##
* *Reflection: Joy
Adding Repetitive Sets of Numbers - Section 2: Teaching the lesson

The students were so excited as they began to graph the data. The graph began to emerge to look like a mountain or a skyscraper. As the middle of the graph grew higher and higher, the students couldn't wait to do the next day.

I wondered if the amount of graphing would be too much, or too confusing for students, but they became excited about the project. They worked hard and were insistent that they wanted to keep going, even when I suggested that we take a break.

They were amazed at how high days 6 and 7 were. They figured out there were 42 of each object from the 2 days.

If students can take ownership of a math project, they will see math as something fun, and something they are good at. What better foundation to set, than one that says, "I like math, I can do math, Math is fun!"

*Excitement*

*Joy: Excitement*

# Adding Repetitive Sets of Numbers

Lesson 10 of 12

## Objective: SWBAT complete repeating addition problems requiring the repetitive addition of each number 1 - 12.

## Big Idea: Repetitive addition is a skill that is a precursor for early multiplication understanding.

*20 minutes*

#### Warm Up

*10 min*

To get students to think about repetitive addition, I put the following on the board:

2 + 2 + 2 = ____

Students quickly see that the sum is 6. I ask them how they got the answer. (Counting by 2s is the desired response. If you don't get this response, keep asking for a better, more "efficient" way.)

Writing and speaking, I ask, "What if I wanted to know 5 + 5 + 5 + 5 = _______ how would I do that?" (Counting by 5s.)

*What if I wanted to know 8 + 8 + 8 + 8 = _______? Is it as easy to count by 8s? What might we do to find the answer with so many eights?* I ask students to find the sum and be ready to explain how they figured it out. I give them a few minutes to write down the work and their answer in math journals. I circulate around to see how students are solving.

We share our answers, but more critically I want to hear how they arrived at their answer. Students have had little practice with repeated addition, so hearing/knowing the students' strategy development now is crucial to exploring this new concept. Most students can do repeated addition with 1, 2, 5 and 10 by skip counting, but beyond those numbers they need to develop appropriate strategies.

While students explain their strategies, I model their explanations on the board. Usually students notice that they can add 8 + 8 which is 16 and then 8 + 8 again for another 16 and then add 16 + 16, putting together tens and ones to get the answer. Other students may rely on counting once they get past 16, using tools such as number lines or number grids.

I tell students that today we will explore adding larger numbers by using the song, "Twelve Days of Christmas." (You can use any appropriate addition counting song or poem for this activity, but for us it is the day before the holiday break so we are celebrating.)

We will also use graphing to display the data derived from the song before we try to do the repeated addition.

*expand content*

#### Teaching the lesson

*10 min*

When sharing the song, "Twelve Days of Christmas", I explain that the song comes from a tradition in England (I show them where England is on the map), where long ago people celebrated for 12 days with feasts and gifts. In listening to and reading the lyrics, we learn that the singer was given gifts every day, for 12 days. We are going to figure out how many presents she received, altogether.

Students are given graph paper (which I discover isn't large enough because I didn't determine how much space our work will require before we started, so I had to adapt by handing out a second sheet and attaching it to the first in the middle of our graphing.)

I project a copy of the blank graph on the board and we talk about how to color in the first day.

We color in the first day, 1 gift, by filling one square. Next we color in 2, for the second day, and one for the first day (remember, she is given every gift from the previous day plus the new day's gifts). We repeat the coloring for each day. I allow students to move ahead if they understand what we are doing. I continue walking through the process, coloring my graph on the board for those who need step-by-step structure.

When the graph is complete, I ask which day does the person in the song receive the most presents? Next, I ask students if they can figure out how many of each gift she received. They can count every square on the graph, or use more efficient (faster, fewer errors) strategies such as - receiving 5 golden rings for 8 days is 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 for 40 golden rings, or counting by fives, eight times. Students are looking for regularity in the numbers as they reason out how to find the total (MP8).

I ask students if they could figure out some of the other numbers of gifts in similar ways? Students work on totaling the different gifts and we share how we found the answers. Noticing the Patterns

Graphing data is a skill that the Common Core Standards have established as important for second graders (2.MD.D.10), and so it is an important aspect of this lesson.

#### Resources

*expand content*

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Where is the Question
- LESSON 2: Playing Teacher - Checking Our Work
- LESSON 3: Estimation - an introduction
- LESSON 4: Using Models to Add and Subtract
- LESSON 5: Comparing Temperatures a Science and Math Exploration Part I
- LESSON 6: Comparing Temperatures A Math and Science Comparison Part II
- LESSON 7: Checking Subtraction
- LESSON 8: Introducing the Addition Algorithm
- LESSON 9: Addition Algorithm Rote or Understanding
- LESSON 10: Adding Repetitive Sets of Numbers
- LESSON 11: Adding and Subtracting in Columns
- LESSON 12: Getting Better At Addition and Subtraction Final Project