Patterns in Multiples of 10, 11, and 12

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SWBAT use patterns to help master the multiples of 10, 11, and 12.

Big Idea

Patterns can be used to find products.


5 minutes

In today's lesson, the students learn to use patterns to help determine if a number is a multiple of 10, 11, or 12. This aligns with 4.0A.B4 because the students recognize that a whole number is a multiple of its factors.

I remind the students that they have learned to use patterns to help you multiply with several factors.  I tell the students, "Today, we will learn to use patterns with factors of 10, 11, & 12."  I ask, "What is a pattern?"  I give the students a chance to think about that for a minute.  I let 2 or 3 students share their ideas of patterns. Possible responses:  1) a pattern is when numbers repeat in a certain order or 2) numbers that follow a rule.

In the videos (Multiples of 10, 11, & 12 video 1 and Multiples of 10, 11, & 12 video 2, you hear the students discuss the lesson.

Direct Instruction

10 minutes

I call the students to the carpet for direct instruction.  Having all the students together in the same area makes it easier to keep all of their attention.  I use the Patterns in Multiples of 10, 11,&12 power point to lead the discussion about patterns of 10, 11, & 12.  

Throughout the discussion, I call on various students to answer the questions within the power point.  I do not just call on the students with their hands raised, but I like to call on students who may look a little timid.  I find that this helps build their confidence because most of the time they know the answer.  I ask the students questions to help them find the correct answer.

I ask," What do you notice about the multiples of 10?"  Student response:  They all end with zero.  Another question that I ask, "How can you use this information to help you find other multiples of 10?"  Student response:  When you multiply by 10, your answer will be the other number with 1 zero."

Possible Misconceptions about the concept:

Because the multiples of 12 are even, some students may misunderstand and think that all even numbers greater than 12 are multiples of 12. 

 Questions to clear up misconception:

1.  How many times can 12 divide into that number?

2.  Will there be a remainder?  If so, did it divide evenly by 12?

3.  What number can you multiply by 12 to get this multiple?

4.  Can you draw an array of this number?

Group Activity

30 minutes

Be for class, print out the Multiple of 10,11,12 Numbers. on different color card stock paper, then cut them out.  Make enough sets of cards for each of your groups. (This is a picture of my materials for your reference.)

I put the students in pairs.  I give each pair a Multiple of 10, 11, 12 or Not activity sheet and a set of numbers (MP5).  The two students will try to find the multiples of 10, 11, & 12 (4.OA.B4).  The first student turns over a card.  This number will be for the tens place.  The second student turns over a card.  This number will be for the ones place.  The students write the number in the place value chart.  The two students should look at the number and determine if it is a multiple of 10, 11, 12, or neither (MP1) (MP6).  The students should answer the following short answer questions upon completing the activity: 1.  How can you tell if a number is a multiple of 12?  2.  How are patterns helpful when finding products? (MP7)

This is a sample of Student Work for this activity.

Early Finishers:  Any pairs that finish the activity early, can go to the computer to practice the skill at the following site:

Independent Activity/Exit Ticket

10 minutes

Group activity is great, but as a teacher,  I need to know what each individual student knows about the skill.  Therefore, I give the students an independent activity.

The students should take out a piece of paper for this activity.  On the Smart board, I display the directions (Independent Assignment Multiples of 10, 11, and 12).  


Write 5 multiples each of 10, 11, and 12.  Tell how you know that these multiples are correct. (MP1) (MP2) (MP7)