Box and Whiskers Plot

So, today I had the opportunity to do something different. I got to work with 8th grade students on Box and Whiskers Plot. Now, I know I am not an expert and I know I missed identifying an outlier, but our goal for this tutorial session was to teach a basic understanding of Box and Whiskers Plot. Their teacher liked my lesson and the kids loved it, so I thought I would share.

My principal asked me if i knew much about Box and Whiskers Plots? I said that I knew a little bit and I have an idea to make it slightly more hands on.

I pulled some data from a textbook and put it on individual pieces of paper creating eight sets.

Here's what I did...

Each table received a sheet of poster paper and a stack of cards with numbers written on them.

My example was taped to a write board with the cards taped in a scattered unorganized manner. I worked through the first data set with them.

Teacher: "What do you call a set of values randomly given?"

I was looking for the word "data". After I guided them there...

Teacher: "What should be the first thing we do with data?"

Students: "Put the data in order from least to greatest."

Teacher: "What are the four measures of central tendency or variability?"

Students: "Mean, Median, Mode, and Range."

I then proceeded to ask the students to define and explain the process used to determine each.

Teacher: "Median is the essential tool in creating a Box and Whiskers Plot."

I then had them find the median of the data.

Teacher: "What is the minimum and maximum value of the data?"

Student: "28 and 67."

Teacher: "Understanding the information in a Box and Whisker Plot is determined by a number line placed below indicating the values used. What would be an appropriate range and scaling for a number line here? ... Another words, what would be a pretty minimum and maximum value that we could use?"

Students: "From 20 to 70 and go by fives."

Each table constructed a number line with the appropriate values and scaling.

Teacher: "Now, let's go back to our data. We need to determine the lower and upper quartile."

I explained the process (similar to median) and why it's called upper, lower, and quartile.

Teacher: "How many significant values have we identified?"

Students: "Five."

Teacher: "Using a short vertical line, let's identify the location of each value along our number line. You then connect the lower quartile to the upper quartile using two parallel lines. What did this create?"

Students: "Two boxes."

Teacher: "Then you connect the minimum to the lower quartile and the upper quartile to the maximum using a single horizontal line. What do you think we call these?"

Students: "Whiskers!"

Teacher: "What do you think is the significance of this type of graph?"

We spent several minutes discussing this before I gave them a new set cards.

I wanted to share this because it was well received. I don't know if it was because I'm not their usual teacher or they were really into it, but this lesson was refreshingly engaging and fun. It was one of those lessons that just worked, flowed, and the kids really connected. If you're a teacher, I'm sure you know what I mean.

Thank you.

 

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Notable Equations

Again focusing on identifying and understanding components of Algebra, I decided to discuss the parts of these two notable equations.

 

 

My students overall liked this page because they now understand what the letters represent in the equations. I heard a lot of "Well, that makes since" and "Now, I see the point".

I was impressed with their overall prior knowledge that they related to me during this lesson. It was refreshing.

 

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My Tool for Finding Slope & Slope Scrabble

Before our test, I decided to review finding slope with the two methods we had studied.

1. Counting Slope on a Graph

2. Slope Formula

Several of my Geometry students used a method earlier in the year that I thought Algebra 1 might appreciate.

• Positive: rise over run
• Negative: fall over crawl

 

We also discussed the staircase within a staircase.

Then we moved over to the slope formula. We also discussed the relationship between coordinate values and slope values of horizontal and vertical lines.

 

SLOPE SCRABBLE! Not as exciting as it sounds right now. We tried this but it was difficult to get the idea across to my students.

They had an excellent time finding slope for all of the problems cards I gave them. I even set up a table with all the solutions laid out so that they could match them.

The idea of slope scrabble is to begin at the origin and, using slope, make your way to the far blue dot in the corner to win. All of the other dots are things like double your slope, draw again, etc. There was some success with my students that have to patience to solve puzzles. Other students wanted to match slope again.

My students have an excellent understanding of slope.

I just wish I could troubleshoot the process and get this game going for them.

 

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Solving Equations is Like Wrapping Presents!

For my first year of teaching Algebra 1, I have made a lot of mistakes. These mistakes all revolve around an assumption. I assume that my students already know this and that. This comes from my experience in state testing remediation for 11th graders for the past three years. I now have realized that I have a chance to teach students to understand Algebra 1 from the beginning. I decided to review solving equations with my students, since this was a nightmare at the beginning of the year. I decided to teach them to understand each component of the process and what solving meant.

