Land of Math

I used to open up the school year with some nice get to know you activities. For example, I might randomly partner students together and have them interview each other. After the students asked each other a few questions, they would introduce their partner to the rest of the class. This was always a nice way to ease into the school year and get to learn a bit about the kids.

As much as I (and the kids) enjoyed these opening day activities I always felt something was lacking. There seemed to be this disconnect with these activities and math. (Also, it seemed like every teacher in the building was doing some variation of this. So the students were doing this all day long. The novelty was lost by the time many got to me.)

Last year I tweaked how opened the school year.

I would still do surveys, but with a more organized purpose. I would make up the surveys with the end goal of the students graphing the results of their surveys.

Normally graphs/charts get shoved to the end of the year (sometimes it gets totally left behind because of snow days). This is such a bummer because there are so many activities during the year that are conducive for using, reading, & analyzing graphs. For example, this year I am planning on a year long Stock Market lesson. Needless to say, graphs are sort of a big deal in this world.

The following are a few of the advantages of opening the school year with this survey/graphing lesson:

You would get to learn about the students as a group/class/grade level.
While students are creating graphs you have the opportunity to interact 1-on-1 with different students which helps to get to know the student.
Lots of hands on activities.
It's not a stressful environment.
Students would be able to move around instead of stuck in their seat the whole period.
Students would be able to interact with other students.
Students would have freedom to be creative.
Students get to collaborate with each other
As a teacher you get to cover 7 different graphs (bar, line, circle, scatter, stem-n-leaf, histogram, box-n-whisker), median, coordinates, angles, intervals, number lines, & degrees of a circle.
Reading and analyzing graphs.
You get to cover an area that many times doesn't get covered, or gets just minimal coverage.
You can use graphs with a variety of units (graphing equations/inequalities for example) during the year.

Below are the steps I took:

STEP 1 - The Survey

The first thing I did was to create a survey. When creating questions I focused on questions that I could use to create different types of graphs and different ways to group students.

(QUESTIONS: gender, class period, how much do you like math (scale of 1-10), how good are you at math (scale of 1-10), grades at Lakewood (k,1,2,3,4,5,6), In the band, sports played, social media, Height, and arm span).

For example, Line Graphs are a bit of a challenge because of the time element needed. To get around this I asked the students to circle the different years they attended our school. This would give us the element of time (grades k-6) that we could use on the x-axis.

Two of the questions (gender & class period) would allow students different ways to group the information.

STEP 2 - Gather and Sort data

Next, students would need to tally up the results of these different survey questions. At times I will let the students figure out how to gather and organize the results. Usually this is chaos. Sometimes chaos is good, but with most students this just leads to anarchy. As a result, I will usually guide/teach students how we can group and record the results of the surveys.

I make sure that the data is split between boys and girls. Because each class is looking at their results, the data is already divided by class period.

STEP 3 - Bar Graph

I like to start with bar graphs because they are the easiest and are the ones the students have been using these for years. This is the sequence I follow when working with bar graphs:

Lesson on bar graphs
1. Parts (x & y axis, title, labeling x & y axis, intervals of y axis, and categories of x axis)
2. How bar graphs can be deceptive (using different intervals and skipping intervals)
3. Different ways to design bar graphs (double bar graphs, stacking bar graphs, vertical vs. horizontal)
Reading Bar graphs - I will create a power point with a couple of bar graphs. I will show these graphs to the class and ask them what information they know from looking at this graph.
Make a couple of basic bar graphs as a class (ex. I might make up info about number of dogs and cats in each class ) period. I show students different ways to group data (by class, gender/class, all students, all students broken down by gender, etc.).
Finally students can make a bar graph of student gender and/or band participation.

STEP 4 - Circle Graph

The next graph I like to use is the circle graph (aka the Pie Chart). Most students are familiar with reading this graph but are weak at making it. In younger grades, students usually will estimate the parts of a circle graph.

The number one struggle for many students is not the math (it's still a struggle), but actually the act of making a circle with a compass. I also opt for the Angle Ruler instead of the Protractor.

Lesson on circle graphs
1. circles are 360 degrees
2. Converting the numbers in a survey to degrees in a circle graph.
  1. I teach 360 divided by number of responses in a survey = degrees of each response. I will show students different ways to round numbers and their impact on the graph.
3. How to use the Compass
4. How to use the Angle Ruler (to measure and create parts of the circle graph)
Reading circle graphs -Just like with bar graphs - I will put a couple samples on a power point and share with the class. Together we will discuss what we know about this graph.
Make a couple of basic circle graphs. For the examples I always (at least at first) use numbers that are multiples of 360 such as 180, 120, 90 etc.
Finally students can make a circle graph of different sports that students are in. (boys only, girls only, boys/girls combined etc.)

STEP 5 - The Box-and-Whisker Graph

For most of my 7th grade students this is a new thing. It's got a goofy name (I just assume some lady that loves cats named this thing) and it looks a bit strange. Sometimes kids can be a bit apprehensive because of how it looks. I spend a bit more time on examples of the Box-n-whisker just because it is new and has has a lot of different parts.

