Teaching CCSS.Math.Content.HSA-SSE.B.4

Sum to finity and…that's about it.

  • Activities: 4
  • Quiz Questions: 0

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Ugh, what is that growing in the back of the fridge? A six-week-old tuna sandwich? Aunt Mary's chicken and chocolate casserole? Your roommate Dave's Something Surprise (not even he knows what's in it)? And more importantly, how fast is that stuff growing? Well, after using the activities in Shmoop's A-SSE.4 Teaching Guide, your students will have no trouble deriving and using the geometric series needed to figure it out.

We recommend that they wear a hazmat suit while confirming their results, though. It is gross in that fridge.

What's Inside Shmoop's Math Teaching Guides

Shmoop is a labor of love from folks who love to teach. Our teaching guides will help you supplement in-classroom learning with fun, engaging, and relatable learning materials that bring math to life.

Inside each guide, you'll find handouts, activity ideas, and more—all written by experts and designed to save you time. Here are the deets on what you get with your teaching guide:

  • 3-5 in-class activities specifically designed with the Common Core in mind.
  • 4 handouts (with separate answer keys!) that'll get your students thinking deeply about the concepts and calculations.
  • Additional resources that'll help make any math topic hip, hot, and happening.
  • A note from Shmoop's teachers to you, telling you what to expect from teaching the standard and how you can overcome the hurdles.

Want more help teaching Teaching CCSS.Math.Content.HSA-SSE.B.4?

Check out all the different parts of our corresponding learning guide.




Instructions for You

Objective: Sadly, there aren't a lot of math-related sports games out there. Sure, there's the Math Olympics, but we always had a hard time with the high-jump. What's a math fan to do?

Play ball, that's what. In this fast-paced game, students will play a little math baseball, stepping up to the plate and answering questions about geometric series and their sums. All the standard baseball rules apply: 3 outs per team per inning, and answering a question correctly gives them a base hit. The team who gets the most batters across home plate will take home the truly magnificent title of World (Geomeric) Series Champion—or at least whatever cool prizes you've got lying around your classroom.

Activity Length: 1 class period
Activity Type:
Full-class game with 2 teams
Materials Needed: Scratch paper, calculator for the student at bat, timer

Preparation: Clear an empty space in the middle of your classroom, and set up four desks in a roughly baseball-diamond shape—these will be 1st, 2nd, and 3rd base, and home plate.

Step 1: Split the class up into two teams and let 'em pick team names. Then explain the rules of The World Geometric Series. If you've got an old-timey baseball outfit to wear while you talk, more power to you. Here's how the game works:

  • There are 9 innings
  • Each team gets to bat (answer a question) once an inning (and every person must bat on the team until 3 outs happen)
  • The pitcher is the teacher
  • Three desks will be the bases
  • One desk will be the batting desk / home plate

If your students don't have it memorized already, write the following formula on your whiteboard so the whole class can see it:

Sum of a finite geometric series:

But you can also just expect them to know the thing, depending on how far along your class is and how much work you've done with geometric series.

Now flip a coin to see which team bats first. Play ball!

Step 2: Read the first question to the first batter on Team A (and have them just go in alphabetical order by last name for their batting order). They have one minute to answer the question, and they can use as much scratch paper as they need. If they get it wrong, it’s an out. If they get it right, they get to move to the 1st base desk. If there's someone on 1st base already, that person moves along to 2nd base (and similarly 2nd to 3rd and 3rd to home).

Once a student makes it to home, that team gets a point. Keep score on your whiteboard using the following format:


Innings123456789TOTAL
Team A
Team B

Once a team gets 3 outs (or after they score 5 runs, if your students are really sharp and not missing any answers), the other team gets to bat. After Team A and Team B have both batted once, the inning's over. Is "batted" even a word, by the way? It looks weird.

Step 3: The following are a bunch of questions to offer for this game. Feel free to add more as your game permits!


QuestionAnswer
What is the common ratio in the series 1/3 + 1/6 + 1/12 + …?1/2
What does the ... mean after 3 numbers in a series?That the series continues in the same pattern
What is the sum of the first 5 terms in the geometric series 1 + 5 + 25 + …?781
What is the sum of the first 6 terms in the geometric series 1 + 5 + 25 + …?3906
What is the sum of the first 9 terms in the geometric series 1 + 5 + 25 + …?488,281
What is the sum of the first 7 terms in the geometric series 1 + 5 + 25 + …?19,531
What is the sum of the first 4 terms in the geometric series 1 + 5 + 25 + …?156
What is the common ratio in the series 12 + 3 + 3/4 + …?1/4
What does "common ration" mean in the geometric series?The number that each term is multiplied by the next term.
What does the n variable stand for in the formula provided?The number of terms.
What is the sum of the first 10 terms in the geometric series 2 + 4 + 8 + …?2046
What is the sum of the first 13 terms in the geometric series 2 + 4 + 8 …?16,382
What is the common ratio in the series -5 – 500 – 5000 – …?100
What's the difference between geometric series and arithmetic series?Geometric series have a common ratio that's multiplied by each term, while arithmetic series have a number that's added to each term.
What is the sum of the first 15 terms in the series 12 + 3 + 3/4 + …?15.99999999
What is the sum of the first 6 terms in the series 12 + 3 + 3/4 + ... ?15.996
What is the sum of the first 3 terms in the series 12 + 3 + 3/4 + …?15.75
What does the a variable stand for in the formula provided?The first term of the series
What is the common ratio in the series -16 + 16 – 16 + … ?-1
What is the sum of the first 100 terms of the series -16 + 16 – 16 + … ?0
What does the r variable stand for in the formulas provided?The common ratio

Step 4: Keep playin' till the end of the period! You probably won't have time for a full 9 innings, so let's just say the team with the most points at the end of the period wins.

Without "batting" an eye "ball" (oh man, we are in Pun Heaven right now), reward your World Geometric Series winners with a sticker, a smile, a pat on the back, or maybe a coupon to your local In & Out Burger.

Instructions for Your Students

Hey, batter batter batter—it's time to combine our two favorite pastimes: baseball and finding the sum of a geometric series. Yes, we're serious. Both involve skill and split-second decision-making, and a big plate of nachos goes great with both. Actually, nachos go great with literally anything.

You'll be facing off against a rival team in the big game, using your powerful math chops to knock question after question out of the park. It should be a ball!

All puns aside, though, this game will show you the ins and outs of geometric series and hopefully cover all your bases with finding their sums. And please, no foul language allowed. Ha!

We can never resist a good sports pun.

Step 1: Split up into two teams (half the class on each team), and come up with a team name and mascot. Are you the Boston Boars? The San Francisco Shellfish? The Georgia Giant Squids? It can be whatever.

Here's how the rules will work (it's pretty basic if you've ever seen a baseball game):

  • There are 9 innings (or however many you can get through in a class period).
  • Each team gets to bat (answer a question) once an inning (and every person must bat on the team until 3 outs happen).
  • The pitcher is the teacher.
  • Three desks will be the bases.
  • One desk will be the batting desk / home plate.

You'll be using the formula for the sum of a finite geometric series to answer questions, so make sure you've got it committed to memory.

Your teacher will flip a coin to see which team bats first. Play ball!

Step 2: Batter up! When it's your turn to bat, sit down at the "home base" desk. Your teacher (the "pitcher") will read you a question about geometric series, and you've got one solid minute to answer. You can go ahead and use a sheet of scratch paper and a calculator to figure it out, if you need to.

If you get it right, that's a base hit! Walk over to the 1st base desk and post up there for a minute. If there's already someone on 1st, they'll advance to 2nd base while you get on 1st.

If you get it wrong, that's an out. After 3 outs or 5 points (whichever comes first), the other team gets to bat instead. Spend your downtime designing an awesome mascot for your team.

Step 3: Repeat Step 2 till the cows come home. Your teacher will keep firing off question after question, and it's your job to knock 'em out of the park.

Step 4: At the end of the game, the team with the most points gets crowned champion. The winning team gets bragging rights the rest of the year. And don't forget to sing "Take Me Out to the Ballgame" during the seventh-inning stretch.