Fourth Grade- Unit 2 Everyday 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 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. 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 The standard seems to suggest a connection between the number pattern and a story. Try to connect function machines and number patterns to a real life situation.

Make And Analyze A Pattern Rule:+5 In Out 1 3 5 7 9 11 13 Notice Think Wonder Rule: +5 In Out 2 4 6 8 10 12 14 Notice Think Wonder

Make And Analyze A Pattern Rule:+5 In Out 1 2 3 4 5 6 7 Notice Think Wonder Rule: +6 In Out 1 2 3 4 5 6 7 Notice Think Wonder

Extend A Pattern Notice Think Wonder Notice Think Wonder Rule: In Out 3 12 21 30 48 66 Notice Think Wonder Rule: In Out 2 7 12 17 22 27 32 Notice Think Wonder

Use Patterns To Solve Problems RULE: 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? RULE: In Out Mary has 32 tickets for the carnival. Each ride costs 5 tickets. How many tickets will she have left after 4 rides?

Functions and Patterns # of triangles # of sides 2 6 3 9 Rule: # of sides = # of triangles x _3__ Bar Model Bar Model 6 3 9 3 Number Model S=2x3 S=6 Number Model S=3x3 S=9

Functions and Patterns Triangles Sides Bar Model Number Model S=___x ___ S=_____ Rule: # of sides = # of triangles x ___ Rectangles Sides Bar Model Number Model S=___x ___ S=_____ Rule: # of sides= # of rectangles x ___

Functions and Patterns Pentagons Sides 2 5 Bar Model Number Model S=___x ___ S=_____ Rule: # of sides = # of pentagons x ____ Hexagons Sides Bar Model Number Model S=___x ___ S=_____ Rule: # of sides= # of hexagons x ___

Each ____________ has _________________________ Rule: # of ___________= # of ____________x________ # of 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 COUNTING Identity Property SKIP COUNTING MultiplES TURN AROUND FACTS Commutative Property PARTS AND WHOLES Distributive Property Focusing on basic math rules and connecting multiplication facts to previous math learning may help students see the patterns and connections between numbers. These slides can, of course, be used in conjunction with other methods you use to help memorize and understand the multiplication facts.

Identity Property Just 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

1 group of objects is the same as the number of objects Identity Property 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100 1 group of objects is the same as the number of objects 1 group of 5=5 1x5=5

Skip Counting…Is Finding Multiples 1 2 3 4 5 6 7 8 9 10 Skip Count Multiplication Fact 5,10,15 3x5-15

Multiples and Multiplication Facts Start Number 2 Groups of Multiple Multiplication Fact 1 2 1x2=2 4 2x2=4 3 6 3x2=6 8 4x2=8 5 10 5x2=10 12 6x2=12 7 14 7x2=14 16 8x2=16 9 18 9x2=18 20 10x2=20

Multiples and Multiplication Facts Start Number Groups of Multiple Multiplication Fact

Number Grids- Finding Multiples 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20

Commutative Property (Addition Turn Around Facts) 10 7+3 = 3+7

Commutative Property (Multipication Turn Around Facts) 18 3x6 = 6x3

Commutative Property (Turn Around Facts) ____ =

Commutative Property (Turn Around Facts) 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

Distributive Property 7 5+2=7 0 0 5x2=10 2x2=4 5x2=10 2x2= 4 7x2=14

Distributive Property 7 X 12 10 + 2 7 x (10+2) (7 x 10) + (7 x 2)

Distributive Property 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100 If students can remember their 1-5 fact for each number, they can find the the 6-10 facts by adding the 5 fact. The reason is that the facts ‘reset to a multiple of 10 at the 5 fact. Let’s look at the 2 facts…2,4,6,8,10 are the first 5 facts….2x6(1+5) is 2(2x1) +10(2x5)…..2x7 (2+5) is 4(2x2)+ = 1 x + 5 x 6 x 2 x 7 x 3 x 8 x 4 x 9 x 10 x

9 Facts What do you notice about the digits? _____________________ 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100 Why do you think that happens? ____________________

9 Facts- Look at The Patterns Factors Product # of tens # of ones x9 9 18 27 36 45 54 63 72 81 90

Solving Problems By Knowing How Numbers Are Connected Equal Groups Bar Model Number Model 1 Equal Groups of 8 8 1x8=8 1 Equal Groups of Students can connect the 2 facts to the 4 facts and 8 facts by doubling one factor and halving the other factor 1x8= 2x4. In this case the factor 1 was doubled and the factor 8 was halved. This can be done in many ways..tripling and thirding, quadrupling and quartering. What do you notice about the how the numbers are changing?

Solving Problems By Knowing How Numbers Are Connected Equal Groups Bar Model Number Model Equal Groups of What do you notice about the how the numbers are changing?

