12 Apples and Bananas

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SWBAT use relationships among different combinations of the number 12. SWBAT find as many 2 addend combinations for 12 as possible.

Big Idea

Early in the year we sang Apples and Bananas and solved for combinations of 7 and 8. Now we are upping the ante and moving in numbers beyond 10. This lesson challenges the students to find all of the possible combinations for the number 12.

Warm Up

5 minutes

I start this part of the lesson by asking the kids to sit in front of the classroom number line.  

"Today we are going to change up our Start At/Stop At routine.  We are going to use the numbers between 60 & 100."  Instead of pulling numbers out of an envelope, I am going to ask you to give me a number between  60 & 100.  Who can give me a number between 60 & 100?  Who could give me another number between 60 & 100?. I will put a green dot on the first number given and a red dot on the 2nd number."  

You should put a green dot on one stick it note and a red dot on the other.  These will be used to focus on where to start and stop.  You can also practice counting back by placing the green dot on the larger of the two numbers given.

I will ask a student to point to each number as we count as a whole group.  I will continue this process as time allows.   In this case students are counting up to and back from 100, starting at any number (CCSS.Math.Content.1.NBT.A.1).  This routine is the process in which I can assure that the students are continuously working toward this standard .

12 Apples and Bananas

30 minutes

"Today I have a new bowl for our apples and bananas.  This time the bowl can hold 12 pieces of fruit.  Your job will be to find all of the combinations of apples and bananas that can fit into the bowl.  How many apples?  How many bananas?  You need to have 12 pieces of fruit in all and you have to have some of each (at least one of each)."

"Remember, you job is to find as many combinations of apples and bananas as you can."

I then give each student a copy of the 12 Apples and Bananas Sheet (section resource).  

As students are working, you should notice how model and solve the problems.  How many combinations do they find, and how do they record their combinations.  You will want to be looking for students who used an organized approach in finding all of the possible combinations.  This will be used in the next section.  The students are meeting the Core Expectation by applying the commutative property of addition (CCSS.MATH.CONTENT.1.OA.B.3

Although, at this point, it is not expected that all of the first graders cant find all of the combinations, this expectation will push them to looking for more rather than fewer combinations.  

I have included an example of students that used an organized approach to find all of the combinations.  I have also included a video of a students who is still needing to use cubes and relies on the guess and check method. 

I am looking to see if students are planning or using a strategy to solve the problems int he task.  The students may also be using concrete models or pictures to help them figure out combinations for the problem (CCSS.MATH.PRACTICE.MP1).  

Lesson Wrap Up

20 minutes

I want to use this time to reinforce and noel the concept of using a strategy to find all of the possible combinations.  I start by making a chart with the title 12 Crayons in All (see section resource).  

"Who can tell me a combination they found (I take a few suggestions)?  As you were working on this task, I noticed that many of you were using strategies to find all of the combinations."

 At this point, I would have identified the students that I wanted to share to the group (based not he strategy they used).  

I will call on students to explain how they worked on the task and illustrate their approach not he chart.  I will be looking for someone who used an ordered list 11+1 thru 1+11 and for someone who used the flip facts or opposites.  Again, the photo in the section resource illustrates both of these approaches.  In this case students are able to analyze the situation and can recognize and use counterexamples. They are justifying their conclusions, communicating them to others, and responding to the statements of others (CCSS.MATH.PRACTICE.MP3). 

Continued Practice: Introducing Mad Minute

15 minutes

During the last trimester of our school year, I want to really focus on fact fluency and build upon the students ability to solve within ten fluently (CCSS.MATH.CONTENT.1.OA.C.6).  I am going to use the Mad Minute Routine.  This is a very "old school" routine that some may question.  However, I truly feel students need practice in performing task for fluency in a timed fashion.  Students need to obtain fact fluency in order to have success with multiplicative reasoning.  Students who don't gain this addition fact fluency by the end of 2nd grade tend to struggle with the multiplicative reasoning in third.  Having this fluency also allows them to work on more complex tasks because the have the fact recall to focus on the higher level concepts.  

I have included a copy of the 1st sheet.  You will need to purchase for own copy of the book in order to have permission to print this sheet and have copies of the additional sheets.  It is a very cheap buy online.

"Today we are going to start a new routine.  It will involve you solving addition equations in a set amount of time.  We will try and do this each and everyday that we have math class.  I would like each of you to find a spot in the room where you can work by yourself.  Once I give you your paper, I will need you to put your name on it.  When I say go you will all start at the same time.  I will give you 1 minute to solve as many problems as you can."

There is a video in the section resource that captures the students working on this during the minute timing.