Poway Unified School District Math Leadership Workshop October

Poway Unified School District Math Leadership Workshop October 28 October 30 Caren Holtzman Rusty Bresser carenholtzman@gmail. com rusty. bresser@gmail. com

Goals for the Day • Extend your knowledge for teaching mathematics. • Deepen your understanding of how children learn mathematics. • Build on your understanding of the Common Core content and practice standards. • Develop your leadership skills. • Reflect on successes and challenges. • Examine differentiating instruction and ability grouping. • Plan for upcoming work in your own classroom and with the teachers at your school. • Plan for upcoming work with math leaders and administrators in your region.

Agenda Session 1: Reflecting on Classroom Practice Session 2: Word Problems Across the Grade Levels 11: 30 -12: 15 Lunch (principals arrive) Session 3: Differentiation Session 4: Planning for Collaboration

District Updates

Session 1: In the Classroom

Last session, we suggested that you try out some of the following lessons: -True, False, & Open Number Sentences -Handfuls, Two Handfuls, Missing Numbers -Breaking Apart Today’s Number -Two of Everything Share with your table group: -Successes? Challenges? -What did you notice about student thinking? -Did you have opportunities to share the lessons with other teachers?

Session 2: Examining Word Problems Goals • Engage in experiences that build procedural fluency and provide opportunities for mathematical discourse. • Deepen our understanding of students’ mathematical thinking. • Further our understanding of different word problem types identified in the Common Core Math Standards.

Challenges students face when solving math word problems • With a partner, talk about some of the challenges that students, especially English language learners, face when reading and then solving math word problems. • Be ready to share your ideas with the group.

Challenges The Language: • Vocabulary • Syntax • Comprehending the message • ? The Math: • Problem solving—choosing the right numbers and operations and determining if the answer is reasonable. • Deciding what information is needed and what information is not needed to solve the problem. • Determining what the question is that needs to be answered. • Problem structure: some problem types are more challenging to solve than others. • ?

Sara’s Candies When working on the following problem, make sure to follow the step-by-step instructions for each phase of the problem solving experience.

Sara’s Candies Sara had a bag of candies. She gave 1/3 to Rebecca. Then Sara gave ¼ of the candies she had left to John. After giving candies to Rebecca and John, Sara had 24 candies left in her bag. *Read the problem. Try to picture the problem. Don’t be concerned with the numbers in the problem. * With a partner, re-tell the problem in your own words. From Harold Asturias, Lawrence Hall of Science

Sara’s Candies Sara had a bag of candies. She gave 1/3 to Rebecca. Then Sara gave ¼ of the candies she had left to John. After giving candies to Rebecca and John, Sara had 24 candies left in her bag. *Read the problem. Identify the question(s) you might have to answer.

Sara’s Candies Sara had a bag of candies. She gave 1/3 to Rebecca. Then Sara gave ¼ of the candies she had left to John. After giving candies to Rebecca and John, Sara had 24 candies left in her bag. How many candies were in the bag to start? *Make a diagram that can help you solve the problem, and label all the information that you know. Share your diagram with a partner.

Sara’s Candies: Solve the Problem Sara had a bag of candies. She gave 1/3 to Rebecca. Then Sara gave ¼ of the candies she had left to John. After giving candies to Rebecca and John, Sara had 24 candies left in her bag. How many candies were in the bag to start?

Understanding a Math Problem in Three Steps 1. Read the problem quickly to get a general understanding. Try to picture the problem. Don’t be concerned with the numbers. Retell the problem in your own words. 1. Read the problem again. Identify the question(s) you are asked to answer. 1. Read the problem a third time. Identify information you need to solve the problem. Make a diagram of the problem and label with all the information you know.

Drawbacks of “Looking for Key Words” • Looking for key words can inhibit children from reading through the problem and making sense of it. • Sometimes children can more easily use a different operation to solve a problem: Jose has 10 candies. Karen has 7 candies. How many more candies does Jose have than Karen?

