EUREKA MODULE 2.1

MATH EUREKA - MODULE 2

PART 1

Index

What are we learning today?

Lesson 11

Lesson 1

Lesson 6

Lesson 16

Lesson 17

Lesson 2

Lesson 7

Lesson 12

Lesson 3

Lesson 8

Lesson 13

Lesson 18

Lesson 4

Lesson 9

Lesson 14

Lesson 19

Lesson 15

Lesson 5

Lesson 10

MidModule Ass.

LESSON 1

Find factor pairs for numbers to 100, and use understanding of factors to define prime and composite.

• I can identify the factors and the product represented in an array.
• I can identify factors to define prime and composite numbers
• I can identify factors of numbers and determine if they are prime or composite.

68÷2=

34

30

60

÷2

96÷3=

32

30

90

÷3

72÷3=

24

20

60

12

÷3

72÷4=

18

15

60

12

÷4

5 x _ = 15

Write the division problem.

15 ÷ 5 = 3

3 x _ = 9

Write the division problem.

9 ÷ 3 = 3

4 x _ = 16

Write the division problem.

16 ÷ 4 = 4

5 x _ = 45

Write the division problem.

45 ÷ 5 = 9

6 x _ = 42

Write the division problem.

42÷ 6 = 7

7 x _ = 56

Write the division problem.

56 ÷ 7 = 8

9 x _ = 72

Write the division problem.

72 ÷ 9 = 8

6 x _ = 54

Write the division problem.

54 ÷ 6 = 9

7 x _ = 63

Write the division problem.

63 ÷ 7 = 9

9 x _ = 54

Write the division problem.

54 ÷ 9 = 6

3 x 2 ones = 6 ones

3x2=

Unit form

3 x 2tens= 6 tens= 60

3x20=

3 tens x 2 tens=

30x20=

6 hundred = 600

4 x 2 ones = 8 ones

4x2=

Unit form

4 x 2tens= 8 tens= 80

4x20=

4 tens x 2 tens=

40x20=

8 hundred = 800

3 x 3 ones = 9 ones

3x3=

Unit form

3 x 3tens= 9 tens= 90

3x30=

3 tens x 3 tens=

30x30=

9 hundred = 900

3 x 4 ones = 12 ones

3x4=

Unit form

3 x 4tens= 12 tens= 90

3x40=

3 tens x 4 tens=

30x40=

12 hundred = 1200

Application problem

8 × ____= 96. Find the unknown side length, or factor. Use an area model to solve the problem.

2x4

1x8

1, 2, 4 and 8 are all factors of 8.

Can you think of any other pair of factors?

1x18

2x9

1, 2, 9 and 18 are all factors of 18.

3 and 6 are factors of 18 too.

3x6

How can we make sure we found all the factors of 18?

1, 2, 3, 6, 9, 18

2x8 = 16

What other multiplication sentences can you write using different factos that will give us the same product?

1x16=16 4x4=16

1, 2, 3, 4, 8, 16

1x7=

Can you find another pair of factors for 7?

How is this different from the examples we have done before?

This one only has two factors: 1 and the number itself.

Can you name pairs of factors for 5?

How is this different from the examples we have done before?

This one only has two factors: 1 and the number itself.

Numbers like 5 and 7 have only two factors: 1 and the number itself.

These are called PRIME numbers.

Can you think of two more PRIME numbers?

How do we call numbers that are not PRIME?

COMPOSITE numbers.

Find the factor pairs of 23.

COMPOSITE

PRIME

1, 23

Find the factor pairs of 35.

COMPOSITE

PRIME

1, 5, 7, 35

Find the factor pairs of 48.

COMPOSITE

PRIME

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

PROBLEM SET

10 minutes Student's book page: 111

Compare the factors in 24 and 12. What do you notice about their factors? Compare the factors in 18 and 9. What do you notice about their factors?

In Problem 1, what numbers have an odd number of factors? Why is that so?

Are all prime numbers odd? Explain why.

Explain your answer to Problem 3(b). Are all even numbers composite? How many even numbers are not composite?

We talked a lot about the number 1 today as being a factor of other numbers, but we have not classified it as prime or composite. What is 1?

EXIT TICKET 1- PG 111

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LESSON 2

I am learning how to test for factors of larger numbers.

• I can use division to find factors of larger numbers.
• I can use the associative property to find additional factors of larger numbers.
• I can use division or the associative property to find factors of larger numbers.

=8

1x8

What is the length of the array? What is the width of the array?

Write the multiplication sentence.

How else can I get 8 by multiplying two numbers?

2x4

=8

Factors of 12?

12x1

6x2

4x3

Factors of 16?

16x1

8x2

4x4

Factors of 18?

18x1

9x2

6x3

Solve 174 x 2 using the standard algorithm.

174 x 2 = 348

What 4 factors of 348 do you know straight away?

1, 2, 174, 348

Solve 348 x 2 using the standard algorithm.

348 x 2 = 696

What 4 factors of 696 do you know straight away?

1, 2, 348, 696

Solve 696 x 2 using the standard algorithm.

696 x 2 = 1392

What 4 factors of 1392 do you know straight away?

1, 2, 696, 1392

Solve 1392 x 2 using the standard algorithm.

1392 x 2 = 2784

What 4 factors of 2781 do you know straight away?

1, 2, 1392, 2781

Find the factor pairs of 7.

COMPOSITE

PRIME

1 , 7

Find the factor pairs of 12.

COMPOSITE

PRIME

1, 2, 3, 4, 6, 12

Find the factor pairs of 15.

COMPOSITE

PRIME

1, 3, 5, 15

Find the factor pairs of 17.

COMPOSITE

PRIME

1, 17

Find the factor pairs of 21.

COMPOSITE

PRIME

1, 3, 7, 21

Application problem

Sasha says that every number in the twenties is a composite number because 2 is even. Amanda says there are two prime numbers in the twenties. Who is correct? How do you know?

28 = 7 x _

How did you find the unknown factor?

We divided 28 by 7.

Is 10 a factor of 28?

10x2= 20; 10x3=30 If you divide 28 by 10 you get a remainder.

Is 3 a factor of 54?

How can I find out?

We divide 54 by 3.

What if I get a remainder?

If we get a remainder then, it is not a factor.

Is 2 a factor of 54?

Yes, because if I divide 54 by 2, I don't have any remainders. I also know 2 is an even number, so it would go evenly into 54.

Is 3 a factor of 78?

How can I find out?

We divide 78 by 3.

78÷3= 26

Yes, 3 is a factor of 78 because I don't have remainders.

Is 4 a factor of 94?

How can I find out?

We divide 94 by 4.

94÷4= 23 R2

No, 4 is not a factor of 94 because I have remainders.

Is 3 a factor of 87?

How can I find out?

We divide 87 by 3.

87÷3= 29

Yes, 3 is a factor of 87 because I don't have remainders.

Do we need to divide 54 to figure out if 5 is a factor of 54? And if 2 is factor of 54?

The even numbers all have 2 for a factor. If the digit in the ones place is odd, then 2 isn't a factor.

Numbers with 5 as a factor have 0 or 5 as a digit in the ones place.

How can we know if 6 a factor of 54?

6 x 9 = 54

We saw that 2 and 3 are both factors of 54. Is this number sentence true? 54 = 6 × 9 = (2 × 3) × 9

54 = 6 x 954 = (2x3) x 9

Move the parentheses so that 3 associates with 9 rather than 2.

3x9= 27 27x2?

