2-week project: math children’s book - · pdf fileproject overview there are a lot of...

Project Overview

There are a lot of really wonderful math children’s stories. However, I have found that most middle schoolers think they are too old for children’s books anymore. Fortunately, I found a way to make these stories appropriate and to extend students learning by having them write their own math children’s story. From this context, we are reading math children’s stories as examples of high quality work. Reading, appreciating, and understanding these stories and the math in them is rewarding enough on its own. Going to the next level to imagine and write their own stories can be extremely valuable to students. This collection of lessons is aimed at helping students to create their own mental math maps. Making connections is a big part of this. Having students write their own math children’s story not only helps them to make connections between math concepts, it also links the learning they do in math class to the learning they do in Language Arts. If possible, it may be nice to partner with the Language Arts teachers to work on the editing and )owing of students stories. “Today we are going to begin a 2 week project in which each of you will be writing a math children’s story. I’ve brought some examples of math children’s stories that have been published. These will serve as examples of high quality work. First let’s go over what the project entails.” Pass out the guidelines and discuss the grading and timeline. Answer any questions students have. I usually read the students a children’s book at the beginning of class every other day through out the project, perhaps beginning with two books on the *rst day. Any math children’s books will work. Here are some possible selections:

The King’s Commissioners by Aileen Friedman Math Curse by Jon Scieszka & Lane Smith A Remainder of One by Elinor J. Pinczes Two Way to Count to Ten by Ruby Dee

Can You Count to a Google? by Robert E. Wells The Greedy Triangle by Marilyn Burns The Grapes of Math by Greg Tang

Anno’s Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno How Big is a Foot? by Rolf Myller

Sir Cumference and the First Round Table by Cindy Neuschwander Sir Cumference and the Dragon of Pi by Cindy Neuschwander

Spaghetti and Meatballs for All by Marilyn Burns

After reading a book aloud to the class, we discuss the following questions:

• What math concepts were in this book?

• How did the author weave this math into the story?

• What made this story sound good when read aloud? (style, rhyme, repetition, etc.)

• How is this book di)erent from the others we’ve read? How is it similar?

• What ideas can you take from this book that might help you make your story better?

I allot 20 minutes each day for the students to work on their story, and the rest they must *nish as homework in order to keep up with our timeline. For the remainder of class time, I teach various math topics as we usually do, sometimes drawing from the topic of the children’s book we read that day.

Encouraging Mathematical Reasoning: www.MathLessonBank.com

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2-Week Project: Math Children’s Book

▣ COMMUNICATE MATHEMATICAL IDEAS USING LANGUAGE

+ TOPICS COVERED IN LESSONS FOR PARTICULAR CHILDREN’S BOOKS

Prerequisites

See individual lessons

Preparation

Math Children’s Book Guidelines for each student Various Math Children’s Books (see list)

During days 6—10 I encourage students switch stories with one another so they may get an outside person’s perspective on their work. On the *nal day, I have students get in groups of 4 and take turns reading their story aloud to the group. The *nal draft must be either printed clearly or typed. I do not make illustrating the book part of this project, although it could be. This would also be a great way to involve the art teachers. Illustrated books could be shared with younger children . . . perhaps a short *eld trip to a near by elementary school could be arranged. Another good extension would be to encourage students to submit their story to various publishers. Researching publishers and writing cover letters could be an educational and rewarding experience (once again a great way to collaborate with the Language Arts teachers.)


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LESSON PAGES

Math Children’s Book Guidelines

/15 points All grammar and spelling is correct.

/15 points Story has a clear beginning, middle, and end.

/15 points Sentences )ow together. (Story is easy to read aloud.)

/30 points Math is an integral part of the story.

/25 points The math in the story is presented clearly. (It is not confusing.)

**Bonus: The math is approached in a really creative or intriguing way.

/100 points TOTAL

Day 1 & 2 Topic Brainstorming:

• What math concept will you write your story around?

• What will the story be about in general?

• What will be the setting?

• Who will be the characters?

• How will you make your story interesting?

Day 3 & 4 Story Outline

• What will happen in the beginning of your story?

