vacaville usd september 4, 2014. agenda problem solving and patterns math practice standards and...

FOURTH GRADESession 1

Vacaville USD

September 4, 2014

AGENDA• Problem Solving and Patterns• Math Practice Standards and Effective Questions• Word Problems• Place Value, Rounding, Reading and Writing

Numbers• Addition/Subtraction Strategies – Mental Math• Multiplication

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.

Regina’s Logo

How many tiles are needed to make a Size 5?

What about a Size 10? a Size 20? A Size 100?

Regina’s Logo

What is a strategy that will let you quickly and easily figure out how many tiles you will need for any given size?

Regina’s Logo

Recursive• Add 3 each time

SIZE # OF TILES

1 5

2 8

3 11

4 14

5 17

Regina’s Logo

3n + 2

Regina’s Logo

2(n + 1) + n

Regina’s Logo

2n + (n + 2)

4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

The Use of Effective Questions

• Questioning plays a critical role in the way

teachers – Guide the class

– Engage students in the content

– Encourage participation

– Foster understanding

CCSS Mathematical PracticesO

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nREASONING 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’s

• So how does the use of effective questioning relate to the Standards for Mathematical Practice?

SMP’s and Questions

• Your group will receive 16 cards– 8 SMP’s– 8 lists of questions related to the SMP’s

• Your job is to match each SMP with the questions designed to support that SMP.

Asking Effective Questions

Pick 2 colors...

1. Use one color to highlight questions that you are already asking.

2. Use the 2nd color to highlight questions that you would like to ask this year.

Additional Resources

• Effective Questions – PBS

Solving Word Problems

1. Read the entire problem, “visualizing” the problem conceptually

2. Determine who and/or what the problem is about

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

5. 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 (show all work!)

7. Write the answer in the sentence and make sure the answer makes sense.

At the flower shop, there are 5 times as many roses as sunflowers. If there are 60 sunflowers, how many roses are there?

At the flower shop, there are 5 times as many roses as sunflowers. If there are 60 roses, how many sunflowers are there?

At the flower shop, there are 5 times as many roses as sunflowers. If there are 60 roses and sunflowers altogether, how many roses are there? How many sunflowers are there?

Standards

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Place ValueRounding

Reading and Writing Numbers

Standards

• What are the place value standards for 4th grade?

• What are students supposed to know and understand from 3rd grade?

Standards

4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Standards

4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Standards

4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place.

Standards

• What are the place value standards for 4th grade?


Tens Times As Many

Put 1 one on your place value mat• What would it mean to have 10 times as

many?• 10 ones = ten• So 1 ten is ten times as much as 1 one

Tens Times As Many

Put 3 ones on your place value mat• What would it mean to have 10 times as

many?• 30 ones = 3 tens• So 3 tens is ten times as much as 3 ones

Tens Times As Many

Look at the 1 ten on your place value mat• What would it mean to have 10 times as

many?• 10 tens = 1 hundred• So 1 hundred is ten times as much as 10

tens

Tens Times As Many

Put 4 tens on your place value mat• What would it mean to have 10 times as

many?• 40 tens = 4 hundreds• So 4 hundreds is ten times as much as 40

tens

Tens Times As Many

Put 2 hundreds on your place value mat• 2 hundreds is 10 times as much as what

number?• 2 hundreds = 20 tens• So 2 hundreds is ten times as much as 2

tens

Tens Times As Many

Put 1 hundred on your place value mat• What would it mean to have 10 times as

many?• 10 hundreds = 1 thousand• So 1 thousand is ten times as much as 1

hundred

Patterns in Place Value

Base 10 blocks

Take out a 1’s piece• What does it look like? • Why does it have a value of 1?

Patterns in Place ValueTake out a 10’s piece

• What does it look like? How is it similar or different from a 1’s piece?

• Why does it have a value of 10?

Patterns in Place ValueTake out a 100’s piece

• What does it look like? How is it similar or different from a 10’s piece?

• Why does it have a value of 100?


Look at the block that I just gave you.• What do we call this block?• How many 100’s would it take to fill this

block?• So 1,000 is ___ times as much as 100• What does it look like? Is it similar to any of

the pieces we have examined so far?

ten


Our number system has some very important structures and patterns

• Place Value• Digits 0 1 2 3 4 5 6 7 8 9• Each place is 10 times as much (or 10

times as large) as the place immediately to its right

Patterns in Place ValueWatch and see if you notice any additional patterns or structures as we continue to look at place value

• So a 1,000’s piece looks a lot like a 1’s piece.

• What do you think it will look like if I put 10 thousand’s pieces together? What piece is it similar to? What do you think we might name this place?

Patterns in Place Value• What do you think it will look like if I put 10

ten-thousand’s pieces together? What piece is it similar to? What do you think we might name this place?

