Second Grade and the CCSS–M

Vacaville USDSeptember 23, 2013

AGENDA The CCSS-M: Math Practice Standards Review Daily Math Word Problems Place Value 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 2nd 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 2nd 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 – 2nd 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!

Problem #1

Tyrone had $17 in his piggy bank. He

added $10 more. What is his total

savings now?

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Problem #2

Ray has 465 tractors and his brother

Ben has 289. How many tractors do

they have altogether?

Problem #3

Jennifer went shopping with $42. She

came home with $9. How much

money did she spend?

Problem #4

Hansel read 235 pages of his book over

the weekend. Gretel read 198 pages of

her book over the weekend. How many

more pages did Hansel read than

Gretel?

Problem #5

A total of 100 raffle tickets were sold

over a 3-day period. If 21 raffle tickets

were sold on Monday, and 67 tickets

were sold on Tuesday, how many raffle

tickets were sold on Wednesday?

Problem #6

There are 5 plates of cookies on the

shelf. If there are 4 cookies on each

plate, how many cookies are there in

all?

Problem #7

There are 20 chairs. Kayla wants to put

the chairs into 4 rows. How many chairs

will be in each row?

Problem #8

12 students need rides to an after school

event. If only 4 students can ride in

each car, how many cars are needed to

transport the students?

2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

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 Put one problem on each card Label the problem type and write the

problem on the front of the card Show the model drawing

representation and possible number sentences on the back.

Example – Front

Put Together/Take ApartAddend Unknown

I have 9 balloons. 3 of them are red and the rest are blue. How many balloons are blue?

Example – Back

I have 9 balloons. 3 of them are red and the rest are blue. How many balloons are blue?

Red

Blue

93 3 + = 9

9 – 3 =

Place Value

Unit Planning

Topic: Place Value  Content Standards:   

CCSS - NBTUnderstand place value.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

a. 100 can be thought of as a bundle of ten tens — called a “hundred.”

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

CCSS - NBTUnderstand place value.2. Count within 1000; skip-count by 2s, 5s, 10s, and 100s. CA3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

CCSS – NBT

8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

CCSS – M Use place value understanding and properties of operations to add and subtract.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.

CCSS – M 7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

CCSS – M 7.1 Use estimation strategies to make reasonable estimates in problem solving. CA9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.

Unit Planning

Practice Standards:   What should students already know and how am I going to help them make connections to that prior knowledge?  

1.NBT Understand place value.2. Understand that the two digits of a

two-digit number represent amounts of tens and ones. Understand the following as special cases:a. 10 can be thought of as a bundle of ten

ones — called a “ten.”b. The numbers from 11 to 19 are composed

of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

d. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

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: 

Unit Planning

What tools, models, and materials are necessary to fully address the standards for this unit?

Base 10 Blocks

ones

tens

“tens” are composed of 10 “ones”

Base 10 Blocks

ones

tenshundreds

“hundreds” are composed of 10 “tens”

Unit Planning

What will students learn and how will I know what they have learned?

Conceptual Understanding: We or trade for a larger piece when

there are more than 10 of any size piece

 

Count out 27 ones From those 27 ones, count out a group

of 10, and arrange them in a line Take one of your 10 sticks Line it up next to your row of 10 ones.

What do you notice? Trade your 10 ones for 1 ten

Look at the ones that are left. Do you think you have enough to make another group of 10?

Count out another group of 10, and arrange them in a line

Take another 10 stick and line it up next to your row of 10 ones.

What do you notice? Trade your 10 ones for 1 ten

Look at the ones that are left. Do you think you have enough to make another group of 10?

Let’s count and check. Do you have enough to make another

group of 10? So, how many ones are left?

Number

27 2 tens 7 ones

42 4 tens 2 ones

35 3 tens 5 ones

16 1 tens 6 ones

23 2 tens 3 ones

Build the number

I am going to show you a number I want you to build it using the fewest

number of pieces possible.

48 How many tens did you use? And the value of those tens is ______ How many ones did you use? And the value of those ones is ______

So we can write 48 as 4 tens and 8 ones

So we can also write 48 as 40 + 8

Number Expanded Form

48 40 + 8

27 20 + 7

64 60 + 4

37 30 + 7

82 80 + 2

Building Numbers

Please build 38 using the least number of pieces

Now please build 51 using the least number of pieces

Which number is larger? How do you know?

Numbers Less thanGreater

than

38 51 38 < 51 51 > 38

62 47 47 < 62 62 > 47

38 23 23 < 38 38 > 23

68 65 65 < 68 68 > 65

84 80 80 < 84 84 > 80

Take your tens I want us to count out 140

I see a problem with our representation of 140. Any ideas?

We have more than 10 tens and our rule so far has been that we always trade for a larger piece when we have more than 10 of something

So, how many tens do we have? From your 14 tens, count out a group of

10 tens Now let’s count them. So ten tens is a hundred.

This is a hundred’s block Take your ten tens. Can you arrange them so they fit

perfectly on top of the hundred’s square?

So we can trade 10 tens for 1 hundred

Number

140 1 hundred 4 tens 0 ones

230 2 hundreds 3 tens 0 ones

163 1 hundred 6 tens 3 ones

216 2 hundreds 1 ten 6 ones

305 3 hundreds 0 tens 5 ones

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