• What will happen in the middle of your story?

• What will happen in the end of your story?

Day 5 & 6 Rough Draft

• Write your story without editing. At this point don’t worry about spelling, grammar, or getting the details correct. Just write the story.

Day 7 & 8 Revisions

• Begin editing. Read your story out loud and concentrate on big things *rst.

• Does your story have a clear beginning, middle, and end?

• Is your story interesting?

• Does your story )ow?

• Is math clearly presented in your story?

Day 9 & 10 Final Draft

• Create the *nal draft of your story. Make sure it is polished and *nished.

• Check all grammar and spelling.

• Read your story aloud. Are there any parts that still need work?

Grading

Timeline

Encouraging Mathematical Reasoning

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MATH CHILDREN’S BOOK PROJECT —

GUIDELINES

Lesson Plan for the Book: The Grapes of Math ▣ ALGEBRAIC PATTERNS & GENERALIZING TO EQUATIONS

Preparation: The Grapes of Math book by Greg Tang Overhead #1 & #2

I began class by reading aloud The Grapes of Math by Greg Tang and then posing the following questions to help further develop their ideas for their own stories:






With this discussion fresh in their minds, I gave them 20 minutes to work on their stories. Afterwards they put their math children’s book away and got into pairs. I passed out Worksheet #1 and displayed Overhead #1 with only part 1 showing. “The Grapes of Math was all about :nding clever ways to make problems simpler to solve. See if you and your partner can :nd a trick to solving this problem. You need to :nd the solution to 1 + 2 + 3 + 4 + … and so on up to 100.” I planned on giving them a few minutes to struggle with the problem before I gave them a hint. I observed as pairs discussed. “How are you supposed to *nd the trick since all the number aren’t even written down?” asked Courtney. “Yeah but we know what they are,” said Tristen. “They’re all the numbers up to 100. Maybe we add all the numbers 1 through 10, then 10 through 20, and 20 through 30 . . .“ Chaz and JePrey were discussing, “You could just add up half of the numbers and just double it . . . no that won’t work.” Alex and Felipe were already busy adding the numbers the hard way. Ariel and Greg had their hands raised, “We’re stuck!” None of the pairs were making any progress, and I wasn’t surprised. I wanted to give them a chance and though the strategies they were trying wouldn’t work on this problem, I liked that they were applying some of the grouping and multiplying techniques from the book. I stopped the class and asked for their attention. “Here is a hint. I’m going to re-read the strawberry problem from The Grapes of Math.” I re-read that page aloud to the class. “Who can explain in their own words how the strawberry problem works?” Kate had her hand raised. “It says it right there. Add the rows that add to 9, and you have 1, 2, 3 of those so the answer is 27.” Storm also had his hand up. “The top row and the bottom row add to 9. The 2nd row and one up from the bottom add to 9. And the middle rows add to 9. That’s 27.” “Oh!” Chaz exclaimed and started talking with his partner. It appeared light bulbs had gone oP for a few students in the room but most still looked like they were waiting to see how that would help with the problem of adding all the numbers from 1 to 100.


