Transcript CCSS Practices and Line Dance
Common Core State Standards Mathematical Practices Jeremy Centeno
You would never hear someone say :
I am not very good at reading.
I can’t read.
You do hear people say:
I am not good at math.
I can’t do math.
When I was a kid math was my worst subject
What is the difference?
The difference between the USA and other higher performing nations is that a culture of learning math is established from the beginning of a students career in school.
Students are informed and taught everyone can do math.
What are the following?
• • • • Cryptanalyst Computational Biologist Mathematical Physicist Actuary $137,780/yr $150,000/yr $166,400/yr $160,000/yr
• • The way we taught students in the past simply does not prepare them for the higher demands of college and careers today and in the future. Your school and schools throughout the country are working to improve teaching and learning to ensure that all children will graduate high school with the skills they need to be successful. In mathematics, this means three major changes. Teachers will concentrate on teaching a more focused set of major math concepts and skills.
This will allow students time to master key math concepts and skills in a more organized way throughout the year and from one grade to the next. It will also call for teachers to use rich and challenging math content and to engage students in solving real-world problems in order to inspire greater interest in mathematics.
Class Building/Corners
• • Look at the posters in the room Pick which is your favorite math concept to teach: – Operations: Addition/Subtraction/Multiplication/Division – Place Value: Skip counting/Base Ten/ Greater Than/ Less Than/ Equal To – Measurement – Geometry Think about the following Question: – Why is this concept your favorite concept to teach?
Timed Rally Robin
Corners Continued
• Pick your corner by least favorite concept to teach Think about the following Question: Why do you feel this concept is your least favorite concept to teach?
Timed Rally Robin:
Team Building/ 4 Corners Name Tag
• • Take a Piece of notebook paper and fold it so that it stands on its own Write Your Name in the Center – – In the Upper Left hand corner draw a shape that represents you In the Upper Right hand corner pick an operation that represents you – – In the Lower Left Corner pick your favorite temperature In the Lower Right Hand corner write your favorite number
• • • • •
Team Interview
Person Number 1 will ask person number 2 to answer upper left hand corner out loud for the group Person Number 2 will be standing and Answer Question Person Number 3 will make a connection Person Number 4 will praise Person 1 turns Mat and Person Number 2 becomes person number 1 and repeats the same process (Continue until I say stop)
Reflection/Talking Chips
• • • • Think about the activities for class building and team building How would you use these activities with students in a math class? Why is it necessary to team build and class build in order to have engaging activities in your classroom?
When the signal word is given anyone can speak but they must put a chip in as they talk.
All chips must be down on the table if there is time pick up chips and continue conversation
Mathematical Practice #1 Problems and Perseverance
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals plan a solution . They make conjectures about the form and meaning of the solution and pathway rather than simply jumping into a solution attempt. They gain insight into its solution. They consider analogous problems, and try special cases and simpler forms of the original problem in order to monitor and evaluate their progress and change course if necessary. … —CCSS
CCSS Mathematical Practice #1
• I can try many times to understand and solve a math problem.
Key Points
• • • • Life Happens (Not just a Chapter in a Book) Puzzler’s Disposition (A good puzzle creates a drive to succeed) Toolkit (Need to solve) Hard problems broken into simpler problems
CCSS Practice #1
Practice: #1 Make Sense of problems and perserver in solving them Three Main Points:
Make a Plan
Self Monitor and Explain
Demonstrate understanding by corresponding Example: Student Friendly Definition:
I can make a plan, explain my answers, and show how I did it; then I can try another way
My Number Bond Name Tag
3 3 3 Jeremy 6 3 + Centeno 7 7 10 10 = 3 + 10 = 13
Choose Three Ways
• • • • Each person will get a math problem On your graphic organizer you will chose three ways to solve your problem and show how you solved it You will work on your own first When you hear the signal word begin
Numbered Head Together
• • • • • • Person number one reads their problem Everyone Answers their problem without looking at each others board As each person gets done stand up When all people are standing discuss how each of you solved the problem Agree and praise/ Or Coach and Praise Repeat with person number 2
Video
• https://www.teachingchannel.org/videos/pro blem-solving-math?fd=1
• http://www.insidemathematics.org/in dex.php/classroom-video visits/public-lessons-word-problem clues/438-word-problem-clues lesson-5
Mathematical Practice #2 Reason Abstractly and Quantitatively
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize— to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to reasoning entails habits of pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. —CCSS
CCSS Mathematical Practice #2
• I can think about the math problem in my head first
Practice: #2: Reason Abstractly and Quantitatively Example:
CCSS Practice #2
Three Main Points:
Makes sense of quantities and their relationship to the problem
Bring complementary abilities together
Use reasoning that entails creating a coherent representation Student Friendly Definition:
I can think about the math problem in my head first
Math Strings Mental Math
• • • • • • The number of fingers on two human hands Subtract the number of toes on one human foot Multiply it by the number doughnuts in a half dozen Divide by the number of eyes on a human face Add to it the number of hearts in a human body The answer is? 16
Math Task Cards/Word Problem Activities
• • Taking a look at Task Cards Taking a Look at Activities
Decontextualizing/ Recontextualizing
• • • How many buses are needed for 99 children if each bus fits 44 students?