More Strategies to Support Students • Use synonyms for unfamiliar words • Identify multiple meaning words and homophones • Model re-telling the problem using synonyms or gestures, then have students practice re-telling in their own words • Act out the problem or use realia to model the problem • Draw a picture or diagram of the problem • Ask students clarifying questions • Help students become of aware of complex or difficult syntax • Help students identify what the numbers stand for • Pose word problems in familiar contexts • Have students write their own story problems

Break

Word Problems and The Common Core • Kindergarten--Addition and subtraction word problems • Grades 1 & 2—One and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions • Grade 3 --Multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities • Grade 4 --Multiplicative compare problems—using multiplication and division • Grade 5 --Word problems involving addition and subtraction of fractions referring to the same whole

• Grades 1 & 2—One and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions

Teaching Addition & Subtraction “In order to use addition and subtraction effectively, children must first attach meaning to these operations. One way for young children to do this is by manipulating concrete objects and connecting their actions to symbols. However, this is not the only way. They extend their understanding of situations involving addition and subtraction by solving word problems. ” -Chapin & Johnson, Math Matters: Understanding the Math You Teach

What do you notice about these word problems? What strategies might students use to solve them? • There are three fireflies inside the jar. We caught seven more and put them in the jar. How many fireflies are inside the jar now? • I see 3 fireflies inside the jar. I see ___fireflies outside the jar. There are 10 fireflies altogether. How many fireflies are outside the jar? • I see 5 fireflies inside the jar. I see 8 fireflies outside the jar. How many more fireflies are outside the jar than inside the jar? • There were 8 fireflies inside the jar. The children took 6 out of the jar. How many fireflies were left inside the jar? • There were some fireflies inside the jar. The children took 3 out of the jar. Now there are 3 fireflies inside the jar. How many fireflies were there in the jar to start with?

A 3 -4 Example

Teaching Multiplication & Division “Students need a strong and complete conceptual knowledge of multiplication and division. If they don’t, they will have difficulty with more advanced multiplicative situations such as proportions, measurement conversion, linear functions, and exponential growth. Therefore, they need to explore many different types of word problems. ” -Chaping & Johnson, Math Matters: Understanding the Math You Teach

What Comes in 2 s, 3 s, and 4 s By Suzanne Aker

Multiplication and Division Equal Grouping Problems: What do you notice about the following word problems? There are 5 octopuses. Each octopus has 8 legs. How many legs altogether? There are 5 octopuses. There are 40 legs altogether. How many legs on each octopus? There are 40 legs altogether. Each octopus has 8 legs. How many octopuses are there?

Multiplication & Division Equal Grouping Problems • With a partner, write a word problem that goes with each number sentence and talk about what strategies students might use to solve them: 6 x 4 = ____ 24 ÷ 6 = ____

A Fifth Grade Word Problem

Word Problems involving Fractions • Solve the following problem individually, then share your answer and strategy with the people at your table: At Olympics Day, two friends are running in a race. One friend is 5/8 of the way to the finish line, and the other friend is ¾ of the way. Who is winning?

Our work with math word problems this morning has included… -Taking a look at challenges that students face when navigating and solving math word problems -Thinking about teaching strategies that support students while solving math word problems -Anticipating how students might solve math word problems -Analyzing student work samples -Examining a variety of word problem types -Solving math word problems -Considering children’s literature as a context for posing math word problems

Word Problem Lesson • Identify word problems in an upcoming lesson in your textbook • Choose one or two that you will pose to your students • Plan a lesson that includes the following parts: Launch, Explore, Summary • Include in your plan: supporting strategies and questions you’ll ask students • Anticipate how your students might solve the problems • Anticipate any confusion your students might experience • Email your typed plan TODAY to: abarraugh@powayusd. com • After the lesson, collect and analyze student work samples • Bring student work samples from the lesson to our December meeting

LUNCH Please return by 12: 15

Session 3: Differentiation Goals: Explore different strategies for meeting the needs of a wide range of learners Experience a tiered math problem (potential problem of the month) Consider the effects of various grouping practices

In what ways do you organize math time to meet the needs of all students?

