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Daily Math Challenge

Greetings Mathematicians,

As a way to stay connected to you during our school closure, I will share a new math challenge with you each day. These activities are optional and meant to be fun. I will try to provide tasks and resources that invite creativity and can be completed with simple materials you can find in your home. Enjoy! 
- Ms. Donahoe
 
 

Friday, May 29:

Let's conclude the week with a paper folding challenge! Choose from four different models at wildmaths.org. There are detailed plans and instructional videos to help you with each model. Which model do you predict will be the most difficult to construct? Why?

 

Thursday, May 28:

Last week at Gather, I encouraged you to consider the ways you are connecting with members of your community, and I shared a bit about my own postcard project. This week, I wanted to share a fun resource for staying connected: Public Math Postcards!

Public Math is dreaming up all kinds of creative ways for folks to engage in mathematical thinking in everyday life. They recently launched a post card project, which allows you to request a Public Math Postcard for yourself and send one to a friend (for free). Brighten someone's day and send them a math-y postcard today!

Wednesday, May 27:

The Julia Robinson Mathematics Festival Activity of the Week is called Nuggets for Sale. This activity includes multiple problems at varying levels of difficulty. 

To access the instructions, click on the file to the right. Click again to open the full document (4 pages).

First page of the PDF file: NuggetsforSale

Tuesday, May 26:

Let's start the week with a photo prompt! Study the photo below and respond to as many of the questions as you can. 

Source: IM Talking Math

Friday, May 22:

For those of you who enjoyed the math art coloring pages last Friday, here are two sample pages from a second book by Alex Bellos, Visions of the Universe: A Coloring Journey Through Math's Great Mysteries.

First page of the PDF file: Visions-of-the-Universe-Sample-Coloring-Pages

Thursday, May 21:

Here's a number puzzle brought to you by #mathwalks. Can you find the missing values? 

Wednesday, May 20:

The Julia Robinson Mathematics Festival Activity of the Week is called Squareland. Grid paper and a ruler might be helpful tools for this exercise! 

To access the instructions, click on the file to the right. Click again to open the full document (4 pages).

First page of the PDF file: Squareland

Tuesday, May 19:

Today I'll share a logic puzzle called Trading Spaces from the site theothermath.com.

Slide the yellow and green pieces along the entire straight path until the green pieces have exchanged positions with the yellow pieces. No two pieces can be on the same circle at the same time. What are the fewest moves possible?

Play the online version here.

 

Monday, May 18:

Time for another Monday photo prompt! Study the photo below and respond to as many of the questions as you can. 

This is El Capitan, one of the most famous rock climbing walls in the world,
in Yosemite National Park, CA. The mountain is about 3,600 feet high.

Source: IM Talking Math

Friday, May 15:

It's Friday! Unplug and spend some time winding down with these printable math art coloring pages. These pages are samples from the math coloring book Patterns of the Universe: A Coloring Adventure in Math and Beauty by Alex Bellos

First page of the PDF file: PatternsoftheUniverseColoringPages

Thursday, May 14:

Math educator and creator of the website Games for Young Minds, Kent Haines, recently shared a fun game that his three children invented called Mathball. To play you'll need a piece of sidewalk chalk and a ball (a kickball or basketball work well).

Below is a description of the game from Kent's most recent newsletter:

How to Play Mathball:

  • To play, you'll want to find a sidewalk, driveway, or other long flat piece of pavement. We use our front walkway. 
  • Draw a "throwing line" on the sidewalk, and then start drawing arrangements of circles extending away from the line. Fill these circles with numbers. We did a couple of 5s, followed by some 10s, 20s, 50s, and 100s.
  • Players take turns standing behind the line and throwing the ball. We have used a small kickball and a basketball, and they each work well. 
  • The goal is to bounce on as many numbers as possible. Every time you bounce on a number, you earn that many points. So you could go for 100, or you could try to bounce on seven different circles throughout the game. Depending on how you've arranged the circles and the numbers, all sorts of different strategies can emerge! 
  • We like to play three or five rounds, calculating scores after each round. My kids are getting a ton of practice with addition!

