I want students to know what mathematical practices we will be focusing on today! So I say, we will be working with the following mathematical practices today. My students are quite familiar with the use of each one, however, I will go over it briefly as a reminder.
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP.3. Construct viable arguments and critique the reasoning of others.
MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.8. Look for and express regularity in repeated reasoning.
To begin, I write a couple of one-digit addition and subtraction problems on the board.
2+7= 5 + 6= 8-5= 7-3=
I ask a couple of student volunteers to solve the problems using illustrations. They seem to do that quite well. So, I decide to probe a bit more. I ask, can anyone tell me another way to solve the problems. Can you explain how you got your answers?
Students offered different ways to represent the given problems, and explained how they got their answers. Since this cluster is connected to the Second Grade Critical Area of Focus#2 Building fluency with subtraction and addition. This activity provides the opportunity for studnts to critique the reasoning of others, and make sense of their own problem solving.
I may work with student a bit more using manipulatives to help them build fluency. However, I want them to be able to experience working on various types of problems throughout the entire lesson.
In this phase of the lesson, the students will explore the relation of addition to subtraction. This process is continued as the students use problem-solving skills to find fact families, including those in which one addend is zero or in which the addends are alike. However, I want to focus students attention to the result unknown, total unknown, and both addends unknown, because as students go deeper into mathematical concepts the complexity changes, and they should be able to make the connection on their own.
My goal is to see my student’s transition from relying on their fingers as tools. However, the use of fingers at this age is normal. However, I encourage them throughout the lesson to rely more on math facts.
After allowing my students to practice reviewing fact families with their group, I move them into a whole group setting.
You will need:
Give each student a paper plate. Ask the students to divide their plate down the middle. Tell them to put four pasta shapes on one side and two pasta shapes on the other side. (The purpose of this lesson is to explore the relationship between addition and subtraction.) Have the students write number sentences using the pieces they have placed on each side to extend their learning.
I also had them to write subtraction sentences using the same numbers to see if they were still using the same numbers in the addition sentence they composed.
They noticed the connections immediately. (Note this would be a good time to introduce “Missing Numbers.”)
Capture The Big Idea:
Finally, ask the students to write the four sentences these two sets suggest. [4 + 2 = 6; 2 + 4 = 6; 6 – 2 = 4; 6 – 4 = 2.] Have volunteers tell stories that fit each of the equations. This activity will help them focus on the relation of subtraction to addition. Now have them put four pasta pieces on one side of their plates and zero pieces on the other side.
Call on a student volunteer to explain and write two addition sentences. Then call on another student to use the same numbers the first volunteer used to compose two subtraction sentences. ( have them to explain aloud)
|4 + 2 = 6||2 + 4 = 6||6 – 2 = 4||6 – 4 = 2|
If the students seem comfortable with this process, move them into their individual seats, and distribute pasta shapes to students. Tell the students to consider this equation: 2 + _ = 8. Remind students that eight is the sum and that the other two numbers are addends.
Ask: What is the missing addend? [Six] Repeat with other examples. Ask the students to record one of the examples and to illustrate it using the pasta and the plate they have already divided into half.
Using what they have learned throughout this lesson the students worked independently solving basic addition and subtraction questions. As students are working I remind them of the intended purpose of this lesson. I say, you guys have been solving addition and subtraction problems to help you develop an algebraic representation of problem solving. I want you all to make meaning of the operations instead of just solving them. I circle the room to probe students. I want to know what they are thinking. I may ask, what can you use to represent your problem. What do you notice about addition/subtraction? Can you tell me the difference between adding and subtracting? Can you explain how you got your answer? Did anyone get anything different? Did you see a pattern? Explain?
Students were able to explain how and why they got their answers. However, some students seem to be puzzled when explaining the difference between adding and subtraction. They know how and when to add/subtract, but lack the skills of explaining it mathematically.
I will work with students in smaller groups to model how to explain how and why they problem-solve mathematically. Student Work-Sample