unit 3 multiplication and division; number sentences

Fourth Grade- Unit 2Everyday Math Unit 3

Unit 3 Multiplication and Division; Number Sentences

4th Grade-Unit 2 (EM3 ) Notes

• *no calculators • *Problem solving 1/week • *Read/write to million *calculations to 100,000 • *DO NOT USE THE WORD BALLPARK * instead of timed fact

tests we strongly suggest doing a “running record” of x facts. ALWAYS do the readiness first

• Use doc camera to show examples or base 10 blocks • * GAMES ARE TO BE PLAYED AND SUPERVISED EVERYDAY!!*

3.1 What’s My Rule: Function Machine

Common Core Focus

4.OA5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that werenot explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in theresulting sequence and observe that the terms appear to alternate between odd and even numbers. Explaininformally why the numbers will continue to alternate in this way.

Lesson

• -Readiness• -Mental Math and Reflexes• -Math Message• -Part 1• -Enrichment• -Math Box no 2,4• -Homelink

Notes• In part 1 have students explain in writing their thinking in a notebook. Ex. Since the rule was -80 and I knew the out number,

to solve I had to turn around and +80

Make And Analyze A Pattern

Rule:+5

In Out

1

3

5

7

9

11

13

Rule: +5

In Out

2

4

6

8

10

12

14

Notice

Think

Wonder

Notice

Think

Wonder

Make And Analyze A Pattern

Rule:+5

In Out

1

2

3

4

5

6

7

Rule: +6

In Out

1

2

3

4

5

6

7

Notice

Think

Wonder

Notice

Think

Wonder

Extend A Pattern

Rule:

In Out

3 12

21

21 30

30

48

48

66

Rule:

In Out

2

7 12

12

17

22 27

27

32

Notice

Think

Wonder

Notice

Think

Wonder

In Out

In Out

Johnny is saving money to buy a new toy for $60. He has $15 saved. He earns $7 a week mowing his neighbor’s lawn. How many weeks will he have to work to save enough money to buy his new toy?

Mary has 32 tickets for the carnival. Each ride costs 5 tickets. How many tickets will she have left after 4 rides?

RULE:

RULE:

Use Patterns To Solve Problems

Functions and Patterns

# of triangles # of sides

2 6

3 9

Rule: # of sides = # of triangles x _3__

6

3 3

Bar Model

Number ModelS=2x3

S=6

9

3 3 3

Bar Model

Number ModelS=3x3

S=9

Functions and PatternsTriangles Sides

Rectangles Sides

Rule: # of sides = # of triangles x ___

Rule: # of sides= # of rectangles x ___

Number Model

S=___x ___

S=_____

Bar Model

Number Model

S=___x ___

S=_____

Bar Model

Functions and PatternsPentagons Sides

2 5

Hexagons Sides

Rule: # of sides = # of pentagons x ____

Rule: # of sides= # of hexagons x ___

Number Model

S=___x ___

S=_____

Bar Model

Number Model

S=___x ___

S=_____

Bar Model

# of # of

Each ____________ has _________________________

Rule: # of ___________= # of ____________x________

Bar Model

Number Grids

In Rule Out

3.2 Multiplication Facts

Common Core Focus• 4.oa.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.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.

Lesson

• -Readiness- do first• -Mental Math and Reflexes• -Math Message• -Part 1• -Part 2• -Math Box no 3,4,5

Notes• Refer to chart as a “factor table/multiples table” NOT x table.

Products

Learning Multiplication Facts

DISTRIBUTIVE PROPERTY

COMMUTATIVE PROPERTY

IDENTITY PROPERTY

MULTIPLESSKIP COUNTING

COUNTING

TURN AROUND FACTS

PARTS AND WHOLES

Identity PropertyJust Count!

1 group of 6 has 6

1x6=6

6 groups of 1 have 6

6x1=6

This means that you can multiply 1 to any number... and it keeps its identity! The number stays the same!

