# Finding Patterns using a Multiplication Chart

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## Objective

SWBAT identify patterns using a multiplication chart.

## Opener

5 minutes

We have already discussed the meanings of multiplication.  The students know that you can use an array to show a multiplication problem.   Also, the students know that you can use the hundred charts to help find patterns in numbers.  In today's lesson, they use their understanding of multiplication to find different patterns using a multiplication chart.  This aligns with 4.OA.C4 because the students are using patterns to find multiples.

To get the students started with the lesson, I ask a question.  "What is a number pattern?"   I give the students a few minutes to think about the question.   I take a few responses from the students.  One student responds, "When you skip count numbers."  I tell the students that this is true, you will have a pattern if you skip count.  Another student adds, "A pattern is how a number repeats.  When you have 5, 10, 15, and 20, the numbers count by 5."  I tell the student that he is correct.  I ask the class, "What do you notice when you count 5's?"  One student responds, they end with 0 and 5.  I let the students know that today they will use a multiplication chart to help them recognize patterns.

## Whole Class Discussion

15 minutes

To begin the lesson, I call the students to the carpet so that they can be close to me.  When I'm at the Smart board, I like for our whole class discussion to be close.  First, we review what we have already learned about patterns.

Review:

You can use a hundreds chart to help find multiples of numbers.  A multiple is the product of a number and any whole number.  With a hundreds chart you can skip count to find your multiples.

For example, some multiples of 2 are 2, 4, 6, 8, 10, and 12. We learned that all multiples of 2 are even numbers.  We learned that all multiples of 5 end with 0 and 5.  We also learned the patterns of 9.  We learned that if you add the digits together, they equal 9 or a multiple of 9.

I tell the students, "Today, I want you to use a different tool  to find other patterns in multiplication."  I go on to tell them, "It is important for you to experience using different tools so that you can be well rounded students."  To give them an example of how to find patterns with a multiplication chart, we work together to find a pattern.

Using the power point, we discuss finding patterns with a multiplication chart.  I tell the students that we can find multiple numbers whose multiples are even.  We have already learned that the multiples of 2 are even. Look at the chart to find another number whose multiples are all even.  I give the students a few minutes to do this.  I call on a student and the student lets me know that the number 8 has all even numbers.  I ask the class to find the next multiple of 8.  One student shares that the multiples of 8 end with 0, 8, 6, 4, and 2.  On the chart for 12 x 8, the number ends with a 6.  So the next number will end with a 4.  I ask the students what is 13 x 8.  Several students figured out that 13 x 8 = 104.  I call on a student to explain how she found the answer for 13 x 8.  The student explains that she knew that the answer was 104 because she added 8 to 96.  She knew her answer was correct because the next pattern would end in a 4.

I challenge the students to get them thinking even more.  Since 8 is double 4, what does this tell you about the multiples of 4?  I do not ask the students to answer this question now.  I just want them to think about it as they are finding patterns in groups.

I send the students back to their seat to practice the skill in groups.

## Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others (MP3).

For this activity, I put the students in pairs.  I give each group a Multiplication Chart.   The students must work together to find patterns of numbers with the multiplication chart.  The students must write down the pattern, then find the next two numbers in the pattern. The students can study the multiplication chart to find any pattern they can discover.  This allows the students the freedom to explore without limitations.  (If we do not put limitations on students, they may discover things that we didn't think about.)  They must communicate precisely to others within their groups (MP6).  They must use clear definitions and terminology as they precisely discuss the patterns they find on the chart (MP1).

During this part of the lesson, I monitor and assess the students' progression of understanding through questioning.  Possible questions to help lead to the solution are as follows:

1.  What pattern do you notice for this number?

2.  Using what you have discovered, how can this help you find the next two numbers?

3.  How does this pattern compare with another number on the chart?

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.ezschool.com/Games/Pattern.html

## Closure

15 minutes

To close the lesson, I have groups share their answers.  This gives those students who still do not understand another opportunity to learn it. I show the multiplication chart on the Smart board while we are discussing the patterns.  Some students are not auditory learners, but understand clearly when the work is put up for them to see. These are some of the patterns found by the students:

1) The multiples of 8 were double the multiples of 4

2) The multiples of 9 add together to equal 9 or a multiple of 9

3) Some of the multiples of 5 are also multiples of 10 because 5 is a factor of 10

4)  Even numbers repeat in the ones place, but odd numbers do not.  (Example: for the multiples of 4, the ones place ends with 4, 8, 2, 6, and 0 repeatedly.)

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples. In the reflection Video - Finding Patterns with a Multiplication Chart, I explain my thoughts on the importance of the multiplication chart in helping the students with this lesson.

Before the class ends, I have the student complete an Exit Ticket Pattern with Multiplication Chart.  This gives me a clear understanding of what each student knows. From this sample of student work (Student Work - Patterns), I can tell that this student understands the connection between a number being a factor of another number; therefore, they will have some of the same multiples.   Those students who need remediation will work with me in small group the next day