This game is intentionally open ended. You can vary the number of circles, the number within each circle, the size and distance between circles. If you are in Kindergarten, you might choose to fill your circles with 1s, 2s, 3s, 4s, and 5s. If you are in 3rd grade you might include  25s, 75s, 125s, and 175s. 4th and 5th graders may want to consider using decimals and fractions in their circles. 


After playing a few rounds, consider the following:

  • How might you alter or adapt the game?
  • How can you incorporate different operations into this game?
  • Can you think of a way for players to earn bonus points?
  • Be creative and have fun!

 

Wednesday, May 13:

The Julia Robinson Mathematics Festival Activity of the Week is called Digit Sums. "The sum of the digits of a number it called its digit sum. For example, the digit sum of 17 is 8 because 1 + 7 = 8. This puzzle involves number theory and graph theory. To play, all you have to do is figure out how the sum of the digits in each empty circle is connected."

To access the game instructions, click on the file to the right. Click again to open the full document (7 pages).

First page of the PDF file: DigitSums

Tuesday, May 12: Celebrating Women in Mathematics!

May 12 is a holiday dedicated to Celebrating Women in Mathematics. The Women's Committee of the Iranian Mathematical Society presented a proposal to recognize this day at the 2018 World Meeting for Women in Mathematics in Rio de Janeiro. The day is celebrated on May 12 in honor of Maryam Mirzakhani's birthday. To date, Maryam Mirzakhani is the only woman to be honored with the prestigious Fields Medal. 

In honor of this important day, I hope you'll enjoy the film below. Journeys of Women in Mathematics is a 20 minute film created by the IMU Committee for Women in Mathematics, featuring math leaders from around the world.

As you watch, reflect on the following:

  • Why is it critically important to encourage and support girls and women in the field of mathematics?
  • How might the stories shared in this film inspire change?
  • What questions or ideas are lingering for you after viewing this film?

Journeys of Women in Mathematics

Monday, May 11:

Time for another Monday photo prompt! Study the photo below and respond to as many of the questions as you can. 

Source: IM Talking Math

 

 

Friday, May 8:

Let's wrap up the week with a maze. Swim from start to finish past dots in this order:
red, yellow, red, yellow, red, yellow . . .

Source: JRMF

Thursday, May 7:

Have you revisited the #mathwalks project site recently? There are lots of interesting problems that have been added over the past couple of weeks. I encourage you to check them out if you are looking for a fun math challenge. Below are two recent posts that I think you'll enjoy working on. 

Wednesday, May 6:

Today's challenge is a "Who's who?" puzzle brought to you by wild.maths.org. Click the link below to view two different graph puzzles. Once you've cracked both of them, try working through the challenge problems at the end. Can you design your own friendship puzzle?

Who's Who?

 

Tuesday, May 5:

The Julia Robinson Mathematics Festival Activity of the Week is called Color Triangles. "Color triangles is an intriguing solitaire puzzle. The triangle develops according to certain rules, and you must predict the outcome. The game has ties to computer science, number theory, and combinatorics. But to play, all you have to know are the colors: red, yellow, and blue."

To access the game instructions, click on the file to the right. Click again to open the full document (5 pages). Once you read through the instructions, you can use this link to access a digital tool for this activity. 

First page of the PDF file: ColorTriangles

Monday, May 4:

Time for another Monday photo prompt! Study the photo below and respond to as many of the questions as you can. 

Source: IM Talking Math

Friday, May 1:

To end the week, I will share a triangle puzzle that is suitable for students of all ages. The puzzle challenges you to consider all of the way you can combine four right-angled isosceles triangles to form a new shape. Click the link below for more details and to access an interactive tool.

