##
* *Reflection: Developing a Conceptual Understanding
Assessment: Finding Combinations for 11 - Section 4: Session Wrap Up

The discussion about the equal sign and its meaning is an important one. Even the strongest of students have trouble defining what equal means (at this point in the year). I want to use this session wrap up to really start pushing students to a conceptual understanding of equality. I have include a video clip of my discussion. It is one child's response. You can see that the student is still hesitant with her understanding. She is a child who uses the sign with her equations and not he surface appeared to understand the concept but the video contradicts that belief.

*Developing a Conceptual Understanding: Talking About Equal*

# Assessment: Finding Combinations for 11

Lesson 1 of 13

## Objective: SWBAT find at least 5 combinations of 11. SWBAT connect written numbers and standard notation.

### Thomas Young

## Big Idea: How are they progressing? Today you will find out who well your students are doing with finding as many combinations of 11 peas and carrots as they can.

#### Warm Up

*5 min*

I have the students sit in a circle. I want them to practice rote counting, counting from a higher number down to a lower number. During this unit we have been working with numbers from 1-30, and tomorrow I will switch to the number range of 31-60. I want to use this time as a quick formative checkin on how students are doing with the first 30. I will designate the start at number and the stop at number.

**"I would like to start at 29. I want to start with Jack and then move around the circle until we get to the stop at number 19."**

*expand content*

You will need to make enough copies of 11 Peas and Carrots for each student in your class.

*"Today you are going to solve another problem, where you are trying to find as many combinations as you can. I am going to read the problem out loud for you to hear:*

* I have 11 vegetables. Some are peas. Some are carrots. How many of each could I have? How many peas? How many carrots?*

* I would like each of you to go find a spot in the room where you can work by yourself. There are connecting cubes out if you need to use them."*

At this point in the year, it is expected that each student can find at least 5 combinations of 11. You will want to look at not only the number of combinations that students are finding but also the approach that they are using. This way you can identify who is using relational thinking when finding combinations, who is just listing all of the known facts, and who is still guessing and checking**. **Looking at students' approaches will help you see how far along students are in engaging with MP1, which states that "mathematically proficient students start a problem by explaining to themselves the meaning of a problem and looking for entry points to its solution (**CCSS.Math.Practice.MP1**)."

As students are working, I will also be circulating to observe how students are solving the problem and to ask any clarifying questions. Below is a video of a student who is exceeding the standard. I have included (in the resource section) a quick clip of his work (he had only been working a few minutes) and a copy of his final piece of work. His work is a good example of MP7, which requires that "students are proficient and look closely to discern a pattern or structure with in a problem (**CCSS.Math.Practice.MP7**)." In this case the student is demonstrating his knowledge of knowing 7+3 means he also knows 3+7 (**CCSS.Math.Content.1.OA.B.3)**.

I have also included two other pieces of student work. One of the pieces is an example of a student using the "guess and check" method for finding the combinations. The other piece is an example of a student who needed a little intervention to get started. She was just sitting at the table holding her head and saying she couldn't do it. I worked with her on using the cubes and noted on her paper that I intervened. Providing concrete manipulatives is a good strategy at this point in the year for some students who still need that support to get to the abstract concept.

*expand content*

#### Center Time

*25 min*

As students finish the combinations problem, I direct them to make a choice from the center time activities that they have been working with during the past few lessons. Before the center time is over, I want to make sure that every child has played *Adding Dice Dots* using the new game board. This piece of work will be needed for the end of session wrap up.

- Recording Sums
- Addition Bingo
- Adding Dice Dots (There is a new game board in this resource section.)

All of these activities have been introduced in a previous lesson. Click the link to get the explanation about each activity.

#### Resources

*expand content*

#### Session Wrap Up

*15 min*

I gather the students to the carpet and have them sit so they can see the whiteboard easel. I hand them each their sheet from the Adding Dice Dots activity they did during Center Time.

I want to start with a conversation about what equal means.

* "What does this sign mean (I show them the equal sign on the easel)?"* I call on a student to share their idea. I will continue this for a few more responses. If someone can clearly define it, I will work with their answer, if not I will state,

*"We have talked a lot about the equal sign. The equal sign means that what is on one side of the sign has the same value as what is on the other side of the sign."*I will then lead them through the following:

I will draw 4+4 with dots on one side of the easel (this matches their recording sheets from Adding Dice Dots). I will then ask for volunteers to give me another way they found to make 8. I will then draw their example with dots. * "So, we now have 4+4 dots on one side of the equal sign and 2+2+4 on the other side of the equal sign. Who can help me write an equation for each set of dots?"* I then have a volunteer tell me how to write each equation. I then take the two equations and write 4+4=2+2+4 on the board.

**We then solve each one as a class and see if the value is the same amount on each side of the equal sign. I continue this routine with a few more examples. By the end of first grade students must "understand the meaning of the equal sign, and determine if equations involving addition are true or false (CCSS.Math.Content.1.OA.D.7)." This activity is an example of building a foundation for that understanding.**

*"Is this true? Are they equal?"**expand content*

#### Continued Practice

*5 min*

Students continue working on complements of 10. I have them partner up and use a 0-9 die. One person rolls and states the number needed to add to the rolled number to make 10. The other partner then has to state the number rolled. I like this activity because, on each roll, both students are having to use their complements of ten on each roll.

*expand content*

This is a fabulous lesson! I love how you used the dot activity to develop the meaning of the equal sign.

| 2 years ago | Reply##### Similar Lessons

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- UNIT 1: Counting Quantities
- UNIT 2: Working with Numbers, Operations, and Story Problems
- UNIT 3: Counting & Comparing
- UNIT 4: Blending
- UNIT 5: Building Numbers
- UNIT 6: Shapes Within Shapes
- UNIT 7: Data and Analysis
- UNIT 8: Non Standard Measuring
- UNIT 9: Shapes Within Shapes
- UNIT 10: Working with Numbers, Operations, and Story Problems
- UNIT 11: The Number 10 and the Addition and Subtraction Concept
- UNIT 12: The Ten Concept: Counting On and Off the Decade and Knowing 10 More/ 10 Less
- UNIT 13: Fraction Action Lessons
- UNIT 14: Counting by Groups
- UNIT 15: Complements of 10 and 20
- UNIT 16: Money!
- UNIT 17: Shapes, Blocks, and Attributes
- UNIT 18: Reviewing Data Collecting and Graphing

- LESSON 1: Assessment: Finding Combinations for 11
- LESSON 2: Story Problems Involving Subtraction
- LESSON 3: Ideas on Subtraction
- LESSON 4: Story Problems: Putting Concepts Into Action
- LESSON 5: Number of the Day
- LESSON 6: Assessment: Addition Story Problem
- LESSON 7: Measuring A Foot
- LESSON 8: Big Numbers For Big Brains
- LESSON 9: More Number Fun
- LESSON 10: 100 Here We Come
- LESSON 11: What Goes Here?
- LESSON 12: Assessing Counting: Number Tapes
- LESSON 13: Assessment of Unit Concepts