Elementary Common Core Team Training Math Lesson Summer 2013. Learning Goals. Increase knowledge of the Standards for Mathematical Practices Unpack the Common C ore S tandards using Unpacking Standards Graphic Organizer Success Criteria - PowerPoint PPT Presentation
Elementary Common Core Team TrainingMath LessonSummer 2013
Thank you for joining us today.Introduce presenters.1Learning GoalsIncrease knowledge of the Standards for Mathematical PracticesUnpack the Common Core Standards using Unpacking Standards Graphic Organizer
Success CriteriaIdentify the Eight Mathematical Practices in a lessonUnpack Common Core Standards using the Unpacking DocumentExplain: Participants are aware that they are here today to get a deeper understanding of the common core math so they can go back to their schools and train their teachers! They will be given this slide show to use.
2Parking Lot Questions
Explain: At any point during the day, if you have a question write it on a sticky note and place it on the Parking Lot. We will go over the questions throughout the training.3Good Math StudentsThink about a few students who are really good in math.
How do they approach problems?How do they solve problems?How do they discuss their strategies?
Common Core will have kids thinking out loud, discussing solutions with each other, and explaining their answers.-Stateimpact.npr.org/florida/2013
Read the three questions. Table talk and have 2 or 3 participants share their responses with the whole group. (2-3 minutes)Read the quote at the bottom.This is what a math classroom needs to look like on a daily basis. Even if you feel that what you are doing is workingCommon Core will enhance the learning and make students better at math. Rather than trying to sift through the text book by chapter or blaze through a curriculum map, we should focus on creating mathematicians.http://www.edutopia.org/blog/why-mathematical-practices-matter-jose-vilson
4Standards for Mathematical PracticeWhat are they?
What do they look like in a K-5 classroom?
10 Minutes: MP Activity Use the next 4 slides during this time.
Prior to going over the MP, pass out a sticky note and have participants write the MPs down as they remember them (slides 7 and 8). On the wall, have a Progression Scale (number line) made out of painters tape with Level 0, Level 1, Level 2, Level 3, and Level 4 (slide 9). Have each participant place themselves on the scale. Refer back to it at conclusion of the PPT and have participants rerate themselves (slide 10).
5Do You Know The Mathematical Practices?INDIVIDUALLY:Take a moment and jot down the Mathematical Practices on the sticky note provided.
Give participants 2 minutes.6Do You Know The Mathematical Practices?WITH A PARTNER:Pair-Share: Share with your partner the list you wrote down. Compare your lists.
Give participants 2 minutes to share.7Do You know The Mathematical Practices?Rate YourselfWhat is your knowledge of the Mathematical Practices today? Place your sticky on the scale.
Read the slide to the participants and explain that the next slide will give them the scale to use.
8Do You Know The Mathematical Practices?Progression ScaleLevel 4- I can state all 8 Mathematical Practices and I use them daily in my classroom.Level 3- I can state all 8 Mathematical Practices and I may use them in my classroom.Level 2- I can state half of the Mathematical Practices.Level 1- I can state 2 of the Mathematical Practices.Level 0- What is a Mathematical Practice?
Give participants 2 minutes to place their sticky notes on the scale.
Discuss:Look at the scale as a group. Where did most of the participants rate themselves?
Now think about your school. Where do you think the teachers at your school would rate themselves?
If the group as a whole rates themselves at a level 3 or 4, we will proceed to slides 11-13, but skim through slides 14-30. If the group as a whole rates themselves lower, more time will be spent on the individual practices. We will pick back up at slide 31 watching a video of the practices in a classroom.
9Standards for Mathematical PracticeMathematical Practices1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.We are building more awareness of the MP and providing ideas for implementation.10Standards for Mathematical PracticeThe Standards for Mathematical Practices describe the behaviors of mathematically proficient students.
Standards for Mathematical Practice are what your students will do daily during math lessons .11Structure of StandardsStandards for Mathematical PracticeA set of 8 standards that describe the ways in which the mathematical content standards should be approached.
Standards for Mathematical ContentThese standards define what students should understand and be able to do in their study of mathematics.12HOWWhatExplain:The Common Core State Standards for Mathematics are structured into two sets of standards: The Standards for Mathematical Practice and the Standards for Mathematics.
First Fly In: The Mathematical Practices are a set of 8 standards for all students in K-12 that describe the varieties of expertise that math educators should seek to develop in their students. They are derived from the NCTM Process Standards and Adding It Up (Adding It Up is a document that explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.) Mathematical Practices are the How.
Second Fly In: The Content Standards define what students should understand and be able to do. They are organized by Domains, Clusters, and Standards. The Content Standards are the What. We will be unpacking the Content Standards this afternoon.12MP 1 - Make Sense of Problems and Persevere in Solving ThemMake sense of the meaning of the taskFind an entry point or a way to start the taskFocus on concrete manipulatives before moving to pictorial representationsDevelop a foundation for problem-solving strategiesReexamine the task when they are stuckAsk, Does my answer make sense?
2b, 3cExplain:Students must be given a chance to tackle problems that they have not been taught explicitly how to solve, as long as they have adequate background to figure out how to make progress. Young children need to build their own toolkit for solving problems, and need opportunities and encouragement to get a handle on hard problems by thinking about similar but simpler problemsOne way to help students make sense of all of the mathematics they learn is to put experience before formality throughout, letting students explore problems and derive methods from the exploration.
13What does MP 1 look like in a classroom?Old problem (little or no rigor) Tina had ten balloons. She gave seven of them away. How many balloons did Tina have then?
New problem (with rigor)Burger Barn has one small table that can seat four people. They also have one large table that can seat double that amount. Fifteen (15) people came in at lunch time. How many people did not get a seat?14Presenters share the two examples. Table talk within groups (2 minutes): Discuss differences between the two problems. What are the teaching implications when using rigorous problems in the classroom?
14MP 2 - Reason Abstractly and QuantitativelyMake sense of quantities and their relationshipsDecontextualizeContextualizeRepresent symbolically (ie. Equations, expressions)153cAbstract reasoning is important because it allows students to apply what they have learned in complex ways.15What does MP 2 look like in a classroom?I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me?
Decontextualize the problem:2 + = 516Explain:Decontextualizing this problem starts with the word problem and the students have to determine the equation. Decontextualizations are representations that preserve some of the original structure of the display, but just in number and not in shape or other features of the picture.
The problem is shown as equation with an addend unknown; two add the unknown represented by a square equals five.
16What does MP 2 look like in a classroom?172 + = 5
Contextualize the problem:
I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me?
Explain:This time we start with the problem. The problem is shown as equation with an addend unknown; two add the unknown represented by a square equals five.
Students must be able to take the numbers and put them into context (contextualize) to show understanding of what the equation means.17What does MP 2 look like in a classroom?18How many buses are needed for 99 children to go on a field trip if each bus seats 44 students?
Is the answer: 2r11 or 2 or 2.25?
Recontextualize to get the answer: 3 busesExplain:In decontextualizing a problem that asks how many buses are needed for 99 children if each bus seats 44, a child might write 9944. But after calculating 2r11 or 2 or 2.25, the student must recontextualize: the context requires a whole number answer, and not, in this case, just the nearest whole number. Successful recontextualization also means that the student knows that the answer is 3 buses, not 3 children or just 3.
Table Talk: (2 minutes) What is the difference between decontextualizing and contextualize? Why is it important for students to be able to do both?
18MP 3 - Construct Viable Arguments and Critique the Reasoning of OthersUse mathematical terms to construct argumentsUse definitions and previously established solutions in their argumentsEngage in discussions about problem-solving strategiesRecognize and discuss reasonableness of strategiesRecognize and discuss similarities and differences between strategies19
2a, 3b, 3cExplain:In order to develop the reasoning that this standard asks children to communicate, the mathematical tasks we give need depth.
Problem that can be solved with only one fairly routine step give students no chance to assemble a mental sequence or argument, even non-verbally.
Certain tasks naturally pull children to explain; ones that are too simple or routine feel unexplainable.
The way children learn language, including mathematical and academic language, is by producing it as well as by hearing it used. When students are given a suitably challenging task and allowed to work on it together, their natural drive to communicate helps develop the academic language they will need in order to construct viable arguments and critique the reasoning of others.
http://thinkmath.edc.org/index.php/Construct_viable_arguments_and_critique_the_reasoning_of_others19What does MP3 look like in a classroom?I can make a plan, called a strategy, to solve the problems and discuss other students strategies too.
http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-proportions-a-ratios/205-proportions-a-ratios-problem-3-part-d?Explain:This video shows students using different strategies to solve a proportions and ratio task. The students in the video have already received the problem and are looking at a sample answer to determine if the work is done correctly.
Ask participants to listen closely for examples of MP3 in the video. They should make note of any examples they hear to share with their table at the end of the video.
Play the 5 minute video.
Stop at 3:01.
Ask participants if anyone has attended a Juli Dixon workshop. One of the most noticeable strategies she uses is asking the students, What did he say? and having the students repeat what another student said was their strategy/answer. It was eye-opening to realize that the students do not listen to each other! We must train our students to listen to each other as well as the teacher or they will not be able to critique the reasoning of others.
20MP 4 - Model with Mathematics.Model with manipulatives and much moreModel with a number sentence or equationCheck to make sure the number sentence matches the context of their problemModel with concrete manipulative representationsModel with pictorial representationsHave matching equations for their representations212e, 3cExplain:Important Note: Student are not simply modeling with manipulatives; model goes well beyond the concrete.
Modeling may involve spatial location: a map or diagram models the real thing. Even children in K and 1 can lay out strips of paper in a grid on the floor, name the streets and avenues, place houses and schools and libraries at various locations, and describe the distances and directions to get from one to another.21What does MP 4 look like in a classroom?22I have three cars. My friend gives me some more cars. Now I have seven cars. How many toy cars did my friend give me?Model with PicturesModel with ToolsModel with Symbols3 + = 7Model with WordsI have three cars. I get four more. Now I have seven cars.Captions:Model with Tools Three green unifix cubes and 4 pink unifix cubes are linked together.Model with Symbols An equation of three add an unknown (represented by a square) equals seven.Model with Pictures Three objects are in the first row and four like objects are in the second row.Model with Words I have three cars. I get four more. Now I have seven cars.22Break
10 minute break23MP 5 - Use Appropriate Tools StrategicallyThe purpose is to move students toward a deeper understanding of these tools.Have access to a variety of tools (counters, place value blocks, hundred boards, number lines, geometric shapes, paper/pencil, etc)Need to express in their own words the what, why, and how to help them clarify, perfect, and organize their thinking.
242c, 2eThink about your classroom: Where are your manipulatives located? When introducing allow time for exploration, the more visible the tool , students are less likely to play and find it new.It requires that their learning include opportunities to decide for themselves which tool serves them best.Mathematical tools are only as useful as students understanding of how to use them.
2425What does MP 5 look like in a classroom?Students have easy access to math tools.Students select their own tools.
Unless you are departmentalized your classroom is set up to immerse your students in print. We need to immerse our students in mathematics too.
Table talk where manipulatives are located in their classroom. 2 minutes
Ask a few participants to share what someone at their table shared. 3 minutes
Access to manipulatives is different among grade levels; K&1 in tubs located on storage carts or 4&5 students may have their own personal toolb...