SVMI Concept Development Lesson

Region 5 Mathematics Network Conference SVMIConcept Development Lesson September 16, 2013 Santa Clara County Office of Education

Participants will have the opportunity to deepen their understanding of formative assessment by exploring: The use of formative assessment to support student learning and A formative assessment resource Concerns Goals of this Session

Classroom Challenge Interpreting Fractions (Concept Development Lesson)

Broadening Our Understanding of Formative Assessment • There are five key strategies for Formative Assessment; one is: an d Introductions “Engineering effective classroom discussions, questions, and learning tasks that elicit evidence of learning” Dylan Wiliam

SVMI FAL: Interpreting Fractions • Read through the task and answer the questions the way you think a“typical” student would. • On the back, jot down what you think the students in your classes (or district[s] you work with) might struggle with and why. • Also jot down the big mathematical ideas in this task.

SVMI FAL: Interpreting Fractions Directions to students: • Attempt this task on your own. • Answer as much as you can. Show your work so I (the teacher) can understand your reasoning. Don’t worry if you can’t do everything. There will be a lesson on this material that will help you improve your work.

SVMI FAL: Interpreting Fractions • Collect students’ responses to the task. Make some notes on what their work reveals about their current levels of understanding and their problem solving strategies. • We suggest that teachers do not score students’ work. The research shows that this will be counterproductive.

Introduction to Interpreting Fractions • On your mini-whiteboard show me a rectangle. • Show me a rectangle divided into two halves. • Show me a circle divided into four fourths. • Show me three fourths of this circle. Write three fourths as a fraction representing this quantity.

Introduction to Interpreting Fractions • On your mini-whiteboard show me a line having a dot at its beginning and a dot at its end. • Show me this line segment divided into four fourths. • Show me this same line segment divided into eight eighths. • Show me on this same line segment where to find seven eighths. Write the fraction representation for this quantity.

Introduction to Interpreting Fractions • On your mini-whiteboard show me a set of six buttons using circles for the buttons. • Show me a one half of this set of buttons. Write the fractional representation for this quantity. • What does this fraction represent? • Who would be willing to justify their numerical representation?

Introduction to Interpreting Fractions • On your mini-whiteboard show me a set of five tiles using a square to represent each tile. • Show me a three fifths of this set of buttons. Write the fractional representation for this quantity. • What does this fraction represent? • Who would be willing to justify their numerical representation?

Broadening Our Understanding of Formative Assessment There are five key strategies for Formative Assessment; one is: a “Clarifying, sharing, and understanding learning intentions and criteria for success” Dylan Wiliam

Collaborative Task (Continues with the same mathematical ideas) • Please move into groups of 2 or 3 (self selected). • Each group will be given five sets of cards: • Set A: Symbolic Notation • Set B: Area Models • Set C: Measurement Models • Set D: Set Models • Set E: Fractional Situations

Collaborative Activity • Take turns matching a fraction represented by a number with an area model. • Each time you find a match, explain your thinking clearly and carefully to your partners. • If you think there is no suitable card that matches, create one of your own. There are some blank cards for doing this. • When you have agreed all the cards, place them side-by-side on your large sheet of paper. • Find another group across the room to share your thinking with; have a discussion.

Collaborative Activity • Take turns matching a measurement modelto your selected pairings from the first match of a fraction represented by a number with an area model. • Each time you find a match, explain your thinking clearly and carefully to your partners. • If you think there is no suitable card that matches, create one of your own. There are some blank cards for doing this. • When you have agreed on all the cards, place them side-by-side on your large sheet of paper. • Find another group across the room to share your thinking with; have a discussion.

Broadening Our Understanding of Formative Assessment There are five key strategies for Formative Assessment; one is: and Introductions ”E“Providing feedback that moves learning forward” Dylan Wiliam

Collaborative Activity • Take turns matching a set model to your selected pairings from of afraction represented by a number, an area model, and a measurement model. • Each time you find a match, explain your thinking clearly and carefully to your partners. • If you think there is no suitable card that matches, create one of your own. There are some blank cards for doing this. • When you have agreed on all the cards, place them side-by-side on your large sheet of paper.

Collaborative Activity • Take turns matching a fractional situation to your selected pairings from of afraction represented by a number, an area model, a measurement model, and a set model. • Each time you find a match, explain your thinking clearly and carefully to your partners. • If you think there is no suitable card that matches, create one of your own. There are some blank cards for doing this. • When you have agreed on all the cards, place them side-by-side on your large sheet of paper.

Broadening Our Understanding of Formative Assessment There are five key strategies for Formative Assessment; one is:an Int Roductions ”“Activating students as instructional resources for each other” Dylan Wiliam

Collaborative Activity: Teacher’s Role • Teachers are to: • Listen and watch students carefully. • Note different student approaches to the task. • Notice any difficulties that students encounter, and the ways they justify and explain to each other. • Try not to make suggestions that move students towards a particular approach to the task. Instead, ask questions that help students to clarify and promote thinking.

Whole Class Discussion Please post completed posters. • Which cards were easiest? Why? • How did you decide which cards to match? • How can you justify why the different types of models convey the same fractional part?

Plenary Discussion • Write the fractions represented by a number with each representation. • On your mini-whiteboard: • Show me three fourths of a whole rectangle. • Now, show me three fourths of a set of sticks. • Show me two thirds of a folded paper stip. • Now, show me two thirds of a set of hearts. • Show me one and one quarter pizzas. • Now, show me one and one quarter on a number line.

SVMI FAL: Interpreting Fractions Directions to students: • “Please do this task on your own.” • Teacher collects tasks to take notes on students’ thinking. • “Look at your original work with the feedback questions.” • “What have you learned from doing this lesson?” • “What are you still struggling with?”

Broadening Our Understanding of Formative Assessment There are five key strategies for Formative Assessment; one is: Ti ”Activating learners as the owners of their own learning” Dylan Wiliam

Lesson Analysis/Reflection • What mathematics can students learn, or deepen their understanding of, with this lesson? • What may they struggle with in this lesson? How is the lesson designed to support struggling students? • How is this lesson like and different from what goes on in your district’s mathematics classrooms? • What do you think are the benefits of using a lesson like this? • What can teachers learn about their students from using lessons like this? What can students learn about themselves from lessons like this?

Links to Common Core Standards • Mathematical Content • Number and Operations with Fractions • 3.G.A. 2: Partition shapes into parts with equal areas • 3.NF.A.1, 2, 3: Develop understanding of fractions as numbers • 4.NF.A.1 & 2: Extend understanding of fraction equivalence and ordering • Mathematical Practice • Can explain correspondences and relationships and draw diagrams to help conceptualize and solve a problem.

The Structure of Formative Assessment Concept Lessons • Lesson:The pre-assessment task and the lesson activities are exemplars of the CCSS (content and Practice Standards which have high DOK levels). • Feedback: The lesson provides opportunities for both teachers and students to gather information about their mathematical understanding/skills. Feedback is givento push thinking and learning forward. Thus, there are no value judgments made or grades given. • Revisions: There are opportunities for students to revise/advance their thinking and their work. • Timing: Formative assessment is happening during instruction where there is still time to adapt the lesson to meet the needs of the students.

Questions, Comments, Concerns After looking at a Formative Assessment ConceptLesson, what questions, comments or concerns do you have? • About the lesson? • Implementation of these lessons in classrooms??

“CLASSROOM CHALLENGES” FORMATIVE ASSESSMENT LESSON MATERIALS Silicon Valley Mathematics Initiative (SVMI) Open source: www.InsideMathematics.org (Coming Soon)

SVMI Concept Development Lesson