students develop understanding of why division procedures work based on the meaning of base-ten...

• Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations.

Students They finalize fluency with multi-digit addition, subtraction, multiplication, and division.

They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths.

They develop fluency in these computations, and make reasonable estimates of their results.

Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense.

They compute products and quotients of decimals to hundredths efficiently and accurately.

Unit 2 Big Ideas

Lesson 2.1 EstimationCommon Core Focus

5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Lesson• MMR: Extended Facts• MM• Do not do Part 1,2 or 3• Do Page 45 from Lesson 2.6• Do R 2.3 (outside resource)• Do P 2.3 (outside resource)• Math Box (Skip #4)• No HW or you may use P 2.3 if you are not able to get to it

Notes• You are teaching the skill of rounding to the place that makes sense for the problem. Rounding is situational.

Extended FactsFactors Product Factors Product Factors Product Factors Product

7x3 7x30 70x30 700x30

4x10 4x60 40x60 400x60

Why do you add a zero in the product for every zero that is in the factors?

Making An EstimateProblem “Friendly” Numbers Estimate

377+213 400+200 600

* Use a number line to help you visualize friendly numbers

EstimationUsing A Number Line To Find Friendly Numbers

___.___ ___.___

___.___ ___.___

___.______ ___.____

Round to the Nearest Hundredth

Round to the Nearest Tenth

Round to the Nearest One


__0 __0

__00 __00

_,000 _,000

Round to the Nearest Thousand

Round to the Nearest Hundred

Round to the Nearest Ten


__0,000 __0,000

__00,000 __00,000

Round to the Nearest Hundred Thousand

Round to the Nearest Ten Thousand

Estimate SumsProblem “Friendly” Numbers Estimate

377+213 400+200 600


Estimate DifferencesProblem “Friendly” Numbers Estimate

377-213 400-200 200


Lesson 2.2: Addition of Whole Numbers and Decimals

Common Core Focus• 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.1Grade 4

expectations in this domain are limited to whole numbers less than or equal to 1,000,000.Lesson

• Readiness: Building numbers with Base 10 Blocks MMR: Expanded Notation• MM• Part 1 and Part 2• Enrichment discussion• Math Box • Study link

Notes• Should be doing column addition, but start with partial sums. Be sure each student understands place value.• *You only need to add and subtract numbers to the hundredths place!

Number(Standard Form)

1000 100 10 1

Base 10 BlocksDraw It

Expanded FormWrite It

Base 10 Models- Representing Numbers

Expanded Form- Showing The PartsNumber

(Standard Form)

Millions HundredThousands

Tenthousands

Thousands

,

Hundreds Tens Ones

1,342,543 1,000,000 300,000 40,000 2,000 500 40 3

Number

Value

Finding Place Value

Number

Value

Number

Value

Number

Value

Change The Value

Original Number Change New Number

37,400 +300 =37,700

Thousands Hundreds Tens

Ones

+

=

Partial Sums Addition

Add The Parts

Put The Sums Together

=

Break The Parts

Thousands + Hundreds + Tens + Ones

+ + +

+ + +

Problem

Column Addition(Adding and Regrouping The Tens)

10,000 1,000 100 10 1

1 1

6 7 4 4

+ 6 2 3 7

= 1 12(10+2) 9 8 11 (10+1)