• Extend our place value mat.– Ones family or units family– Thousands family

10 times as manyWork at your tables (number off)• 1 and 2 are partners; 3 and 4 are partners;

etc.• Odd numbers start with the chart; trade off

with your partner• Person 2 – Starts with the calculator;

passes around the table after each problem

10 times as many

• I’m going to give you a number• Odd numbers record the number on the

chart• Person 2 – calculate 10 times that number• Odd numbers record the new number

10 times as many• I’m going to give you a number

476• Odds: record that number on your chart• Person 2: calculate 10 times that number• Odds: record the new number

4 7 64 7 6 0

10 times as manyLet’s try again• Evens: record that number on your chart• Person 3: calculate 10 times that number• Evens: record the new number

5,920

10 times as many

Keep trading and recording• 607• 3,600• 1,234• 71,900

What do you notice?

• What happens to the digits in each number when we multiply by 10?

• WHY?

100 times as many

• What do you think would happen to the digits in each number if we multiplied by 100?

• Let’s check and see if our prediction is correct.

Metric Conversions

Find the equivalent measures.

• 1 m = __________ cm

• That means that a meter is ______ times as

large as a centimeter.

100

100

Metric Conversions


• 1 m = __________ cm

• 3 m = __________ cm

• 80 m = __________ cm

• __________ m = 1200 cm

100

300

8,000

12

Metric Conversions


• 1 km = __________ m

• 4 km = __________ m

• 7 km = __________ m

• __________ km = 18,000 m

1,000

4,000

7,000

18

Other Place Value Concepts

• Expanded Form• Reading• Writing• Comparing• Rounding

Expanded Form

45,793

• 40,000 + 5,000 + 700 + 90 + 3

• 4 x 10,000 + 51,000 + 7100 + 910 + 31

ReadingRead: 452,807

• First group the number into families

thousand, ones• Now read the numbers in each family

– Remember they are all 3 digits or less

Four hundred fifty two thousand

Eight hundred seven

452 807

• Write in number form:

Two hundred three thousand five hundred forty

• Break the number into families and write it one part at a time

Writing Numbers

203,540

Comparing

Go back to your place value recording mats

• Odds: Record the number 72,498• Evens: Underneath that number, record

the number 72,600

Comparing

• Which is larger?

• Write the relationship using ____ > ____

• Write the relationship using ____ > ____

Comparing

• Which is larger?

145,299 or 95,387

How do you know?

• Complete using >, <, or =

89,432 157,308

Rounding

• What does it mean to round a number to the nearest thousand?

• If I were to count by thousands, which number would be the closest to my number.

Rounding

• Count by 1,000 starting at 0

• Count by 1,000 starting at 30,000

• Count by 100 starting at 427,000

• How many 1,000’s?• Count by 1,000.

What’s next? • What’s in the middle

of 2,000 and 3,000?• Is 2,784 closer to

2,000 or 3,000?

3,000

2,000

2,500

= 20 hundreds

= 30 hundreds

= 25 hundreds

Round 2,784 to the nearest thousand

Round 372,584 to the nearest hundred thousand

• How many 100,000’s?• Count by 100,000. What’s

next? • What’s the midpoint of

300,000 and 400,000?• Is 372,584 closer to 300,000

or 400,000?

400,000

300,000

350,000

Rounding

Round 372,584to the nearest • hundred thousand

400,000

Round 372,584 to the nearest ten thousand

• How many 10,000’s?• Count by10,000. What’s

next?• What’s the midpoint?• Is 372,584 closer to 370,000

or 380,000?

380,000

370,000

375,000

Rounding

Round 372,584to the nearest • hundred thousand

400,000• ten thousand

370,000

Try a couple!

• Round 347,523 to the nearest ten-thousand

• Round 347,523 to the nearest thousand

Addition and Subtraction

Standards

• What are the addition and subtraction standards for 4th grade?


Standards

4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Standards

• What are the addition and subtraction standards for 4th grade?


Progression

• Concrete• Pictorial or Representational• Abstract

– Invented and Alternative Algorithms– Traditional Algorithms

Mental Math

135 + 48

400 – 165

Multiplication

Standards

4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.OA.2 and OA.3 Word Problems

4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Standards

• So, what are students supposed to know and understand about multiplication from 3rd grade?

Multiplication

• Solve 23 x 4 at your tables.

• Use at least 4 different methods!– Concrete– Representational– Abstract

Using Groups to Multiply

23

x 4

Using Arrays to Multiply

23

x 4

4 rows of 3

4 rows of 20

= 12 = 80

12 80 92

Area Model

Area Representation

23x 4

20 + 3

4 4 2080

3 412

Abstract

23

23

23

+ 23

92

20 + 3

20 + 3

20 + 3

+ 20 + 3

80 + 12

Partial Products

23

x 4

4 x 20

4 x 3

80 12 92

Using Arrays to Multiply

• Use Base 10 blocks and an area model to solve the following:

21 x 13

31 x 14 =

Pictorial Representation

30 + 1 10

+

4

10 30300

10 110

4 30120

4 14

31x 14

Partial Products

31 x 1 4300

10120 4434

(10 30)

(10 1)

(4 30)

(4 1)

Partial Products

3 1x 1 4

412010

300434

(4 1)

(4 30)

(10 1)

(10 30)

Pictorial Representation

84x 57

80 + 4 50

+

7

50 804,000

50 4

7 80 7 4

200

560 28

vacaville usd september 4, 2014. agenda problem solving and patterns math practice standards and...

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