This document provides an overview of a math lesson on multiplying and dividing by 9. The lesson includes fluency practice with dividing by 8 and decomposing multiples of 9. The concept development teaches patterns for multiplying by 9, such as the digit in the tens place being one less than the number of groups and the ones place being 10 minus the number of groups. Students apply these patterns to solve nines facts from 1 to 10. An application problem has students use nines facts to check their work. A problem set, debrief, exit ticket and homework assignment conclude the lesson.

1. Multiplication and Division
Using Units 9
Module 3: Lesson 13
Objective: Identify and use arithmetic patterns to
multiply.

2. Fluency Practice
(15 Minutes)
Divide by 8 Sprints
• Sprint A: Do as many problems as you can!
• Sprint B: Try to get one more right than you did
on Sprint A!

3. Fluency Practice
(15 minutes)
Group Counting (4 minutes)
Count forward and backward, occasionally
changing the direction of the count:
• Sixes to 60
• Sevens to 70
• Eights to 80
• Nines to 90

4. Fluency Practice
(15 minutes)
Decompose Multiples of 9 (3 minutes)
45
18 ?
Complete the missing part of the number bond.
Continue with the following possible sequence: whole of 90 and 27 as a
part, whole of 54 and 36 as a part, whole of 72 and 27 as a part, whole of
63 and 18 as a part.

5. Concept Development (20 minutes)
Materials: (S) Personal White Boards
Part 1: Identify patterns in multiples of 9.
During the fluency, we group counted nines to say
the multiplies of nine. When we skip-count by
nines what are we adding each time? Right 9!
Adding nines can be tricky. What’s a simplifying
strategy for adding ? Right, add 10 and subtract 1.

6. Concept Development (24 minutes)
Materials: (S) Personal White Boards

7. Concept Development
(20 minutes)
Compare the digits in the ones and the tens places of
the multiples. What pattern do you notice?
Yes! The digit in the tens place increases by 1 and the
digit in the ones place decreases by 1.
With your partner, analyze the sum of the digits for
each multiple of 9. What pattern do you notice?

8. Concept Development
(20 minutes)
Yes! Every multiple has a sum of the digits equal to 9.
Example: 9 + 10 = 19, 19 – 1 = 18 9x2= 18.
Knowing this can help you because you can check your
answer by adding up the digits. If the sum isn’t 9, then
there is a mistake.

9. Concept Development
(20 minutes)
Part 2: Apply strategies to solve nines facts.
Solve all the facts from 1 x 9 to 10 x 9 in a
column on your personal white boards.
Let’s examine 1 x 9 = 9. What is 9 multiplied by?
1.
So what digit is in tens place of the product 9x1?
Right, 0! How is this number related to 1? Zero is
one less than 1.

10. Concept Development
(20 minutes)
On my signal, say the product of 9x2. 18!
Which digit is in the tens place of the product? 1!
How is the digit in the tens place related to the 2? It is
one less again; 1 is one less than 2!
• Repeat the process with 3 x 9 and 4 x 9.
What pattern do you notice with the digit in the tens
place for each of those products?
The number in the tens place is one less than the
number of groups.
Does this pattern fit for the rest of the nines facts? Yes!

11. Concept Development
(20 minutes)
Let’s see if there is a pattern involving the ones
place.
2 x 9 = 18 Well, the 2 and the 8 are related in
some way.
3 x 9 = 27 The 3 and 7 are also related in the
same way. How are they related?
2 + 8 = 10 & 3 + 7 = 10 and 10 – 2 = 8 &
10 – 3 =7.

12. Concept Development
(20 minutes)
2 + 8 = 10 & 3 + 7 = 10 and 10 – 2 = 8 & 10 – 3 =7.
When you take the number of groups and
subtract it from 10, what do you get?
Right! The ones place in the product! On your
white boards, see if this pattern fits for the rest
of the nines facts.
Did it work for every fact 1 x 9 through 10 x 9?
Yes!

13. Concept Development
(20 minutes)
Let’s try 11 x 9. What is the product? 99
What is the number of groups? 11
Does the pattern work for 11 x 9? Why or why
not?
No, because you can’t have 11 in the ones place
and 10 – 11 doesn’t give us a whole number.
This pattern will only work for the nines facts 1-
10.

14. Application Problem
(15 minutes)
Michaela and Gilda read the same book. It takes
Michaela about 8 minutes to read a chapter, and
Gilda about 10 minutes. There are 9 chapters in
the book. How many fewer minutes does
Michaela spend reading than Gilda?
Use RDW to solve the problem. Check your
answer to the nines fact using a trick that you
learned today!

15. Application Problem
(15 minutes)

16. Problem Set (10 minutes)
You have 10 minutes to complete the problem set pages.
Debrief (10 minutes)
Let’s review your solutions for the problem set.

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

18. Homework
3-3 Lesson 9
Homework
Worksheet
Is Due Tomorrow!