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“What are the similarities between the strawberry problem and the problem were trying to solve?” I asked. “It’s the same thing with adding the *rst and the last,” explained Chaz, “and then the 2nd and the 2nd to last.” Quite a few more heads began nodding and there was some commotion as pairs talked about the idea. I let the class work and visited a few pairs that still looked confused. I was careful not to help too much and focused on having them verbalize to me their understanding of the strategy being used to the strawberry problem. That seemed to be enough to get them started on the problem in part 1. After most pairs *nished and were getting restless, I called the class to attention. “Did anyone :gure out a trick for solving the problem in part 1?” Lots of hands were raised and most seemed eager to share. I called on Katherine. “It’s easy. You add the 1 and the 100 and get 101 and the 2 and the 99 and get 101 again and you keep doing that until you used up all the numbers. There’s *fty 101’s, which gives you 5,050.” “Can you come up to the board and show us what you mean?” Katherine came to the board and drew something like this: Next I uncovered part 2. “For part 2 you need to add all the numbers up to 11 and then back down to 1 again. See if you and your partner can :nd a trick for this one too.” Some pairs thought the problem was easy and saw the trick right away, others struggled. They tried adding the *rst and the last number like they had in part 1 but that didn’t help. Race and Grecia asked for my help. “What makes this problem more diDcult from the last?” I probed. “You can’t add the *rst and the last number because it goes back down again.” “Where does it go back down?” I asked and Grecia pointed to the second 10 she had written on their paper. “So if the problem ended here. . .” I covered up the problem from the second 10 and beyond, “would it be easier to solve?” Both Race and Grecia were in agreement that that part of the problem would be very easy to solve. “Well maybe you should begin with the part of the problem that is easy for you to solve and then :gure out the rest later.” Most pairs were *nishing, and we discussed their methods which fell into two basic categories. First were those who broke the problem into two parts, adding 1 through 11 and then adding 10 through 1. The solution they got from these two parts were then added together to get the *nal answer. Adding 1 through 11 did bring up one snag that some students didn’t catch. Since 11 is odd, adding the *rst and last number, and the second number and second to last number, and so on still left a number in the middle (which is 6).


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The second method students used was to add the numbers 1 through 10, double that number since 10 through 1 would be the same answer, and then add 11. Here’s what the two methods look like: I uncovered part 3. “Here’s another challenge. This one is di)erent from parts 1 and 2 but there is still a trick to solving. See if you and your partner can :nd it.” I circulated. About 1/3 of the class came upon the trick after struggling for a bit. Even if students didn’t discover the answer, I felt there was great value in attempting the problem because it got them to search for a diPerent way to see things. We shared what we found as a class. Alex observed, “You start with 1 because 100 - 99 is one. Then you add 98 to it but right after that you take away 97 of what you just added so it is the same as if you just added 1. And you keep doing this. We *gured out you add 1, 50 times, so the answer is 50.” Felipe had another way to explain, “If you do all the subtraction problems *rst you get 1 + 1 + 1 … and you do that 50 times, just like Alex said.” Felipe came to the overhead and showed us what he meant. Once the other students saw the solution, it seemed obvious. Next I displayed Overhead #2 and read aloud, “Lynn’s Imports gets a new shipment of semi-precious gems each morning. She o)ers incredibly low pricing, and they usually sell out by 1:00 or 2:00 in the afternoon. Lynn sells the :rst gem for $1, the second gem for $2, the third gem for $3, and so on until she runs out of gems. If she receives a shipment of 10 gems on Monday, how much money will she collect by the time she sells out in the afternoon? How much for a shipment of 13 gems?” After pairs found answers to both questions I asked, “How did you solve for the money Lynn collects on a shipment of 10 gems?” “It’s just like problem we solved before. You add the 1 and the 10, and the 2 and the 9, and so on. You end up with 5 elevens to get 55,” explained Michael.


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Then I asked, “How was solving for a shipment of 13 gems di)erent?” “When you add the *rst and last you get 14,” oPered Art. “There’s a number left in the middle like with part 2,” Ariel pointed out who came to the board and drew: “What do we do with this number in the middle?” “You just add it at the end,” explained Kelsey. “14 added 6 times gets you 84 and 7 more gets you 91.” “Why do you think a shipment of 13 gems left a number in the middle and 10 gems did not?” I asked. The class was in agreement that it was because 13 was odd. I uncovered the second part of the question. “Now I’d like you to :gure it out for a shipment of 32 gems and a shipment of 45 gems.” Pairs were engaged and purposeful in their work. It seemed the task provided the right amount of challenge. Most found that the numbers were too big to draw a complete picture, which is what I was hoping for because it was a step towards being able to generalize the process. After observing I had students share. A shipment of 32 was rather easy for them. Each pair of numbers added to 33 (starting with the *rst and last number). There were 16 pairs of numbers so 33 x 16 = 528. 45 posed more problems for student. Each pair added to 46 (starting with the *rst and the last number) but the question was how many were there? Alex had her hand raised. “If you take out the middle number you have 44 numbers which will make 22 pairs. That’s why you do 46 x 22. Then you have to *nd the middle number.” “How do you :nd the middle number?” I asked. I called on Michael. “You have to have equal counting numbers on top and on bottom. Since there are 22 pairs, then the middle number is 23.” I wasn’t sure what he meant so I asked him to show us. Michael pointed to the example for 13 which was still on the board. “All the numbers except the middle get paired up. Since there were 6 pairs that means 6 is the number that comes right before the middle number.” Alex had another way to look at it. “I found a trick. If you divide the biggest number in half it will always be something-point-*ve … that’s if the number is odd. And if you add 0.5 to the answer you get the middle number.” “Now I want you to write instructions for how you would solve for a shipment of any number of gems.” At this point in the year students were used to me asking them to write in math class and to describe their thought process. Predictably even numbers were easier to explain than odd numbers. Some students *nished much quicker than others. I had Chaz and JePrey write their process for even numbers on to an overhead. I then called the class I set Chaz and JePrey’s overhead aside for the moment and called the class to attention. “What if we wanted to write an equation for :nding the amount of money Lynn would make on any size shipment. Let’s look at two methods. First let’s pretend this is a round of the function game, and you are trying to guess the rule. Let’s focus on only the even numbers for right now.” I wrote the following on the board.