Find the Answer How did I come about my answer? (recontexualize)
Video
• https://www.teachingchannel.org/videos/thir d-grade-mental-math
• http://insidemathematics.org/index.p
hp/classroom-video-visits/public lessons-proportions-a-ratios/199 proportions-a-ratios-problem-1
Mathematical Practice #3 Construct Arguments and Critique Reasoning
Mathematically proficient students … justify their conclusions , communicate them to others, and respond to the arguments of others. They … … Elementary students can distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. construct arguments using concrete referents listen or read such as objects, drawings, diagrams, and actions. Such arguments can improve the arguments. —CCSS make sense and be correct, even though they are not generalized or made formal until later grades. … Students at all grades can the arguments of others, decide whether they make sense, and ask useful questions to clarify or
CCSS Mathematical Practice #3
• I can make a plan, called a strategy, to solve the problem and discuss other students’ strategies to make sense.
Key Points
• • • • • • • Children like to talk but explanation is difficult Focus on “Shared Context” Interest Based Student should not critique from desk Key is to “Show as well as tell” Give Depth not one process problems Challenging problems worked on together creates a natural pull to reason
CCSS Practice #3
Practice: #3: Construct viable arguments and critique the reasoning of others Example: Three Main Points:
Understand and use stated assumptions and definitions
Construct arguments using objects, drawings, and actions
Listen, read, and critique to find out what makes sense Student Friendly Definition:
I can make a plan.
I can tell my partner how I did it and listen to how they did it too!
Talk about it!
Find the Fiction
• My number is 100.
1.I can be broken into 4 parts equally 2.I represent a millennium 3.My quantity in pennies is equal to a dollar
Find the Fiction
• • • • • On your board write the number of the statement that is fiction and write the word fiction next to that number (DO NOT SHOW ANYONE) Example: 4 Fiction When you hear the signal word discuss with your group one at a time your answer. Come to a consensus Answer: 2 is the Fiction Praise: Expert Thinking
Page 6.32
Partners take turns, One solving a problem while the other coaches.
100% Engagement!
Teacher Coach 0 % Engagement
How Many Ways Task
• • • • How many ways can I make 28 cents?
How many ways can I make 28 cents without quarters?
How many ways can I make a 5 inch tower with 1 inch cubes using 1 white cube and 4 blue cubes?
Now try with 3 white and 2 blue cubes.
Consideration
• Young students should not developmentally be held accountable for critiquing another students argument.
• http://insidemathematics.org/index.p
hp/classroom-video-visits/public lessons-proportions-a-ratios/204 proportions-a-ratios-problem-3-part-c
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Mathematical Practice #4 Model Mathematics
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life…. In early grades, this might be as simple as writing an addition equation to describe a situation.… Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation…. They are able to quantities in a practical situation and relationships using such tools as diagrams, two way tables, graphs…. They… identify reflect important map their on whether the results make sense…. —CCSS
CCSS Mathematical Practice #4
• I can use math symbols and numbers to solve the problem.
Practice: #4 Model with mathematics Example:
CCSS Practice #4
Three Main Points:
Reflect on whether the results make sense
Apply the math they know to solve problem in everyday life
Map relationships using tools Student Friendly Definition:
I can use symbols and numbers to solve problems
Children are Curious about the World
• • • • • Use of real life interest Play: Experiment, Tinker, and Push Buttons to see what happens Curiosity: Size, Shape, Fit, Quantity, and Number To catch a ball what does one need to figure?
Math is not a collection of skills that are demonstrated
What does this Array tell us?
Why Arrays?
Peter Penguins Clues
• • • • • • As a team use your mats to see who is person 1,2,3, or 4 Person 1: Pass out clue cards Person 2: Colors in Answer Sheet when done Person 3: Checks all Answers Person 4: Praises if correct Turn board for next game
• http://www.insidemathematics.org/in dex.php/classroom-video visits/public-lessons-proportions-a ratios/202-proportions-a-ratios problem-3-part-a
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Mathematical Practice #5 Use Tools Appropriately
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet…. Proficient students are sufficiently course to make familiar sound decisions with tools appropriate for their grade or about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. —CCSS
CCSS Mathematical Practice #5
• I can use math tools, pictures, drawings, and objects to solve problems
CCSS Practice #5
Practice: #5 Use appropriate tools strategically Three Main Points:
Be familiar with and consider all available tools
Use Technology tools to deepen understanding
Identify and Use other math resources Example: Student Friendly Definition:
I can use all available tools and technology appropriately when solving math problems
Key Notes
• • • • • • • Make a list of standard tools in classrooms Pencil and Paper Area Model of Multiplication Many Choice Options for Students Student made decisions on tools Different problems to create choice of tools Proscribed or Prescribed tool activities
Number Lines
• • • • • • •
Blind Sequence
Person Number 1 distributes one card face down to each person Each person puts their initials on the back to identify their own card Each person looks at their card and describes it to the group Once they have completed that keeping cards face down the group will sequence the cards Once the group feels they have properly sequenced they will turn cards over If correct praise if incorrect discuss how the cards should be placed then praise If a person forgets what they have they may look at their card only
• http://www.insidemathematics.org/in dex.php/classroom-video visits/public-lessons-numerical patterning/223-numerical-patterning problem-2
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Mathematical Practice #6 Attend to Precision
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They careful state the meaning sign consistently and appropriately. They are quantities in a problem. They of the symbols they choose, including using the equal about specifying units of measure, and labeling axes to clarify the correspondence with calculate accurately and efficiently …. In the elementary grades, students give carefully formulated explanations to each other…. —CCSS
CCSS Mathematical Practice #6
• I can check to see if my strategy or calculations are correct.