Step 1: "Unwrapping Your Solution"

I love reading educational material and Danika McKellar is one of my preferred authors. I remember her referencing gift-wrapping as a metaphor for solving equations. The idea of operations applied to a solution is similar to wrapping an object to hide its identity. To reveal the item, one has to reverse the process of wrapping, which is similar to finding a solution by reversing the applied operations.

It didn't turn out as spectacular as I would have preferred. However, this was a day well spent because my students no longer feared equations (for the most part).

First we started with x=3. Next, the students selected different operations and values to "wrap it up". Then in order to solve we reversed to process. When finished, we a concluded that solving is reversing the original operations. Hooray!!

 

Step 2: Properties Used to Solve

We identified the most common properties used in solving equations. Within the notes, we used the same equation to demonstrate how similar operations can be applied to acquire the desired result.

Step 3: How to Solve Those Equations

With the use of multi-door flap foldables, students identified each step in solving an equation by technical property and then by general vocabulary accumulated by the class. This step was critical in building their fluency in solving equations. Even lower level students that were hesitant in the process could solve.

Example1: We always started with the inside process.

Then finish by summing up with general words to help them identify the steps.

Example 2:

Step 4:

We moved from the in-depth process to identifying the general steps. By now, my students were using the vocabulary-properties, names of terms, quick steps, etc.

Step 5:

We reviewed with the giant Sorry board game. During this step, students started with a given equation including the solution and focused on the solving process.

Step 6:

TEST: I gave them a test in standardized format and received outstanding results! :)

 

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Slope Dude.... Win!

Slope Dude followed Pedro the Penguin in our journal. Pedro the Penguin was a great story that gave the students a visual to relate the idea of slope to. I also use the fact that we read a book from left to right means we also read a graph from left to right.

After building an internal understanding of slope, I wanted to provide the students with a memorable visual that my students could easily draw to reference. They love slope dude. I made sure to explain each component of his face as the students named each type of slope. It made slope dude all the more important.

Then I decided to take it one step further and go over what these slopes look like on a grid. I noticed that even though they knew the types, some of my students had trouble transferring the concept to a grid.

And I was right. As they graphed examples, I provided verbal guidance and feedback on their examples.

 

They were retested with a test previously given in the first semester and I had a significant increase in recognition and understanding on the concept of slope thanks to slope dude and the next few journal pages...

 

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Making a Change in Algebra 1

I just want to say thank you to all of you out there for your great ideas and passion for teaching. I feel rejuvenated and my Algebra 1 class is full of energy. Let me share some of the chaos as of late...

PEDRO THE PENGUIN

My students were having a hard time connecting the description of slopes with the actual graphs. While I was tutoring several students from other schools, one student shared an idea he learned of a skiing penguin for slope. My mind exploded with a story-Pedro the Penguin. I googled a skiing penguin as my inspiration to illustrate the rest of the story and my Algebra 1 girls wrote the story! We have no idea where the name Pedro came from.

 

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GIANT SORRY BOARD GAME

We were solving equations and it came down to the day before the test. My students tell me that they do better solving on the marker boards, one question at a time, and with some sort of an engaging, high energy activity. Of course, right?!

Again, my brain goes into overdrive and out pops this insane idea of a giant board game.

I assigned the task to my geometry students and they succeeded. They put my tables into a closed rectangle, unrolled white poster paper all the way around, and taped it together. They finished by cutting and pasting colored squares for the track, circle for the start, mini squares for the safe zone, and a pentagon for home.

They decided to construct cubes of different colors for the playing pieces.

I googled sorry game cards and found some vintage printable cards.

Then, it was up to me to figure out how to use this for a review. Since I didn't assign a specific math concept to the game, I can reuse the board game for a multitude of activities (hopefully). I printed and pasted differing levels of equations on different colored index cards. I sat in the middle of the tables and rotated clockwise. On the first rotation, each student drew an equation and solved; and the second rotation was to verify solution and allow them to draw a sorry game card. (Idea: Have a leading student be the monkey in the middle.)

Troubleshooting: We quickly realized that the teacher looking up solutions took too long.

Solution: Each solution is written below the equation. Thus the solution was no longer the focus. The solving process became the focus of our time. WOW! You wouldn't believe the results. That small change resulted in student teaching students, collaboration, and justification of the process to me!