Solving Problems By Knowing How Numbers Are Connected 2 x 5 = 1 x 10 4 x 5 = 2 x 10 x 5 = x 10 x 5 = x 10

Solving Problems By Knowing How Numbers Are Connected 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 Model Equal Groups of

Arrays, Number Models and Bar Models Array 6 3 Number Model 3x6=18 Bar Model 18 6

Arrays, Number Models and Bar Models Array 3 6 Number Model 6x3=18 Bar Model 18 3

Multiplication Bar Modeling (Factors and Products) Number Model: _____________x_____________=_____________

Square Numbers

Square Numbers 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

Square Numbers-Noticing Patterns Difference 1 2 4 3 9 5 6 7 8 10

2 x____=____ 3 x____=___ 4 x____=____ 5 x____=____ 6 x____=____ Use bar modeling cards- fill out cards. Bend them in the middle 8 x____=____ 9 x____=____ 10 x____=____

x2 x3 x4

x5 x6 x7

x8 x9 x10

3.2b Discovering Prime and Composite 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 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:_____________ Have students create all of the possible arrays for a number. If they can only create arrays with 1 row and 1 column for a number, it is prime. Numbers with multiple arrays are composite.

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. 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: 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____=____ Use bar modeling cards- fill out cards. Bend them in the middle 8 x____=____ 9 x____=____ 10 x____=____

Factor Captor

3.2d Prime and Composite Numbers (1.6 from Grade 5) 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 Mental Math and Reflexes -Math Message -Part 1 (NO pt 2,) Boxes No 1 - Homelink1.6 Notes

Prime and Composite Numbers Use Learning carpet…have students place all cards in coorect location. Take off all multiples of 2, 3, 4 etc… If a card is already gone place a marker to represent additional multiples/factors ( 6 would be gone already because it is a multiple of 2, place a marker down when multiples of 3 land on it.) Combine with next slide.

Prime and Composite Number 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 Use Learning carpet…have students place all cards in coorect location. Take off all multiples of 2, 3, 4 etc… If a card is already gone place a marker to represent additional multiples/factors ( 6 would be gone already because it is a multiple of 2, place a marker down when multiples of 3 land on it.)

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

3.3 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-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

3.4 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 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 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- 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 Bar Models 20 5 # in each Group (5) # of groups (4) Number Models 4x5=20 20/4=5

Multiplication and Division Bar Models 20 4 # in each Group (4) # of groups (5) Number Models 5x4=20 20/5=4

Multiplication and Division: Bar Models and Number Models ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___ ___x___=___ ___/___ =___

Multiples Or Products

12 12/2=x 4 4x3=x 45 9 45/x=9

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 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? 4 John J= Mary M=

Using Bar Models to Solve ‘As Many’ Problems 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? Mary M= John J=

Bar Modeling- Multiplication Total Equal part Equal Part Number Model: _____________x_____________=_____________

Bar Modeling- Multiplication Start 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) Number Model: 6÷2=3

Multiplication Bar Modeling Number Model: _____________x_____________=_____________

Multiplication Bar Modeling Number Model: _____________x_____________=_____________

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 Ted bought 4 bags of apples. Altogether, there were 36 apples. How many apples were in each bag? 4xA=36 # of Groups Unknown Picture Ted bought $40 worth of books for his friends. Each book cost $8. How many books did he buy? 40=Bx8 e 12 36 A 40 8 B

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

Amount Per Group Unknown Bar Modeling: Joining Equal Groups (Multiplication) (Remember to split bottom bar in TA and APG examples) Total Amount Unknown Number Model Amount Per Group Unknown # of Groups Unknown

Amount Per Group Unknown Bar Modeling: Joining Equal Groups (Multiplication) (Remember to split bottom bar in TA and APG examples) Total Amount Unknown # Story ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Amount Per Group Unknown # of Groups Unknown ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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

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

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

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

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

Amount Per Group Unknown 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 Model Number of Groups Unknown

Bar Models and Factor Strings 18 6 Number Model 18=3x6 24 2 Number Model 24=3x3x2

Multiplying Along the Number Line Bar Model __________x___________=_______ Bar Model

3.9 True or False 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 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

Pan Balance Equations ( Equal: = ) Number Model

Pan Balance Equations ( Less Than: < ) Picture

Pan Balance Equations ( Less Than: < ) Number Model

Pan Balance Equations ( Greater Than: > ) Picture

Pan Balance Equations ( Greater Than: > ) Number Model

Pan Balance Equations # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.10- Parentheses in Number Stories (May Need t0 find some problems) 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 -Mental Math and Reflexes -Math Message -Part 1 -Part 2 Note Only do the problems that already have (), Putting () in is a 5th 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. 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 -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