54 = 6 x 9 54= (2x3)x9 54=2x(3x9)

54

ASSOCIATIVE property shows that both 2 and 3 are factors of 54.

Use the associative property to see if 2 and 3 are also factors of 42.

42 = 6 x _

42 = 6 x 7 42 = (2x3) x 7 42= 2x (3x7)

42

Since 6 is a factor of 60, both 2 and 3 are also factors.

Can you prove this statement?

60 = 6 x _60 = 6 x 10 60 = (2x3) x 10 60 = 2 x (3x10)

Since 6 is a factor of 60, both 2 and 3 are also factors.

Can you prove this statement?

60 = 6 x _60 = 6 x 10 60 = (2x3) x 10 60 = 2 x (3x10)

6 x 12 =

6 x 12 = 72

Using either division or the associative property, work with your partner to prove that since 6 is a factor of 72, 2 and 3 are also factors.

72 = 6 x 1272 = (2x3) x 12 72 = 2 x (3x12)

PROBLEM SET

10 minutes Student's book page:

How did answering Problem 1, Part (a) help you answer Problem 1, Part (b)? Was it necessary to divide?

What relationship do you notice between Problem 1, Parts (a), (c), and (e)? What about between Problem 1, Parts (d), (f), and (h)?

Discuss with your partner what is similar and what is different about Problem 1a, 1c and 1e and Problem 1d, 1f and 1h.

What’s the difference between the statements in Problem 4? Why is one false and the other true?

When we divided 72 by 3, we saw that there was no remainder. Another way to say that is “72 is divisible by 3.” Is 24 divisible by 3? Is 25 divisible by 3?

We can use number patterns to determine if 2 and 5 are factors of other numbers. What other numbers do you think have patterns? Do you see a pattern for determining which numbers 3 is a factor of? Can you describe one?

If 8 is a factor of 96, what other numbers must also be factors of 96? How can we use theassociative property to prove this?

Once someone tried to tell me that the two statements in Problem 4 say the same thing. How would you explain that the two statements are different??

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LESSON 3

I am learning how to determine if a whole number is a multiple of another number.

• I can determine the meaning of the word multiple.
• I can determine if one number is a multiple of another number, and list multiples of given numbers.
• I can use the associative property to see that any multiple of 6 is also a multiple of 3 and 2.

Can you count in groups of...?

2 to 20

3 to 30

4 to 40

5 to 50

6 to 60

10 to 100

Find the factor pairs of 5.

COMPOSITE

PRIME

1, 5

Find the factor pairs of 15.

COMPOSITE

PRIME

1, 3, 5, 15

Find the factor pairs of 12.

COMPOSITE

PRIME

1, 2, 3, 4, 6, 12

Find the factor pairs of 19.

COMPOSITE

PRIME

1, 19

Find the factor pairs of 24.

COMPOSITE

PRIME

1, 2, 3, 4, 6, 8, 12, 24

What number has 10 as a factor?

30

30

56

45

48

Write the division to prove both 5 and 2 are factors of 30

What numbers have 6 as a factor?

30

30

56

45

48

48

Prove that both 3 and 2 are factors of 30 an 48 using the associative property.

What numbers have 8 as a factor?

30

56

45

48

48

56

Prove that both 3 and 2 are factors of 48 an 56 using the associative property.

Application problem

8 cm × 12 cm = 96 cm2. Imagine a rectangle with an area of 96 cm2 and a side length of 4 cm. What is the length of its unknown side? How will it look when compared to the 8 cm by 12 cm rectangle? Draw and label both rectangles.

When we skip count by a whole number, the numbers that we say are called multiples.

Factors are the numbers we multiply together to get a certain product, whilst multiples are the number we say when we skip count.

Why is 24 a multiple of 4?

What about 8? Is 24 a multiple of 8?

How can we know if 96 is a multiple of 3?

Since zero times any numbers equals zero, zero is multiple of every number.

We could consider it the firts multiple of every number.

Shout out a multiple of 6.

Is any multiple of 6 also multiple of 2 and 3?

60 = 10 x 6= 10 x(2x3) =(10x2)x3 = 20 x3

Let's use a letter to represent the number of sixes to see if this is true for all sixes.

The multiples of a number are also multiples of its factors.

n x 6 =n x (2x3)n x 6= (nx2) x 3 n x 6=(n x 3) x 2

PROBLEM SET

10 minutes Student's book page: 123

What strategy did you use in Problem 2?

In Problem 5, Parts (c) and (d), what patterns did you discover about multiples of 5 and 10?

Explain the difference between factors and multiples.

Which number is a multiple of every number?

In Problem 1, which multiples were the easiest to write: the fives, fours, or sixes? Why?

How can the associative property help you to know if a number is a multiple of another number?

Did anybody answer no on Problem 4? What about 1? Are prime numbers multiples of 1?

In the lesson, we found that when counting by fours, the multiples followed a pattern of having 0, 4, 8, 2, and 6 in the ones digit. Does that mean any even number is a multiple of 4?

True or False? 3 is a factor of 12. 12 is a multiple of 3. 12 is divisible by 3.

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LESSON 4

I am learning the properties of prime and composite numbers to 100.

• I can define and identify prime and composite numbers to 100.
• I can describe the properties of prime and composite numbers to 100.
• I can use multiples to determine prime and composite numbers.

What number has 10 as a factor?

40

40

42

64

54

Write the division to prove both 5 and 2 are factors of 40

40= 10 x 4 40 = (5x2) x4 40= 5 x (2x4) 40= 2 x (5x4)

What numbers have 6 as a factor?

42

40

42

64

54

54

Write the division to prove both 3 and 2 are factors of 54 and 42

42= 6 x 7 42 = (3x2) x7 42= 3 x (2x7) 42= 2 x (3x7)

54= 6x9 54 = (3x2) x9 54= 3 x (2x9) 54= 2 x (3x9)

What numbers have 8 as a factor?

40

40

42

64

54

64

Write the division to prove both 4 and 2 are factors of 54 and 42

40= 8x5 40 = (4x2) x5 40= 4 x (2x5) 40= 2 x (4x5)

64= 8x8 64 = (4x2) x8 64= 4 x (2x8) 64= 2 x (4x8)

In your tables, count in 4s for the next two minutes. One number each, in order.

Could you have keep counting by 4 after I told you to stop?

We know multiples are infinite, they go on forever. How is this different from factors?

Every number has only a certain amount of factors but an unlimited number of multiples.

Find the factor pairs of 10.

COMPOSITE

PRIME

1, 2, 5, 10

Find the factor pairs of 13.

COMPOSITE

PRIME

1, 13

Find the factor pairs of 20.

COMPOSITE

PRIME

1, 2, 4, 5, 10, 20

Find the factor pairs of 21.

COMPOSITE

PRIME

1, 3, 7, 21

Find the factor pairs of 81.

COMPOSITE

PRIME

1, 3, 9, 27, 81

PROBLEM SET

TODAY WE ARE GOING TO WORK TOGETHER THROUGH THE PROBLEM SET.

PROBLEM SET 1

Which numbers are circled? Which numbers are crossed out?

We started this Problem Set by coloring number 1 red and beginning our work with the multiples of 2. Why didn’t we cross out the multiples of 1?

Are any prime numbers even? Are all odd numbers prime?

We crossed off multiples of 2, 3, 5, and 7. Why didn’t we have to cross off multiples of 4 or 6?

How did you know some of the larger numbers, like 53 and 79, were prime?

How can we find the prime numbers between 1 and 200?