(Rule of Ms. Haley's class: Oral explanations only! You cannot write on others' marker boards/sheet protectors or touch others' calculators. All explanations and directions are to be given orally; therefore, students are putting any process into words.)

 

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Looking Forward...

On a brighter note, I am looking forward to my next unit in Algebra thanks to Pinterest and all of these wonderful blogs that I following.

We will be solving equations and discussing slope. I plan to teach solving using the door flaps fold for a step by step process, over and over. I can't wait to introduce SLOPE DUDE! Majority of my Algebra class is boys and they will love SLOPE DUDE because they loved SLEEPY MAN.

Overwhelming...

I am finding the section on circles quite overwhelming. There are so many relationships, theorems, and formulas. Is there anything out there that provides an organized overview of circles??

 

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What happened??!?!?

"What happened?" is the question that just seems to resonate in my brain. My Algebra 1 kids bombed their test. I had such high expectations. All I want to do is cry....

A few tears later...

Alright, I will figure this out and we will come back stronger and better.

Game plan:

1. I gridded student responses (right/wrong) against names.
2. We have tutorials 7:30 am to 8 am and 3:35 pm to 4 pm. Starting tomorrow afternoon, I will have students that missed certain questions attend tutorials on a certain day. Example: All students that missed number one will attend morning tutorials Thursday. A revised question will be a half credit towards the original test grade.
3. I plan on the students completing an in depth revision for each question by identifying properties, writing explanations, and justifying their solution. I use the Cornell notes systems as a guide for organizing the process.
4. During class I will give what I call quiz strips. These consist of two to three problems. I create two to three sets of differing questions. Purpose: Students cannot cheat, but they can collaborate and teach each other about the concept.
5. I will administer accumulative quizzes. These quizzes focus on several concepts at once with a few questions.
6. We will retest. This method of repetitive practice and accumulation has proven true with my juniors in Algebra 2. There's not a function that they cannot transform or a transformation they cannot read. They love transformations of functions.
7. OVERALL: I am focusing on my level of questioning. I have several versions of Bloom's Taxonomy printed and posted around my classroom to help prompt and remind me of the higher level of vocabulary to use.

Looking for...

I am looking for strategies in Algebra 1 to build fluency in the foundational skills. Game ideas, practice methods, anything???

 

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Algebra Review Game

Monday's seem to be my worst day of the week. I give a weekly grade report to students, and, it never fails, there are certain students that throw fits, argue that they turned assignments in, or dispute every grade given back. My classes are not hard, but the key is-don't miss class. Many of my students have picked up on this. Anyways, I was determined to make today a high energy, fun day. I did and it was a great day. My favorite was, surprisingly, my Algebra 1 classes.

 

 

We reviewed for tomorrow's test by answering questions as a team competing with other teams. I wrote down 3 sets of the same problems on different colored paper and gave each group a set. We used marker boards.

(GREAT IDEA: GO TO LOWES OR HOME DEPOT AND HAVE A SHEET ($12) OF TILE BOARD CUT UP INTO MINI WHITEBOARDS FOR YOUR STUDENTS. They will cut them for you!)

 

 

How it works:

The students may choose to work together or split up the questions and work individually. Once they solve the problem, a student raises their hand and I come around to check. If right on the first try, they get three tokens. If incorrect, I usually provide some guidance or show a incorrect step. For the second attempt, if correct, they receive two tokens. If incorrect, try a third time for one token. Today, all of my students answered it by the second round. I made sure to monitor and provide verbal cues.

THEY LOVED THIS!!! We all had so much fun.

In the beginning, I tried to keep exact track of the number of attempts; however, they got so into it that it wasn't worth the concern. It turned out to be better to reward them for their effort and energy than to try and focus on the specifics.

My 5th period played the game right and took their time solving and collaborating. (Mostly girls.)

However, my 8th period (all boys) figured out how to cheat the system. My policy for the game is that I have to see your work. I'm much more observant than my students give me credit. They figured out that if they solved and answered correctly, then they could quickly show another teammate how to correctly answer the question to accumulate points faster. At first, I was going to deny them this strategy, but I then saw them teaching and collaborating on strategies. A class that usually struggles with engagement was blowing my mind with enthusiasm and hard work.

I really enjoyed this activity because of the diversity it produced with the learning. I had some students teaching, and others learning from peers. I saw a lot of different strategies used to solve the same problem, heard debates over which method is better, and observed a classroom full of pride and determination.

I'm very excited to see how we do on the test tomorrow.

 

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