Individualized Instruction as a Formative Assessment Tool

• Content objectives – Translate and solve one-step equations from real-world scenarios
• Literacy/language objectives – Translate and solve mathematical equations by reading, annotating, and discussing problems in groups
• Engagement/interaction objectives – Work in groups to solve one-step equations

Common Core State Standards for Mathematics

• CCSS.Math.Content.6.EE.B.7
  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.
• CCSS.Math.Practice.MP1
  Make sense of problems and persevere in solving them.

The Unit
The focus of this unit was expressions and equations. It spanned several weeks and fell in the second quarter of the school year. The lesson on translating real-world scenarios into algebraic equations occurred at the end of the unit.

Before the Video
Students learned first about expressions and the concept of mathematical phrases being unsolvable. They practiced translating phrases into expressions and vice versa. Students then learned about equations (and the difference between equations and expressions) and how to translate equations. In preparation for the lesson on solving translated equations, Ms. Gay placed students in groups and used examples from language arts to explain the group roles of reader, annotator, translator, and double-checker. She helped students understand the importance of translating problems into equations before they are solved.

During the Video
Ms. Gay began the lesson by reviewing the content and language objectives with students and talking again about the significance of translating equations. She reviewed the group role assignments and duties with students and added a few new words to the word wall. Then, Ms. Gay began direct instruction by modeling how to solve an equation through reading, annotating, translating, and double-checking. She had five stations set up throughout the room, each with a one-step equation based on a real-world scenario. In groups of four, students translated and solved the station’s problem in their assigned roles. As they moved from station to station, their roles shifted. By the end, each group had completed between one and three problems. Each group shared one answer with the class, and Ms. Gay addressed questions or inaccuracies. She assessed student understanding with a “line of learning” and exit ticket.

After the Video
The following day, Ms. Gay spent a bit more time on translation before introducing one-step inequalities. Students applied the five-step method that they had used to solve equations to now solve real-world problem-based inequalities.

Teacher Prep
Ms. Gay planned her lesson and created the worksheets and problems for students to solve, the PowerPoint describing each role, and the line of learning assessment. She determined how she would assign roles and groups, made nametags, and planned for later lessons in the unit that incorporated the same roles.

Prior Knowledge
To participate in this lesson, students needed to have an understanding of translating, annotating, solving one-step equations, and how to work effectively in groups within the learning environment.

Differentiated Instruction
Ms. Gay posted vocabulary words and concepts to a word wall, which provided a visual for students to refer to when helpful (especially for visual and English language learners). She incorporated movement into the lesson for kinesthetic learners by having some students get up to post new words. A PowerPoint slide explaining the duties of each role within the group remained on the projector throughout the lesson as a reference. The “line of learning” assessment tool encouraged students to work in their own way and at their own ability level (through annotated pictures, bulleted lists, essays, etc.).

Group Interaction
Ms. Gay used recent quiz scores on expressions to determine roles. She assigned the students with the highest scores and strongest grasp of translating to be group leaders and those with good scores who clearly understood the concept to be translators. Students with average scores became double-checkers and those who struggled the most were assigned the role of reader (to engage them in the lesson and build confidence right from the start). The students with strong reading skills were assigned to be annotators. Ms. Gay then built the groups of four based on personalities. She believes strongly in creating groups with intention and assigning roles so that each student has a purpose and can lean on one another and learn from others’ understanding. Throughout the year, she placed an emphasis on collaboration and learning from peers and offered students the opportunity and autonomy to choose to work in partners at any time.

• Word Problems handout
• Station Scenarios handout
• Translating Equations Line of Learning handout
• Ellie Mall Word Problem handout
• ELMO projector

Formative Assessment
Ms. Gay walked around the classroom to observe work, listen to conversations, and get a sense of each student’s understanding. To determine if students understood the new skill and were ready to move on, she used a “line of learning.” This assessment tool showed Ms. Gay how students were interpreting the knowledge that they were receiving. Students were given a problem and asked how they would explain the process of solving it to another student (they could answer in any manner they chose). They were also asked to write about what they learned in that day’s lesson. (Sometimes, Ms. Gay grades and returns the line of learning. Sometimes, she asks students to improve their work. Other times, she reviews them and hands them back anonymously so that each student has one that is not his or her own and can learn from others’ work—mistakes included.)

Student Self-Assessment
During the group work, students needed to be accountable to their peers and had to assess for themselves if they were performing the duties of the role that they were assigned and were working collaboratively. Through the line of learning, students were able to assess their own knowledge—did they understand it well enough to explain it to another student? At the end of the lesson, Ms. Gay reviewed the student objectives for the day and asked students if they felt that they had met them.

Summative Assessment
To check individual understanding, Ms. Gay gave students an exit ticket with another real-world-scenario one-step equation to complete on their own. They had to be able to read, annotate, translate, solve, and double-check the answer. For those students who did not solve the equation properly, she reviewed their work one-on-one the following day.

Impact of Assessment
Ms. Gay modified the lesson as she went, based on formative assessments. She noticed that it was taking students much longer than expected to solve the first problem, so she adjusted the time parameters in response. She heard good discussion among groups and, in response, gave them more autonomy as they moved to the next station.