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

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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

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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