The process of crossing out multiples to find primes is called the sieve of Eratosthenes. Eratosthenes was an ancient Greek mathematician. Why do you think this is called a sieve?

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LESSON 5

I am learning how to multiply multi-digit whole numbers and multiples of 10

• I can use my knowledge of place value units and basic facts to multiply multi-digit whole numbers and multiples of 10.
• I can apply the distributive property to multiply multi-digit whole numbers and multiples of 10.
• I can apply the associative property to multiply multi-digit whole numbers and multiples of 10.

3 x 100

3 x 1000

3 x 10

0.005x1000

5 x 1,000

0.05x100

50x100

30x 1,000

30x100

0.32x 1,000

32x1,000

5.2x100

52x100

0.4x10

4x10

30.45x1,000

0.45x1,000

72x100

7x100

7.002x100

How many ones?

4 tens

4 ten thousandss

How many ones?

4 hundred thousandss

How many ones?

7 millions

How many ones?

2 thousands

How many ones?

3 tens

How many ones?

53 tens

How many ones?

6 ten thousands

How many ones?

86 ten thousands

How many ones?

8 hundred thousands

How many ones?

36 ten thousands

How many ones?

8 millions

How many ones?

24 ten thousands

How many ones?

8 millions

How many ones?

17 hundred thousands

How many ones?

1,034 hundred thousands

How many ones?

ROUND TO THE NEAREST...

Thousand

Hundred

Ten

ROUND TO THE NEAREST...

Thousand

Hundred

Ten

Application problem

The top surface of a desk has a length of 5.6 feet. The length is 4 times its width. What is the width of the desk?

4x30=

12 tens

4x 3 tens=

40x30=

12 hundreds

4tens x 3 tens=

40x300=

4tens x 3 hundreds=

(4x10) x (3x100)=

(4x3) x (10x100)=

12 x 1,000=

12,000

4,000x30=

4 thousands x 3 tens

(4x1,000) x (3x10)=

(4x3) x (1,000x10)=

12 x 10,000=

120,000

60x5=

6 tens x 5=

300

(6x10) x 5=

(6x5) x 10=

When we change the order of the factors, we are using the commutative (any-order) property.When we group the factors differently, we are using the associative property of multiplication.

60x50=

6 tens x 5 tens=

3,000

(6x10) x (5x10)=

(6x5) x (10x10)=

When we change the order of the factors, we are using the commutative (any-order) property.When we group the factors differently, we are using the associative property of multiplication.

60x500=

6 tens x 5 hundreds=

30,000

(6x10) x (5x100)=

(6x5) x (10x100)=

When we change the order of the factors, we are using the commutative (any-order) property.When we group the factors differently, we are using the associative property of multiplication.

60x5,000=

6 tens x 5 thousands=

300,000

(6x10) x (5x1,000)=

(6x5) x (10x1,000)=

When we change the order of the factors, we are using the commutative (any-order) property.When we group the factors differently, we are using the associative property of multiplication.

3,608

451x8=

451 x (8x10)

451 x 80=

(451 x 8) x10

3,608 x 10

36,080

3,608

451x8=

(451x10) x (8x10)

4,510 x 80=

(451 x 8) x (10x10)

3,608 x 100

360,800

3,608

451x8=

(451x10) x (8x100)

4,510 x 800=

(451 x 8) x (10x100)

3,608 x 1,000

3,608,000

PROBLEM SET

10 minutes Student's book page: 133

Problem 3. Discuss how the parentheses that are used to show thinking directs us toward which part of the equation was grouped and, thus, which part of the expression is evaluated first.

In Problem 3, for which problem was the distributive property most useful when solving? For which problems is the distributive property unnecessary?

In Problem 2, was it necessary to solve each expression in order to compare the values? Why or why not?

How does understanding place value help you decompose large numbers to make them easier to multiply?

About 36 million gallons of water leak from the New York City water supply every day. About how many gallons of water leak in one 30-day month? How can the patterns we discovered today about multiplying by 10s, 100s, and 1,000s help us solve this problem?

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LESSON 6

I am learning how to estimate multi-digit products.

• I can estimate multi-digit products by rounding factors to a basic fact.
• I can estimate multi-digit products by using place value knowledge and rounding.
• I can reason if the estimate will be higher or lower than the actual amount.

SPRINT - Pg 31

INDEPENDENT WORK!

SPRINT - Pg 31

MARK YOUR WORK!

ROUND TO THE NEAREST...

Between which two ten thousands is 48,625?

What's the midpoint?

Would it round up or down?

ROUND TO THE NEAREST...

Between which two thousands is 48,625?

What's the midpoint?

Would it round up or down?

ROUND TO THE NEAREST...

Between which two hundreds is 48,625?

What's the midpoint?

Would it round up or down?

ROUND TO THE NEAREST...

Between which two tens is 48,625?

What's the midpoint?

Would it round up or down?

310

31x10=

620

310x2=

310x20=

6,200

310x2x10=

230

23x10=

920

230x4=

230x40=

9,200

230x4x10=

320

32x10=

960

320x3

320x30

9,600

320x3x10=

Application problem

Jonas practices guitar 1 hour a day for 2 years. Bradley practices the guitar 2 hours a day more than Jonas.How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years?

How many students do we have in the classroom?

Do all classroom have the same amount of students?

We have 21 classrooms in the school, how could I find a number that is close to the actual number of students?

What number could help me make an estumate for the number of students in each class?

What number could I round the number of students so it is easier to multiply? And the number of classrooms?

How would I estimate the total number of students?

456x42=

Supose I don't need to know the exact product, just an estimate. How could I round the factos to estimate the product?

Round to the nearest ten

Still hard to work on mentally, can I round 456 to a different place value to make the product easier to find?

460x40=

500x40

5 hundreds x 4 tens= 20 thousands

20,000

1,320x88=

Supose I don't need to know the exact product, just an estimate. How could I round the factos to estimate the product?

How are these connected?

The factors are greater, about 10 times larger each. Let's round.

13,205 x880

10,000 x 900

10,000 x (9x100)= 10,000 x 100 x 9

1,000,000x9= 9,000,000

3,120x880=

Supose I don't need to know the exact product, just an estimate. How could I round the factos to estimate the product?

How are these connected?

The factors are greater, about 10 times larger each. Let's round.

31,200 x880

30,000 x 900

(3x10,000) x (9x100)= (3x9) x (10,000 x 100)

27x 1,000,000= 27,000,000

PROBLEM SET

10 minutes Student's book page: 143

In Problem 6, there are many ways to estimate the solution. Discuss the precision of each one. Which is the closest estimate? Does it matter in the context of this problem?

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LESSON 7

I am learning how to write and interpret numerical expressions.

• I can rewrite math statements from word form to numerical expressions and represent them with diagrams.
• I can rewrite numerical expressions in word form.
• I can compare expressions in word form and numerical form.

21x40

21x4x10

84x10

840

213x30

210x3x10

630x10

6,300

4,213x20

4,213x2x10

8,426x10

84,260

421x18

Supose I don't need to know the exact product, just an estimate. How could I round the factors to estimate the product?

400 x 20=

8,000

323x21=

Supose I don't need to know the exact product, just an estimate. How could I round the factors to estimate the product?

300x20=

6,000

1,950x42=

Supose I don't need to know the exact product, just an estimate. How could I round the factors to estimate the product?

2,000x40=

80,000

2,480x27

Supose I don't need to know the exact product, just an estimate. How could I round the factors to estimate the product?