1 2, 9 8 1


10,000 1,000 100 10 1

+

=

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 1

920

21 22 23 24 25 26 27 28 29

30

31 32 33 34 35 36 37 38 39

40

41 42 43 44 45 46 47 48 49

50

51 52 53 54 55 56 57 58 59

60

61 62 63 64 65 66 67 68 69

70

71 72 73 74 75 76 77 78 79

80

81 82 83 84 85 86 87 88 89

90

91 92 93 94 95 96 97 98 99

100

.01 .02 .03 .04 .05 .06 .07 .08 .09 .10

.11 .12 .13 .14 .15 .16 .17 .18 .19 .20

.21 .22 .23 .24 .25 .26 .27 .28 .29 .30

.31 .32 .33 .34 .35 .36 .37 .38 .39 .40

.41 .42 .43 .44 .45 .46 .47 .48 .49 .50

.51 .52 .53 .54 .55 .56 .57 .58 .59 .60

.61 .62 .63 .64 .65 .66 .67 .68 .69 .70

.71 .72 .73 .74 .75 .76 .77 .78 .79 .80

.81 .82 .83 .84 .85 .86 .87 .88 .89 .90

.91 .92 .93 .94 .95 .96 .97 .98 .99 1.00

Decimals:Breaking One

Into Groups of 10 and 100

Tens Ones Tenths

Hundredths

+

=

Partial Sums Addition

Add The Parts

Put The Sums Together

=

Break The Parts

Tens + Ones + Tenths + Hundredths

+ + +

+ + +

Problem


10,000 1,000 100 10 1 .10 .01

+

=

Place Value # Line

+10,000

+1,000

+100

Place Value # Line

+10

+1

+.1

+.01

Using A Number Line: Adding Ones and Tens

38+23=w

38 41

+3 +20

61

38 58

+20

61

+3

Adding On A Number Line

Number Model Bar Model

2.3 Subtraction of Whole Numbers and Decimals

Common Core Focus• 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.1Grade 4 expectations in this

domain are limited to whole numbers less than or equal to 1,000,000.Lesson

• Readiness• MMR• MM• Part 1 (use SRB as directed)• Part 2• Math Box • Study Link

Notes• Trade first and counting up only.• **No partial differences**

Column Subtraction(Subtracting and Borrowing The Tens)

10,000 1,000 100 10 1

10+7 (17) 10+4(14)

9 (8+1) 7 8 (7+1) 4

- 6 8 3 7

= 2 9 4 7

9784-6837=t


10,000 1,000 100 10 1

-

=

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 1

920

21 22 23 24 25 26 27 28 29

30

31 32 33 34 35 36 37 38 39

40

41 42 43 44 45 46 47 48 49

50

51 52 53 54 55 56 57 58 59

60

61 62 63 64 65 66 67 68 69

70

71 72 73 74 75 76 77 78 79

80

81 82 83 84 85 86 87 88 89

90

91 92 93 94 95 96 97 98 99

100

.01 .02 .03 .04 .05 .06 .07 .08 .09 .10

.11 .12 .13 .14 .15 .16 .17 .18 .19 .20

.21 .22 .23 .24 .25 .26 .27 .28 .29 .30

.31 .32 .33 .34 .35 .36 .37 .38 .39 .40

.41 .42 .43 .44 .45 .46 .47 .48 .49 .50

.51 .52 .53 .54 .55 .56 .57 .58 .59 .60

.61 .62 .63 .64 .65 .66 .67 .68 .69 .70

.71 .72 .73 .74 .75 .76 .77 .78 .79 .80

.81 .82 .83 .84 .85 .86 .87 .88 .89 .90

.91 .92 .93 .94 .95 .96 .97 .98 .99 1.00

Decimals:Breaking One Into Groups of

10,100


10,000 1,000 100 10 1 .10 .01

-

=

Place Value # Line

-10,000

-1,000

-100

Place Value # Line

-10

-1

-.1

-.01

Using A Number Line: Subtracting Ones and Tens

61-23=w

38 41

---3

-20

61

38 58

-20

61

-3

Subtracting on A Number Line

Number Model Bar Model

2.4a Addition and Subtraction Number Stories

Common Core Focus• 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.1Grade 4 expectations in this

domain are limited to whole numbers less than or equal to 1,000,000.

