##
* *Reflection: Developing a Conceptual Understanding
Tallying it Up - Section 2: Collaborate

As I assessed students' work-samples, I noticed a common error. Several students were organizing six to a bundle as opposed to five. To clear up this misconception I used a small group setting to re-teach. I asked students to recount the number of tally marks by ones (have them to mark each line as they count to make sure they were counting correctly). Then, I had them to write the number out beside each tally mark. I ask them what they noticed about the number they counted and the number each tally mark represented.

To reaffirm their learning, I ask students to tell me what number each tally mark represented? Most of them said five and corrected their problems. However, some students were unable to correct their mistakes. I had them to repeat the given task until a level of understanding was reached.

*Developing a Conceptual Understanding: Student's Work Sample*

# Tallying it Up

Lesson 9 of 10

## Objective: SWBAT generate data flipping coins, record the data using tally marks, and count the tally marks by skip counting by fives.

## Big Idea: In this collaborative lesson students will use "Head, or Tails" to learn how to tally count by fives and add on left over numbers.

*60 minutes*

#### Warm Up

*20 min*

I start this lesson by saying, “How many of you would like a penny?”

After that, I say, “Today you will learn how to tally and how to count by fives using pennies!” Then, I invite students to the carpet. I give them all a penny. I ask them to look at their pennies carefully. I ask them, “What do you notice about your penny?” If students notice that each penny has two sides, I ask, “Does anyone know what they are called?” (Heads and tails).

**Resource: **Heads and tails

I ask, “Why do you think they are called that?

Some students note the side with the face on it is the head, and the side without the face is the tail. I tell students we will be flipping their pennies to see how many times it falls on heads or tails. They all seem pretty excited about flipping coins!

I want students to connect making bunches of five while tallying to the idea of bunching five pennies together to make a nickel - all within the context of exploring a problem.

**MP1- Make Sense of Problems & persevering in solving them.**

I collect the pennies from students and ask them to move into smaller groups no larger than six.

#### Resources

*expand content*

#### Collaborate

*20 min*

After the students move into their small groups, I tell them we are going to try a fun experiment.

"Each group will be given five pennies, one per student, to shake in your hand. Then each of you will open your hands and gently put the pennies on your desk. After that each group will count how many times the pennies land heads up and how many times the pennies land tails up."

I demonstrate how to shake the pennies and how to mark their tally marks on their tally sheet. While I am demonstrating I ask students howto determine how many tally marks to mark. I also ask them to tell me how to correctly count their tally marks (Counting by fives).

When a level of understanding is reached, I let students go to work.

While students are working, I keep track of the number of heads and the number of tails on the dry erase board that I placed at each group. Since this is their first time taking tally marks, I want them to check their marks with the marks I placed on the board. I hope that they will use my marks as a guide to assist them in the learning process. To reinforce learning I continue asking probing questions to check for understanding:

- Can some explain what you are going to be doing?
- How many heads/tails are there?
- Do you agree? Why or why not?
- Does anyone have the same answer but a different way to explain it?
- Have you compared your work with anyone else’s?
- What did other members of your group try?
- How would you describe the problem in your own words?

See: Group work sample

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#### Making the Connection

*10 min*

After students have reached a level of comfort in this exercise, I call them back to the carpet. I ask several questions to check for understanding, and to help them make the connection between tallying and counting by fives:

- Do you think the pennies landed heads up more often or tails up more often?
- How do you know?

Some students are able to make the connection by counting by fives using the tally marks. However, some students continue to add by ones. I make a note of this to address throughout the lesson.

Then, I ask students to count to check how many tally marks are in each group? We started counting the tally marks in the heads column first from each group (I used a large tally board to write the tally marks on). Then we count the tally marks for the tails column. After we finished writing all of the tally marks, I ask students to think of a way to use skip counting to help us count faster. I tell them the more they practice counting the better they will become. They all seem to agree that practice makes perfect.

I ask student volunteers to write next to each group of five tally marks as you count by fives (see: example chart). I repeat the same for the tails column. I ask students, “What do you notice about our chart?” I allowed them time to observe the chart, and to make connections (each complete tally marks represent five, when we to count tally marks we can do it faster by counting by fives.)

I ask students to count by five with me as I write the numbers. I begin at the bottom by writing 0 and then 5 above it (see: counting strip). I tell students we will use this strip to help us count forward and backwards by fives each morning. I post this strip on the board, and ask students to return to their seats. **MP6-Attending to precision.**

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#### Closing

*10 min*

For the closing students are back at their seats and eager to talk about what they have learned. I have students model and explain what they learned about tallying.

I ask students who would like to show us how to write 15 using tally marks? I ask them to demonstrate how to use tally marks to show 15 on the board. After that, I ask students to count by fives to check their answer. Then, I ask students to tell how many groups of five tally marks do we have? (3) How many extra tally marks do we have? (0) I repeat with 7, 25, 16, 38, and 41.

I pay particular attention to some of my students struggling to explain how to add on left over numbers by counting by ones. This tells me I need to adjust future lessons on skip counting with marks left over **( MP6)**.

*expand content*

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- LESSON 1: Comparing Things!
- LESSON 2: Finding the Right Place!
- LESSON 3: Applying The Basics!
- LESSON 4: Watch my number grow!
- LESSON 5: Mentally Speaking!
- LESSON 6: Keep On Doing!
- LESSON 7: Abracadabra
- LESSON 8: What's in Your Zoo?
- LESSON 9: Tallying it Up
- LESSON 10: Identifying Tens and Ones