Download Dividing using friendly multiples worked well for two digit dividends

Lesson 5.1: Finding Multiples (4.OA.B.4)
Lesson Objective: The students will write multiples for a given
number.
Video Lesson: Finding multiples
You are supposed to bring a snack for your team’s game this week.
There are 25 people of the team. You think that power bars would be a
great treat to push your team to victory. They come in packs of 3. How
many packs are you going to need?
Multiples of a number can be found by counting by groups of that number. If I wanted to find
the first five multiples of 6 I could just count by six. Let’s look at what that would look like on a
number line:
+6
6
12
18
24
30
When we hear the word multiples multiply jumpy out at our ears. That is because that is what
we are doing. Let’s fill in the chart below to show how multiplication can give us multiples as
well.
Multiples of 6
6*
Product
1
6
2
18
4
30
There are certain multiples I would like to point out here that help us in some situations (like
dividing). They occur when we take the numbers times 10 or 100. These are sometimes
referred to as the parents (*10) of a number or the grandparents (*100). For instance, the
parents of 3 would be _____. The grandparents would be ________.
In the chart below, list the parents and grandparents of the numbers on the left:
Number
7
1
8
4
Parent (times 10)
Grandparent (times 100)
So you are at the grocery store and need to buy those snacks. Use the
number line below to show how many packs of three you need for the 25
players.
Practice:
1. Fill in the chart of parent and grandparent multiples:
Number
Parent (times 10)
Grandparent (times 100)
2
90
12
17
2. List five multiples for 9.
3. Write 5 multiples for 7
4.Use the number line to show 5 multiples for 2
Lesson 5.2: Division Meanings (4.M.NBT.06)
Lesson Objective: The students will understand what it means
to divide a group up.
Video Lesson: Dividing by subtracting equal groups
The carnival is a great place to go! You and three friends have just
gotten 36 tokens to play games. How are you going to fairly share these
with each other?
One way to divide numbers is to take and break the number you are dividing up (the Quotient)
and put them into the equal groups you are looking for (the divisor) by subtracting. This is
called dividing using repeated subtraction. Let’s show this below for 12 4 using pictures and
repeated subtraction:
1. 12 – 3 =______
2. __ - 3 = ______
3. ____ - ___ = _____
4.____ - ___ = _____
To get the answer for 12/3 you count up how many groups of three you had or to say it another
way, how many times you subtracted. In the above example we had to subtract 4 times. So,
our answer to 12 divided by 3 is 4.
We have been working a lot on how to multiply numbers this year. Now we are going to try
doing the inverse (opposite) of that and move into division. In math each operation has an
opposite or inverse operation that will undo it. For addition it would be ______________. For
____________________ it would be addition. For multiplication it is _______________. And
finally, for division it is __________________.
Looking at 12 ÷ 3 = 4, what multiplication sentence would help us solve it:
____________________________________________
We should be able to see a fact family here.
12 ÷ 4 = 3,
12 ÷ 3 = 4,
3 * 4 = 12,
4 * 3 = 12
Let’s try to solve another division problem using multiplication. 24 ÷ 6 = ?
(hint: What times 6 gives you 24?)
_____________________________________
What fact family can be shown using the three numbers above (24, 6, and the answer)?
Remember you are at the carnival with three friends and 36 tokens.
How many should each person get?
1. Give the fact family for 24 ÷ 8 = ?
3. Use repeated subtraction to solve:
36 ÷ 9 =
1. Use repeated subtraction to solve:
42
7
2. Give the fact family for 56 ÷ 7 = ?
Lesson 5.3: Dividing using friendly
multiples (4.M.NBT.06)
Lesson Objective: The students will divide a quotient by
subtracting friendly multiples.
Video Lesson: Partial quotient
Taking your 36 game tokens and dividing them amongst you and your
three friends was easy yesterday because you know your math facts.
The problem now is with those tokens you all won 88 tickets! How are
you four going to divide those up? You cannot think of something that
multiplies by 4 to give you 88.
Repeated subtraction is fine if a number is small. When our dividend (the number you are
dividing up) gets bigger, than you need a bigger tool. This is where friendly multiples come in.
78 divided by 5 is a situation where I would not want to use repeated subtraction. Let’s look at
what friendly multiples we can use to subtract from 78 to get our answer. (hint: try to start
with parent and grandparent multiples to make things easier)
Division problem
5 78
- 50
28
- 25
3
Friendly multiple
Total groups of 5
5 * 10 = 50
10 groups
+ 5 groups
15 total groups with three
left over
5 * 5 = 25
We can subtract groups of 5 to make things faster, rather than subtracting them one at a time.
Fill in the chart below to practice this method. What would be a good friendly multiple to start
with?
Division problem
Friendly multiple
4 92
How many of those 88 tickets will be yours?
Total groups of 5
1. 75 ÷ 8
2. 32 ÷ 2
3. 99 ÷ 8
Lesson 5.4: Dividing Larger Numbers
(4.M.NBT.06)
Lesson Objective: The students will divide 4-5 digit dividends.
Video Lesson: larger dividend tool
Dividing using friendly multiples worked well for two digit dividends.
How can I use it to divide larger numbers?
If we have 12,376 and are dividing it by 6, how do we determine what a friendly multiple would
be? The grandfather of 6 is 600 (6 * 100). That seems like it would take a while to subtract that
out. How could I get a larger number?
__________________________________________________________________________
I guess we could multiply 6 by 1,000 and subtract 6,000. That would make for a lot less
subtractions. What if we took a multiple of 1,000. I know 6 * 2 gives me 12, so what would
happen if we took this:
6 * 2,000? _________________
That would make it a lot faster. Let’s finish this out below:
Division problem
6 12,376
- 12,000
376
600
76
60
16
12
4
Friendly multiple
Total groups
6 * 2,000 = 12,000
2,000 groups
100 groups
10 groups
+ 2 groups
With ____ remaining
6 * 100 = 600
6 * 10 = 60
6 * 2 = 12
Let’s try one together:
Division problem:
4,529 divided by 4
Friendly multiple
Total groups
Using words, how can you divide bigger dividends using the partial
quotient method?
Practice:
1. 3,542 ÷ 2
2. 7,495 ÷ 6