Lesson• Readiness with bar models• MMR• MM• Part 1: Do this together and use bar models• Part 2: Game• Math Box • Study link

Notes• Review problem solving strategies from Sweethome problem solving model.• • Frank - Bar Models need to be made for• p. 37/38 and readiness

2.4b- Continue With Lesson 2.4a

Bar Modeling Teaches The Importance of Language When Solving Math Problems

CHANGE

and Wholes

CompaRe

Parts Parts Parts Parts Parts Parts

Change-Addition

Start Change End

+ =

4 butterflies were sitting on a branch. 2 more landed on the branch. How many butterflies were on the branch now?

Bar Modeling: Joining (Addition-Change)

Total Amount Unknown # Story•The team had 8 runs. They scored 2 more. How many do they have in all?

•8+2=R

Amount Joined Unknown •John has $2 in his piggy bank. He needs $10 to buy the new toy he wants. How much more does he need to save to have enough money?

•2+D=10

Initial Amount Unknown •Mary added 5 books to her library. Now she has 10 books in her library. How many books did she start with?

•B+5=10

R

8 2

10

2 D

10

B 5

Change-Subtraction

Start Change End

- =

There were 5 butterflies sitting on a branch. 2 flew away. How many were left?

Bar Modeling: Separating (Change- Subtraction)

Amount Remaining Unknown # Story•Suzie had $10. She spent $8 on lunch. How much money does she have left over?

•10-8=x

Amount Separated Unknown •John had to read 10 books over the summer. He only has 2 left to read. How many books did he read?

•10-x=8

Initial Amount Unknown •Jim ate 5 cookies out of the box. He only has 5 left. How many were in the box?

•X-5=5

10

8 x

10

x 8

x

5 5

Part/Part/Whole

1st Part 2nd Part End

+ =

There were 4 butterflies and 2 ladybugs sitting on a branch. How many insects were sitting on the branch?

Bar Modeling: Part/Part/Whole

Whole Unknown # Story•There were 2 apples and 8 bananas in the fruit bowl? How many pieces of fruit were in the bowl?

•F=2+8

First Part Unknown •Jim had 10 brothers and sisters. How many sisters did he have if head 2 brothers?

•10=s+2

Second Part Unknown •Jim had 10 brothers and sisters. If he had 5 brothers, how many sisters did he have?

•10=5+B

F

2 8

10

S 2

10

5 x

Bar Modeling- Comparison

LARGER AMOUNT

Number Model:

_________-__________=_________ (more or less)

SMALLER AMOUNTDIFFERENCE

Bar Modeling- Comparison

Larger SmallerAmount Amount

- =

Jim has 5 butterflies. Mary has 2. How many more butterflies does Jim have than Mary?

Bar Modeling: Comparison- All(Finding The Difference)

Amount More (or Less) Unknown

c Difference

# Story

•Ted has 10 crayons. Neil has 4 crayons. • How many more crayons does Ted have than Neil?• How many fewer crayons does Neil have than Ted?

•10-4=c

Smaller Amount Unknown

6 Difference

•Ted had 10 crayons. Neil has 6 less than Ted. How many crayons does Neil have?

•10-6=c

Larger Part Unknown

5 Difference

•Ted Has 5 crayons. Neil has 5 more than Ted. How many crayons does Neil have?

•5+5=c

10

4

10

c

c

5

Addition and Subtraction Number Stories

1.)

M

18 27 34

Number Model:

Solution

Number Model:

Solution

Bar Model

Bar Model

2.)

Number Model:

Solution

Number Model:

Solution

Bar Model

Bar Model

3.)

4.)

Addition and Subtraction Number StoriesNumber Model:

Solution

Number Model:

Solution

Bar Model

Bar Model

6.)

Number Model:

Solution

Number Model:

Solution

Bar Model

Bar Model

7.)

8.)

5.)

2.5 Estimate Your Reaction Time

Common Core Focus

Lesson• Readiness!!! Do 1 and 2 on board and talk about them.• Blue teaching box in TM 105 is the mini- lesson.• See line plots on TM 106: that will be the model we use• Use the following website:• http://getyourwebsitehere.com/jswb/rttest01.html• • Math Box • Study link

Notes

• do it yourself first. • *Will probably need a number sheet from 0.1 to 0.4 with enough space to write hundredths between.• *DOMINANT HAND only• *emphasis is on rounding decimals and plotting them on line plot NOT landmarks.

