Finding the Hidden Addend

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SWBAT solve a problem in which the total and one part are known. SWBAT represent their "action" with an equation.

Big Idea

CSI First Grade! Today your young investigators will try to find the missing addend while playing two different missing addend games.

Warm Up

10 minutes

We have been playing this game as part of our Morning Meeting (with my 1st and 2nd graders). Today, I will introduce it to all of the 1st graders (some come from another classroom).  

Advanced preparation:  Draw a chart with three columns.  The first column is labeled 10's, the second column is labeled 1's, and the third column is labeled total.  Get ten tongue depressors and on one side of each stick make 10 dots (2 groups of 5) and on the other side of each stick put one dot.  

I ask the students to come sit in a circle.  I show them the sticks.

There are 10 sticks altogether.  Each stick has ten dots on one side and one dot on the other side.  I am going to drop them on the floor.  Once they are dropped, I am going to ask someone to sort them by 10's and 1's.  We will then record the total number of tens, the total number of ones, and the total number of dots.

 I will then play a few rounds with the students.  I won't make the connection of the groups of 10's and 1's being recorded in the total number but rather wait for students to start to notice this on their own.  I want them to make this connection on their own because it will then have meaning by the ones who discover it.  Then I can have them explain it to others and start making predictions about how other groups will be written.  There is a video clip of this activity in the resource section.

The CCSS state that 1st grade students need to be able to understand that the two digits of a two-digit number represent amounts of tens and ones (CCSS.Math.Content.1.NBT.B.2).  As they continue throughout the year they will develop this concept and be expected to transfer it to the 3 digit concept in 2nd grade.  

Introduction to Games Involving Missing Addends.

15 minutes

I will introduce one new and one previously played game today.  Both of the games focus on students solving a problem where one of the parts and the total are known.  I will also reinforce the concept of the missing addend by having the student record an equation with a missing addend and fill it in once the missing part is identified.  There is a video in the resource section of two students modeling one of the games.  

I quickly reintroduce the How Many In My Hand? to the students.  I will use 7 cubes for this reintroduction.  

How many cubes do I have?  (the kids will count them with you)  I am going to put them behind my back and break them into two stacks.  I will keep one stack behind my back, in my hand, and place the other stack in front of me for you to see.  

I break off three and place four in front of me on the floor.  

There are 4 here.  How many are in my hand?  Think about what you already know.  We know that there are 7 altogether.  What else do we know?  How many are there all together? 

I then call on students to share their strategies and answers.  I then show them the recording sheet How Many In My Hand? (see section resource).  I model how to fill out the sheet and writing the equation as a missing addend problem.  See the section resource for a video sample of this (Cup Activity Video).  There are also samples of student work in the resource section.   

I then introduce What's Under the Cup.  I introduce this game the exact same way as I did with the game above except I show them how to hide cubes under the cup instead of in their hand. Once they get the idea, I introduce the recording sheet titled What's Under the Cup (see section resource).  

These activities both have students solving for a missing addend. The CCSS expect that students can determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.CCSS.Math.Content.1.OA.D.8.

Center Time

30 minutes

Students choose from the two activities that were just introduced in the previous section.  As students are engaging themselves in there activity choice, you should be circulating and taking notice of the following:

  1. How do the students figure out how many cubes are hidden?  In other words, what strategy are they using?
  2. How are they doing with the use of an equation?
  3. Do they understand that the total never changes?

As you are circulating, take note of two or three students that are using the strategy of counting on to solve the missing addend.  Their work will be highlighted in the Wrap Up section of the lesson.

It is important to let students choose their own strategy because it is developmental and each one is based on an understanding of the previous one.  To not allow this choice would be to not allow a student to go through the developmental process of understanding addition.  

Wrap Up

15 minutes

I call all of the students to come join me on the carpet area and asks them to take 7 cubes and sit in a circle.  

I noticed a variety of strategies that students were using while playing How Many In My Hand?  I would like you to watch how "Johnny" (choose a student who was using the strategy of counting on to model how they used that strategy to find the hidden number of cubes) solves for the hidden number of cubes.  

I will hide some in my hand and show the rest.  Hide 2 and show 5.  Then Johnny will model his strategy.  I will narrate his action to the class to make sure it is clear for everyone.  I will then call on a few more students (who I observed counting on during Center Time).