2,000x30=

60,000

9x3=

(5x3) + (4x3)=

15 + 12=

27

7x4=

(4x4) + (3x4)=

16 + 12=

28

8x2=

(4x2) + (4x2)=

8 + 8=

16

9x6=

(4x6) + (5x6)=

24 + 30=

54

Application problem

Robin is 11 years old. Her mother, Gwen, is 2 years more than 3 times Robin’s age. How old is Gwen?

What expression describes the total value of these 3 equal units?

3x5

What about 3 times an unknown amount called A?

3xA

3 times the sum of a number and 4

n+4

3x(n+4)

6 times the difference between 60 and 51

Show a strip diagram and expression to match these words.

6x(60-51) or (60-51)x6

(60-51)

6x(60-51) or (60-51)x6Are these expressions equal?

COMMUTATIVE PROPERTY

6 times the difference between 60 and some number.

Show a strip diagram and expression to match these words.

6x(60-n) or (60-n)x6

(60-n)

6x(60-n) or (60-n)x6Are these expressions equal?

COMMUTATIVE PROPERTY

The sum of 2 twelves and 4 threes

Show a strip diagram and expression to match these words.

(2x12)+(4x3)

12

12

The sum of 2 copies of some number and 4 copies of adifferent unknown number.

Show a strip diagram and expression to match these words.

(2xm)+(4xn)

5 times the sum of 16 and 14.

Show a strip diagram and expression to match these words.

5x (16+14)

(16+14)

Sum of 2 tens and 3 of some unknown number.

Show a strip diagram and expression to match these words.

(2x10)+ (3xn)

10

10

Say it: 8x(43-13)

8 times 43 minus 13.

8x43-13 = we should multiply 8 by 43 and then take away 13. Is this correct?

What are the two factors we are multiplying?

The difference of 43 and 13 is being multiplied by 8.

8 and (43-13)

8 times the difference of 43 and 13

Say it: (16+9)x4

16 plus 9 times 4

16+9x4 = we should multiply 9 by 4 and then add it to 16. Is this correct?

What are the two factors we are multiplying?

The sum of 16 and 9 is being multiplied by 4.

(16+9) and 4

4 times the sum of 16 and 9

Say it: (20x3)+(5x3)

20 times 3 plus 5 times 3

20x(3+5)x3= we should multiply 20 by the sum of 3 and 5 and then multiply by 3. Is this correct?

What are the two numbers we are adding?

The product of 20 and 3 is being added to the product of 5 and 3.

(20x3) and (5x3)

The sum of 20 times 3 and 5 times 3.

Bigger, smaller or equal?

9x13 ? 8 thirteens

9 x 13 ? 8x13

9x13 > 8x13

Bigger, smaller or equal?

The sum of 10 and 9, doubled ? (2x10)+(2x9)

(10+9)x2 ? (2x10)+(2x9)

19x2 ? 20+18 = 38 ? 38

The sum of 10 and 9, doubled = (2x10)+(2x9)

Bigger, smaller or equal?

30 fifteens minus 1 fifteen ? 29x15

(30x15)-15 ? 29x15

450-15 ? 435 = 435 ? 435

30 fifteens minus 1 fifteen = 29x15

PROBLEM SET

10 minutes Student's book page: 149

Return to the Application Problem. Create a numerical expression to represent Gwen’s age.

In Problem 1(b) some of you wrote 4 × (14 + 26) and others wrote (14 + 26) × 4. Are both expressions acceptable? Explain.

When evaluating the expression in Problem 2(a), a student got 85. Can you identify the error in thinking?

Look at Problem 3(b). Talk in groups about how you know the expressions are not equal. How can you change the second expression to make it equivalent to 18 × 27?

EXIT TICKET 7- PG 153

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 8

I am learning how to convert numerical expressions into unit form.

• I can designate the unit and relate the unit to the expression.
• I can use the commutative property when designating units.
• I can draw a diagram to represent expressions in unit form
• I can use place value understanding to decompose factors and solve for products mentally.
• I can solve for products using the unit form strategy to support mental math.

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

409x32=

____ x ____ =

400x20=

8,000

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

287x64=

____ x ____ =

300x60

18,000

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

3,875x92=

____ x ____ =

4,000x100

400,000

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

6,130x37

____ x ____ =

6,000x40

240,000

Decompose the multiplication sentece

12x3=

(8x3) + (4x3)=

24 + 12=

36

Decompose the multiplication sentece

14x4=

(10x4)+ (4x4)=

40 + 16=

56

Decompose the multiplication sentece

13x3=

(10x3)+ (3x3)=

30 + 9=

39

Decompose the multiplication sentece

15x6=

(10x6)+ (5x6)=

60 + 30

90

Simplify the expresion:

11 x (15+5)=

11 x 20=

220

Simplify the expresion:

(41-11) x 12 =

30 x 12=

360

Simplify the expresion:

(75+25) x 38 =

100 x 38=

3800

Simplify the expresion:

(20x2) + (6x2) =

40 x 12 =

480

Application problem

Jaxon earned $39 raking leaves. His brother, Dayawn, earned 7times as much waiting on tables. Write a numerical expression to show Dayawn’s earnings. How much money did Dayawn earn?

What does this expression mean when I designate 31 as the unit?

8x31

31

Does our choice of unit change the product of the two factors?

8x31 = 31x8

Commutative property says that the order of the products doesn't matter. The product will be the same.

Let's designate 8 as the unit.

8x31 8x30

8x31

...

...

8x30

How does 8x30 help us solve 8x31?

8x31 is the same as 8x30 plus 1 eight

8x31= (8x30)+(8x1)

Let's designate 20 as the unit.

49x20

20

50x20

20

20

20

20

...

20

20

20

20

20

...

49x20

49x20 = (50x20)-(1x20)= 1,000 - 20 = 980

Create an equivalente expression to solve 51x20

Let's designate 20 as the unit.

51x20

20

51x20

20

20

20

20

...

20

20

20

20

20

...

50x20

51x20 = (50x20)+(1x20)= 1,000 + 20 = 1,020

Designate 12 as the unit.

12

101x12

12

12

12

12

...

12

12

12

12

12

...

100x12

12

12

12

12

12

...

101x12

101x12 12x98

101x12 = (12x100) + (12x1)

98x12 = (12x100) - (12x2)

PROBLEM SET

10 minutes Student's book page: 157

What mental math strategy did you learn today? Choose a problem in the Problem Set to support your answer.

How did the Application Problem connect to today’s lesson? Which factor did you decide todesignate as the unit?

In Problem 1(b) the first two possible expressions are very similar. How did you decide which one was not equivalent?

Look at Problem 2. How did the think prompts help to guide you as you evaluated these expressions? Turn and talk.

What was different about the think prompts in Problem 2 and Problem 3?

Explain to your partner how to solve Problem 5(a).

EXIT TICKET 8- PG 161

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 9 & 10

I am learning how to multiply using partial products.

• I can represent units using strip diagrams and area models.
• I can represent products using area models and standard algorithms.
• I can connect area models and the distributive property to partial products of the standard algorithm with and without renaming.

SPRINT - Pg 35

INDEPENDENT WORK!

SPRINT - Pg 35

MARK YOUR WORK!

Multiply mentally

9x10= 90

9x9 = 90-9

81

Multiply mentally

9x100= 900

9x99 = 900-9

891

Multiply mentally

15x10= 150

15x9= 150 - 15

135

Multiply mentally

29x100= 2900

29x99= 2900-29

2,871

Multiply by multiples of 100.