1x8=8 8x1=8 1x67=67 67x1=67

1x234=234 234x1=234

Identity Property1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

1 group of objects is the same as the number of objects1 group of 5=5

1x5=5

Skip Counting…Is Finding Multiples

1 2 3 4 5 6 7 8 9 10

2

5

10

Skip Count Multiplication Fact

5,10,15 3x5-15

Multiples and

Multiplication FactsStart Number

2

Groups of Multiple MultiplicationFact

1 2 1x2=2

2 4 2x2=4

3 6 3x2=6

4 8 4x2=8

5 10 5x2=10

6 12 6x2=12

7 14 7x2=14

8 16 8x2=16

9 18 9x2=18

10 20 10x2=20

Multiples and

Multiplication FactsStart Number

Groups of Multiple MultiplicationFact

Number Grids- Finding Multiples

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3

4

5

6

7

8

9

10

Commutative Property(Addition Turn Around Facts)

7+3 = 3+7

10

Commutative Property(Multipication Turn Around Facts)

3x6 = 6x3

18

Commutative Property(Turn Around Facts)

=

____

Commutative Property(Turn Around Facts)

1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Distributive Property

7

5+2=7

0 0 0 0 0 0 0 0 0 0 0 0 0 0

5x2=10 2x2=4

5x2=102x2= 47x2=14

Distributive Property

7 X 12

10 + 2

7 x (10+2)

(7 x 10) + (7 x 2)

Distributive Property1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10

12

14

16

18

20

3 3 6 9 12

15

18

21

24

27

30

4 4 8 12

16

20

24

28

32

36

40

5 5 10

15

20

25

30

35

40

45

50

6 6 12

18

24

30

36

42

48

54

60

7 7 14

21

28

35

42

49

56

63

70

8 8 16

24

32

40

48

56

64

72

80

9 9 18

27

36

45

54

63

72

81

90

10

10

20

30

40

50

60

70

80

90

100

= = =

1 x + 5 x = 6 x

2 x + 5 x = 7 x

3 x + 5 x = 8 x

4 x + 5 x = 9 x

5 x + 5 x = 10 x

9 Facts1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

What do you notice about the digits?

_________________________________________________________________________________________________________

Why do you think that happens?

____________________________________________________________________________________________________

Factors Product # of tens # of ones

x9 9

x9 18

x9 27

x9 36

x9 45

x9 54

x9 63

x9 72

x9 81

x9 90

9 Facts- Look at The Patterns

Solving Problems By Knowing How Numbers Are Connected

Equal Groups Bar Model Number Model

1 Equal Groups of 8 8 1x8=81 1 1 1 1 1 1 1

Equal Groups of

Equal Groups of

Equal Groups of

•What do you notice about the how the numbers are changing?


Equal Groups Bar Model Number ModelEqual Groups of

Equal Groups of

Equal Groups of

Equal Groups of

•What do you notice about the how the numbers are changing?

2 x 5 = 1 x 10

4 x 5 = 2 x 10

x 5 = x 10

x 5 = x 10



• Based on what you discovered from the number beads, explain how you can use numbers that are connected to solve multiplication problems. Remember to explain the ‘rule’ and give an example._____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Equal Groups Bar Model Number ModelEqual Groups of

Equal Groups of

Arrays, Number Models and Bar Models

Array 6 3

Number Model 3x6=18

18

6 6 6

BAR MODEL

Arrays, Number Models and Bar Models

Array

3

6

Number Model 6x3=18

18

3 3 3 3 3 3

BAR MODEL

Multiplication Bar Modeling(Factors and Products)

Product

Factor Factor Factor Factor

Number Model:

_____________x_____________=_____________

Square Numbers

Square Numbers

1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Square Numbers-Noticing Patternst t2 Difference

1 1

2 4 3

3 9 5

4

5

6

7

8

9

10

2 x____=____ 3 x____=___ 4 x____=____

5 x____=____ 6 x____=____ 7 x____=____

8 x____=____ 9 x____=____ 10 x____=____

x2

x3

x4

x5

x6

x7

x8

x9

x10

3.2b Discovering Prime and Composite




Lesson• Prime/Composite Numbers• -Enrichment from 3.2- MM 77• - INSERT project 1 from Grade 5- make sure each child has 8 different colored pencils• -Study link 3.2

Notes• Insert guided/independent practice for Prime/composite numbers• With project- notice the #’s that have more than 1 factor- keep paper in their folders for reference

PRIME AND COMPOSITE NUMBERS

•Create all the possible arrays for:_____________

3.2c Factors (Grade 5- 1.4) Common Core Focus

• 4.oa.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.


