SWBAT generate equivalent expressions for a number. SWBAT use numbers and standard notation (+,-,&=) to record. SWBAT use a strategy to count and combine groups of dots.

Students will revisit an old routine as they work with larger groups of dots and record the number of dots that were flashed before them. Students will represent a variety of ways to represent the number 10.

5 minutes

Advanced preparation: You will need to print out both sets of number cards from the resource section. Cut out the 31-60 cards and put them into one envelope and do the same with the 61-90 and put them in their own envelope.

I start this part of the lesson by asking the kids to sit in front of the classroom number line.

**"Today we are going to change up our Start At/Stop At routine. We are going to add the numbers 61-90." I will pull one card out of the 31-60 envelope and we will use that as our start at number. I will then pull out a card from our 61-90 envelope and use that as our Stop At number. We will then count as a class from our starting number to our ending number."**

I will ask a student to point to each number as we count as a whole group. I will continue this process as time allows. I will also mix in counting backwards by starting at the higher number and counting to the lower number. The Core Standards expect 1st graders to be able to count to 120, starting at any number, by the end of 1st grade. This routine is the process in which I can assure that the students are continuously working toward that standard (CCSS.Math.Content.1.NBT.A.1).

20 minutes

Advanced Preparation: You will need blank paper and pencils for the students. You will also need to make a copy of the Quick Flash Cards in this section's resource.

I want to start this unit and lesson by doing several quick flashes that focus on different arrangements of 10 dots. You will begin by flashing one of the image cards for 5 seconds (I use my document camera). Then give students time to draw it. Then flash the image again (for 5 more seconds). Again, allow time for them to check their work and draw it. Then show the image a final time and ask students to describe who they remembered the image.

*"Who can tell me how they remembered what to draw, or How did you see the image? What strategies helped you?"*

You are looking for how kids visually broke the dots down.

As students come up to the projection and show how they saw it, you should draw a circle around each set they identify and then write an equation to represent their thinking.

*"Joe saw it as groups of 2 dots and 3 dots and 5 dots. Who can we write that as an equation to tell how many altogether?"*

It is important to model a few examples for each image. You don't want students to think theirs is the only one way to see the set of dots.

This activity really supports MP4 because it promotes proficiency with model with mathematics and apply what they know to simplify a situation (CCSS.Math.Practice.MP4).

30 minutes

Advanced Preparation: You will need to make enough copies of the Number of the Day: 10 Sheet. I have included the .pdf and notebook version of the sheet. If you have notebook software, you can open the file and change the sheet for future lessons as well.

**"We are going to wok with the 'Friendly" number of ten! We call this number friendly because it is easy to count and is a benchmark number. We can use our knowledge of ten to build all kinds of numbers. (I then use the easel as I discuss the following) I can show ten by writing the number, writing the word ten, and/or writing 10 dots."**

* "What are some ways that we can represent ten?"* I record these on the white board easel as well. There is a picture in the section resource (number of the day:10.png) that shows what the students came up with.

I remind students that they can use more than two numbers and that they can also use subtraction but that they should focus on using numbers and equations and not pictures. The Core expects students to apply properties of operations as strategies to add and subtract.^{2}*Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)(CCSS.Math.Content.1.OA.B.3) It also expects first graders to a*dd and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)(CCSS.Math.Content.1.OA.C.6).

*"Now I want you to take your own ten sheet and find as many ways as you can to make 10. I will come around and ask you to explain how you are coming up with different ways."*

There are several resources included. Here is an explanation of each one for your convenience:

- Number of the Day 10.notebook: This is the notebook file that can be edited and used for future lessons.
- Number of the Day 10.pdf: This is the pdf file of the same resource.
- Representing 10 with a Strategy.m4v: This video demonstrates a student explaining the strategy that was used in finding combinations. He clearly points out how he is changing each addend by one.
- Student Using A Systematic Strategy For 10.png: This is a copy of the recording sheet of a student who clearly used a strategic approach to finding combinations.
- Number of the Day 20.notebook: This is for differentiation and explained in the Reflection part of this section.
- Number of the Day 20.pdf: Same as above but pdf. file instead f the notebook file.
- Student Work Representing 10.m4v: Another student explaining how they used a strategy to find combinations.

While students are working, you should circulate and observe how students are coming up with combinations to make 10 and how are they recording their work?

10 minutes

The purpose of this discussion is to generate equivalent expressions for the number ten (as a class). Students are using standard notation (=, -, & =).

I call the class to the carpet and have them face the easel.

** "I want you to share ways that you found to make 10."** I start by asking the student who used a strategy to find two addend equations to make 10. I then call in someone who used subtraction and finally some own who used three or more addends. There is a photo in the section resource of our completed chart.

During this unit, more and more students will start to use a strategy or method for finding combinations of a number. It is important to model this whenever the opportunity arrises.

I also used cubes to reinforce the visual model of equations with three addends. There is a photo in the section resource of this model.

The Core Standards expect students to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning (**CCSS.Math.Practice.MP6**). In this case, the students are sharing strategies that they used. They are modeling how they recorded their equations and explaining their thinking. As the teacher I can make connections to each strategy. For example, if someone say 8+2=10. I can show how that can easily become 8+1+1=10.

5 minutes

I continue to reinforce the complements of 10 by having student use ten sticks. There is a video that demonstrates who this activity works.

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