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g = number of gems

m = amount of money Lynn collects

g process m

“You can :ll in the table with the numbers we’ve already :gured out, and you could also add more of your own. Once you think you have enough information, you can guess the equation and then check it.” I walked around as students worked. Courtney and Tristen had the equation “g + 1 x 1/2 = m”. “Explain to me how you would use this formula to solve for a shipment of 10 gems.” I said. Courtney explained, “You would go 10 + 1 x 5 . . . 55” “Where did the 5 come from?” “5 is half of 10,” said Tristen. “If I used your equation, I would write ’10 + 1 x 1/2’, not ‘10 + 1 x 5’. How can you :x that?” I left Tristen and Courtney to work further on their equation. After ample time for pairs to work, I wrote the following on the board:

g + 1 x ½ = m

g + 1 x g ÷ 2 = m

g + 1 x ½ g = m

“Here are three di)erent equations people have come up with. Do they make sense?” Tristen answered, “The *rst equation is wrong. That’s what we had, but you aren’t multiplying by 1/2, you’re multiplying by half of whatever the number is.” Michael had his hand raised, “Ours is the second one and it works. We tested it.” I pointed to the second equation. “A number of groups had this equation. According to the order of operations which part of this equation would we do :rst?” We discussed that the multiplication part would come *rst but what we wanted to begin with was the addition therefore we needed to add parenthesis around g + 1


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which I did. We also talked about how we want to do the division part before the multiplication part, so we added

parenthesis around the division part too.

g + 1 x ½ = m

( g + 1 ) x ( g ÷ 2 ) = m

g + 1 x ½ g = m

“So does the second equation make sense now? How can we check?” We tested the second equation using both 10 gems and 32 gems. Each worked. “Does the last equation make sense?” We discussed that it also needed parenthesis around the g + 1, so I added them. “Does the last equation make sense now?” There was some confusion as to whether you could just write 1/2 g. Also did ½ g need parenthesis? “Now for the second method for writing an equation. We can translate your descriptions into equations. Here’s the description Chaz and Je)rey wrote for even number of gems.” I displayed their overhead.

Even: take the number of gems plus 1 and multiply times half the number of gems.

I underlined the *rst part “take the number of gems”. “How would you write that in an equation?” I asked. “g” a number of students said aloud. I wrote g on the board. Then I underlined “plus 1” and wrote “+ 1” next to the “g”. Next I underlined “multiply” and I wrote “x” in our equation. Finally I underlined “half the number of gems” “How would we write half the number of gems in an equation?” Someone oPered “g ÷ 2”, another student oPered “½ g”. “Wow, that was a lot easier!” said Alex. The class was in agreement that this was a much easier way to write equations. I was glad to give them alternative strategies for future problems. “We’re missing something.” I said. “Parenthesis” was a chorus through the room. I added parenthesis as we had before. “There is still something missing.” I said. “= m.” oPered Felipe. I *nished our equation by writing “= m”. “That means we’re missing something from our description. How can we :x it?” I called on Chaz. “We should add at the end ‘equals the money Lynn makes’.” I made the correction on the overhead. “Now I want you to test an odd number on these equations and see if they work.” The student were surprised to see that they didn’t need a diPerent equation for the odd numbers. “Why does the same equations work on odd numbers?” No one had an answer so I decided to demonstrate with an example. “Let’s take 45 gems. We end up with 22 pairs that add up to 46 plus the middle number, 23. One way to think of that is that we have 22 ½ pairs of 46, because 23 is half of 46. If we use the equation, we do g + 1 which is 46 and multiply that times half of 45 which is 22.5. So we have 22.5 forty-sixes! Raise your hand with an open hand if you followed my reasoning, and with a closed :st if it is still a bit confusing.” Only about a third of the class indicated that they followed my explanation.


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I needed to wrap up the lesson so I decided to leave the discussion there and to end the class with a journal question. Journal Question: The Grapes of Math is all about *nding tricks to make solving math problems easier. Choose one trick you learned today and explain how it works so that a student that missed today’s class would understand how to use it.


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Part 1.

What is the solution to

1 + 2 + 3 + 4 + 5 + 6 + 7 + . . . + 99 + 100 ?

Part 3.


100 - 99 + 98 - 97 + 96 - 95 + . . . 3 + 2 - 1 ?

Part 2.


1 + 2 + 3 + . . . + 10 + 11 + 10 + . . . + 3 + 2 + 1 ?


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OVERHEAD #1

Lynn’s Imports gets a new shipment of semi-precious

gems each morning. She o+ers incredibly low pricing,

and they usually sells out by 1:00 or 2:00 in the

afternoon. Lynn sells the 0rst gem for $1, the second

gem for $2, the third gem for $3, and so on until she runs

out of gems. If she receives a shipment of 10 gems on

Monday, how much money will she collect by the time

she sells out in the afternoon? How much for a shipment

of 13 gems?

22 gems? 35 gems?

How could you 0gure it out for any number of gems?


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OVERHEAD #2

Lesson Plan for the Book: Spaghetti & Meatballs for All ▣ USE TABLES AND SYMBOLS TO REPRESENT & DESCRIBE PROPORTIONAL RELATIONSHIPS & GENERATE FORMULAS

▣ COMMUNICATE MATHEMATICAL IDEAS USING LANGUAGE & GRAPHICAL, NUMERIC, PHYSICAL, OR ALEGRAIC MODELS

▣ EVALUATE THE EFFECTIVENESS OF DIFFERENT REPRESENTATIONS TO COMMUNICATE IDEAS

▣ RATIO PROBLEM SOLVING

Preparation: Spaghetti & Meatballs for All book by Marilyn Burns Worksheet #1, #2 & #3

I began class by reading aloud Spaghetti & Meatballs for All by Marilyn Burns and then posing the following questions to help further develop their ideas for their own stories:






With this discussion fresh in their minds, I gave them 20 minutes to work on their stories. Afterwards they put their math children’s book away and got into pairs. I passed out Worksheet #1 and color tiles. “Here’s our own Spaghetti & Meatballs for All type problem. Event tables can be made by pushing square tables together to make long rectangular tables. You can use color tiles to stand for the square tables. One square table seats 4 people. Two square tables pushed together seats 6 people. Three square tables pushed together seats 8 people. If you pushed four square tables together, how many could you seat? 10 square tables? 15 square tables? 50 square tables? Describe how you could :gure it out for any number of tables.” Circulate while students work. Each time pairs solve the next problem, they should get a stronger handle on the problem and be closer to seeing how to generalize. It may be helpful to prompt students by asking:

• Are you doing the same steps over and over? What are they? What changes each time? What

stays the same?

• Do you see any patterns in how you are solving these problems?

• How did you :gure out the number of people you could seat without drawing all 50 tables the

picture?

