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Transcript of K-2 Standards and Support Training Office of Standards and Learning Mary L. Ruzga [email protected]...
K-2 Standards and Support Training
Office of Standards and Learning
Mary L. [email protected] Summer 2015
Introductions• Introduce yourself to your table mates
• Show of hands – How many• Pre-K, K, 1st, 2nd, etc., Principal/Assistant,
District Leader, other?• have participated in Numeracy Leader
training?• have read the new standards?• are comfortable with the new standards?
What will we do today:
1. Quick overview of format of the standards
2. Review the standards by engaging in activities which explain and demonstrate the need for possible new pedagogical techniques
3. Review and explore the K-2 portion of the Mathematics Support Document
Accessing the Standards and Resourceswww.ed.sc.gov
BASIC COURTESIES/REMINDERS
Please turn off phones (emergency vibrate)
Please refrain from texting, emailing, etc.
No formal break – take care of personal needs
Logistics (lunch, restrooms)
Participate and respect those around you
Content Standards Process Standards
Portrait of SC Graduate
Process Standards
Mathematical Process Standards
1. Make sense of problems and persevere in solving them.
2. Reason both contextually and abstractly.3. Use critical thinking skills to justify
mathematical reasoning and critique the reasoning of others.
4. Connect mathematical ideas and real-world situations through modeling.
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
Mathematical Process Standards
5. Use a variety of mathematical tools effectively and strategically.
6. Communicate mathematically and approach mathematical situations with precision.
7. Identify and utilize structure and patterns.
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
Content Standards
Format of Mathematics Content Standards
K – 8 Grade Level Content Standards
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
Format of Mathematics Content Standards
K – 8 Grade Level Content Standards
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
In grades K – 8:GradeLevel.KeyConcept.Standard
Number (e.g., K.NS.1) or, if applicable,GradeLevel.KeyConcept.Standard
NumberStandardLetter (e.g., K.NS.4a)
Format of Math Content Standards
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
Termsincluding - references content that must
be mastered (See K.G.1)
e.g. - references possible illustrative examples. (See 1.NSBT.2c)
i.e. - references the only examples or terms that should be used. (See 2.MDA.3)
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
TermsFluently and fluency describe a student’s ability
to compute with accuracy, flexibility, and efficiency (Kilpatrick, Swafford, & Findell, 2001).
Real-world refers to authentic contexts through which students engage in mathematics and should serve as a stepping-stone for thinking about important mathematical concepts.
Source: South Carolina College- and Career-Ready Standards for Mathematics 2015
Digging Into the K-2 Standards for Mathematics
K 1st Grade 2nd Grade 3rd Grade 4th Grade 5th GradeNumber Sense
Number Sense and Base Ten
Number Sense and Base Ten
Number Sense and Base Ten
Number Sense and Base Ten
Number Sense and Base Ten
Number Sense and Base Ten
Number Sense - Fractions
Number Sense and Operations - Fractions
Number Sense and Operations - Fractions
Algebraic Thinking and Operations
Algebraic Thinking and Operations
Algebraic Thinking and Operations
Algebraic Thinking and Operations
Algebraic Thinking and Operations
Algebraic Thinking and Operations
Geometry Geometry Geometry Geometry Geometry Geometry
Measurement and Data Analysis
Measurement and Data Analysis
Measurement and Data Analysis
Measurement and Data Analysis
Measurement and Data Analysis
Measurement and Data Analysis
Progression of Key Concepts
Digging Into the Standards
Look at the standards for Grades K-1. Discuss with your tablemates:
• If you count the standards and the a,b,c, etc. which Key Concept is the largest in each grade?
• Why do you think that is so?
Digging Into the Standards
Look at the standards for Grade 2. Discuss with your tablemates:
• If you count the standards and the a,b,c, etc. which Key Concepts are the largest?
• Why do you think that is so and what is the relationship between those concepts?
Digging Into the Standards
If grades K-1 have the largest amount of standards devoted to number sense where should the bulk of our teaching time for mathematics be spent?
Two types of Number Sense:• Pre-operational• Operational
Pre-operational mathematical development is one of the most important predictors to future mathematical success.