3100

31x100=

6200

3100x2=

31x100x2

31x200=

6200

Multiply by multiples of 100.

2400

24x100=

7200

2400x3=

24x100x3

24x300=

7200

Multiply by multiples of 100.

3400

34x100=

6800

3400x2=

34x100x2

34x200=

6800

Application problem

Aneisha is setting up a play space for her new puppy. She will be building a rectangular fence around part ofher yard that measures 29 feet by 12 feet. How many square feet of play space will her new puppy have? If you have time, solve in more than one way.

Let's designate 5 as the unit.

1x5

20x5

21

21x5

21x5

...

...

20x5

Imagine all 21 boxes stacked vertically.

It looks like an area model.

What values could we write?

Could we count 5 groups of 21?

31x23

Let's designate 23 as a unit.

Does it matter how we split the rectangle? Does it change the area (product)?

30

23

(23x30)+(23x1)

23

690

343x21

Let's designate 343 as a unit.

Does it matter how we split the rectangle? Does it change the area (product)?

20

343

(343x20)+(343x1)

343

6860

231x32

Let's designate 231 as a unit.

Does it matter how we split the rectangle? Does it change the area (product)?

30

231

(231x30)+(231x2)

462

6930

64x73

Let's designate 73 as a unit.

Does it matter how we split the rectangle? Does it change the area (product)?

4200+280+180+12=4672

60

70

280

4200

12

180

Can you work out the answer using the standard algorithm?

814x39

Let's designate 814 as a unit.

Does it matter how we split the rectangle? Does it change the area (product)?

30

800

10

Can you work out the answer using the standard algorithm?

7200

24000

90

300

36

120

7,200+24,000+90+300+36+120=31,746

624x82

Let's designate 814 as a unit.

Does it matter how we split the rectangle? Does it change the area (product)?

80

600

20

Can you work out the answer using the standard algorithm?

1,200

48,000

40

1,600

320

48,000+1,200+1,600+40+320+8= 51,168

PROBLEM SET

25 minutes Student's book page: 171 (1,2,3) 179 (1,2,3)

Look at the area models in Problems 1(a) and 1(b). What is the same about these two problems?

How could you use Problem 1 to help you solve Problem 2?

How is multiplying three digits by two digits different from multiplying two digits by two digits? How is it the same?

What is different about Problem 4? Does using a decimal value like 12.1 as the unit being counted change the way you must think about the partial products?

Application problem

Scientists are creating a material that may replace damaged cartilage in human joints. This hydrogel can stretch to 21 times its original length. If a strip of hydrogel measures 3.2 cm, what would its length be when stretched to capacity?

What pattern did you notice between Parts (a) and (b) of Problem 1? How did this slight difference in factors impact your final product?

Explain to your partner how you recorded the regrouping in Problem 2(a). What were you thinking and what did you write as you multiplied9 tens times 5 tens?

Let’s think about a problem like 23 × 45 and solve it with the algorithm. What is the first partial product that we would find? The second? Would this be the only order in which we could find the partial products?What else could we do?

What information did you need before you could find the cost of the carpet in Problem 3? How did you find that information? Why is area measured in square units?

Look at Problem 4. Discuss your thought process as you worked on solving this problem. There is more than one way to solve this problem. Work with your partner to show another way. Howdoes your expression change?

EXIT TICKET 9 & 10- PG 163 + 175

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 11

I am learning how to multiply multi-digit whole numbers and estimate for reasonableness.

• I can connect area models and the distributive property to the partial products of the standard algorithm.
• I can multiply multi-digit whole numbers using the standard algorithm.
• I can estimate products by rounding factors to check for reasonableness.

SPRINT - Pg 37

INDEPENDENT WORK!

SPRINT - Pg 35

MARK YOUR WORK!

24x15

200+100+40+20=360

10

20

200

100

40

20

10

800

20

824x15

4,000

8,000

100

200

20

40

4,000+8,000+200+100+20+40= 12,360

Application problem

The length of a school bus is 12.6 meters. If 9 school buses park end-to-end with 2 meters between each one, what’s the total length from the front of the first bus to the end of the last bus?

30

500

20

100

524x136

3000

15000

50000

120

600

2000

24

120

400

3,000+15,000+50,000+120+600+2,000+24+120+400= 71,264

20

4,000

500

10

300

4,519x326

24,000

80,000

1,200,000

3,000

10,000

150,000

60

200

3,000

54

180

2,700

1,200,000+80,000+24,000+3,000+10,000+150,000+60+200+3,000+54+180+2,700=1,469,934

4,000

500

300

4,509x306

24,000

1,200,000

3,000

150,000

54

2,700

1,200,000+24,000+3,000+150,000+54+2,700=1,379,754

PROBLEM SET

10 minutes Student's book page: 111

Explain why a multiplication problem with a three-digit multiplier will not always have three partial products. Use Problems 1(a) and (b) asexamples.

How are the area models for Problems 2(a) and (b) alike, and how are they different?

What pattern did you notice in Problem 3?

Does it matter which factor goes on the top of the model or the algorithm? Why or why not?

How many ways can you decompose the length? The width?

What are you thinking about as you make these decisions on how to split the area into parts?

Do any of these choices affect the size of the area (the product)? Why or why not?

What new (or significant) math vocabulary did we use today to communicate precisely?

EXIT TICKET 11- PG 183

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 12

I am learning how to multiply multi-digit whole numbers and estimate for reasonableness.

• I can connect area models and the distributive property to the partial products of the standard algorithm.
• I can multiply multi-digit whole numbers using the standard algorithm.
• I can estimate products by rounding factors to check for reasonableness.

4,000

500

300

4,509x306

24,000

1,200,000

3,000

150,000

54

2,700

1,200,000+24,000+3,000+150,000+54+2,700=1,379,754

Application problem

Erin and Frannie entered a rug design contest. The rules stated that the rug’s dimensions must be 32 inches × 45 inches and that they must be rectangular. They drew the following for their entries, showing their rug designs and the measurements of each part of their design. Show at least three other designs they could have entered in the contest. Calculate the area of eachsection, and the total area of the rugs.

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

314x236=

____ x ____ =

300x200

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

60,000

74,104

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

1,882x296

____ x ____ =

2,000x300

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

600,000

557,072

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

4,902x408

____ x ____ =

5,000x400

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

2,000,000

2,000,016

PROBLEM SET

10 minutes Student's book page: 111

What is the benefit of estimating before solving?

Look at Problems 1 (b) and (c). What do you notice about the estimated products? Analyze why the estimates are the same, yet the products are so different.

How could the cost of the chairs have been found using the unit form mental math strategy?

In Problem 4, Carmella estimated that she had 3,000 cards. How did she most likely round her factors?

Would rounding the number of boxes of cards to 20 have been a better choice? Why or why not?

Do we always have to round to a multiple of 10, 100, or 1,000? Is there a number between 10 and20 that would have been a better choice for Carmella?

Can you identify a situation in a real-life example where overestimating would be most appropriate?Can you identify a situation in the real world where underestimation would be most appropriate?

EXIT TICKET 12- PG

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 13

I am learning how to fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

• I can solve multiplication multi-digit word problems using the standard algorithm.

Write 45 tenths as a decimal.

Four and five tenths = Four point five.

4.5 x 100 =

Write 4 tenths as a decimal.

Four tenths = Zero point five.

0.4 x 100 =

0.4 ÷ 100 =

Write 3,895 thousandths as a decimal.

