SWBAT show what they know about integer operations, rational number operations, and equations on the first mock math assessment of the year.

This is a two day test; day two includes open response questions

90 minutes

Students have 90 minutes, one math period, to complete the mock assessment. It is set up like a state exam. Desks are separated, dividers are spread through-out the class, along with noise-canceling headphones.

All students received a reflection assignment yesterday. Students are reminded that it is due the next day. Those who do not complete the tests are given additional time during study halls, but are warned this will not happen on future mock assessments. The test includes 10 open response questions; the challenge on this day is not timing, it is showing work, and often, students finishing too quickly. I motivate students to take their time annotating and showing work on their papers by telling them that I will be rewarding students with paycheck points if I see them doing these things during the test. I have a yellow notepad where I write down names for those who earn paycheck credits or deductions on a daily basis. Students are well aware of what I am writing as I walk around the room with my notepad. Being open and transparent about my actions also puts anxious students at ease.

60 minutes

I calculated the average number of points scored for each question by all students. Then I compared each of these values to the total number of points possible per question. This is how I was able to come up with the three questions most challenging to students: #43, #38, and #40

The resource document attached depicts each of these three questions and solutions. The following are some skills I review with students during class or during remediation periods along with some feedback and strategies to improve performance on open response questions. I determine whether the question needs to be reviewed whole class or during individual one-on-one conferences by taking a close look at the frequency of points earned per question. I use question 43 below to model how I break down each of the three questions and their skills to guide my instruction or conferences with students.

**Question #43: Fractions **

**Skills**:

- Calculating fractional pieces of pizzas with 12 slices
- Use total number of slices to calculate number of pizzas consumed as a mixed number
- Applying knowledge of fractional pieces to make inferences about whole pieces
- Applying information from part A to answer question in part C
- Synthesizing facts from the problem and calculated facts to form a holistic understanding of the context of the situation

**Questions to ask:**

- What does Part A ask you to find? The number of slices or the number of pizzas?
- The information for the amount consumed by each friend is given in two different ways. How is this information given for each friend?
- How can you use the information provided to calculate the total number of pizzas consumed?
- How much pizza did Darius, Hannah, and eat? How many slices is that? How many did Alex eat? How do we calculate that?
- Once we calculate the total number of slices consumed, how can we calculate the number of pizzas this reflects? Does is HAVE to be a whole number?
- In part B, the answer does need to be a whole number. How can we use the information from part A to answer part B?
- Draw a picture for part C. How many slices does each pizza have?
- How do you calculate the amount left over?

**Strategies to discuss:**

- Drawing a picture
- Making a list of important information
- For Qs about fractions: keeping separate the facts about whole pieces and fractional pieces

**When to address:**

Since 49 out of 67 students (73%) received zero points for this question, not only am I prepared to review this question during class rather than remediation blocks, I am also using the skills and concepts used to inform my future instruction, such as the problems I choose to include in Do Now, Exit Ticket and Homework assignments.

As stated in the previous lesson, these data analysis processes are time intensive, but are also great tools to inform instruction and remediate major concepts.

As a last point, I am very fortunate to have a data team that is responsible for collecting this data and managing a platform, Illuminateed.com that allows me to save time creating and analyzing data. Once upon a time however, I was responsible for doing this on my own and found ways to use Excel to create formulas that would allow me to analyze frequencies in open response questions. Here's a video tutorial that shows how I used "countif" formulas to help analyze my data: