I have already introduced doubles this year, but we all know that students need work on using their facts, even doubles, in problem solving. I also want my students to be able to explain what they are doing mathematically. So at the beginning of this lesson the students are to write their definition of what a double is in their math notebook. Not only does this help them with fluency when it comes to their doubles facts, but it also encourages them to communicate precisely (MP6). Additionally, in order to accomplish this introductory task, students need to look for and make use of structure (MP7) within the Common Core Standard 1.OA.6, which states that first graders need to be able to add and subtract within 20. Doubles are one structure students can use to build that fluency.
Under the definition they are to write at least 5 doubles facts they know in their head, without using any counting or getting to a friendly number. (for example: saying 9+9=18 I know that because 10 +10=20 and if I took 2 away from that it would be 18)
I am adding this piece because I want to see what they think they know as a fact.
I will give them about 5 minutes or so and then we will head over to the carpet with our notebooks - no pencils because I want them to be actively participating and not writing, and to share out some of our thinking.
I want them to build upon their prior knowledge and then we will build upon that in the next section.
I have a book, "The Babysitting Twins." It is from an old math series. It is about a brother and sister who are twins and everything they do, they do with the exact same number, and then a sibling comes in and needs just one more. I like to use this book to introduce the doubles +1 concept.
For example: on page 4-5, the older brother and sister each have their own train, each with 7 cars. There is a flap that you lift up and then, the little brother comes along and adds "one more."
I might say: "How does this page show us doubles?" I will pose the question and then expect the students to articulate their thinking. The mathematical practice standards expect students to attend to precision when they are communicating (MP6) and construct viable arguments (MP3). To get students engaged in these practices, I encourage students to use "math talk." In other words, I tell them to talk like a mathematician. A mathematician might say, "I know that 7+7=14 is a doubles fact. A doubles fact means both addends are the same number."
We'll read the story and then write an equations to reflect a few different pages. For page 4 and page 5 we would record the equations 7+7=14 and then 7+8=15.
If you can't find a copy of the book you could easily make your own version.
We are using math journals today. I like to write my own problems for the students to solve. I try and use them as the main characters. Today Zoey is our character. I do this because it helps to make the problem more relevant for the students. The number choices I used all lend themselves to the doubles +1 strategy. CCSS (1.oa.1) first graders are to solve word problems within 20. That is exactly what they are doing in this lesson, and the problem is about someone they know.
At the carpet I will read the problem that the students are going to solve in their notebooks.
Zoey has 6 bracelets. She gets 7 more from her Grandma. How many bracelets does Zoey have now?
Together we will unpack the problem. When we unpack the problem, I don't want the students to tell me the answer. Right now we are thinking about what the problem is asking of us (MP1).
I will ask them: What do we know and what do we need to find out?
What do we know? (Zoey has 6 bracelets) Do we know anything else? (She got 7 more from her grandma). I'll ask something like: if she gets more bracelets, then what happens to her group? Is it larger or smaller, how do you know?
Do we know anything else? (no)
What do we need to find out? (how many bracelets Zoey has now)
The students will work with a partner. They will each have their own math journals, with the problem already taped inside. They are given multiple number choices to solve for, they don't have to get through all of them, but they do need to solve one set then share out their strategy with their partner. Are the strategies they used the same or are they different? Then move onto the next number set.
I want to make sure everyone has multiple chances to make sense of the problem and persevere (MP1). They are also constructing viable arguments and beginning to critique others (MP3). I want the students to understand there are multiple ways to solve a problem. When they are sharing out if they don't match on the answer I want them to be able to go back and decide if someone made a counting error or a number mix up etc...
While the students are working I am conferencing with groups and looking for efficient strategies for the students to share out during the wrap up section of the lesson.
Students will come back to their seats and we will share out strategies using the document camera. I try and be very strategic with my sharing out. I look for a direct modeler, someone who counts everything, then move to a counting on. I will ask how are the strategies the same and how are they different?
If I don't have a direct modeler then I move right to the counter. I want the students to see strategies that work, but also that are efficient. If someone is counting everything I want them to see a peer who is counting on.