Three and eigth hundred ninety five thousandths = Three point eight nine five,

3.895x1,000=

Write 5,472 ones as a decimal.

Five thousand four hundred seventy two.

5,472÷1,000=

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

412x231

____ x ____ =

400x200

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

80,000

95,172

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

523x298

____ x ____ =

500x300

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

150,000

155,854

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

684x347

____ x ____ =

700x300

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

210,000

237,348

Estimate the answer rounding each factor to arrive at a reasonable estimate of the product.

Will the answer be more or less than the estimation? Why?

908x297

____ x ____ =

900x300

Use the traditional algorithm to work out the answer. Then, compare it to your estimation. Is it a reasonable answer?

270,000

269,676

Problem 1: An office space in New York City measures 48 feet by 56 feet. If it sells for $565 per square foot, what is the total cost of the office space?

Problem 2: Gemma and Leah are both jewelry makers. Gemma made 106 beaded necklaces. Leah made 39 more necklaces than Gemma. a. Each necklace they make has exactly 104 beads on it. How many beads did both girls use altogether while making their necklaces? b. At a recent craft fair, Gemma sold each of her necklaces for $14. Leah sold each of her necklaces for $10 more. Who made more money at the craft fair? How much more?

PROBLEM SET

10 minutes Student's book page: ?

Share and explain to your partner the numerical expressions you wrote to help you solve Problems 3 and 5.

Explain how Problems 3 and 5 could both be solved in more than one way.

What type of problem are Problem 1 and Problem 5? How are these two problems different from the others?

EXIT TICKET 13- PG

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 14

I am learning how to multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

• I can estimate the product
• I can multiply the decimal factor with tens and multiply as if both factors are whole numbers.
• I can divide the product by tens to find the original answer when a factor was a decimal.

3x2=

3x2x10÷10=

Why are the products the same when we multiply by 10 and then divide by 10?

1.5

5x0.3=

1.5

5x0.3x10÷10=

Why are the products the same when we multiply by 10 and then divide by 10?

7.5

3x2.5=

7.5

3x2.5x10÷10=

Why are the products the same when we multiply by 10 and then divide by 10?

6.8

2x3.4=

6.8

2x3.4x10÷10=

Why are the products the same when we multiply by 10 and then divide by 10?

7.463=

7 and 463 thousandths

7.463

7 ones

463 thousandths

Represent this number in a two-part number bond with ones as one part and thousandths as the other part.

7.463=

7 and 463 thousandths

7.463

74 tenths

63 thousandths

Represent this number in a two-part number bond with tenths and thousandths.

7.463

746 hundredths

3 thousandths

7.463=

7 and 463 thousandths

Represent this number in a two-part number bond with hundredths and thousandths.

8.972=

8 and 972 thousandths

8.972

8 ones

972thousandths

Represent this number in a two-part number bond with ones as one part and thousandths as the other part.

8.972=

8 and 972 thousandths

8.972

89 tenths

72thousandths

Represent this number in a two-part number bond with tenths and thousandths.

8.972

897 hundredths

2thousandths

8.972=

8 and 972 thousandths

Represent this number in a two-part number bond with hundredths and thousandths.

6.849=

6 and 849 thousandths

6.849

6 ones

849thousandths

Represent this number in a two-part number bond with ones as one part and thousandths as the other part.

6.849=

6 and 849 thousandths

6.849

68 tenths

49thousandths

Represent this number in a two-part number bond with tenths and thousandths.

6.849

684 hundredths

9thousandths

6.849=

6 and 849 thousandths

Represent this number in a two-part number bond with hundredths and thousandths.

Application problem

The fifth-grade craft club is making aprons to sell. Each apron takes 1.25 yards of fabric that costs $3 per yard and 4.5 yards of trim that costs $2 per yard. What does it cost the club to make one apron? If the club wants to make $1.75 profit on each apron, how much should they charge per apron?

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

43x2.4

40x2

We have 43 units of 2.4. I’d like to rename 2.4 using only tenths. How many tenths would that be?

40

20

4 tenths

80

60 tenths

800 tenths

160 tenths

12 tenths

1032 tenths= 103.2

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

3.5X42

4X40

We have 42 units of 3.5. I’d like to rename 3.5 using only tenths. How many tenths would that be?

40

30

5 tenths

160

60 tenths

1,200 tenths

200 tenths

10 tenths

1470 tenths= 147

LET'S WORK OUT THE ANSWER:

Name 3.5 in tenths and use the standard algorithm.

3.5X42

LET'S WORK OUT THE ANSWER:

Multiply 3.5 by 10, then multiply by 42. Once finished divide by 10

3.5X42

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

15.6x73

20x70

We have 73 units of 15.6. I’d like to rename 15.6 using only tenths. How many tenths would that be?

1400

70

100

6 tenths

50

300 tenths

7,000 tenths

3,500 tenths

150 tenths

60 tenths

440 tenths

11,388 tenths= 1,138.8

PROBLEM SET

10 minutes Student's book page: 201

​Discuss Michelle’s error in Problem 3 by allowing students to share their representations and explanations.

​How does being fluent in whole number multi-digit multiplication help you multiply decimals?

0.3 ×​42. How would you draw an area model and/or record this case vertically? Discuss how putting the single-digit numeral (3 tenths) as the top number affects the recording of partial products?

EXIT TICKET 14- PG 203

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 15

I am learning how to multiply decimal fractions by multi-digit whole numbersthrough conversion to a whole number problem and reasoning about the placement of the decimal.

• I estimate the product.
• I can solve, using the standard algorithm.
• I can explain my thinking when placing the decimal in the product.

SPRINT - Pg 43

INDEPENDENT WORK!

SPRINT - Pg 43

MARK YOUR WORK!

3x4.1=

12.3

12.3

12.3x10÷10=

12.3

3x4.1x1÷1=

12.3

3x4.1x17.6÷17.6=

3x2.4=

7.2

7.2

7.2x10÷10=

7.2

3x2.4x1÷1=

7.2

3x2.4x13.2÷13.2=

Application problem

Mr. Mohr wants to build a rectangular patio using concrete tiles that are 1 square foot. The patio will measure 13.5 feet by 43 feet. What is the area of the patio? How many concrete tiles will he need to complete the patio?

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

7.38x41

10x40

We have 41 units of 7.38. I’d like to rename 7.38 using only hundredths. How many hundredths would that be?

400

70

700

8 hundredths

30

560 hundredths

240 hundredths

90 hundredths

2,100 hundredths

49,000 hundredths

2,100 hundredths

30,258 hundredths= 302.58

Solve using the standar algorithm

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

8.26x128

10x40

We have 128 units of 8.26. I’d like to rename 8.26 using only hundredths. How many hundredths would that be?

20

800

6 hundredths

20

400

120 hundredths

48 hundredths

160 hundredths

400 hundredths

16,000 hundredths

6,400 hundredths

80,000 hundredths

2,000 hundredths

600 hundredths

105,728 hundredths= 1,057.28

Solve using the standar algorithm

100

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

82.61x63

80x60

We have 63 units of 82.61. I’d like to rename 82.61 using only hundredths. How many hundredths would that be?

70

8,000

1 hundredths

200

60

4,800

4,200 hundredths

180 hundredths

600 hundredths

1,400 hundredths

560,000 hundredths

24,000 hundredths

3 hundredths

70 hundredths

520,443 hundredths= 5,204.43

Solve using the standar algorithm

PROBLEM SET

10 minutes Student's book page: 207

For Problem 1, what did you write in your think bubbles? Compare what you wrote with a partner.

