Session 3 Overview 5 th Grade Level II Course Time Content Materials Needed 8:30 Session Starts Agenda Review Norms Overview the Day s Objectives 8:35 Naked Numbers The Importance of Context Slide 6: Introduce this topic by having teachers share at a table or with a partner why it is important to teach concepts in context. Student Journals Bubble Wrap Task (instructor movie files Day 3) Slide 7-10: Share the next 4 slides that explain the importance of teaching in context. Guide a group discussion around the importance of context and include in the discussion the challenges that teachers face when trying to put concepts into context. Slide 11: Share the next slide on purposeful planning as a solution or one way to address some of the challenges of finding ways to put concepts into context. Emphasize the importance of grade- level planning and delegating different jobs to reduce the challenges of time and work load. Slide 12: Use Dan Meyer s Bubble Wrap Three Act Task to demonstrate the use of context at its best (see http://threeacts.mrmeyer.com/bubblewrap/ for the resources and materials). Have participants experience the three act task. To wrap the session on teaching math context, ask participants to share examples of experiences they use with their students to create those real- life connections. 9:35 Slide 13: Transition to Fractions Important to reinforce the focus of this next section centers around the following standard. Participants can refer to their standards handout. Grade 5 Math Standard NBT.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or Student Journal Fraction Manipulatives
difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Slide 14: Warm Up Task: The Out in Front activity connects yesterday s work with conceptual understanding and estimation to today s work with computation. It simply serves as a refresher. Participants need to be able to describe and model both the whole and the parts. If participants are struggling with how to model; feel free to suggest linear (number line or fraction strips), grid model, or even a circular model will work (this could be a challenge to see if anyone can clearly explain how a student might use the circle model to describe distance as a part of a whole. Slide 15 Using the Frayer Model, ask participants to complete a model for each of the following terms as related to fractions: Whole, Parts, Numerator, Denominator as a table group. Participants will be responsible for having all four completed, but their tablemates will help them fill in the ones they don t do on their own. Frayer Model Sheets (Double- sided, 2 per person) These definitions and working models are important before teachers begin any work with computation of fractions. Students need to go through the same process (in their math journals) in order for them to have a deeper understanding that will lead to the algorithms they will encounter. Slide 16: Van De Walle s Definitions:! Fractional parts are equal shares or equal- sized portions of a whole or unit. They have names that tell how many parts make up the whole. The more fractional parts that make up the whole, the smaller the size of the part.! Denominators tell by what number the whole has been divided and is therefore a divisor. It is the kind of fractional part that is being considered.! Numerators count or tell how many of the fractional parts are being used or considered and are actually multipliers.! The whole is the unit under consideration. It may be a length, an area, or a set of objects.
Slide 17: Building a Strong Foundation! Vocabulary work builds a common language for students and teachers to work.! Students need time internalizing the meaning of fractions before we move to the abstract.! Students need to understand and be able to visualize of as it relates to the various types of the whole. Isabel Beckman suggests that, Students from elementary school through college can correct many mistakes in their work with fractions if they can identify the whole associated with a fraction.! Students need immersion in Fair Sharing before they can begin to add and subtract and understand the need for common denominators. These slides lay the foundation for the work we need to do before we begin addition and subtraction of fractions. Time spent developing this deeper understanding of what we are doing as we work with fraction computation. You may want to discuss why we don t spend the time upfront to be sure students have this conceptual understanding and instead just rush into the algorithm. What are the outcomes of jumping straight into computation without meaning? Slide 18 These problems are provided to open the discussion of building thinking around the whole as compared to the parts. Students often struggle with understanding the whole when it isn t provided. Providing them with opportunities to explore the imagined whole facilitates that bigger picture. Slide 19- The focus here is on developing teachers ability to model thinking and representations for students and allow adequate time for students to explore equal size parts and the fractional names attached to those parts. Question 4 This can be done through overlapping parts of a circle with the parts being halves, fourths, thirds, eighths, and twelfths. Blank Paper (one per participant) Fraction Bars Fraction Addition and Subtraction Video (in instructor movie files Day 3) Slide 20: Illustrating Common Denominators: An 8 minute video showing the conceptual understanding of adding and subtracting fractions with common denominators.
