First Grade and the CCSS–M
Vacaville USDOctober 4, 2013
Demographic Form
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AGENDA The CCSS-M: Math Practice Standards Review Daily Math The Bakery Problems Word Problems Teaching Facts Planning/Discussions
Expectations
We are each responsible for our own learning and for the learning of the group.
We respect each others learning styles and work together to make this time successful for everyone.
We value the opinions and knowledge of all participants.
Sharing
At your tables, discuss What you have tried since our first session What successes you have had What questions and/or concerns you have?
Pick one success and one question/concern to share with the group.
Standards for Mathematical Practice
CCSS Mathematical Practices
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REASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and
critique the reasoning of others
MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in
repeated reasoning
SMP Matrix
SMP MatrixIndividual Reflection Look over the matrix For each of the SMP’s,
where are your students on the matrix? where are 1st grade students at your site
on the matrix?
SMP MatrixSite Reflection:Based on your individual reflections with regards to the SMP’s, Discuss as a group
Where do you believe most of your 1st grade students are on the matrix?
Plan as a group What SMP do you want to work on as a
team? What are your next steps?
Review of Daily Math
Word Problems
Bakery Problem #1
A bakery sold 235 boxes of cookies.
They sold 119 more boxes of cookies
than cupcakes. How many boxes of
cupcakes were sold?
Bakery Problem #2
Another bakery sold 3 times as
many boxes of cookies than
cupcakes. If they sold 126 more
boxes of cookies than cupcakes, how
many boxes of cookies were sold?
Lessons Learned From Research
Sense-making is important! In learning and remembering
mathematics In developing mathematical thinking
and reasoning
How many two-foot boards can be cut from two five-foot boards? (Verschaffel, 2007)
Nearly 70% of the upper elementary school students given this problem say that the answer is “five”
Why?
How many two-foot boards can be cut from two five-foot boards? (Verschaffel, 2007)
Because 5 + 5 = 10 and 10 ÷ 2 = 5.
What did the students forget? the “real world” context
Kurt Reusser asked 97 1st and 2nd graders the following question:
There are 26 sheep and 10 goats on a ship. How old is the captain?
76 of the 97 students “solve” this problem - by combining the numbers.
H. Radatz gave students non-problems such as:
Alan drove 50 miles from Berkeley to Palo Alto at 8 a.m. On the way he picked up 3 friends.
NO QUESTION IS ASKED!
Yet, from K-6, an increasing % of students “solve” the problem by combining the numbers and producing an “answer.”
The Serious Question
Where does such behavior come from?
A Serious Answer Students develop their
understanding of the nature of the mathematical enterprise from their experience with classroom mathematics.
Therefore….. If the curriculum doesn’t induce
them to see mathematics as a sense-making activity, they won’t engage with mathematics in sensible ways.
What about using “key words” to help elementary school kids solve word problems?For example…….
Using Key Words.
John had 7 apples. He gave 4 apples to
Mary. How many apples did John have
left?
7 - 4 = 3
Nick Branca gave students problems like these:
John had 7 apples. He left the room to get another 4 apples. How many apples does John have?
Mr. Left had 7 apples…
Can you guess what happened?
Juan has 9 marbles. He gives 5 marbles to Kim. How many marbles does he have now?
Juan has 9 marbles. Kim gives 5 marbles to him. How many marbles does he have now?
** Problems can use the same key words but have different meanings
Jon has 5 red blocks and 3 blue blocks. How many blocks does he have in all?
Jon has 5 bags with 3 red blocks in each bag. How many blocks does he have in all?
Key Word Strategies Biggest concern –
Research shows that students stop reading for meaning
Students need to be taught to reason through a problem – to make sense of what is happening
Personal Example
Mary practiced the piano for 2 hours on Monday. This was 20% of her total practice time for the week. How many hours does Mary practice the piano each week?
Personal Example
Mary practiced the piano for 2 hours on Monday. This was 20% of her total practice time for the week. How many hours does Mary practice the piano each week?
Domains – 1st Grade
Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry
Key to algebraic thinking is developing representations of the operations using Objects Drawing Story contexts
And connecting these to symbols
Such manipulatives or pictures are not merely “crutches” but are
essential tools for thinking
Word Problems and Model Drawing
Model Drawing A strategy used to help students
understand and solve word problems
Pictorial stage in the learning sequence of
concrete – pictorial – abstract
Model Drawing Develops visual-thinking
capabilities and algebraic thinking.
If used regularly, helps students spiral their understanding and use of mathematics
Steps to Model Drawing
1) Read the entire problem, “visualizing” the problem conceptually
2) Decide and write down (label) who and/or what the problem is about
H
Steps to Model Drawing
3) Rewrite the question in sentence form leaving a space for the answer.
4) Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem
H
Steps to Model Drawing5) Chunk the problem, adjust the
unit bars to reflect the information in the problem, and fill in the question mark.
6) Correctly compute and solve the problem.
7) Write the answer in the sentence and make sure the answer makes sense.
Representation
Getting students to focus on the relationships and NOT the numbers!
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards)
Word Problems
What can we do when to make word problems more interesting and engaging for our students?
Group Task
Work with your group to write a variety of problems appropriate for your grade level
Example
Put Together/Take ApartAddend Unknown
I have 9 balloons. 3 of them are red and the rest are blue. How many balloons are blue?
Five Facts and Ten Facts
Five Facts
3 + 2 = 5
Five Facts
4 + 1 = 5
Ten Facts
7 + 3 = 10
Ten Facts
4 + 6 = 10
The Teen Numbers
Developing Reasoning
https://www.teachingchannel.org/videos/kindergarten-counting-cardinality-lesson
Addition Facts
Subtraction Facts
Subtraction
John had 9 ghosts at his house but
3 of them left to go visit Caspar.
How many ghosts are in his house
now?
Subtraction
John has 9 ghosts at his house
while Mika only has 3 ghosts at her
house. How many more ghosts are
in John’s house?
Subtraction
Vanessa has 7 monsters and 12
ghosts at her Halloween party. How
many more ghosts are at the party?
Subtraction
Vanessa had 12 monsters at her
Halloween party but 7 of them had
to go back to work at the Fright
Factory. How many monsters are
left at the party?
Subtraction
Show me 2 different ways to model
11 – 5
Unit Planning
Topic: Subtraction Facts to 12 Content Standards:
Unit Planning
Practice Standards: What should students already know and how am I going to help them make connections to that prior knowledge?
Unit Planning
What will students learn and how will I know what they have learned?
Concrete – Representational – Abstract
Unit Planning
What will students learn and how will I know what they have learned?
Conceptual Understanding:• Subtraction as take-away AND • Subtraction as compare
• Relationship between addition and subtraction
Unit Planning
What tools, models, and materials are necessary to fully address the standards for this unit?
Unit Planning
What will students learn and how will I know what they have learned?
Procedures and Skills:
Unit Planning
What will students learn and how will I know what they have learned?
Applications and Problem Solving:
Unit Planning
What will students learn and how will I know what they have learned? Key Vocabulary
Unit Planning
What tools, models, and materials are necessary to fully address the standards for this unit?
Unit Planning
Anticipated Number of Days: ______
• Conceptual understanding: ____ days
• Procedures and skills: ___ days
• Applications and problem solving: ___
days
Unit Planning
Sketch of Unit by Days (Overview)
Planning Actual Lessons
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