What strategies did you use to solve Problem 2(d)? Does the decimal number affect the process for solving? Why or why not?

What is the relationship between the relative size of the factors in the whole number problems and the factors in the decimal problems? What is the relationship between the products?

EXIT TICKET 15- PG 211

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 16

I am learning how to reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation.

• I estimate the product.
• I can solve, using the standard algorithm.
• I can represent the product using an area model.

12 in ≈ ____ ft.

12 in ≈ 1 ft.

2 ft.

24 in ≈

12 in ≈ 1 ft.

3 ft.

36 in ≈

12 in ≈ 1 ft.

4 ft.

48 in ≈

12 in ≈ 1 ft.

10 ft.

120 in ≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

24 in

2 ft.≈

1 ft. ≈ 12 in

30 in

2.5 ft. ≈

1 ft. ≈ 12 in

36 in

3 ft. ≈

1 ft. ≈ 12 in

42 in

3.5 ft. ≈

1 ft. ≈ 12 in

48 in

4 ft. ≈

1 ft. ≈ 12 in

54 in

4.5 ft. ≈

1 ft. ≈ 12 in

108 in

9 ft. ≈

1 ft. ≈ 12 in

114 in

9.5 ft. ≈

1 ft. ≈ 12 in

324 in

27 ft. ≈

1 ft. ≈ 12 in

330 in

27.5 ft. ≈

Say the number as you would write it: 8 tenths.

0.8 Zero point eight

Say the number as you would write it: 9 tenths.

0.9 Zero point nine

Say the number as you would write it: 10 tenths.

1 One

Say the number as you would write it: 11 tenths.

11 One point one

Say the number as you would write it: 19 tenths.

1.9 One point nine

Say the number as you would write it: 20 tenths.

2 Two

Say the number as you would write it: 30 tenths.

3 Three

Say the number as you would write it: 35 tenths.

3.5 Three point five

Say the number as you would write it: 45 tenths.

4.5 Four point five

Say the number as you would write it: 85 tenths.

8.5 Eight point five

Say the number as you would write it: 83 tenths.

8.3 Eight point three

Say the number as you would write it: 63 tenths.

6.3 Six point three

Say the number as you would write it: 47 tenths.

4.7 Four point seven

Say the number as you would write it: 8 hundredths

0.08 Zero point zero eight

Say the number as you would write it: 9 hundredths

0.09 Zero point zero nine

Say the number as you would write it: 10 hundredths

0.1 Zero point one

Say the number as you would write it: 20 hundredths

0.2 Zero point two

Say the number as you would write it: 30 hundredths

0.3 Zero point three

Say the number as you would write it: 90 hundredths

0.9 Zero point nine

Say the number as you would write it: 95 hundredths

0.95 Zero point nine five

Say the number as you would write it: 99 hundredths

0.99 Zero point nine nine

Say the number as you would write it: 199 hundredths

1.99 One point nine nine

Say the number as you would write it: 299 hundredths

2.99 Two point nine nine

Say the number as you would write it: 357 hundredths

3.57 Three point five seven

Say the number as you would write it: 463 hundredths

4.63 Four point sixty three

Application problem

Thirty-two cyclists make a seven-day trip. Each cyclist requires 8.33 kilograms of food for the entire trip. If each cyclist wants to eat an equal amount of food each day, how many kilograms of food will the group becarrying at the end of Day 5?

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

8.26x128

10x40

We have 128 units of 8.26. I’d like to rename 8.26 using only hundredths. How many hundredths would that be?

20

800

6 hundredths

20

400

120 hundredths

48 hundredths

160 hundredths

400 hundredths

16,000 hundredths

6,400 hundredths

80,000 hundredths

2,000 hundredths

600 hundredths

105,728 hundredths= 1,057.28

Solve using the standar algorithm

100

PROBLEM SET

10 minutes Student's book page: ?

Discuss the estimates for Problems 2(b) and 2(d). What effectdoes this have on the products?

Continue to discuss the relationships between the actual problem and the parallel whole number problem you use to obtain the digits of the product.

EXIT TICKET 16- PG

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 17

I am learning how to use whole number multiplication to express equivalent measurements.

• I can rename units using equivalency statements.
• I can use equivalency statements to determine equivalent measurements

30x0.1=

30

1 tenth

30 tenths

300x0.01=

300

1 hundredth

300 hundredths

3,000x0.001=

3,000

1 thousandth

3,000 thousandths

5,000x0.001=

5,000

1 thousandth

5,000 thousandths

50x0.1=

50

1 tenth

50 tenths

500x0.01=

500

1 hundredth

500 hundredths

50

5,000x0.01=

5,000

1 hundredth

5,000 hundredths

30

3,000x0.01=

3,000

1 hundredth

3,000 hundredths

30

30,000x0.001=

30,000

1 thousandth

30,000 thousandths

50

50,000x0.001=

50,000

1 thousandth

50,000 thousandths

40x0.1=

40

1 tenth

40 tenths

400

4,000x0.1=

4,000

1 tenth

4,000 tenths

4,000

40,000x0.1=

40,000

1 tenth

40,000 tenths

700x0.01=

700

1 hundredth

700 hundredths

70

7,000x0.01=

7,000

1 hundredth

7,000 hundredths

700

70,000x0.01=

70,000

1 hundredth

70,000 hundredths

7,000

700,000x0.01=

700,000

1 hundredth

700,000 hundredths

7,000,000x0.001=

7,000

7,000,000

1 thousandth

7,000,000 thousandths

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

5.21x34

5x30

We have 34 units of 5.21. I’d like to rename 5.21 using only tenths. How many tenths would that be?

150

30

500

1 tenths

20

2,000 tenths

15,000 tenths

600 tenths

80 tenths

4 tenths

30 tenths

17,714 tenths= 177.14

Round the factors to estimate the product.

Will the answer be more or less than the estimation? Why?

8.35x73

10x70

We have 73 units of 8.35. I’d like to rename 8.35 using only tenths. How many tenths would that be?

700

30

5 tenths

800

70

2,400 tenths

56,000 tenths

2,100 tenths

90 tenths

15 tenths

350 tenths

60,955 tenths= 609.55

1 ft. ≈ ____ in

1 ft. ≈ 12 in

24 in

2 ft.≈

1 ft. ≈ 12 in

36 in

3 ft. ≈

1 ft. ≈ 12 in

48 in

4 ft. ≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

24 in

2 ft.≈

1 ft. ≈ 12 in

36 in

3 ft. ≈

1 ft. ≈ 12 in

120 in

10 ft. ≈

1 ft. ≈ 12 in

60 in

5 ft. ≈

1 ft. ≈ 12 in

84 in

7 ft. ≈

100 cm = 1 m

3 m

300 cm=

100 cm = 1 m

6 m

600 cm=

100 cm = 1 m

8 m

800 cm=

100 cm = 1 m

9 m

900 cm=

Application problem

Meter strip!

3 weeks = ______ days?

3 weeks = 3 x (1 week)

3 weeks = 3 x (7 days)

3 weeks = 21 days

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the amount of time stayed the same.

3 hours = ______ minutes?

3 hours = 3 x (1 hour)

3 hours = 3 x (60 minutes)

3 hours = 180 minutes

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the amount of time stayed the same.

1.05 m = ______ cm?