Ways to Differentiate Tiering Opening Up Problems (providing more entry points) Offering Choice (different numbers, ___ and ___) Mild, Medium, Spicy Pre-teaching/Premediation (language, set up for challenge) Menu Structure Time as a Variable, Not a Constant (MIT, Growth Mindset) Expectations Extensions/Challenges Individual/Pair/Grouping

An Example of a Differentiated Task

Arches (a possible problem of the month) • Read the task. • Answer the questions from each of the tiers with which you are comfortable. • Try to challenge yourself!

Differentiating by Tiering Tasks • All the tiers involve the same growing pattern. • All students are given an opportunity to engage in algebraic thinking at their level—and everyone has access to the same curriculum content. • The tiers offer a challenge for everyone, while providing access for everyone. • Everyone can participate in the same classroom discussion because everyone is working on the same growing pattern.

Another Example of Differentiation

Differentiating Tasks by Providing Choice Mrs. Garrison’s class found ____ insects. ___ were beetles and the rest were butterflies. How many butterflies did Mrs. Garrison’s class find? 10, 6 13, 8 23, 9 25, 13 ___, ___

Ways to Make 12

Differentiating by Grouping Students • How are the groups are made? • Flexible or fixed? • Within a class (ability) or between classes (tracking)? • Heterogeneous or homogeneous?

What does Jo Boaler say? Students Work to Highest Level

Table Talk What are the key points? What concerns you? What discussions might be productive at your school site?

More Research on Grouping Within class grouping allows for more flexibility than whole grade level grouping. Low ability groups receive lower quality instruction (less content, more drill, more emphasis on management, less encouragement from teachers). The criteria used to determine ability groups is narrow and subjective. Lower income and African American and Latino students are over-represented in low groups. Grouping by skill/need can be productive when it’s targeted and short term. There’s a big range of students even within a group. Ability grouping leads to labeling and differing expectations.

Break

Session 3: Big Picture Planning Goals: Review the regional collaboration model, roles and goals Consider the types of collaboration already occurring in the district Plan for specific collaboration “next steps”

The Model

The District Math Plan PUSD Elementary Math Leadership Roles 1 Math Coach 1 Math Professional Learning Facilitator 1 District Instructional Leader 1 District Instructional Leader 1 Math Professional Learning Facilitator Mentor School Collaborative Schools

Roles The Math Coach supports classroom instruction through grade level planning, demo lessons, co-planning/copd assists with collaboration across region The District Instructional Leader (DIL) becomes strong math teacher and role model works with Lynne H on curriculum units and assessment The Professional Learning Facilitator (PLF) becomes strong math teacher and role model works with grade level works with math coach and principal to identify school pd opportunities The Principal supports math leaders’ work seeks out opportunities to collaborate and pool resources with other regional principals Math Transformations Team (Rusty, Andrea, Care) helps develop district math leaders supports district vision implementation teaching,

Creativity and Collaboration Examples of Regional Work (with support from coach): Number Talk Focus Problem of the Month Grade Level Planning Shared PD Site Math Leaders Exchanging Lessons and Resources Canvas Web Page by Grade Level Within Regions Observations at District Mentor School (Valley) Site specific TLCs opened to other teachers in region (e. g Lesson Study TLC at Valley)

Setting Clear Goals: What do we hope to accomplish through structuring school and regional collaboration?

Expanding Opportunities Read the questions on the posters. Respond with ideas, suggestions, questions.

Regional Planning Get in regional groups with your coach. Discuss where you are, next steps, big leaps. Identify 3 -5 tangible action items including dates and persons responsible for each part.

Summary

Reflections

Thank you!