2.7 Estimating Products

Common Core Focus

Lesson• Readiness• MMR• MM• Part 1• Math Box –skip 1,6• Study link• Additional worksheets you may want to use to reinforce the skill:• R 3.3 and P 3.3 (outside resource – whole numbers)• R 6.2 and P 6.2 (outside resource – decimals)

Notes*emphasis is on “about how big” not magnitude (substitute wording) Force the habit of kids estimating before ANY calculation.

Reward this behavior!

Estimate Products

10 20

60 70

700

70

10

Area Model EstimateRound To A Friendly Number

14

68

Estimate Products

______

______

____

____

Area Model EstimateRound To A Friendly Number

P.S. DAY

THE FOURS PROBLEM from Journal 2, Pages 317-318

Common Core Focus

LessonNotes

2.8 Multiplication of Whole Numbers and Decimals

(Day 1)

Common Core Focus• 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

Lesson• Readiness: must use base 10 blocks• MMR• MM• Part 1 – Have them solve all the problems using partial products.

• Note• USE the base 10 blocks• Use document camera to show whole class• Do an exit slip with one 2 digit x 2 digit partial product to assess.• Need to carefully check each student for proficiency. Is the problem with the algorithm or with knowing basic facts?

Area Models and Partial Products

600

80

60 8

30 4

20

2

34x 22

Area Model

20x30 600

20x4 80

2x30 60

2x4 8

784

784

Area Models and Partial Products

Area Model

Problem

2.8 – Day 2-3


Lesson• Part 2: Journal page 52, use Bar Models to solve. • Enrichment activity: Very important for ALL students• Study Link 2.8

Note• You will determine how many days to spend on Partial Products. You may need to extend this lesson 1 or 2 days. It is

essential that the kids to have a strong understanding of PP before they move into lesson 2.9

Addition and Subtraction Number Stories

1.)

Number Model:

Solution

Number Model:

Solution

Bar Model

Bar Model

2.)

Number Model:

Solution

Number Model:

Solution

Bar Model

Bar Model

3.)

4.)

2.9 Transition to Standard Algorithm:

(Day 1)Traditional Method:Multiplication 2 digit by 1 digit


Lesson• MMR• MM• Teach the Traditional method: start with some 2 digit by 1 digit problems and 3 digit by 1 digit problems.• *Give students some practice problems and let them use Base 10 blocks to help them gain a better understanding of how

the traditional method works.• • Use R 3.6 to help explain what the kids need to think as they solve the problems.• Use P 3.6 for additional practice and homework.• Math Box

Notes• NO LATTICE METHOD - will use Traditional method.• • In this lesson, continue to reinforce that the students need to make an est. before solving each problem and have them

write that est. before they solve it.

Estimate Products

40 50

450

50

Area Model Estimate

Round To A Friendly Number9

45 47

47x9

Problem

Area Model Multiplication- 2 Digit by 1 Digit

360 63

Add The Products

360

+ 63

= 423

9

40 7

Traditional Multiplication- 2 Digit by 2 Digit

Traditional Method Expanded

+ 6 47

__x9__ 3 (63)

(36+6) 42(0) 423

Traditional Method

1 47 X9423

Estimate Products

___

Area Model Estimate

Round To A Friendly Number__

Problem

Area Model Multiplication

____ ____

Add The Products

+=

Traditional Method

___

Area Model___ ___

2.9 Transition to Standard Algorithm: (Day 2)

Traditional Method:2 digit by 2 digit


Lesson• Teach the Traditional method: 2 digit by 2 digit• Use R 3.7 to help explain what the kids need to think as they solve the problems.• Use P 3.7 for additional practice and homework.

