Using the Timed Tests ap on their iPad, my students spend 10 minutes taking their timed tests as a warm up in the morning before they are off to specials, or anytime they are free to practice. The tests are set for individual goals. Some have them set at as many as 100 problems in both division and multiplication. Other students may have the timed test set at as low as 80 problems in 4 to 5 minutes with a range of facts 1-10 or 3-12, depending upon their needs. The idea is that they need to achieve growth, no matter how small. I set the ranges individually for them, so that their personal goals are met. While fluent multiplication facts should have been mastered in third grade according to 3.OA.A.3, my students need to be more fluent in order to prepare them for learning their factor pairs to 100 as the standard 4.OA.B.4 demands.
The ap has a records page where the percentages are displayed along with the date. This is a great resource tool to create a graph from. Sample Timed Test record
Closure of Warm up: I asked for all students to look at their records. I asked how many students had shown growth? How do you know that from looking at your records? Is it easy to tell from how it looks on this page?
Students raised hands, and offered up their opinions about how they were amazed that it really helps to practice. I know there was a lot of anxiety about studying math facts in my classroom. This ap relieves it because they know their goals are correctly set for their needs.
Guiding Students to Understand the Purpose of Graphing: After we discussed finding the data on their timed tests, I asked the question: Would there be an easier way to show your progress than just a written list on your iPad or notebook? What would be a really quick way to see if you were growing or not over time?
To help them understand the question better, I showed images of graphs from the internet on the SB. The first image showed a column graph "Our Favorite Fruits." This particular graph opened up conversation about what a bar graph is intended to do. We searched for more to examine more thoroughly and compare.
Examine a Bar Graph Online: We chose a bar graph from mathisfun.com to examine more closely. We identified the title and discerned what the graph was saying to us. From the graph, I created a list and then we compared it to the chart that is shown on that page ( click "visit site.") We compared our understanding with the chart as students could see how we made a chart from the graph. I explained that soon we would make a bar or column graph from a chart of our personal data.
Prepare for the Activity: We listed on the white board important points about bar graphs on the right. Lesson Notes on Whiteboard Students copied these in their notebooks. Notes on Data and Bar Graph (This photo is the complete set of notes just prior to graphing.) We discussed how the bar graph we were looking at was a little confusing because the numbers were not listed on the lines, but on the bars. We decided that it would be more clear if the numbers were located right on the lines. That way, if we needed to use a number in between, we could graph it more accurately.
I asked if graphing our data would be a way to show our data more clearly? They agreed. I asked them if a bar graph would show a comparison? What would we be comparing? Many students kept saying that we would compare the "multiplication facts." I had to guide them to understand that they were comparing their growth of fluency of math facts over a time period.
Giving the Graph an Overall Title: We decided together that the best overall title that would specify what the graph is about, would be: My Multiplication Facts Growth Over Time. We decided, with my guidance, how we would label the two axes. On one axis, we decided to label it: Number of Problems Mastered. On the other axis: Date of Test. We would talk about the scale of the graph when we were ready to begin graphing.
Student Inquiry for Further Discussion: One student asked if she could make a line graph. I told them that a line graph would be perfectly appropriate and I brought a line graph up in one of the image samples from online. I told them that I wanted them to work with a bar graph first. This decision was based on my class data from MAPS testing that shows that these students have not mastered bar graph concepts yet from standard 2.MD.D.10 & 3.MD.B.3. I can't move onto teaching them about line plots using fractions until these standards are more fluent!
One student asked about stem and leaf plots. I brought up a sample so they could see how a stem and leaf plot would not be an appropriate graph, because the "time" factor would not be represented. We talked about how it would be more appropriate for things like weights or test scores in a whole class. I was pleased that he was showing some thinking about other graphs.
(This whole section of this lesson supports MP5: Use appropriate tools strategically because of all the use of technology, data, and our discussion about the graphs. )
I asked students what they thought we should do with their data from their Timed Test ap? One girl replied that we should make a graph next. I told my students that I wanted them to be thinking how they would show the data on a graph.
I knew I needed to help them understand that the data needed to be really clear and that it should show their progress. I mentioned that some students did multiple tests on a given day. How would we show the growth from day to day if there was 3 or 4 entries on one day? We discussed this and decided that it was best to take the greatest score from that day. I told them that we needed to remember that we were comparing data over a period of time. This supports MP2 and MP3. These students were using their reasoning and logic skills to come to the conclusion that they only numbers that mattered for any given day were the largest score! Student noticing his progress. One student mentioned that if we wanted to show growth on that given day, we could make that particular bar as many different colors as necessary to show the different tests that day. That was a great idea!
I think they will be mastering their 3rd grade standard after this lesson because of their extended reasoning that was showing up in their discussion.This indicates the conceptual development that CCSS and the Math Practice Standards support.
Students listed their data in their notebooks in either a chart or list. Personal Data Listed
After the data was listed in their notebooks, I visited students to see if they could predict what their bar graph bars would look like. I did this so students could visualize how their graph would look before they drew it. I interviewed two of my students: Predicting how the graph will look. This student mentions her fluctuations in scores and can predict that the graph will be "up and down, up and down." The second student had data that showed steady progress and she could easily predict that the bars would go up. Predicting how the graph will look: Take Two.
As soon as my students were done listing their data in their notebooks, I called them back to the Smart Board to discuss the meaning of "scale".
I asked: How do we know what numbers to put up the vertical axis of the graph? I defined axis for them. I asked: Which way is best for our graph paper to be, vertical or horizontal ?
I opened a page on the SB that I had prepared with a grid. I titled it with our title and drew and wrote the word "scale" on it. I defined the word "scale" for them. This supported their third grade standard. I guided them along to realize that they needed to set their scale according to the highest score in their data.
One student asked a great question! "Some people have one hundred percent. How will it fit?" We tried counting by tens and saw that it made it about halfway up the paper. I told them I wanted us to use most of the paper. One student commented that the scale could be counted by fives. He wondered: "But if it is horizontal, would it make it?" We counted by fives together. We counted off the page! We discovered we needed to turn the paper vertically and count by fives. We could easily allow room for the title and the list of dates below. I drew a quick sample using the grid on the Smart Board. We discovered it was better not to graph the bars right together and to skip a column.
We talked about prior knowledge of what features need to be included on our graph to make it clear to the audience: Title, scale and label axis. They went to work! We used simple 1 cm graph paper, colored pencils and pens.
Below are a couple of samples. Each of them did a good job and the one student listed that he had changed to 100 problems.
Graph 1 & a Closeup of Dates listed on one axis :: This student mastered being able to scale the graph correctly, labeled it correctly and gave it a title. The work was very clean and accurate. If we take a closer look, she listed each date they had tested. Through this, the graph takes on a new meaning for the student. She listed some dates where she made minimal progress , close to the zero mark. It showed her clearly that she did well on days that she made her mind up to work hard. This message to her was eye opening. We discussed how the ap lists the numbers, but when we see it graphed, it reveals our progress and effort too!
Graph sample 2: I adjust the ap when a student masters a particular amount of problems. In this graph, we see that they noted when they switched from 80 to 100 problems. This was a landmark accomplishment for this student.
Although some students were not completely finished with their graphs, I decided to stop the work time and pull them together to discuss their observations and pose questions about what the graph shows.
I asked: What does your graph show you about your own progress?
Students raised hands one by one sharing how they could see that practicing on this particular ap had helped them. One student mentioned that she never thought she would progress to 100 problems in 4 minutes. Another student said he needed to practice more because he noticed that his graph should be "going up higher" like some of his classmates. I decided that he got a clear message from this activity about his possibilities and that hard work pays off!