Meaning Attached to Counting. . .
“Generally, children at midyear in kindergarten should have a fair understanding of counting, but children must construct this idea. It cannot be forced. Only the counting sequence is a rote process. The meaning attached to counting is the key conceptual idea on which all other number concepts are developed.” (Emphasis added)
John A. Van de Walle
Digging Into the Standards
What is meant by Pre-operational Number Sense?
Compare: K.NS.1 and K.NS.2 to
K.NS.3, K.NS.4 and K.NS.5
Discuss with your tablemates:• How do the expectations in the first two standards
differ from the expectations of the second three standards?
Rote vs meaningful counting
Digging Into the Standards. . .
Pre-Operational Number Sense (meaningful counting)
Look at:K.NS.4a (cardinality)
• Counting Strategy• 1, 2, 3, 4, 5 How many?• 1, 2, 3, 4, 5 How many?
K.NS.4b (conservation of number)
• Arrangement Strategy• Count, spread out and re-count
K.NS.4c (increasing/decreasing magnitude)
• One/two more/less K.NS.5 (one-to-one correspondence)
Digging Into the Standards
Comparison of Quantities - Number Relationships
Discuss with your tablemates:• How do K.NS.7 and K.NS.8 differ from
each other and how do both relate to K.NS.4c?
All three deal with number relationships – how does one quantity relate to the other (increasing/decreasing magnitude).
Digging Into the Standards
Comparison of QuantitiesNumber Relationships versus Operations
Think about:If comparisons are number relationships – how one quantity relates to the other – then is that counting or is it operations and as a teacher does it matter?
Re-read K.NS.4c
Let’s explore through an activity.
Is it counting or is it operations? Does it matter?
K – Play “More/Less Than” with five frameNeed: 5 frame; baggie of pink cards and paper
clip; spinner on “Spinning More or Less”, “One More Than Recording Sheet”; and follow directions on recording sheet
1st and 2nd Grade – Play “Spinning More/Less” (Bingo)Need: one die, paper clip from baggie of pink
cards; several two-color counters (one color for you; other for partner); “Spinning More/Less”, and follow directions on spinning sheet
Is it counting or is it operations? Does it matter?
Talk with your tablemates:• Which game would most likely support a
counting solution strategy and which one an operational solution strategy?
Read 1.ATO.5Talk with your tablemates:• How does counting relate to addition and
subtraction?
Digging Into the Standards
Read the following Standards:• 1.NSBT.5• 2.NSBT.2• 2.NSBT.8
Then discuss with your tablemates:• How does the K concept of counting “one
more/less” relate to the above standards?• If students are struggling with the above
standards, what might you need to consider?
Extending Number Relationships to Multiples
Understanding the increasing/decreasing principle (number relationships) is necessary in order to count and add by multiples.
One ten and one more ten is?
In addition to number relationships, students also need to have developed the concept of subitizing in order to count on or “add on”.
Digging Into the Standards
Visualization“Sight Words/Numbers/Quantities”
Look at KNS.6 • Perceptual Subitizing• Conceptual Subitizing
Beginning of counting on . . . (Add)
• Perceptual Subitizing – instantly seeing how many in a small set of 2-3 objects; recognizing a # without operational knowledge
• Conceptual Subitizing – similar to the ability to recognize a # without operational knowledge but with larger sets and recognizing the number as both a whole and as its composite parts
Digging Into the Standards
Visualization“Sight Words/Numbers/Quantities”
Look at KNS.6 • Perceptual Subitizing• Conceptual Subitizing
Beginning of counting on –
Play “What Number Do You See?”
Digging Into the Standards
Read:K.ATO.4, 1.NSBT.2 - all parts 1.ATO.3, & 6, 2.NSBT.1 - all parts 2.ATO.2
Then discuss with your tablemates:• How does the ability to perceptually and
conceptually subitize relate to the above?
• If a student is struggling with the concepts in the above standards, what might you check for?
How might the concept of subitizing be developed in relation to operations? (Play How Many are Hiding? )
Subitizing/Visualization Needed for Counting On and as Foundation for Operations. . .
