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 and hundreds grids. 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!
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 2/4 to 0.62
To begin, I asked students to compare 2/5 and 0.62 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, a student volunteered to come up to the board to show her thinking: Student Modeling 2:4<0.62
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: Student Number Line 2:4<0.62 and Student Hundreds Grid 0.62 > 2:4.
Task #2: Compare 9/10 to 0.80
Next, we moved on to comparing 9/10 and 0.80. Again, students immediately began comparing the two numbers using a number line, Student Number Line9:10 > 0.80, and their hundreds grids, Student Hundreds Grid 9:10 > 0.80.
A few students explained their thinking on the board: Students Modeling 9:10 > 0.80.
Task #3: Compare 130/100 to 1.25
Finally, students compared 130/100 to 1.25 using their number lines, Student Number Line 130:100 > 1.25, and hundreds grid: Student Hundreds Grid 130:100 > 1.25. Here, students label and identify the location of these numbers on the board: Students Modeling 130:100 > 1.25.
To provide students with an engaging way to document decimal-fraction conversions, I created a Google Presentation called Decimals Presentation. I then shared this document with students so that any student could modify the presentation on their own computers.
Goal & Lesson Introduction
I began by introducing today's goal on Slide01: I can use decimal notation for fractions. I explained: Through our daily Number Talks, you have learned that decimals can also be represented using fractions. Today, we are going to explore the relationship between fractions and decimals further!
Slide 2: Making Observations
We then went on to Slide02. I invited students to raise their hands to share observations. By encouraging students to make observations, I'm also hoping students will engage in Math Practice 8:Look for and express regularity in repeated reasoning.
As each student shared an observation, I asked them to add another bullet in the text box and type their observation. This was a bit hectic as several students were typing at one time, but it was also much more powerful than a teacher documenting observations on the board.
One student pointed out, "After the decimal, you count backwards: tenths, hundredths, thousandths." Others said, "There is no such thing as oneths." Here's the list of Student Observations Slide 2.
Slide 3: Making Observations
Going to Slide03, students eagerly raised their hands again, hoping to share their observations (both aloud and by typing it into the shared document)!
One student said, "Every number has a one with a different meaning in it." We discussed how the 1 in 100 means one hundred dollar bill and how the 1 in 1/00 means 1 penny. Here's the list of Student Observations Slide 3.
Saying & Writing Decimal Numbers
Before moving on, I invited students to join me on the front carpet. I explained: Let's take a look at how we say and write decimal numbers. I began creating this list on the board: How to Say Tenths.
For example, when we see this decimal number (I wrote 0.2 on the board) we sometimes call it "zero point two." However, this number has a special name (I wrote "two tenths" off to the side).
Next, I wrote the number, 0.6, and asked: If 0.2 is "two tenths," then how do you think you should say 0.6? Turn and talk! A few moments later, students said, "Six tenths!"
We continued in this same fashion, discussing, turning & talking, and writing the correct way to read and write decimals next to each of the following numbers 1.5, 0.8, and 5.4. We also discussed how we say "and" at the decimal point when there is a whole number in the decimal number.
Then, we moved on to making a list with How to Say Hundredths. Again, I started off by writing "0.01" and explaining, The special name for this number is "one hundredth." We then discussed how to read and write 0.12, 0.56, 0.08, and 1.99.
Decimal Process Grid
Prior to the lesson, I drew a grid for comparing decimals to fractions. I labeled each column: decimal, written form, equivalent fractions, and visual models. Here's what the completed Decimal Process Grid will look like at the end of today's lesson. I want students to look for pattern, categorize information, and, once again, be engaged in Math Practice 8:Look for and express regularity in repeated reasoning.
I explained: Let's start off by looking at the decimal, 0.01. How do you say and write this decimal? Students said, "One hundredth!" I wrote these words on the chart.
Let's skip over to the visual models column. I glued down a hundreds grid and asked: How many squares should I color in out of 100 squares to represent this decimal number? Due our daily Number Talks, students immediately said, "1 out of 100!" I then colored in one square out of the hundreds grid.
Finally, we looked at equivalent fractions. Students pointed out that 1/100 = 2/200. We discussed how we could decompose each 1/00 into two parts so that there would be 200 parts. If we colored into 2 out of 200, it would be the same as coloring in 1 out of 100.
At this point, I wanted students to apply this new learning!
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!
Google Presentation Practice
I asked students to make a copy of the class Google Presentation called, Decimals Presentation. Next, students went to Slide04. On this slide, I modeled how to enter the same decimal from our first row in the process grid: 0.01 in the decimal box. Then, we entered the name in the name box and discussed equivalent fractions. Finally, I showed students how to shade in parts of the hundred grid to represent decimal numbers. The students absolutely loved begin able to use the computer to represent decimals!
As students were ready, I wrote the next decimal number on the Decimal Process Grid: 0.10, 0.16, 0.92, and 0.5. In between writing each decimal number, students represented their own thinking on the next slide on their own computers and turned and talked about their thinking with partners. Then we discussed the decimal numbers as a class and completed the decimal grid, one row at a time.
When students finished, I challenged them to copy and paste new slides to represent 0.1, 0.7, and 0.9.
Monitoring Student Understanding
While students were 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).
During this conference, Examining 0.1, I guide the student to make the connections between 0.1 = 1/10 = 10/100 = 1 dime = 10 pennies.
Here, Examining 0.9, another student explains how 0.9 = 9/10 using the hundreds grid model.
Here is an example of a student's finished presentation: Student Example Decimals Presentation.