##
* *Reflection: Developing a Conceptual Understanding
Working with Multiples Using the Factor 3 - Section 4: Practicing With 3's Multiplication

The students did a great job skip counting to find the missing product. Many used their fingers to keep track of their counts, but I am still uncertain they really know what they are counting. Several more lessons with actually drawing the groups or building the expression with cubes are necessary. However, this lesson does help the students with their accuracy. We now need to pair that with fluency work.

In third grade, fluency is not automaticity. It is knowing and correctly using appropriate strategies, using objects, pictures, words and symbols. The strategies that 3rd grade students use are expected to become increasingly sophisticated, as their skills develop. (3.OA.7) "By the end of Grade 3, know from memory all products of two one-digit numbers". Know from memory is not solely intended as a focus on timed tests of memory recall. It is intended to insure that students have many experiences working with manipulatives, drawings, and models such as arrays, so that they have a deep understanding of the basic facts.

*How Did They Do*

*Developing a Conceptual Understanding: How Did They Do*

# Working with Multiples Using the Factor 3

Lesson 5 of 5

## Objective: Students will use their knowledge of skip counting to build their accuracy with multiplication facts with a factor of 3 and learn what the vocabulary word "multiples" means.

## Big Idea: Children don't readily "see" threes. In this lesson, we work to find connections to 3 in our skip counting, which we will identify as working with multiples.

*50 minutes*

#### Warm Up

*10 min*

In order to check for application of our "quick array" strategy, I put a prompt on the board to begin math class. The students copy the prompt into their reflection journals and begin answering it according to their current understanding. The prompt also introduces a product of the 3's.

Following about 5 minutes of work, we then share out, verbally, what several of the children did. You may want to encourage students to add to their journals if they hear a peer express an idea that is interesting and new. This is a nice way to step into the Mathematical Practice of Critiquing the Reasoning of Others (MP3).

Also, if a student struggles with finding the correct vocabulary to explain his/her thinking, it is completely appropriate to have them share their visual and you, or their peers, help with the wording. One way I like to do this is to put the piece up and ask, "What do you think _______did here? Can you explain?" This way, the student sharing does not have to feel criticized or less able, and the class is pushed to critique and explain. Everyone wins.

#### Resources

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#### What Comes In 3's

*5 min*

To engage the students, I ask them to think about things in the world that come in sets of three. Then I list these on the board and ask them to find commonalities in the words.

*Look at these words boys and girls:*

*tricycle*

*triangle*

*triplets*

*triathlon*

*tripoly*

*triple*

*third*

*What do you see in common in these words?*

The students identify "tri" in every word except for the word *third*. At this point it is beneficial to explain that "tri" is a signal that there are 3. One of my students surprises me, saying, "But third and thirds at least start with a t! I wonder if all words meaning 3 start with a t?"

*Today, mathematicians we will talk about multiples of 3. We can think about these things we see all the time when we are counting sets of three today. *

*Let's watch this short clip to review the multiples of three. *

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#### Grouping 3's

*25 min*

The routine in my room when introducing new multiples is to create equal groups and label those groups with the total number of objects. Counting by 3's is not as easy as our previous multiples lessons, so I take this part slowly.

*Mathematicians, will you please use your math boards to make 10 groups of 3? When you are done, label the total number of items next to each group. We will talk about patterns you notice in the multiples of 3.*

As students are working, I walk around and watch how they attack the groupings. It is important the children at this point understand (and apply) that when we multiply we are counting equal groups of items. This is a key concept outlined by the Common Core. One of the patterns the students often times don't see is that the ten's place changes after 3 equal counts. I think this is important to point out if no one in the class does.

Following the discussion about the patterns they see in the multiples, we begin to write the multiplication expressions down. We then look for patterns in the equations and discuss them together as a class. You may also choose to have partners or table groups share first, before a class discussion.

Last, I ask the students to write out the associated repetitive addition facts next to the multiplication expressions. I do this to continue practice with adding "equal groups". At this point we discuss how 7 x 3 = 21 and 3 x 7 = 21 because of the commutative property, but that the story for each would be different because the equal groups are different.

*Students, would someone like to make up a word problem that would make sense with 3 x 7 = 21? *

"There are 7 marbles in each bag. I bought 3 bags. I have 21 marbles total."

*How about for 7 x 3 = 21? How would your story be different?*

*"There are 3 marbles in each bag. I bought 7 bags. I have 21 marbles total."*

*Excellent. So the difference is you bought different equal amounts of marbles. Which one of these stories represents our multiple work today? Write the story of the bags with 3 marbles each!*

#### Resources

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In order to practice using multiples of 3, I have my students engage in a game found on the K-5 Math Teaching Resources site. There is a Multiples game for several numbers and causes the students to use important vocabulary.

This clip shows two of my students playing the game. On each turn the student rolls a die and multiplies that number by 3. They then can place their marker on the product. If the product is already covered by their color, they must remove it. The first person to use all 5 of their markers wins.

#### Resources

*expand content*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities