Counting and Combining Groups of Objects

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SWBAT count and combine items that come in groups of 2 and 4.

Big Idea

Today your students will solve story problems that ask them to find totals the involve groups of 2 and 4.

Warm Up

10 minutes

I start the class by having my students sit in a circle on the carpet.  I want to focus on finding the complement of 20 when given a number.  My next unit, will focus on complements of 20 and fluency with them, so this activity allows students to start thinking about combinations to 20 and allows me to informally see where students are with this concept.

I included a video, How Many to 20, that models how to play this game and the types of questions you could ask.

To make these 20 sticks, I used beads from the dollar store and barbecue skewers.  I glue round wooden balls at the end to seal the skewers.

Talking About 2s & 4s

10 minutes

I start by asking the students to make a circle on the carpet.  

"We will count around the group to find the number of eyes in the whole class.  When it is your turn you can either say the next 2s number or if you need you can do the whisper shout count.  Remember, this is where you whisper the first number (for the first eye) and say the 2nd number aloud."

I repeat this activity several times but starting with different students each round.  I want to them to see that it doesn't matter where we start, the total number will always be the same.  

"Does it matter what student we start with?  Will we always get the same number?  What if we counted knees or elbows?  Would the total number still be the same?  Why?"

The video, "Will It Still Be the Same?.m4v," captures a student's thinking about these questions.

I then turn the discussion to the idea of groups of 4.  

"We just talked about body parts that come in groups of 2.  I now want to switch our thinking and move away from our body.  I want to focus on the number four.  Can anyone think of anything that comes in groups of 4?"

There is a picture of the Things That Come In Fours chart that we created.

"Today you are going to work on problems that deal with the number of tires on a car."  

The opening activity and the preview for the activities that include items that are grouped by 4s allow the students to relate counting to addition by adding two or four for every 2s or 4s count (CCSS.MATH.CONTENT.1.OA.C.5).

How Many Wheels

30 minutes

The students will now work on the Toy Cars & How Many problems. You will need to make enough copies of this for each student in your class.

"I am going to ask that you solve the Toy Car problems.  I will read the first one to you and then ask you to get to work.  Remember to show your thinking and represent your work with an equation."

The How Many problem is meant to challenge students who need it.  In this case the problems are giving the students the total number of wheels and then asking them to figure out how many cars would be represented.

These tasks have students using addition within 20 to solve word problems involving situations of adding to, putting together, and comparing by identifying groups and then combining the groups to find a total (CCSS.MATH.CONTENT.1.OA.A.1) and solving problems that call for addition of three whole numbers whose sum is less than or equal to 20 (CCSS.MATH.CONTENT.1.OA.A.2).  

The CCSS expect students to solve story problems by explaining to themselves the meaning of a problem and looking for entry points to its solution (CCSS.MATH.PRACTICE.MP1).  In this case the students are trying to decipher how many groups of 4 would be represented for each car.

Sharing Strategies

10 minutes

Once the students are finished the problems, I gather them back to the carpet for a discussion about the first task.  

"I would like you to help me model the 1st problem with cubes."

I lay out 4 cubes for each car (Representing 4 Cars With Cubes.png), and then lead a discussion about who saw the tires as 2 front plus 2 back for each car and then added 2+2 eight times.  I will also have those who saw it as 4+4+4+4.  I will then ask for others to share how they solved the problem.  This way those who might have added all 1s can share their approach too.

As students share their strategies, you should record their approach on a piece of chart paper.

During this discussion, the students are analyzing each approach and recognize and use counterexamples. They are justifying their conclusions, communicating them to others, and responding to the arguments of others (CCSS.MATH.PRACTICE.MP3).

I have included a variety of approaches that represent the thinking of my students.

Drawing Pictures.pdf

Being Efficient.m4v

adding and double checking by counting each one.pdf

Writing Equations.pdf

Applying Discussion Concepts

5 minutes

After the discussion, I want to see if students can apply the discussion concepts into action.  You will need to make enough "Use the Clues.docx" copies for your whole class.  

"I want you to think about the strategies that we just discussed and models with the cubes.  I would like each of you to work on your own on this sheet.  I want you to show me how you are adding groups in each situation." 

This tasks allows students to identify and use repeated reasoning with the repeated addition of groups of 2s and 4s (CCSS.MATH.PRACTICE.MP8)

Continued Practice

5 minutes

I will ask the students to meet me on the carpet and hand out their sheet for today's Mad Minute exercise.  This routine was introduced in a previous lesson.  Please check out the link to get a full overview of this routine.

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, but 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.