Discovering the Unknown

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SWBAT determine the unknown whole number in a subtraction problem.

Big Idea

My First Graders have been working hard to learn multiple strategies to solve subtraction. This lesson will have them incorporate all those skills to solve for the unknown.

Rev Them Up

5 minutes

I will have my students use mental math as a warm up exercise. Mental math is not something I would use at the beginning of the year in First Grade because it would be too much of a challenge. The majority of the class are still in the concrete stage at that point. Right now I am in the early spring and my class can handle thinking abstractly about numbers because they have developed solid one-to-one number match and can solve abstract problems quantitatively (MP2). If you still have a few students who would struggle with this activity, give him or her a partner or provide paper to allow them to draw out what is happening instead of solely relying on mental math.

I will state several problems slowly and provide a wait time for students to attempt to solve for their answer. There will be a variation in how fast my students find the correct answer. After I state the problem, I will tell students to raise their hands when they have an answer, and I will count to 10 in my head before asking for a volunteer.

I will use problems like the following:

  • Start with 5, add 2, then subtract 1...answer 6.
  • Start with 9, subtract 3, add 0...answer 6.
  • Start with 10, add 10, subtract 1...answer 19.

Whole Group Interaction

10 minutes

First graders are expected to solve for the unknown whole number in a subtraction problem. Finding this unknown quantity can be solved using many different strategies, including addition, fact families, and the use of manipulatives or drawings (1.OA.D.8). My students have been working hard to learn multiple strategies and to develop understandings around the identity property and the commutative property. Learning these strategies and properties are necessary for students to be able to solve for a missing unknown number. 

I will ask my students to help me identify all the ways we have learned to subtract and make a list. I will guide them towards ideas like:

  • If 0 is subtracted from a number, we know the answer will be the number.
  • We can make a model using a drawing or cubes.
  • We can use the number line.
  • Doubles facts help us solve; if we know 4+4=8, then we can solve 8-?=4
  • If we know 2+3=5, then we can solve 5-?=2.

I will make a list of subtraction problems on the board with missing whole numbers and ask my students to help me use any strategy that works for them to solve for the missing number. Problems like:

  • 9-?=4
  • 6-?=3
  • 8-?=3

You may have some students who still need manipulatives to solve with or even paper to draw a picture. Make sure and have some supplies for these strategies on hand. Watch our class discussion to see how it goes for us. Finding a missing addend always seems to be an easier concept for First Graders to grasp then finding a missing whole number in subtraction. Subtraction in itself is difficult for students to master because it is a less intuitive operation than addition. You can read more about it here. Acting out and drawing a picture is another strategy that can be used for students to solve for a missing whole number.

You can represent one of the problems above with a drawing or using students within the room. Example: I had 9 students in my room when the bell rang. (Have 9 students come stand at the front of the room) Some of my students left to go to the office and only 4 were left in my room. (Separate 4 students from the group of 9 and hand the group left a ? mark sign to hold in their hands) Now point to the questions mark on the chalkboard within the equation and tell them the students holding the sign belong in that blank. How many students left for the office? 5

Making the concept of a missing whole number into a concrete activity will help them identify the answer.

Independent Practice

15 minutes

I will have my students play this game at K-5 Math Resources. This game is a mixture of missing addend, missing whole number, subtraction and addition. I chose this game because it is built in review of previously taught skills and incorporates today's instruction on finding missing whole numbers. It is a partner game where students will draw a number and look at their game sheet to see if that number answers any of their problems. There are multiple game sheets for students to complete, which results in lots of practice. The students must think about each problem separately and decide what method to use to solve. Before I allow my partners to begin their game I will pass out the game sheets and ask them to talk with me about what they see, how will they solve, and what kind of strategies will they use.

If you have students who continue to have difficulty with these types of problems, or completing this kind of variety of problems all at once, you may examine how fluent they are with their addition facts. First Graders should be very fluent in solving addition facts before moving forward with subtraction and missing whole numbers. You might bring a small group to work with you on addition fact fluency, determining an unknown number in a subtraction problem, or another type of problem at this time if you feel they aren't ready for the game, which integrates so many types of problems at once.

My students really enjoyed playing the game.

Lesson Closure

5 minutes

I will print enough copies of the exit ticket to give my students one card each. As I have them line up for restroom break, they will have to bring their card to me and answer the problem. This allows me an opportunity to check what they have learned and see if I need to reteach.