Play – “How Many are Hiding?” K – use 5 cubes; 1st and 2nd grade - use 10 cubes
Need: Paper plate, cm cubes1. Count out cubes; Partner A grab some of the cubes and hide under plate; ask Partner B –
• How many are hiding?• How do you know?
2. Partner B states:• I know ___ are hiding because ____ and ___
more equal 5/10.
3. Count to verify Partner B’s response4. Exchange Roles and Repeat
Subitizing/Visualization Needed for Counting On and as Foundation for Operations. . .
“How Many are Hiding?”
Handouts• Continuum of Understanding• Stages of Counting by Multiples
Read K.ATO.2 1.ATO.1 2.ATO.1Addition is a Joining/Part-Part Whole action Parts of the Whole, Separation, Comparison
Digging Into the Standards
Operations:K.ATO.1 and 2
Digging Into the Standards – “Start Unknown”
1.ATO.4 Understand subtraction as an unknown addend problem.
Sandra had some pennies. George gave her 4 more. Now Sandra has 12 pennies. How many pennies did Sandra have to begin with? (Join: Initial Unknown/ Add to: Start Unknown)
_____ + 4 = 12 Semantic Form of the equation12 – 4 = _____ Computational Form
What might we do in our classrooms to help students come to see the two forms as equivalent?
Once you know students can subitize and count on, focus on the operations – Subtraction as Think Addition and vice versa .
How would the game, “How Many are Hiding” relate to 1.ATO.4 if students were required to write the number sentences?
How many are hiding and how do you know?• I know 7 are hiding because 10 – 3 (amount showing) = 7 (amount hiding)
You are right, 7 are hiding because 3 + 7 = 10
3. Count to verify number sentences4. Exchange Roles and Repeat5. Results can re recorded in a variety of forms.
18
7
38
11
24
35Number Bonds
Funnel Machine
24
4
10
10
38
31
7
Number Machine
Another design for Number Bonds
Digging Into the Standards
The tendency in the US is to have children solve a lot of problems in a class period and focus on the correct answer rather than focusing in-depth on one or two well-chosen problems at a time, the relationship between the structures of the problems and the variety of approaches to the solutions. John A. Van De Walle
Digging Into the Standards
1.ATO.3 vs 2.ATO.4 Read the above two standards then discuss with your tablemates:How do the student expectations in these two standards differ?
• Equal Groups • concrete objects
• Size of each group (4)• Lesson 2 Handout
• Number of groups (3)
4 + 4 + 4 = 12Handout x 2
Important Considerations at each Grade K-2• Rote Counting• Meaningful Counting
Cardinality (last number spoken) Conservation of Number (arrangement) Increasing/decreasing Magnitude Principle
(one/two more/less) (number relationships) One-to-One Correspondence Subitizing (visualization) Comparisons (quantity relationships) Check for student solution strategies in
order to determine: Is it counting or is it operations? This determines how to move the student forward in understanding.
Support Document
Support Document Overview
Mathematics Support Document Overview
“Overview”
http://ed.sc.gov/agency/ccr/Standards-Learning/Mathematics.cfm
o Mathematics Edmo Group
Mathematics Support Document
Review Process: Work by grade levels – YOUR DECISONo Move into Grade Alike Groupso Open browser
http://maryruzga.weebly.com Not hyperlinked at this time
Grade Levels Review/explore Share out one activity/lesson/resource
SCDE Mathematics Team: https://edmo.do/j/snmcix
1. Create an account. (If you have an account, log in.)
2. Enter URL above.3. Different Grade Band “Folders”
Joining Mathematics Edmodo Group
Office of Standards and Learning: https://edmo.do/j/fu7i2y
1. Create an account. (If you have an account, log in.)
2. Enter URL above.
Joining Office Edmodo Group
Mathematics Support Document
Feedback and Certificate of Participation
https://scde.formstack.com/forms/summer_plo_evaluation_form_copy_1_copy
See Yellow Handout for link or the QR code
Geometry Handout
My Contact Information
Mary L. [email protected]
Thank you for spending time with me today.