welcome to math 6 today’s lesson is called: “be fruitful” and multiply

Welcome to Math 6

Today’s lesson is called:

“Be Fruitful” and Multiply

The Connector…

I am going to give a brief background on multiplication in this lesson. Also I will discuss some properties of multiplication which you can use. Some of what I discuss may be familiar to you.

KEY VOCABULARY FOR THIS LESSON

Algorithm. An established step-by-step procedure used to achieve a desired result. For example, the addition algorithm for the sum of two two-digit numbers where carrying is required.

82

27

55

+¿𝟏

KEY VOCABULARY FOR THIS LESSON

Distributive property- the property indicating a special way in which multiplication is applied to addition of two (or more) numbers.

For example,5 x 23 =

5 x (20 + 3) =

5 x 20 + 5 x 3 =

100 + 15 = 115.

OBJECTIVES:

Each student will:

1. Be able to explain the distributive property.

2. Understand that multiplication works because of the distributive property

3. Use the standard algorithm of multiplication to find a product.

Using multiples of 10, 100, 1000 etc.

When you know the basic multiplication facts, you can recognize and use patterns to find products of multiples of 10.

3 x 6 = 18

3 x 60 = 180

3 x 600 = 1800

Review place value

3 x 6 = 18 (basic math fact)

3 x 60 = 180

three x 6 tens = 18 tens

3 x 600 = 1800

3 x 6 thousands = 18 thousands

3 x 60,000 = 180,000

3 x 6 = 18

3 x 60 = 180

three times six tens

= 18 tens

3 x 600 = 1800

three times six hundreds

= 18 hundreds

4 x 6= 24

40 x 6= 240

4 x 60= 240

40 x 60= 2,400

40 x 600= 24,000

400 x 600= 240,000

40 x 6,000= 240,000

4,000 x 6= 24,000

4,000 x 60= 240,000

Note how we use the basic fact, then count the combined number of zeros in both factors, and tack that number of zeros onto the product.

http://mathforum.org/dr.math



The basis of any method of multiplying is the distributive property:

a x (b + c) = (a x b) + (a x c)

The distributive property

9 x 185=9 x (100 + 80 + 5)=(9x100) + (9x80) + (9x5)=900 + 720 + 45=900 + 700 + 20 + 40 + 5=1600 + 60 + 51665

37 x 469

= (30 + 7) x (400 + 60 + 9)

= 30 x (400 + 60 + 9) +

= 12,000 +1800 +270

+ 7 x (400 + 60 + 9)

2800 + 420 +63

= 12,000 + 1800 +2800 + 270 +420 +63

=12,000 + 4,600 + 690 + 63

=16,600 + 600 + 90 + 60 +3

=17,200 + 153 = 17,353

Break each number up into a sum of terms, one term for each digit, and the product will be the sum of all possible products of a term from one number and a term from the other.

This may seem like a complicated trick, but if you have a sound mastery of the multiplication (and addition) tables, and a solid grasp of using the patterns with multiplying by multiples of ten, it is not too difficult a skill once you practice it. In other words, “practice makes perfect.”

But what about a written algorithm?

How can we do that easily?

A multiplication table does the same thing - a table of all products.

So let's make a multiplication table for these terms:

Lattice 1_0001.pdf

THE DISTRIBUTIVE PROPERTY

When we take a multi-digit number- and break it into expanded form:

460 = 400 + 60

and multiply each term

by each term in the other factor,

37 = 30 + 7

we are using the distributive property. Then we add it up to get the total product.

The "easy way" to multiply in columns

THE PARTIAL

PRODUCTS ALGORITHM

Multiply the ones.

Multiply the tens. Place the result underneath.

Then add.

Multiply the ones.

Multiply the tens.

Add.

64 × 8

32

64 × 8

32

480

64 × 8

32

+ 480

512

Multiply the ones first.

Then multiply the tens.

Then multiply the hundreds.

Then add.

184 × 3

12

184 × 3

12

240

184 × 3

12

240 300

184 × 3

12

240 + 300

552

3 × 4 = 12

3 × 80 = 240

3 × 100 = 300

THE

STANDARD MULTIPLICATION

ALGORITHM

Now the “standard” algorithm is still based on the exact same principle (the distributive property). You simply multiply ones and tens separately, and add.

But this time the adding is done immediately after you multiply the tens.

Regrouping Choices: Where can we show the regrouping?

Here

Or Here

Regrouping Choices: Where can we show the regrouping?

Regrouping Choices

Multiplication regrouping

Addition regrouping

A

Multiplication regrouping

Addition regrouping

Regrouping ChoicesB

GUIDED PRACTICE

Guided Practice 1 The school hired buses for a field trip. Each bus can seat 43 passengers. If 7 buses were used, what was the greatest number of passengers that could have rode a bus?

Guided Practice 2

There are 297 kids going on the trip. Teachers will chaperone no more than 7 kids each. If 25 teachers are going, will more chaperones still be needed?

Guided Practice 3Robert buys a brand new car by paying a certain amount in cash. The rest of the amount is paid by loan. He pays $197 as equal monthly installments for 3 years. Find the total amount paid in equal monthly installments after 3 years.

Guided Practice 4

Mark uses the computer for 12 hours. If the average power consumption of a computer per hour is 299 watt, how much power does Mark use?

Guided Practice 5

Thomson bolt manufacturing company packs 599 bolts into each carton. How many bolts are needed to pack 59 cartons?

Guided Practice 7

A broken scale reads 11 inches. Kathy uses the broken scale to measure the length of a rope. She finds the length of the rope is 113 times the length of the broken scale. Find the length of the rope.

GUIDED PRACTICESolutions

Guided Practice 1: The school hired buses for a field trip. Each bus can seat 43 passengers. If 7 buses were used, what was the greatest number of passengers that could have rode a bus?

Solutions

Guided Practice 2

There are 297 kids going on the trip. Teachers will chaperone no more than 7 kids each. If 25 teachers are going, will more chaperones still be needed?

Solutions

Guided Practice 3Robert buys a brand new car by paying a certain amount in cash. The rest of the amount is paid by loan. He pays $197 as equal monthly installments for 3 years. Find the total amount paid in equal monthly installments after 3 years.

Solutions

Guided Practice 4Mark uses the computer for 12 hours. If the average power consumption of a computer per hour is 299 watt, how much power does Mark use?

Solutions

Guided Practice 5Thomson bolt manufacturing company packs 599 bolts into each carton. How many bolts are needed to pack 59 cartons?

Solutions

Guided Practice 6

A broken scale reads 11 inches. Kathy uses the broken scale to measure the length of a rope. She finds the length of the rope is 113 times the length of the broken scale. Find the length of the rope.

Solutions

INDEPENDENT PRACTICE

Independent Practice 1

There are 6 adult members in John’s family and they plan to make a trip to London. It costs $1236 for an adult from New York City to London. What will be the total air fare cost?

Independent Practice 2Steve receives $1525 as a scholarship in a year. How much does he receive as scholarship in 3 years?


Madison runs 5032 meters in 1 hour. If she runs at this rate, how far does she run in 4 hours?


Hamlet ordered 9 pizzas. Each pizza costs $13.95. How much does he need to pay?

Independent Practice 5A broken scale is used to measure the height of a plant. The length of the broken scale is 12 cm. The height of the plant is 14.15 times greater than the broken scale. What is the height of the plant?

Independent Practice 6David and Dora study in the same school. David’s home is 6.87 miles away from school. Dora’s home is 7 times as far as David’s home from school. Find the distance between Dora’s school and her home.


There were 137 birdwatchers participating in the Great Backyard Bird Count in Brunswick County. If they each saw at least 23 Carolina Chickadees, how many Carolina Chickadees were spotted all together.


During the Great Backyard Bird Count, there were 7 counties in which 250 people spotted over 50 birds. Altogether how many people spotted over 50 birds?


A person earns $110 per day at her job. How much could she earn for 73 days?

Independent Practice 10If a teacher works with 23 students per year for 35 years, what is the total number of students he could work with in that time?

INDEPENDENT PRACTICE

Solutions


There are 6 adult members in John’s family and they plan to make a trip to London. It costs $1236 for an adult from New York City to London. What will be the total air fare cost?

Solutions


Steve receives $1525 as a scholarship in a year. How much does he receive as scholarship in 3 years?

Solutions


Madison runs 5032 meters in 1 hour. If she runs at this rate, how far does she run in 4 hours?

Solutions


Hamlet ordered 9 pizzas. Each pizza costs $13.95. How much does he need to pay?

Solutions


A broken scale is used to measure the height of the plant. The length of the broken scale is 12 cm. The height of the plant is 14.15 times greater than the broken scale. What is the height of the plant?

Solutions


David and Dora study in the same school. David’s home is 6.87 miles away from school. Dora’s home is 7 times as far as David’s home from school. Find the distance between Dora’s school and her home.

Solutions


There were 137 birdwatchers participating in the Great Backyard Bird Count in Brunswick County. If they each saw at least 23 Carolina Chickadees, how many Carolina Chickadees were spotted all together.


During the Great Backyard Bird Count, there were 7 counties in which 250 people spotted over 50 birds. Altogether how many people spotted over 50 birds?


A person earns $110 per day at her job. How much could she earn for 73 days?


If a teacher works with 23 students per year for 35 years, what is the total number of students he could work with in that time?

Assignment 1Complete the page entitled “patterns with multiples of ten.

Assignment 2

Fill in the multiplication grid. The one in the assignments section is partially filled in already. It will make a great study aid for you if you have not yet mastered the time tables up to 12 x 12.

Complete the “Reading Challenge” assignment found in the supplementary materials section. It will really test your mastery of multiplication.

Assignment 3

Useful Websites

Final thought…

Although multiplication was something you first learned a long time ago, it is a skill you will be relying on more in the future- not less.

Its not too late to learn everything you can. In the coming lessons we will do lots more with multiplication.

welcome to math 6 today’s lesson is called: “be fruitful” and multiply

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