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: 2/10 + 0.90
To begin, I asked students to add 2/10 + 0.90 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. Here are a few examples of student work during this time: 2:10 + 0.90 Student Hundreds Grid and 2:10 + 0.90 Student Number Line.
Students then volunteered to model their thinking on the board. During this time, I continually asked clarifying questions to encourage students to make connections between fractions and decimals and to consider more exact language: Students Modeling 2:10 + 0.90.
Task #2: 40/100 + 3/10
Students then modeled their thinking on the board: Students Modeling 40:100 + 3:10.
Goal & Lesson Introduction
To begin, I introduced today's goal: I can measure and identify angles. I explained: Today, you will learn how to correctly use a protractor. Then, you will use your protractors to make and analyze three different angle types: right, obtuse, and acute. I was careful to not define these math terms as I wanted students to discover the meaning of each through exploration.
I continued: Let's start by discussing some key vocabulary. We then discussed the meaning of an angle (Angle Poster) as well as the meaning of a point and line segment (Point & Line Segment Poster). I try to always create vocabulary posters with a picture and definition. This way, students can refer to our math wall, full of vocabulary posters whenever needed throughout the year.
Prior to today's lesson, I created a Protractor Poster. All of the labeling on the poster occurred during the lesson. This is because students remember the labeling better if they are able to take part in (or witness) the process instead of seeing it after the fact.
I explained: A protractor is a measuring instrument used to measure angles using degrees. Just like we use a ruler to measure distance using inches or a stopwatch to measure time using seconds, we use a protractor to measure degrees!
We then discussed the outer scale, inner scale, zero edge, and center mark. Next, we discussed two important points to keep in mind when using a protractor to measure an angle: 1. Line up the vertex with the center mark. 2. Check to see if the angle is more or less than 90 degrees.
This was a perfect opportunity to introduce the meaning of right angles using the Right Angle Poster.
As a side note: I purposefully avoided "telling" students the meaning of acute and obtuse angles. Later on, I will provide students with the opportunity to analyze angles and develop definitions for acute and obtuse angles based on their own observations.
Students couldn't wait to get their hands on these protractors! To provide students with an opportunity to practice using the protractors, I handed out a practice page: Angles Practice. I explained: All of the angles on the left side of the page are more than 90 degrees and all the angles on the right side are less than 90 degrees. Keep this in mind when you are determining which scale to use!
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).
I found that students struggled in two areas particularly:
Here, a student determined which scale to use, the inner or the outer: Choosing a Scale.
Another student extended the rays of an angle to get a more precise measurement: Precise Measurements.
As students finished, they met up at the back table to go over answers. I find this to be an effective way to "buy more time" for students who are still working and it also provides the perfect opportunity for students to engage in Math Practice 3: Construct viable arguments and critique the reasoning of others.Whenever there's a discrepancy in answers, students generally grab a protractor to "prove their thinking."
Here's an example of a completed page: Angles Page.
This was the most successful part of this lesson! I asked students to get computers out and to go to the following link: Measuring Angles with a Protractor. There were two great components to this site:
1. Students didn't have to worry about lining up the center point. They could simply focus on measuring the angle.
2. Every student was provided with immediate feedback. This way students knew immediately if they were correctly using the protractor and could adjust accordingly.
Again, I conferenced with as many students as possible and made sure all students were proficient at measuring angles before moving on to our next activity.
Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills.
I passed out Obtuse & Acute Angles and explained: Now for the final part of today's lesson! I'm going to pass out copies of obtuse and acute angles. I'd like for you to work together with your math partners to analyze each set of angles. Based on your observations, come up with a definition for acute angles and then for obtuse angles!
I loved watching students literally put their heads together: Students Working Together. Once again, I knew students were actively engaged in Math Practice 3: Construct viable arguments and critique the reasoning of others. Students were "justifying their conclusions, communicating them to others, and responding to the arguments of others."
As students finished, I asked them to check their work with other groups.
During this time, I continued conferencing with students, checking for proper protractor use, and pushing student thinking using questioning. These angles were a bit trickier than the the first practice page as some were up-side down. Some students asked, "How do I place the protractor?" I love how conferencing always provides opportunities for one-on-one instruction.
Acute Angle Exploration
First, students began measuring and observing acute angles: Measuring Acute Angles. Many students decided that an acute angle is "any angle that measures less than 90 degrees."
Obtuse Angle Exploration
Next, students moved on to exploring obtuse angles: Creating a Definition for Obtuse Angles. Most students found that obtuse angles "measure over 90 degrees."
Here, Definitions for Obtuse & Acute, a student explains her group's findings for both angle types.
I then asked students to join me on the front carpet with their acute and obtuse papers. We then discussed the meaning of acute and obtuse angles. As soon as students shared their thinking, I revealed our Acute Angle Poster and Obtuse Angle Poster. Students then made revisions to their own working definitions.
Here's one group's completed work: Acute Angle Definition and Obtuse Angle Definition. You'll notice that they revised their definition of obtuse angles after our class discussion by adding, "but not larger than 180 degrees."
To complete today's lesson, I taught students how to sing the Angles Song. This is only the second time singing the song, so they're a bit rusty yet!