# Pattern Block

Team Members and grade level they teach:
• Tammy Kraft – LBSS (Algebra 1 Honors) – June 12
• Becky Morgan – (Math 6 AAP 5th grade) – May 29
• Stacey Mayo – LBSS (Math 7) – June 10 Changes indicated in red signify adjustments to the lesson for my 7th grade Power Math class.
• Tricia Drummond – Sangster(Math 7 AAP 6th Grade) – June 2
• Julie Green – LBSS (Math 7 Sped) – June 6
Standard(s):
PRS 1 : Represents numbers accurately and demonstrates an understanding of number relationships.
PRS 2: Computes numbers with fluency and makes reasonable estimates.
7.1.c: Compare and order fractions, decimals, and percents and numbers written in scientific notation.
ALG 1.1 : The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.
Lesson Study Title:
If this is a whole……and that is a whole made of different sized parts shared with different numbers of people, who gets more?
Overview of the the lesson and how it connects to STEAM: (Please attach the task & blackline masters)
Our lesson explores equivalencies, reasoning up and down, and using non-standard representations to determine equivalencies among different representations of wholes. STEAM connection – Connect proportional thinking to planning and executing designs in art, engineering, architecture, and multiple other disciplines. Students will explore, discover and understand that basic fractions, ratios, and proportions are the foundation upon which many advanced mathematical concepts and algorithms are derived.
Adjusted lesson for Math 7 Power Math (support class): After working through pattern blocks activities and other different representations of whole/part relationship, students in Power Math support class reported that solving problems using different methods of representing their thinking was very helpful in helping them remember how to work with numbers in fraction and ratio form. They requested MORE problems, especially in the area of comparing and ordering rational numbers in fraction form. This skill relates to all areas of STEAM but as two of my students related, being able to compare fractions mentally using different strategies will help them identify correct wrench sizes when working on car engines and accessories. Other students identified scaling recipes up or down as a situation in which knowing how to compare ratios would be helpful. Since not all students in the class were interested in wrenches or recipes, but all were interested in the end-of-the-year pizza celebration, we (the class and I together) wrote a problem to determine which of my two support class would get more pizza per student.
Anticipated student strategies: (BOARD PLAN with Sequencing and connections)

TLW:
• Use manipulatives & pattern block packets to explore different representations of wholes.
• Determine which of the two support classes will get more pizza per student at the end of year Pizza Celebration.
• work, present in individual and small collaborative groups
• Use various representations to compare and contrast strategies to include: posters, graphs, charts, enlarged marker work from whiteboards
• Connect reasoning from one presentation to another, will follow and connect reasoning of other groups

Formative Assessment strategies: (Rubric/checklist)
• Assess through observation
• comprehension questions
• reflection sheet
• misconception sheet

Goals
What are your mathematical goals for the lesson:
1) What do you want students to understand as a result of this lesson? …as a result of this unit?
2) What mathematical processes are you working to develop?
3) How does this lesson contribute to their continuing development as learners?
Prior Knowledge
In what ways does the task build on students’ previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin to work on the task? What questions will you ask to help students access their prior knowledge? Goals:
• abstract reasoning and critical thinking skills
• perseverance in problem solving
• understanding that “wholes” are represented differently
• Compare part/whole relationships: Students will be able to correctly determine the portion of a pizza order (more than one pizza, cut into different numbers of slices) a person from two different size groups will get, and determine which group gets more pizza per person.
Anticipating Student Responses
Identify the ways in which the task can be solved.
· Which of these methods do you think your students will use?
· What misconceptions might students encounter?
· What errors might a student make?
Expectations
What are your expectations for students as they work on and complete this task?
· What resources or tools will students have to use in their work?
· How will the students work — independently, in small groups, or in pairs — to explore this task? How long will they work individually or in small groups/pairs? Will students be partnered in a specific way? If so in what way?
· How will students record and report their work? • Pattern blocks
• number cubes
• whiteboard markers
• paper and colored pencils
• student constructed paper fraction circles (available; no students chose this option)
• draw pictures
• system of equations (did not apply to our problem)
• guess & check
• mental math
• Same Number of Pieces strategy (this was the strategy I used when solving this problem outside of context)
• Fair Shares strategy (some way to divide multiple pizzas into equal shares)
• Students may divide all pizzas into eighths (common commercial practice), which will leave leftover slices to divide among the individuals in the group.
• Students may not realize they must divide leftover slices among the individuals in the group.
• Students may set up ratios without labeling part and whole correctly; or may set up correctly labeled ratios without making sense of computations.

Launch
How will you introduce students to the task so as not to reduce the problem solving aspects of the task(s)?
What will you hear that lets you know students understand the task(s)?
Explore/Monitoring
As students are working independently or in small groups:
· What questions will you ask to focus their thinking?
· What will you see and hear that lets you know how students are thinking about the mathematical ideas?
· What questions will you ask to assess students’ understanding of key mathematical ideas, problem solving strategies, or their representations?
· What questions will you ask to advance students’ understanding of the mathematical ideas?
· What questions will you ask to encourage students to share their thinking with others or to assess their understanding of their peers’ ideas?
How will you ensure that students remain engaged in the task?
· What will you do if a student does not know how to begin to solve the task?
· What will you do if a student finishes the task almost immediately and becomes bored or disruptive?
· What will you do if students focus on non-mathematical aspects of the activity (e.g., spend most of their time making a beautiful poster of their work)?
Whole Class Discussion/Selecting, Sequencing, Connecting
Which solution paths do you want to have shared during the class discussion in order to accomplish the goals for the lesson?
· Which will be shared first, second, etc.? Why?
· In what ways will the order of the solution paths helps students make connections between the strategies and mathematical ideas? Introduction option 1:
• Hand students a pattern block handout and have them work though to determine the relationships between the picture and the fraction.
• Discussion to follow.

Introduction option2:
• Hand students the department store handout and manipulatives and have them work individually to solve the problem to determine the relationships between the patterns.

• Group students and ask them to work on option 1 pattern block packet.
• Discussion to follow

Introduction Option 3:
• Heart activity: They will divide the sets up into different parts.

Introduction Option 4:
After completing pattern blocks, heart and Fractions and Their Parts activities, present the number of pizzas ordered and students in each Power Math class. (8 pizzas ordered for seventh grade class of 14 students; 4 pizzas ordered for eighth grade class of 9 students).

Since the seventh grade students were the class of 14 designated to share 8 pizzas, they were immediately and totally engaged in the task, tenaciously involved in making sure the party plans were “fair.” I knew that the task would challenge them but for early finishers a follow up task planned was to propose a “best” way to equalize the amounts of pizza between the two classes.

Students in this class tend to spend more time on presentation than on reasoning. I chose to eliminate posters for presentations, allowing students to use whiteboard markers on desks or labeled manipulatives, photographed and displayed large on the interactive board for explanation.

Sequencing: I expected to find pizza/people as well as people/pizza strategies, and wanted to show both ways as equally valuable if handled correctly. I wanted a pizza/people strategy first, then a people/pizza strategy second — incomplete or incorrect work OK. Third, I wanted a complete, perhaps incorrect solution using either strategy, and fourth, I wanted complete, correct solutions using both strategies.

Assessment
What will you see and hear that lets you know that students in the class understand the mathematical ideas addressed in the lesson? When students are able to correctly identify that pizza/people is a comparable quantity AND that a higher unit rate (pizza/ 1 person) OR a lower unit rate (people per 1 pizza) is better, I will know that students understand the mathematical ideas addressed in the lesson.
References: