M3 P14

1. Multiplication and Division with Units of 0,
1, 6-9, and Multiples of 10
Topic D: Multiplication and Division Using
Units of 9
Module 3: Lesson 14
Objective: Identify and use arithmetic patterns
to multiply.

2. Fluency Practice
(7 minutes)
Multiply by 9 (7 minutes)
Materials: Multiply by 9 Pattern Sheet (1-5)
Let’s skip-count by nines to find the answer to
5 x 9 = ____. I’ll raise a finger for each nine.
Let’s skip-count up by nines again to find the
answer to 3 x 9 = ____, and I’ll count with my
fingers for each nine again.

3. Fluency Practice
(7 minutes)
Let’s see how we can skip-count down to find the
answer to 3 x 9 = ____, too. Start at 45 with 5 fingers,
1 for each nine, and count down with your fingers as
you say the numbers.
Repeat the process for 4 x 9.
Now let’s practice multiplying by 9 on the Pattern Sheet.
You have 2 minutes to do as many problems as you can.
Be sure to work left to right across the page and use
skip-counting strategies to solve unknown facts.

4. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
How is the 9 = 10 – 1 strategy –- or add ten, subtract 1 –-
from yesterday used to solve 2 x 9?
That’s right! You can do 1 x 9 = 9, then add ten and
subtract one like this: (9 + 10) – 1 = 18.
Let’s use this strategy to find 2 x 9 another way!
First, draw a 2 x 10 array. When we start with 2 x 10,
how many tens do we have?
In unit form, what is the fact we are finding?
That’s right – 2 nines.

5. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
To get 1 nine, we subtract 1 from a ten. In our problem
there are 2 nines, so we need to subtract 2 from our 2 tens.
When we subtract 2, how many tens are left?
What happened to the other ten?
2 x 9 = 18.
Tell your partner how we used the 9 = 10 – 1 strategy
with 2 x 10 to find 2 x 9.

6. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
Let’s use the 9 = 10 – 1 strategy to solve 3 x 9.
First, draw an array for 3 x 10.
To solve this problem, how many should we subtract?
Tell your partner why it’s 3.
That’s right! Because we are trying to find 3 nines and
we made 3 tens in our array, we have to take 1 away
from each 10 to make it 3 nines. So you subtract 3.

7. Cross off 3 from your array, then talk to your partner:
How many tens and ones are left in the array?
That’s right! There are till 2 complete tens, but only 7
ones in the third row.
What does our array show is the product of 3 x 9? 27!
Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.

8. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
How is the array related to the strategy of using the
number of groups, 3, to help you solve 3 x 9?
That’s right! There are only 2 tens in 27, and 3 – 1 = 2.
There are 7 ones in 27, and 10 – 3 = 7.
You can use your fingers to quickly solve a nines fact
using this strategy!
Put your hands out in front of you with all 10 fingers up,
with your palms facing away from you.

9. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
Imagine your fingers are numbered 1 through 10, with
your pinky on the left being number 1, and your pinky
on the right being number 10.
Let’s count from 1 to 10 together, lowering the finger
that matches each number.
To solve a nines fact, lower the finger that matches the
number of nines.
Let’s try together with 3 x 9. Hands out, fingers up!

10. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
For 3 x 9, which finger matches the number of nines?
That’s right – your third finger from the left!
Lower that finger. How many fingers are to the left of
the lowered finger?
That’s right - 2 fingers! 2 is the digit in the tens place.
How many fingers are to the right of the lowered finger?
That’s right – 7 fingers! 7 is the digit in the ones place.

11. Concept Development (43 minutes)
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.
What is the product of 3 x 9 shown by our fingers?
Does it match the product we found using our array?

12. Concept Development (43 minutes)
Continue with the following possible suggestions:
7 x 9 and 10 x 9
Why is the finger strategy limited to facts where the
number of groups is between 0 and 10?
How is the finger strategy related to the strategy of
using the number of groups to help solve a nines fact?
Talk with your partner.
Part 1: Extend the 9 = 10 – 1 strategy of
multiplying with units of 9.

13. Concept Development (43 minutes)
Now you’re going to get into small groups and rotate
through five stations! At each station you will use a
different strategy to solve nines facts.
 Station 1: Use the add 10, subtract 1 strategy
to list facts from 1 x 9 to 10 x 9.
 Station 2: Use 9 x n = (10 x n) – (1 x n),
a distributive strategy, to solve facts
from 1 x 9 to 10 x 9.
Part 2: Apply strategies for solving nines facts
and reason about their effectiveness.

14. Concept Development (43 minutes)
 Station 3: Use the finger strategy to solve facts from
1 x 9 to 10 x 9.
 Station 4: Use the number of groups to find the digits
in the tens and ones places of the product
to solve facts from 6 x 9 to 9 x 9.
 Station 5: Use 9 x n = (5 x n) + (4 x n),
a distributive strategy, to solve facts
from 6 x 9 to 9 x 9.
Part 2: Apply strategies for solving nines facts
and reason about their effectiveness.

15. Concept Development (43 minutes)
Let’s discuss the effectiveness of the strategies you used
to solve nines facts!
 Is there a strategy that is easiest for you? What
makes it easier than the others?
 What strategy helps you solve a nines fact with a
large number of groups, such as 12 x 9 = n, the most
quickly? Which strategies would not work for such a
large fact?
 Which strategies could easily be used to solve a
division fact?
Part 2: Apply strategies for solving nines facts
and reason about their effectiveness.

16. Problem Set (10 minutes)
Do your personal best to complete the Problem Set
in 10 minutes.
Debrief (10 minutes)
Let’s review your solutions for the Problem Set.
First, turn to your partner and compare answers.
Why is it important to know several strategies for solving larger
multiplication facts? Which strategies for solving nines facts
can be modified to apply to a different set of facts (sixes,
sevens, and eights, for example)?

17. Exit Ticket
(3 minutes)
This is where you are going to show
that you understand what we learned today!
Are you ready for the next lesson?!

18. Homework
3-3 Lesson 14
Homework
Is Due Tomorrow!