CCSS Practice #6
Practice: #6 Attend to Precision
Three Main Points:
Communicate precisely and use clear definitions State the meaning of the symbol Specify units of measure Example: Student Friendly Definition:
I can carefully explain to my partner how I came across my answer and why I think it is correct
Key Points
• Focus on: – Precision of Communication – Speech and Writing – Specify units in numerical answers, graphs, and diagrams
Vocabulary
• • • • • • • • Use in context Children build their own definitions Refine definitions Make Precise Holistic Imagery Draw a triangle Meticulous use of vocabulary and symbols Clarity of Communication
Draw a Triangle
Match Mine
• • • • • • Assign roles of sender and reciever Sender Creates the arrangement Sender Directs Reciever Partners Check Praise and Plan Switch Roles
• http://insidemathematics.org/index.p
hp/classroom-video-visits/public lessons-numerical-patterning/221 numerical-patterning-introduction part-c
•
Mathematical Practice #7 Look/Make Use of Structure
Mathematically proficient students look closely to discern a pattern or structure . Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property…. They also can step back for an overview and shift perspective . They can objects…. —CCSS see complicated things objects or as being composed of several , such as some algebraic expressions, as single
CCSS Mathematical Practice #7
• I can use what I already know about math to solve the problem.
CCSS Practice #7
Practice: #7 Look for and make use of structures Three Main Points:
Find a pattern
Use what you know
Solve the problem!!!
Example: Student Friendly Definition:
I can use what I already know to solve a problem using patterns
• •
Key Points
Children look for structure Mathematics is a structured language – Children learn orally – Two Sheep plus three sheep makes five sheep – Two hundred plus three hundred makes five hundred – Two wugs plus three wugs makes five wugs no matter what a wug might be – So two eighths plus three eighths makes five eighths
Word Problem Take a Deep Breath!
• • • • • • • Mr. Centeno had a fruit fly problem On day 1 there were two fruit flies.
On day 2 there were four fruit flies.
On day 3 there were six fruit flies.
How many fruit flies would Mr. Centeno have on day 5?
Answer: 10 What was the pattern? +2
Line Ups
• • • • • • Students each receive a card When the signal word is given students must line up according to sequence They may or may not talk during the line up If they talk they must discuss why and where they should go Once done look at line up and determine if correct Praise when done
• http://insidemathematics.org/index.p
hp/classroom-video-visits/public lesson-number-operations/179 multiplication-a-divison-problem-3 part-b
Mathematical Practice #8 Repeated Reasoning
• Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal…. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details . They continually evaluate the reasonableness of their intermediate results. —CCSS
CCSS Mathematical Practice #8
• I can use a strategy I used to solve another math problem.
CCSS Practice #8
Practice: #8 Look for and express regularity in repeated reasoning
Three Main Points:
Notice if calculations are repeated by looking for methods Attend to detail Often evaluate results (check understanding) Example: Student Friendly Definition:
I can look for shortcuts, use steps to solve problems, and see if it makes sense
Key Points
• • • Students should draw conjectures Look for patterns in results Look for patterns in what is being done
Repeated Pattern Activity
Directions. Multiply the middle number by itself. Multiply the outer numbers to each other. Compare the products 5,6,7 3,4,5 6,7,8 What conjecture can you come up with?
What is 29x31 and why?
What would the Algebraic formula look like?
Expressing Regularity
Start with 28 and Respond to me: +10 Repeat Start with 28 and Respond to me: +9 Repeat What conjecture can you make?
Start with 100 and Respond to me: +10 +99
• • • • • • •
Quiz Quiz Trade
Students stand up, hand up, and pair up with a partner Partner A quizzes partner B Partner B answers Partner A praises partner B if he or she answers correctly/Coach if not Switch roles Trade Cards Repeat
Video
• http://www.youtube.com/watch?v=k ZxNldBEU6o
Resource
• http://www.k 5mathteachingresources.com/1st grade-number-activities.html
Contact Me
Jeremy Centeno [email protected]
Website: https://sites.google.com/a/bay.k12.fl.u
s/jeremy-centeno/