12:00 Lunch 12:45 Slide 21: Is the setup for the task on slide 22. It provides a specific overview of the instructional sequence for teaching addition/subtraction of fractions. Slide 22:Task Participants will develop a learning sequence that begins with the concrete through the representational to the abstract. The focus is to carefully think through the instructional sequence rather than create an elaborate and creative problem. You may want the participants to think of their thinking with regards to the sequence. As they work through the task, have them complete the strategy graphic organizer. Possible questions to provide them with: 1. How will I know if my students are ready for fractional computation? 2. How can I intentionally plan for misconceptions? 3. What open- ended questions can I ask as students are working through each level CRA? Do I need a rubric to assess student work? Strategy Graphic Organizer (1 per participant) Fraction Capture Game (1 per participant) Fraction Dice Game Directions/Fraction Game Board (1 per participant back to back) Create Break for Addition and Subtraction of Fractions (1 copy per participant) If Time or for Fast Finishers: 3 opportunities are provided for participants to explore practice games. If the whole class is finished; divide them into 3 groups. They can rotate through each of the sections: Fraction Capture, Fraction Dice Game or Create Break for Addition and Subtraction of Fractions. You will want to have a space organized for each activity. These activities are designed specifically for practice of concepts the students have mastered. 2:00 Afternoon Break 2:15 Slide 23- - Setting Learning Objectives and Self- Assessment The intent of this portion of the day is to go over the power of setting learning objectives that students are aware of and have the opportunity to self- assess themselves on their current level of understanding as a way to provide feedback to themselves and the teacher. Slide 24- - To start, have participants read Power of Myth. When they have finished reading the article have them highlight a word, phrase, sentence or paragraph that strikes them most. Then, in their table groups have them take turns sharing their word, phrase, sentence or paragraph and why Power of Myth (1 copy per participant) Video: Carol Dweck Two Types of Mindset (instructor files) Student Journal Video Clip: Carol Dweck Math
they chose it. This article is the introduction to the concept of mindset and its connection to learning. Slide 25 Carol Dweck s, a professor at Stanford, published her research findings about the characteristics of successful people in her latest book Mindset: The New Psychology of Success. (Instructor Note: If you haven t read this book I would encourage you to do so just to build your background knowledge) Slide 26 Watch a video that further elaborates on the two types of mindsets. Slide 27 Have participants fold a page in their journal in half to make a quick T- Chart. One side of the T- Chart will be Fixed Mindset and the other side Growth Mindset. Have participants generate ideas for each side of the T- Chart with a partner or their table from what they read and the video clip they watched. Slide 28 & 29 Then to ensure they have a clear understanding of the two types of mindset, talk to them about the characteristics of the two types. Self Assessment Template #1 (on website) Self- Assessment Template #2 (on website) Self Assessment Template #3 (on website) Capacity Building Series Article (on website) Assessment Sort (if you want to ;)(instructor files Day 3) Slide 30 So do you want your students to have a growth mindset? Yes or No? (Anita s way) Turn and Talk discuss why you would want them to have a growth mindset. Call on a few participants to share out the reasons they discussed with their partner. Slide 31 One way to develop students with a growth mindset is by having them self- assess their learning. Slide 32 Video Clip Start at 4:34 Dweck talks about how to develop math students with a growth mindset. Have participants share one idea with a partner of how they could help students be in a growth mindset that either Dweck shared or that her ideas made them think of. Slide 33 Hattie s Barometer of Influence John Hattie did a metanalysis of over 800 studies to find what instructional practices have the largest effect size. The graphic on the slide shows the effect sizes that decrease achievement, what students could achieve without schooling, typical effects of teachers, and the zone of desired effects. His work pointed
out that anything above a.4 effect size has significant effects. Slide 34 Student Self- Assessment and Grading has the highest effect size out of all 138 of the instructional practices reviewed. The effect size is 1.44!! That is huge! There is no other practice that out performs this. Slides 35-40 Have participants do a Cloze Reading of this quote from Hattie. You read the quote and they read the red words as you click. Make sure you look at these slides so you know when to click. Slide 41- How to Do It? Engage students in setting challenging goals they have to be part of the process and the need to understand what success looks like what is the goal for the day, lesson, week, unit, etc. Learning goals should emphasize progress, not ability. It should be connected to student effort and involve students giving feedback to teachers to where they are in the learning progression towards that goal. Slide 42 By doing these things (what was mentioned on previous slide), our students will learn: How to assess their own progress by asking key questions about their learning such as:! Where am I now?! Where am I trying to go?! What do I need to get there?! How will I know I have accomplished what I set out to do? Slide 43 When students are engaged in this kind of process, there are many benefits. Some of those benefits include:! Development of metacognitive skills students become more skilled at adjusting what they are doing to improve the quality of their work! Positive effects for low achievers reducing achievement gaps! Development and refinement of students capacity for critical thinking! Increased mathematics problem- solving ability! Reduction in disruptive behavior Slide 44 Transition to- - So how do you do it? Slide 45 There are lots of sample tools for having students
engage in the process of knowing the learning objectives and then assessing their own understanding of the set objectives. Let s look at a few Slide 46-49 These are some example tools you can use to have students record the learning objectives and self- assess themselves. Participants may have other ideas of things they do that they can share, too. Slide 50 This particular template has students measure not only their understanding, but also the amount of effort they exerted. This is a great template to connect the concept of growth mindset and the importance of effort. Slide 51 This is an example of the template filled in for the 5 th grade standard NBT.3. Talk them through the objectives may not seem as student friendly, but if the language/vocabulary of mathematics is being explicitly taught then students will understand the objectives. Slide 52 This is an example of a template that can be used for the whole day in an elementary setting for all content areas. There is a key at the bottom that tells students what a 1, 2, 3, or 4 means so they can rank their understanding. Slide 53 Another example template. Slide 54 Learning Task Have participants work on developing a set of learning objectives for a standard of their choosing. Give them some time to review the Core Standard and think about the progression of that standard over the course of a week or more. Have them try and develop some learning objectives for that standard and select a learning objective template to put them into the templates are on the website. Do whatever type of grouping you would prefer (individual, partner, small group, etc.) Give them 10-20 minutes (depending on your time) to start their planning. Then as the ending time nears ask a few participants to share out. Slide 55 Additional Resources for more information Education Leadership Resilience and Learning Issue Capacity Building Series file on website Slide 56 Another Resource- - From Jane E. Pollock new book
(co- author of Classroom Instruction that Works with Marzano Feedback: The Hinge that Joins Teaching and Learning.! Closing Quote: Feedback fills the gap between what is understood and what is aimed to be understood. From Hattie and Timperley, 2007 (75 minutes) 3:30 Slide 57- - Session Ends Closing Close the session by asking participants what questions they have and any compliments they have for the group could be things they learned from each other or the instructors. Slide 58- - Ask participants to bring their district curriculum materials for a concept/standard they would like to spend time fleshing out tomorrow. If they have access online, that is fine, too.