Lesson

• Readiness: Fact Families: Use 3 questions to write in notebooks• Mental Math and Reflexes• Message• Part 1• Part 2• NO boxes• Homelink: use!

Notes• Teach and Play Factor Captor

2 x____=____ 3 x____=___ 4 x____=____

5 x____=____ 6 x____=____ 7 x____=____

8 x____=____ 9 x____=____ 10 x____=____

FACTOR CAPTOR

3.2d Prime and Composite Numbers (1.6 from Grade 5)




Lesson

• Mental Math and Reflexes• -Math Message• -Part 1• (NO pt 2,)• Boxes No 1• - Homelink1.6

Notes

Prime and Composite Numbers

Prime and CompositeNumber Factors Prime or

CompositeNumber Factors Prime or

CompositeNumber Factors Prime or

Composite

1 14 27

2 15 28

3 16 29

4 17 30

5 18 31

6 19 32

7 20 33

8 21 34

9 22 35

10 23 36

11 24 37

12 25 38

13 26 39

Prime Numbers

• A prime number is a number that has exactly 2 factors- 1 and itself. In the box below, list all of the prime numbers.

• Can a composite number have 2 factors? _____• If yes, give an example.____________________

Problem Solving Activity





Lesson• -Readiness-make sure students write about pattern• -Mental Math and Reflexes• -Math Message• -Part 1- • -Part 2• -Math Box no 4• -Homelink

Notes• Of the facts you don’t know- practice ONLY 2 cards a week.

• Refer back to bar model cards patterns and strategies shown previously


Common Core Focus

• 4.oa.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.


Lesson• Play: -Factor Captor, x top-it, baseball x• -Mental Math and Reflexes• - MORE FACT PRACTICE• -Homelink

Notes• Can use this day to take a running record of individual x facts. Teach x fact strategies, practice strategies• Refer back to bar model cards patterns and strategies shown previously

3.5 Multiplication and Division




Lesson• Readiness- great game• -Mental Math and Reflexes• -Math Message• -Part 1• -Part 2• - -Math Box NO 2,4• -Homelink

Notes• USE MANY MANIPULATIVES

Multiplication and Division

20

5 5 5 5 # in each Group

(5)

# of groups (4)

Number Models

Bar Models

4x5=20 20/4=5

Multiplication and Division

20

4 4 4 4 4 # in each Group

(4)

# of groups (5)

Number Models

Bar Models

5x4=20 20/5=4

Multiplication and Division: Bar Models and Number Models

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

___x___=______/___ =___

MultiplesOr

Products

12

4 4 4

45

9

12/2=x

4x3=x

45/x=9

3 3 3 3 3

3.8 Solving Number Stories

Common Core Focus• 4.oa.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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. 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.1

• 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.

Lesson• -Readiness- use bar models• -Mental Math and Reflexes• Play high number toss• Intro problem solving with SRB 175• Insert a problem• Math Box• Studylink

Note

Using Bar Models to Solve ‘As Many’ Problems

4

JohnJ=

MaryM=

John and Mary had a garage sale. John earned $4. Mary earned 3 times as much as John.

How much did Mary earn?

How much did they earn altogether?

Using Bar Models to Solve ‘As Many’ Problems

MaryM=

JohnJ=

John and Mary earned $15 at a garage sale. John earned 4 times as much as Mary.

How much did Mary earn?

How much did John?

Bar Modeling- Multiplication

Total

Equal part Equal Part

Number Model:

_____________x_____________=_____________

Bar Modeling- MultiplicationStart Join

X=

Jim collects butterflies. There were 3 butterflies in each container. He had 2 containers. How many butterflies does Jim have in his collection?