Pass out Worksheet #2. “Here is a Relationship Study for the event table problem. The work you’ve already done should help you in creating the table representation. Your description for how to :gure it out for any number of square tables may help you in writing the equation. It may also be helpful to think of the table like a round of the function game to try and :gure out the process column and the equation. My suggestion is to start with which ever representation seems easiest to you, and see if that representation helps you create any others.” I’ve found it is best to allow students to work through the relationship study in the order they chose and using strategies that make sense to them. As students work you may want to ask:

• Which representation did you start with? Did that help you create any other representations?

• Which representation is the easiest for you to :gure out? What makes it easy?

• Which representation is the most diDcult for you to :gure out? What make it so diDcult?

• Have you developed any strategies that help you with any part of relationship studies?

• How did you decide how to number your graph? What does this point on your graph mean?


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• Which representation did you think would be most helpful for White Weddings Inc. to create a

pricing sheet? Why? If someone called up and said they needed 3 long event tables that seated a

total of 300 people, how many square tables would be needed? If the tables rent for $10 each,

how much would the tables for the wedding cost?

Pass out Worksheet #3. This takes the lesson that has mostly been about geometry and algebra (speci*cally perimeter and *nding rules to generalize a procedure) into a lesson about proportional reasoning (speci*cally ratio).


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PAGHETTI &


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Name: Date:

Event Tables

Event tables can be made by pushing square tables together to make long rectangular tables. One square table seats 4

people. Two square tables pushed together seats 6 people. Three square tables pushed together seats 8 people. See

picture below:

If you pushed four square tables together, how many could you seat? 10 square tables? 15 square tables? 50 square

tables? Describe how you could *gure it out for any number of tables.


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PAGHETTI &


WORKSHEET #1

Name: Date:

Relationship Study: Event Tables

S Process P

Table Representation

Equation Representation

Verbal Representation

(Do not forget to de0ne your variables)

Graph Representation

Decision

Brides often call wedding planners with their guest list. White Weddings Inc. wants to create a price sheet to show clients how much the event tables will cost for their size guest list. Which representation would be most helpful in creating this price sheet? Why?


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PAGHETTI &


WORKSHEET #2

Name: Date:

Johnson Family Dinner

A Johnson family gathering is held with a 5-square table for the adults and a 4-square table for the kids. Three dishes of

lasagna is served to the kid’s table and 4 dishes of lasagna are served to the adult’s table. If the lasagna is shared equally at

the table, do the kids and the adults get the same amount of lasagna?


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PAGHETTI &


WORKSHEET #3

Lesson Plan for the Book: The Greedy Triangle ▣ USE GEOMETRIC VOCABULARY TO DESCRIBE, COMPARE & CLASSIFY TWO– AND THREE–DIMENSIONAL FIGURES

Preparation: The Greedy Triangle book by Marilyn Burns Worksheet #1

I began class by reading aloud The Greedy Triangle by Marilyn Burns and then posing the following questions to help further develop their ideas for their own stories:






With this discussion fresh in their minds, I gave them 20 minutes to work on their stories. Afterwards they put their math children’s book away and got ready for a Geometry Scavenger Hunt. I passed out Worksheet #1 and took the students outside. “When Marilyn Burns wrote The Greedy Triangle, she used the fact that shapes are all around us every day. For this Geometry Scavenger Hunt, you are to work on your own to :nd examples of each of the items on the list, and then record a description and sketch a picture.” Most students are just excited to break free of the classroom for a bit. I think most are surprised how easy the items are to *nd in the lines of the school building, a near by tree, or the distant parking lot. It been my experience that this simple scavenger hunt heightens students awareness of the geometry in their everyday lives. For this reason Math Curse by Jon Scieszka and Lane Smith may be a good book to read next. After the scavenger hunt, you may want to ask the class:

• Were you able to :nd all the items on your list?

• Were there a lot of a particular term, and very few of another? Which ones?

• Which were the easiest to :nd? The most diDcult?

• Was anyone able to :nd a pentagon? Where? What about a trapezoid?

• Do you ever normally look at these things and think “Oh, there’s a hexagon.”?

• Did you :nd any geometry terms we didn’t have on the list?


