I have told my students in the past that one day they would be using alphabet letters in their math equations. Today, will be my chance to introduce this idea to them and explain the why behind it. First Graders need to tackle problems where the unknown is represented by letters or symbols. This prepares them for algebraic problems in later grades. (1.OA.D.8).
I want my students to begin thinking about problem-solving on word problems. I will verbally state several problems for them to start using their critical thinking skills and imagery to solve.
Tom held up 5 fingers and Sherri held up 3 fingers. How many fingers did they hold up altogether?
Justin had 9 crayons and Terri gave him 4 more crayons. How many crayons does Justin have now?
Mrs. Moon passed out 4 pieces of paper to Ashley and 8 pieces to Taylor. How many pieces of paper did Mrs. Moon pass out?
I started with a problem that my students could access action pieces easily (their fingers). Then I built on that and moved towards problems that they could use manipulatives if necessary, otherwise they could solve abstractly with imagery. (MP2). This will get them using their critical thinking skills and making connections before our lesson begins.
I will use a story problem to introduce the concept of an unknown addend. I will use the following problem and discussion points.
Tom was playing with 10 legos. Brad gave him 6 legos and he got the rest from Sara. How many did he get from Sara?
Teach: Tom has the total =10
Brad gave him part;6
Sara is our question, we don’t know what she gave him so we are going to call it x. I will write the equation x+6=10; we are looking for a number that if we join it with 6 our answer will be 10. When we find the answer, we will replace the x with the correct number. Then we will check to see if what we found makes the number sentence true.
I will use unifix cubes and connect 10, break off 6 to find what is left, answer is 4. I will point out to my students that we are using subtraction to figure out what is being added. I am using this concrete method with cubes to introduce this concept to my students because I know it is somewhat abstract. There are multiple strategies that can be used to solve an unknown addition equation, but I am starting with the concrete method to explain, teach, and hopefully reach all of my students. (1.OA.D.8). I have several students that have the higher order thinking skills to use counting up and/or math fact fluency to solve for unknown whole numbers in an equation. But introducing this concept with a concrete connection will help all of my students to see the connection with using an x for the unknown. The process of solving for the unknown is an abstract thought process that First Graders are building towards. (MP2). They must become proficient in selecting strategies to assist them in reasoning quantitatively. Please look at the picture in the resource section for a perfect example of one student using counting up and another student using her cube tower to solve. I will complete two more problems with my class, similar to the one above.
Need: Print the practice sheet below and copy per student
I will go here to print and copy a practice worksheet for my students. I will provide unifix cubes to those students who need the concrete manipulatives to solve their problems. I have many students who mastered counting on in previous lessons and I will remind them of this strategy. Watch the video in the resource section to see one student using counting on. I will have some students who need extra support when I release them to work independently. I will encourage them to attempt their equations and then have them come sit by. My rule of thumb is to provide enough support for them to accomplish 3 problems successfully, then I send them back to their desk to attempt the rest independently.
Every student has their own method for making sense and solving for an unknown addend. I want to offer my students a chance to conduct a share out with their classmates on how they solved for an unknown addend and we can make a list of the ideas offered. I will provide a problem and ask students to raise their hand and tell me how they solved it.
Sherri had 16 pencils in her desk. She brought 5 of them from home. How many did she already have in her desk?
Some of the ideas I hope to hear from my students are: