students in order to help them work through any confusing parts of the activity and to push student thinking. 

Here, Finding Equivalent Fractions, a student identified the fraction of each colored candy. At the end of our conference together, I encouraged her to identify equivalent fractions.

I loved watching this student graph his Smarties: Conference Graphing. I took the time to help him connect fractions with graphs as students often struggle with identifying the whole amount represented and the fractional parts. 

Here's a student example: Completed Activity Student Example.

Finding Equivalent Fractions

As students finished, I asked them to flip over their Smarties Activity paper. I then showed them how to fold the paper in 1/2... and then in half again... and then in half once more to create 8 rows. We then flattened the paper, drew lines along the folds, and also created four columns. Here's what the end result of this activity will look like for a reference: Teacher Model of Equivalent Fractions.

I explained and wrote the column headings at the same time: In the first column, let's write "Colors." In the next column, let's make one whole roll of Smarties. I then modeled how to write the colors in the colors column and the fraction of each color in the "1 Whole" column. Students did the same, only using the fractional amounts of each color from their own rolls. We then wrote a fraction to represent the total candies in each roll: 15/15.

Two Whole Rolls of Smarties

Next, I asked: What if I gave you had two rolls? And what if you had the same fraction of each color in the second roll as you have had in the first roll? So if you had 1/15 white in the first roll, you'll have 1/15 white in the second roll. And if you had 2/15 pink in the first roll, you'll have 2/15 pink in the second roll. 

I wrote "2 Wholes" at the top of the next column. I then asked: What will the total number of candies be in two rolls? (30/30) We then wrote this in the bottom row. What fraction of the Smarties would be white? Students said, "2/30!" So would you say that 1/15 is equal to 2/30? "Yes!" What do we call these fractions? "Equivalent fractions!"

Three Whole Rolls of Smarties

After students completed listing the equivalent fractions for each color under the column, "2 Wholes," we moved on to the last column and wrote "3 Wholes." I asked: What would happen if we had three whole rolls of Smarties? What fraction would represent the total? (45/45) And what if each roll had the same fraction of each color as the first roll? How many Smarties would be white? (3/45) What fraction of Smarties would be pink? (6/45)

Student Work

Again, students completed their own equivalent fraction charts using their own number of Smarties. Here are a couple examples: 

Student Practice

30 minutes

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Before students began working, I asked them to discuss how they would like to support each other today. I gave them many examples: Do you want to take turns talking out loud? Do you want to solve quietly and then check with each other? Or do you want to turn and talk anytime you get stuck? Students always love being able to develop a "game plan" with their partners! 

Practice

I explained: For practice today, I'd like for you to continue finding equivalent fractions! I passed out copies of Equivalent Fractions Practice found at Math-Aids.

Instead of modeling how to complete each problem, I challenged students to figure out how to solve each problem with others. 

Monitoring Student Understanding

Once students began working, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3). 

  1. Can you explain what you know?
  2. What step did you take first?
  3. What pattern did you notice? 
  4. What are you doing to find the missing numerators/denominators? 
  5. Are some problems easier/harder than others? Why?

Conferences

During this conference, Conference 1, I loved listening to the students trying to explain the practice page to one another. The most difficult part of this activity was that students had to find fractions with common denominators to solve each problem. Often, they would have a fraction, such as 3/6, next to a fraction, such as x/8 (missing numerator). Then, students would get confused when 6 wan't a factor of 8!

Here, Conference 2, I showed students how to find the missing denominator for 4/x (missing denominator) as the fraction, 4/5 could be used to find all the other equivalent fractions. I was so proud of students for persevering! 

Completed Work

Here's a Student Work Example.