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Name: Date:

Geometry Scavenger Hunt

Description Sketch

Circle

Non-Square Rectangle

Radius

Perimeter

Area

Right Angle

Parallel Lines


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WORKSHEET #1

Description Sketch

Square

Trapezoid

Hexagon

Obtuse Angle

Acute Angle

Pentagon

Perpendicular Lines

Parallelogram


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WORKSHEET #1

Lesson Plan for the Book: Can You Count to a Google ▣ ESTIMATE MEASUREMENTS & SOLVE APPLICATION PROBLEMS INVOLVING VOLUME

Preparation: Can You Count to a Google book by Robert E. Wells Worksheet #1 Rulers Calculators

This is very important! Do not read Can You Count to a Google by Robert E. Wells until AFTER the lesson. Begin by having students get in pairs and posing the following question: “How thick is a piece of paper? This is a task for you and your partner to solve.” Indicate what tools are available to students including rulers and calculators. Allow time to work. If pairs are stuck, have them visit with other pairs that have developed a strategy (such as measuring how thick their math book is without the covers and then dividing by the number of pages in the book). Afterward discuss diPerent pairs approach to the problem and their answers. Are their answers close to each other? Is there one answer they think is more accurate than another? Why? Passing out Worksheet #1 and read aloud “Someone hands you a suitcase :lled with 5, 10, and 20 dollar bills that total 1 million dollars. Approximately how big is the suitcase? Part of being a good problem solver is knowing what questions to ask. What questions come to mind that you’ll need to :gure out? Brainstorm with your partner and then we’ll share as a class.” Possible questions students may come with include:

• How much is a million? How many zeros?

• How many of each 5, 10, and 20 dollar bills would there be if we had a million dollars?

• Are we supposed to assume there are an equal amount of each type of bill? Would that equal a million

dollars? If not, how do we know how many of each we have?

• How wide and long is a dollar bill? Are 5, 10, and 20 dollar bills the same size?

• What am I going to spend the money on? :)

Record questions on the board and then ask, “I had you :gure out the thickness of a piece of paper before starting this problem because I thought that would help you. Can anyone see how this would help?” Discuss and then allow students time to work through the problem.

This question is intentionally vague in regards to the number of 5, 10, and 20 dollar bills there are. I let students know that whatever combination they come up with that totals to a million dollars will work for the problem, as long as there are at least a couple of each type of bill. This means they could choose four 5-dollar bills, two 10-dollar bills, and the rest 20-dollar bills . . . or two 20-dollar bills, two 10-dollar bills, and the rest 5-dollar bills . . . or a much more even mixture of the three. Some students who are used to exact answers may feel uncomfortable with the freedom to choose this aspect of the problem. This is part of this lesson, since most real life math is “messy” and therefore it is good to include messiness in our classroom problems. Student’s solutions are likely to vary quite a bit, not only because of the freedom to choose the mixture of bills in the suitcase, and their judgment on which estimation to use for the thickness of a bill, but also because they may decide to make the suitcase shaped like a traditional suitcase versus something that more closely resembles a cube. This is a great problem to have pairs record on blank overheads and share as a class so students can see the variety of approaches each group took. Your class discussion may include questions such as:

• What is similar about the various solutions we’ve seen? What is di)erent?

• Why do you think there were such di)erent solutions?

• Were you surprised how big of a suitcase you would need?

• Do you think you could carry the suitcase of $1 million dollars?

• How much money do you think you could carry?

• If the suitcase contained 100-dollar bills, how do you think that would change the answer?

Afterwards read Can You Count to a Google? by Robert E. Wells and discuss how this lesson relates to the book, speci*cally creating benchmarks for grasping the size of large numbers.


pg. 21 of 22

MATH CHILDREN’S BOOK PROJECT: C

AN YOU COUNT TO A GOOGLE —

LESSON PAGES

Name: Date:

Suitcase of Money

Someone hands you a suitcase *lled with 5, 10, and 20-dollar bills that totals 1 million dollars. Approximately how big is

the suitcase? Explain in complete sentences how you *gured it out.


pg. 22 of 22

MATH CHILDREN’S BOOK PROJECT: C

AN YOU COUNT TO A GOOGLE? —

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