How can we assess 3.MD.B.3?

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. [3.MD.B.3]

Teaching-Learning Cycle

Teachers use #MTBoS as a way to find interesting and effective math lessons. Recently, some of us have noticed that assessments are often lacking as this community shares in the work of teaching. So I am proposing the #MTBoSAP (Math Teacher Blog-o-Sphere Assessment Project) as a way to pass along our wisdom and experience assessing students in our mathematics classes. I figured I could start by sharing some work I am doing in one of my courses for preservice elementary teachers.

The teachers are currently researching assessment items related to the Measurement & Data Domain (focusing on Data) from the Common Core State Standards (CCSS) in Mathematics. One of the third-grade standards in that domain is written at the beginning of this post. Because we are partnering with a school district that uses EngageNY, we looked for assessment items that already existed within that curriculum. This is an exit ticket that we found in the Grade 3, Module 6, Lesson 4. 

We thought that this item did a fair job of assessing the last part of 3.MB.B.3 but completely missed the first part, "Draw a scaled picture graph and a scaled bar graph..." So we looked through the rest of the lesson and thought this item from the problem set looked promising.

This item has students "draw a scaled bar graph" (still no scaled picture graph) and asks that they solve "two-step 'how many more' and 'how many less' problems." As we thought about it further, however, we were concerned that it was not clear whether students would use the chart or the graph to answer the questions.

Therefore, I decided to try to modify the original exit ticket in order to assess more of the standard. I got rid of two of the bars and wrote questions intended to have them "draw (a part of) a scaled bar graph" and answer multi-step questions that require some "information presented in scaled bar graphs."

Please complete the bar graph using the following information. 

• The number of books checked out on Thursday was 10 more than the number of books checked out on Tuesday. Draw the Thursday bar.
• 1,480 books were checked out Monday through Friday. Draw the Friday bar.

What are your thoughts about using this modified assessment item to gather data on students' mathematical understanding related to 3.MD.B.3? Do you have a good item for this standard that you'd be willing to share? If so, please share the item or a link to the item in the comments. Also, If you have any other effective CCSS assessment items, please share them on Twitter using #MTBoSAP. Thank you in advance for all you do to advance the profession.

How Many in a Handful?

One of the projects in #MTH221 involves hosting activity stations during a Family Math Night at local schools. Our preservice elementary teachers are assigned a topic (patterning, measurement, data, or probability) and asked to find an activity related to that topic that might interest K-5 students. As a group, they decide on two that they want to run and begin gathering/developing the resource they need to make the activity work.

For example, I found I Have a Handful in the November 1999 issue of Teaching Children Mathematics in the Math by the Month department. I made a poster and began identifying Common Core State Standards in Mathematics (CCSSM) that this activity might address. We encourage our teachers to connect at least two Standards for Mathematical Practice and two content standards. For I Have a Handful, I decided to focus on:

Standard for Mathematical Practice:

• Model with Mathematics [SMP 4]
• Use Appropriate Tools Strategically [SMP 5]

Content Standards:

• Kindergarten: Classify objects and count the number of objects in each category [K.MD.3]
• Grades 1, 2, and 3: Represent and interpret data [1.MD.4, 2.MD.10, 3.MD.3]
• Grade 6: Develop understanding of statistical variability [6.SP.1]
• Grade 6: Summarize and describe distribution [6.SP.4, 6.SP.5a]

Next, I identified some questions I might ask to help make students' thinking visible during the activity and aligned them with the CCSSM.

1. Which shape shows up most often and how do you know? [K.MD.3]
2. How could you record your result on a graph? [SMP 4, 1.MD.4, 2.MD.10, 3.MD.3, 6.SP.4]
3. Why did you use this type of graph to represent your results? [SMP 5]
4. Which shape occurred the most? The least? How many more? [SMP 4, 1.MD4, 2.MD.10, 3.MD.3, 6.SP.5a]
5. What would happen if you grabbed another handful? Why? [6.SP.1]

I decided to concentrate on the first three questions, and using the framework from Orchestrating Discussion (5 Practices), I began to anticipate possible student responses (Practice 1). This lead to the monitoring sheet (Practice 2) that is provided below.

On the second page, I tried to arrange the responses in such a way that they represent movement from a concrete approach to an abstract one. In essence, a rubric reflecting various levels of comprehension related to the idea of creating a display of the results from the activity. It was not as evident, to me, how to break up the questions on pages 1 and 3 using this approach. Perhaps seeing people engage with the activity will make these responses easier to arrange.

In the next post, I will share the results of carrying out the activity and address the remaining Practices (Selecting, Sequencing, and Connecting).