1.05 m = 1.05 x (1 m)

1.05 m = 1.05 x (100cm)

1.05 m = 105 cm

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the distance stayed the same.

0.09 m = ______ cm?

0.09 m = 0.09 x (1 m)

0.09 m = 0.09 x (100cm)

0.09 m = 9 cm

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the distance stayed the same.

0.09 m = ______ mm?

0.09 m = 0.09 x (1 m)

0.09 m = 0.09 x (1,000mm)

0.09 m = 90 mm

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the distance stayed the same.

A crate of apple weighs 5.7 kg. Convert the weight to grams.

5.7 kg = ______ g?

5.7 kg = 5.7 x (1 kg)

5.7 kg = 5.7 x (1,000 g)

5.7 kg = 5,700 g

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the weight stayed the same.

A sack holds 56.75 pounds of sand. Convert the weight to ounces.

56.75 lb = ______ oz?

56.75 lb = 56.75 x (1lb)

56.75 lb = 56.75 x (16 oz)

56.75 kg = 908 oz

Since we converted to a smaller unit (CONVERSION FACTOR), the number units increased, but the weight stayed the same.

PROBLEM SET

10 minutes Student's book page: 111

In the conversion you completed for Problem 1(d), explain your process as you worked. How did you decide what to multiply by?

Although we multiplied by 100 to convert 1.05 meters to 105 centimeters, the length remainedthe same. Why?

Explain the term conversion factor.

What would be the conversion factor if we wanted to convert years to days? Years to months? Why isn’t there one conversion factor to convert months to days? Why isn’t there one conversion factor to convert years to days?

Can you name some situations in which measurement conversion might be useful and/or necessary?

EXIT TICKET 17- PG

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 18

I am learning how to use decimal multiplication to express equivalent measurements.

• I can use unit statements to show the relationship between metric units.
• I can set up measurements as equivalent expressions with the unit as a factor.
• I can convert between measurements.

420 ÷ 20 = 21

÷2

÷10

42

420 ÷ 10 =

21

42 ÷ 2 =

960 ÷ 30 =

÷3

÷10

96

960 ÷ 10 =

32

96 ÷ 3 =

680 ÷ 20 =

÷2

÷10

68

680 ÷ 10 =

34

68 ÷ 2 =

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

1 ft. 1 in≈

13 in

(12 in) + 1 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

1 ft. 2 in≈

14 in

(12 in) + 2 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

1 ft. 3 in≈

15 in

(12 in) + 3 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

1 ft. 10 in≈

22 in

(12 in) + 10 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

1 ft. 8 in≈

20 in

(12 in) + 8 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

2 ft≈

24 in

(12 in) x 2≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

2 ft. 1 in≈

25 in

(24 in) + 1 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

2 ft. 10 in≈

34 in

(24 in) + 10 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

2 ft. 6 in≈

30 in

(24 in) + 6 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

3 ft≈

36 in

(12 in) x 3≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

3 ft. 10 in≈

46 in

(36 in) + 10 in≈

1 ft. ≈ ____ in

1 ft. ≈ 12 in

? in

3 ft. 4 in≈

40 in

(36 in) + 4 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

13 in≈

1 ft 1 in

(12 in) + 1 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

14 in≈

1 ft 2 in

(12 in) + 2 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

22 in≈

1 ft 10 in

(12 in) + 10 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

24 in≈

2 ft

(12 in) + (12 in)≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

34 in≈

2 ft 10 in

(24 in) + 10 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

25 in≈

2 ft 1 in

(24 in) + 1 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

36 in≈

3 ft

(24 in)+(12 in)≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

46 in≈

3 ft 10 in

(36 in)+ 10 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

40 in≈

3 ft 4 in

(36 in)+ 4 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

48 in≈

4 ft

(36 in)+ (12 in)≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

47 in≈

3 ft 11 in

(36 in)+ 11 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

49 in≈

4 ft 1 in

(48 in)+ 1 in≈

12 in ≈ ?

12 in ≈ 1 ft

? ft ? in

58 in≈

4 ft 10 in

(48 in)+ 10 in≈

Prime or composite?

10

1, 2, 5, 10

Composite

Prime or composite?

10

1, 2, 5, 10

Composite

Prime or composite?

13

1, 13

Prime

Prime or composite?

20

1, 2, 4, 5, 10, 20

Composite

Prime or composite?

21

1, 3, 7, 21

Composite

Prime or composite?

81

1, 3, 9, 27, 81

Composite

Application problem

Draw and label a strip diagram to representeach of the following: 1. Express 1 day as a fraction of 1 week. 2. Express 1 foot as a fraction of 1 yard. 3. Express 1 quart as a fraction of 1 gallon. 4. Express 1 centimeter as a fraction of 1 meter. (Decimal form.) 5. Express 1 meter as a fraction of 1 kilometer. (Decimal form.)

195 cm = ____ m?

195 cm = 195 x (1cm)

195 cm = 195 x (0.01m)

195 cm = 1.95 m

Since we converted to a bigger unit (CONVERSION FACTOR), the number units decreased, but the distance stayed the same.

4,500 g = ____ kg?

4,500 g = 4,500 x (1 g)

4,500 g = 4,500 x (0.001kg)

4,500 g = 4.5 kg

Since we converted to a bigger unit (CONVERSION FACTOR), the number units decreased, but the weight stayed the same.

578 ml = ____ L?

578 ml= 578 x (1 ml)

578 ml = 578 x (0.001L)

578 ml =0.578 L

Since we converted to a bigger unit (CONVERSION FACTOR), the number units decreased, but the volume stayed the same.

A truck weighs 1,675,280 grams. Convert the weight to kg.

1,675,280 g = ____ kg?

1,675,280 g = 1,675,280 x (1 g)

1,675,280 g = 1,675,280 x (0.001kg)

4,500 g = 4.5 kg

Since we converted to a bigger unit (CONVERSION FACTOR), the number units decreased, but the weight stayed the same.

PROBLEM SET

10 minutes Student's book page: 111

In the conversion you completed for Problem 1(d), explain your process as you worked. How did you decide what to multiply by?

When our conversion factor is a fraction, we are converting to larger units. When our conversion factor is a whole number, we are converting to smaller units. Explain this using examples from your Problem Set and memory.

Whether we are converting small units to large units or large units to small units, we are multiplying. Explain why this is true.

EXIT TICKET 18- PG

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

LESSON 19

LO: I am learning how to solve two-step word problems involving measurement conversions.

• I can convert from larger to smaller units.
• I can convert from smaller to larger units.

SPRINT - Pg 47

INDEPENDENT WORK!

SPRINT - Pg 47

MARK YOUR WORK!

480 ÷ 20 = 24

÷2

÷10

48

480 ÷ 10 =

24

48 ÷ 2 =

690 ÷ 300 = 2.3

÷3

÷100

6.9

690 ÷ 100 =

2.3

6.9 ÷ 3 =

8,480 ÷ 400 = 21.2

÷4

÷100

8,480 ÷ 100 =

84.8

21.2

84.8 ÷ 4 =

Application problem - Concept development - Problem set

Liza's cat had six kittens! When Liza and her brother weighed all the kittens and

PROBLEM SET

10 minutes Work on problems 2, 3 and 4.

Look back at Problem 4(b). Is there another way to solve it?

Which problems involved converting from larger to smaller units, and which involved converting smaller to larger units? Which conversion is more challenging for you?

EXIT TICKET 19- PG

ONCE FINISHED, DROP IT BY THE TEACHER'S DESK.

MID MODULE ASSESSMENT