Save Dave! Decomposing 4

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SWBAT work with a group to solve a problem & illustrate the different combinations for 4.

Big Idea

This is a problem-solving, group based activity that illustrates a real-world reason to find different number combinations for 4.

Attention Grabber/Introduction

10 minutes

[I asked my student, David, ahead of time, if I could make a math lesson about him.  I picked David on purpose—he’s a good buddy to everyone, and he doesn’t take things too seriously.  I wouldn’t pick a kiddo who’s really shy and sensitive or who gets in trouble frequently.]

“Okay friends, we are pretending today for math,” I begin, and some of my buddies get very confused looks on their faces.  “Mmm hmm,” I continue, “Let’s pretend it’s a little after Christmas, and David finds chocolate candies like these in his house.”  (David shows a red and a silver Hershey’s kiss in his hand with a big grin.)

“Yum…” a few kids say.

“So what would you do if you found yummy chocolates?” I ask.

“Eat them!” students proclaim.

“Exactly!” I agree.  “So just as David was finishing up the last green candy, his sister Bryanna came in.

“’That’s MY candy!’” she said, sounding very unhappy.  Oh no.  David knew he would get in trouble for eating his sister’s candy, and he really didn’t take her stuff!

 “His mom asked, “’Bryanna, do you remember what your Hershey’s kisses looked like?  That way we can check for sure to see if David has your candy.’”

 “Bryanna said, “’Yes.  I had 2 red kisses, and 2 silver kisses.’”  (I show 2 red and 2 silver kisses on the “big screen.”)

 “David did not take his sister’s candy.  He will show his candy to prove it.  What possible groups (or combinations) of candies could David have?

“Hmm… I see some of you are really thinking about Dave’s candy troubles.”  A couple of my really bright little kiddos are beginning to make combinations in their heads already.  Cool!

“So here’s what you’re going to do,” I continue.  You will get a paper like this,” I say, projecting the “Save Dave” recording sheet on the “big screen.” 

“Now, you need to work as a team,” I say.  “Your table will work together to find out what groups (or combinations) David could have.  You will need to show what you figure out for Dave, so your group has recording strips like this [holding up strip with 4 blank Hershey’s kisses] to color in.”

“What color will you need?” I ask.

A student says, “Red and green!”

“Well, remember… the green ones are all gone.  Since it’s hard to find a silver crayon, let’s leave the silver crayons white and color the red candies…”

“Red!” students proclaim.

“Absolutely.  Now here’s the teamwork rule:  You all need to sign your names on your recording sheet.  You are a team.  Here’s the rule of the crayon:  if you have an idea for a group (or combination), you cannot color it in.  Someone else on your team much color the recording strip.  So you have to talk to each other!  After you color one group, you must pass the crayon to someone else in your group.”

We go over the specifics with a few clarifying questions.  I try to keep the questions flowing quickly but naturally, so all groups, and all students are included in our “quick check.”  When it’s clear that we have the procedure down, I ask David to help me pass out recording sheets so we can get started.

“Don’t worry, David,” one student says, “We will help you out!”

Shared Problem Solving

15 minutes

After the supplies are distributed, I notice there’s an uncertain pause.  They don’t know how to begin!

I call on the help of my one buddy—a little guy who is so used to being last to be called on, so he’s absolutely thrilled.  “Start us off, buddy,” I urge.  “What is one group of candies that David can have—one group different than Bryanna’s 2 reds and 2 silvers.”

Without missing a beat, the little guy says, “3 red and 1 silver!”

“Hmm...” I say in my “making the obvious super obvious” mode.  “3 red, and 1 silver is not 2 red and 2 silver… would it work?

“Yes!” the entire class agrees, suddenly confident.  (“Secret mission, secretly accomplished!” I think to myself!)

“Let’s say, ‘Thanks, Jason!” and color in that first group of 3 red and 1 silver (or white).  Then, its up to your groups to figure out David’s other possible groups.  You need to SAVE DAVE!”

Students get working right away, and for the most part, our review questions really worked!  Occasionally, I will have to get a student to step back and share with his or her group, and once or twice, I have to help a group when they’re “stuck.”  We keep working, and time goes quickly.  The combinations are looking fantastic!


5 minutes

After a 2-minute warning, I ask that all red crayons be set down, and honestly, only 1 of our 4 groups is still coloring.  (The other groups have just finished up.) 

I ask a pair from one group to come up font, with a shy kiddo holding the group’s recording sheet, and a buddy to tell us their combinations.  We go over each combination, and I ask the other groups, “Do you have 4 reds, too?! (and so on, going over each combination).  The groups high-5 after each successful combination

Oddly, every group except for David’s group found every possible combination to save Dave.  Being a super good-natured kid, David just keeps smiling.

I ask the kids for their thoughts.  They say it was tricky, but they got used to the teamwork part.  (One little guy laments that he never got his chance to color.  I sympathetically agreed that it would be a bummer.) 

“Do you realize,” I say finally, noticing that we are out of time on our short day of school, “That we found all the ways to make 4… if you include Bryanna’s 2 and 2?  All of those groupings that you colored so nicely—those are different combinations to get 4!”  (In my perfect world, I would have 5 more minutes to ask strategic questions to get the students to come up with that realization, but time took its toll at the end.)