Multiplication

Total(6)

Separate Equal Part(3)

Separate Equal Part(3)

Number Model:

6÷2=3

Multiplication Bar Modeling

Number Model:

_____________x_____________=_____________

Bar Modeling: Joining Equal Groups (Multiplication)

Total Amount Unknown Example•Ted has 5 cartons of eggs. Each carton has 12 eggs in it. How many eggs does Ted have?

•E=12x5

Amount Per Group Unknown Example

•Ted bought 4 bags of apples. Altogether, there were 36 apples. How many apples were in each bag?

•4xA=36

# of Groups Unknown PictureTed bought $40 worth of books for his friends. Each book cost $8. How many books did he buy?

40=Bx8

e

12

12

12

12

12

36

A A A A

40

8 B

Bar Modeling: Joining Equal Groups (Multiplication)(Remember to split bottom bar in TA and APG examples)

Total Amount Unknown Picture

Amount Per Group Unknown Picture

# of Groups Unknown Picture


Total Amount Unknown Number Model

Amount Per Group Unknown Number Model

# of Groups Unknown Number Model


Total Amount Unknown # Story____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Amount Per Group Unknown # Story____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

# of Groups Unknown # Story______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Joining Equal Groups (Multiplication)- Total Amount Unknown(Remember to split bottom bar in TA and APG examples)




Bar Modeling: Joining Equal Groups (Multiplication) Total Amount Unknown(Remember to split bottom bar in TA and APG examples)




Bar Modeling: Joining Equal Groups (Multiplication) Total Amount Unknown(Remember to split bottom bar in TA and APG examples)



Total Amount Unknown # Story______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Joining Equal Groups (Multiplication)- Amount Per Group Unknown(Remember to split bottom bar in TA and APG examples)




Bar Modeling: Joining Equal Groups (Multiplication) Amount Per group Unknown(Remember to split bottom bar in TA and APG examples)



Amount Per Group Unknown # Story______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Joining Equal Groups (Multiplication)- Number of Groups Unknown

Number of Groups Unknown Number Model



Bar Models and Factor Strings

24

2 2 2 2 2 2 2 2 2

18

6 6 6

Number Model18=3x6

Number Model24=3x3x2

Multiplying Along the Number Line

__________x___________=_______

__________x___________=_______

__________x___________=_______

__________x___________=_______

Bar Model

Bar Model

3.9 True or False Number Stories





Lesson• Mental Math and Reflexes• -Part 1• -Part 2• -Math Box no 4,6• -Homelink

Note

Balanced Equations(Turn Around Equations)

<

=

>

Pan Balance Equations ( Equal: = )

=Picture

=

=Picture

=

=Picture

=

Pan Balance Equations ( Equal: = )

=Number Model

=

=Number Model

=

=Number Model

=

Pan Balance Equations ( Less Than: < )

<Picture

<

<Picture

<

<Picture

<

Pan Balance Equations ( Less Than: < )

<Number Model

<

<Number Model

<

<Number Model

<

Pan Balance Equations ( Greater Than: > )

>Picture

>

>Picture

>

>Picture

>

Pan Balance Equations ( Greater Than: > )

>Number Model

>

>Number Model

>

>Number Model

>

Pan Balance Equations

# Story______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.10- Parentheses in Number Stories(May Need t0 find some problems)





Lesson• -Mental Math and Reflexes• -Math Message• -Part 1• -Part 2

Note• Only do the problems that already have (), Putting () in is a 5 th grade skill

3.10- Open Sentence(Use variables- CC uses the word unknown)

Common Core Focus• 4.oa.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.



Lesson• --Readiness• -Mental Math and Reflexes• -Math Message• -Part 1• -Math Box no 4• -Homelink- skip 9-12

Note• Enrichment problem (MM 101)- do as a problem solving day.• Write a reflection. • SEE PREVIOUS SLIDES

Problem Solving

Assessment

Make Unit 3 Assessment •.Open Response- do as series of equations, , so () are not needed.•Boxes- no 2,4

unit 3 multiplication and division; number sentences

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