Lesson on Box-and-whisker graphs
1. Parts of the Box-and-Whisker
  1. Extremes, Quartiles, median, number line, box, whiskers
2. The four parts of Box-and-Whisker that are each 25%.
Reading Box-and-Whisker graphs -I usually start with a double Box-and-Whisker Graph sample. For example, I usually will have two "random" classes and their quiz scores. The first teacher (Mr. Smith for example) I will make sure his extremes are both larger than the other teacher's extremes (let's call her Mrs. Jones). I will make the quartiles and median for Mrs. Jones larger than Mr. Smith's. Actually I line up Mrs. Jones' median with Mr. Smith's Upper Quartile and her Lower Quartile with his Median. This leads nicely to a discussion about which class did better on the quiz. You can make an argument for each class.
Next I have the students make different box-and-whisker graphs. To make a Box-and-Whisker you are finding three Medians: Whole, smallest half and largest half. There are four different situations that occur:
1. Total is an odd amount of numbers and halves are odd an amount of numbers
2. Total is an odd amount of numbers and halves are an even amount of numbers
3. Total is an even amount of numbers and halves are an odd amount of numbers
4. Total is an even amount of numbers and halves are an even amount of numbers
Finally, students can make a Box-and Whisker Graph of the total number of students that are good at math. ***Make sure that the extremes, quartiles and medium are five different numbers***. If you do have duplicate numbers you will want to look at either "students that like math," "student heights," or "student arm spans."

STEP 6 - Line Graph

Line graphs are another graph that students have used. A key focus is the element of time (minutes, days, weeks, years) on the x axis. The biggest mistakes I are usually intervals not being consistent (x and y axis) and when plotting points, not using the grid lines to help plot the points.

Lesson on Line graphs
1. Parts (x & y axis, title, labeling x & y axis, intervals of x and y axis, and some element of time on the x axis)
2. Having consistent intervals on x and y axis
3. Showing how to correctly plot the points on line graph.
4. Show how bar graphs can be deceptive. For example, the greater the intervals on the y axis the smaller the bars (the smaller the intervals the greater the size of the bars.)
Reading Line graphs - I will create a power point with a couple of line graphs. I almost always use a graph of a companies stock price over the years (I look for a company with a lot of price swings and that the kids like.) I will also introduce double line graphs which compare two different items (such as two different companies).
Next, I'll have students complete a couple of easy line graphs (usually multiples of 5 or 10)
Finally, I will have the kids make line graphs of the number of students attending Lakewood over the past 7 years. If I want, I can make a line representing each of the classes, boys and girls or my students vs. the other math teachers students.

STEP 7 - Histogram

Histograms look a lot like bar graphs. Most people would just assume they are same. In my 7th grade classes, very few of my students have ever heard of a histogram. The biggest difference between a bar graph and a histogram is the x axis. The bar graph will show categories (like types of colors, favorite pets etc.) while the histogram will show a sequence.

Lesson on Histogram
1. Focus on how the Bar and Histogram are nearly the same with the exception of the x axis which the Histogram uses some type of a sequence (such as time, weight, ages).
Parts
1. x and y axis, intervals, labeling each axis, bars (bars - which must touch)
Reading a histogram
1. Reading a histogram in many ways is more like reading a line graph, especially if the sequence on the x axis is an element of time. Like the other graphs I will have a couple examples to look at.
I usually just have one simple histogram for students to do before we work on the survey histogram.
Students will make a histogram of the number of students attending Lakewood each year. (yes I know it's the same topic as with the line graph).

STEP 8 - Stem-n-Leaf Graph

The stem-n-leaf graph is really ideal for gathering and recording large amounts of data. The advantage of the graph is that you only need to record half the numbers. It also can be a nice graph to compare to amounts side by side.

Lesson on Stem-N-Leaf
1. Show students how the numbers drawn vertically represent the tens place. Only the number found in the ones place is written next to the vertical numbers. make sure numbers are written in numerical order (left to right on the right side of the stem and right to left if written on the left side).
Parts of the Stem-n-leaf graph
1. Stem, leaf (numbers written horizontally), a second stem if using a double stem-n-leaf and title
Reading a Stem and leaf graph
1. Reading a Stem-n-Leaf is very different from other graphs. A single Stem-n-leaf you read like a book - top down and left to right. In the case of a double steam-n-leaf graph you read the "leafs" on the left, top down, BUT right to left.
I will do a couple (one single and one double) Stem-n-leaf graphs with the students using basic numbers. In addition, I will show how how to write numbers that are over 100.
Students will make a a double Stem-n-leaf graph using the height and arm span of 7th grade students)

STEP 9 - Scatter Plot

Even though the Scatter Plot is not a required graph to teach it doesn't take long to teach and it's great at showing trends/patterns.

Lesson on Scatter plots
1. The biggest thing that is new for the scattered plot is reading coordinates (x,y). I really try to focus on having students use the vertical and horizontal lines when plotting points.
Parts of Scatter Plot
1. The set up of the scatter plot is similar to bar, line, or histogram.
Reading Scatter Plot.
1. The biggest thing is the relationship between the x and y axis.
  1. How to read - x first and then the y
2. looking for trends/patterns
  1. When looking at the graph we are looking for a pattern for example...
    1. If you work more (x axis) the y axis (money) also increases.
    2. If you run more (x axis) your weight (y axis) will decrease.
    3. sometimes there is now trend (waffles you eat and your height)
As with the other we will do a couple of basic examples
Students will use their height and arm span to see if there is a correlation between their height and arm span. I will have one massive coordinate grid which all students will plot their coordinate.
Next I will draw a line (not quite a fitted line) that connects all coordinates with the same Height and Arm Span. Students will discuss how their coordinates compare to the line (most are on or below). Finally, I will plot the coordinates of NBA players preparing fore the NBA draft. Students will notice how most (if not all) the players are located above the line. We will then discuss how this is an difference in height and arm span is a huge advantage for basketball.

At the very end of the lesson we have students brainstorm all the different things about their class that they can determine from reading the graphs. This is a nice chance to overlap with Language Arts. We put the results on a hallway bulletin board (it's big) to share with our fellow classmates.