Notes• Traditional Method• • In this lesson, continue to reinforce that the students need to make an est. before solving each problem and have them


Estimate Products

10 20

60

Area Model Estimate

Round To A Friendly Number

1513

56x13

Problem

50 55 56 60

10


500 60

150 18

Add The Products

500150

60+ 18= 728

Traditional Method

+ 1 56

_x13__ 8 (18)

(36+6) 16(0) 6(0) 5(00) 728

10

50 6

3

Traditional Method Expanded

+1 56

_x13__ 8 (18)

(15+1) 16(0) 6(0) 5(00) 728

Traditional Method

56x13168

56(0)728

Traditional Method: 2 Digit by 2 Digit

Estimate ProductsArea Model Estimate


Problem

____

___


____ ____

____ ____

Add The Products

+=

Traditional Method

___

___

___ ___


(Day 3)Traditional Method:3 digit by 2 digit


Lesson• Teach the Traditional method: 3 digit by 2 digit• *****You do not need to multiply numbers larger than 3 digit by 2 digit*****• • Use R 3.8 to help explain what the kids need to think as they solve the problems.• • Use P 3.8 for additional practice and homework.

Notes• Traditional Method• • In this lesson, continue to reinforce that the students need to make an est. before solving each problem and have them


Estimate Products

12000

Area Model Estimate


317x42

Problem

300

40

300 317 400

40 42 50


12000 400 280

600 20 14

Add The Products

12000 800 280 600 40 +14

= 13214

40

2

300 10 7

Traditional Method

2 1

317 X42 63412580

13214

Traditional MethodExpanded

2 1 317 x42 4 (14) (2+1) 3(0) 6(00) 8(0) (280) (4+2) 6(00) 12(000) 13214

Traditional Method

Estimate ProductsArea Model Estimate


Problem

____

___


___ ___ ___

___ ___ ___

Add The Products

=

___ ___ ___

___

___


(Day 4)Traditional Method: Decimals

Common Core Focus

Lesson• Teach the Traditional method: Using numbers with decimals. • *****You will not need to multiply any numbers that goes to the thousandths place. Use only decimals up the

hundredths place***** • Use P 6.5 and P 6.6 for additional practice.• Homework: Study Link 2.9 but they have to use traditional method … Not Lattice

Notes• Traditional Method• In this lesson, continue to reinforce that the students need to make an est. before solving each problem and have them


Multiplying by Decimals- All About the tens and tenths

x 100 x 10 x 1 x .1 (1/10) x .01 (1/100)

4 400 40 4 .4 .0423 2300 230 23 2.3 .23

• Do the digits change when multiplying whole number and decimals?

•Does the value of the digits change when multiplying whole numbers and differences?

33 3 3

4x3=t t=

4x.3=t t=

Multiplying Decimals and Whole Numbers

Similar Different


(Day 5)PP and Traditional, Side by Side

• Common Core Focus

Lesson• You are going to have the kids solve some multiplication problems in their notebooks. We would like you to model solving

the problems using PP and Traditional, side by side. Make sure they estimate before answering the problems. • Use all problems on 54, 55 in EM Journal to model pp/traditional side by side and have them practice in their notebooks. • INSERTED HW 2.9HW1 and 2.9HW2

Notes

• Show Educreations video from June to show transitions... You can find this on the Wiki

2.10 Comparing Large Numbers Through Games

Common Core Focus

Lesson• Readiness: play game• MMR• MM• Part 1: Ask the questions on Teacher Manual pg 79.• NO journal pages• Part 2: play game and Number Top-It• Study link

Notes

Comparing Number SituationsWhat can you buy with…

$2? $2,000? $20,000?

What type of transportation would you use to travel….

2 Miles? 20 Miles? 20,000 Miles?

How long would it take to read…

2 Pages? 200 Pages? 2,000 pages?

Number Millions Hundred Thousands

Ten Thousands Thousands

Hundreds Tens Ones

>

Comparing Numbers

Number Top ItPlayer 1 <,> o r= Player 2

students develop understanding of why division procedures work based on the meaning of base-ten...

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