Four Triangle Puzzle

Source: NRICH Maths

 

Thursday, April 30:

My daughters and I have enjoyed playing with our SumBlox this week. We built this wall a few days ago.

  • What do you notice?
  • What do you wonder?
  • What patterns do you recognize?
  • Assuming you have unlimited blocks to represent the numbers 1-10, what are all of the possible combinations you could use to construct a tower of 20?
  • What have you been building at home lately? What are your favorite construction materials? How have you used math to help you build or play? Send me a photo of something you've built at home! I would love to feature all of the fun ways you've been playing with math at home on this page. (mdonahoe@phillipsbrooks.org)

 

 

Wednesday, April 29:

The Julia Robinson Mathematics Festival Game of the Week is called Blue Dot Solitaire. As the name implies, this is a single player activity, but feel free to work collaboratively with a family member. The game encourages you to identify and analyze patterns in order to play strategically. 

To access the game instructions, click on the file to the right. Click again to open the full document (4 pages). Once you read through the instructions, you can use this link to access virtual manipulatives for this activity. 

For additional challenge, be sure to spend some time working through the questions on the final page of the document. 

 

First page of the PDF file: BlueDotSolitaire

Tuesday, April 28:

Some of our 5th graders worked on this maze at our first PBS Julia Robinson Mathematics Festival in January.

Can you solve this challenge? Try to find a way to get from start to finish, while following these rules:

  • Right turns only (no left turns)
  • No u-turns
  • Stay off the grass

 

First page of the PDF file: CrittersFloorMaze

Monday, April 27:

Time for a new Monday photo prompt! 

After a sunny weekend, I thought I'd share a photo of solar panels. They use the sun's light or heat to create electricity. What do you notice? What do you wonder? If you are interested in learning more about solar energy, you can read more here: A Brief History of Solar Panels

Study the photo below and respond to as many of the questions as you can. 

Source: IM Talking Math

Friday, April 24:

Today's task is a game called Shut the Box, brought to you by youcubed.org. "This is a paper and pencil version of an old game. It is fun for young children and anyone can enjoy the game of chance mixed with the fun of finding a strategy. There is even more opportunity for conversation about odds and probability."

To get started, you'll need a piece of paper, a pencil, and two dice. Click the link below to learn how to play.

Shut the Box Instructions

Thursday, April 23:

Today I encourage you to play a few rounds of the game Same or Different. It's a great game to play with a sibling or family member because you can make it as simple or challenging as needed.

Consider these questions:

  • How does this game connect to mathematics? 
  • What are some attributes you compare in math?

Watch the video below to learn how to play Same or Different. Then, visit the idea gallery at mathanywhere.org and filter by Same or Different to view a variety of different images you can play with. If you're feeling creative, you can even create your own same or different pictures (click on the PDF below for a template).

First page of the PDF file: SameOrDifferent

Wednesday, April 22:

In honor of Earth Day, I will share two activities:

1) Follow a recipe and make a batch of Earth Day Cookies. Challenge: try doubling or halving the recipe!

2) Explore a collection of data sets compiled by the Exploratorium that illustrate how our planet is changing over time. 

  • What do you notice? What do you wonder?
  • How do the graphs and visual representations illustrate change?
  • What is one change you can make in your daily life that will help protect our planet?

Tuesday, April 21:

This week's game of the week from Julia Robinson Mathematics Festival is Super Tic-Tac-Toe. This game is exactly what it sounds like - it takes the simple and familiar game of Tic-Tac-Toe and introduces an added level of strategic play. I recommend using a different colored writing utensil for each player. It will help you keep track of your progress in a visual way. To access the game, click on the file to the right. Click again to open the full document (5 pages).

As you play, consider the following:

  • How does Super Tic-Tac-Toe differ from the traditional version?
  • What strategies lead to a win?
  • Is there a strategic starting point that gives you an advantage over your opponent?
  • If you could introduce one additional rule to this game, what would it be?

Enjoy!

First page of the PDF file: SuperTicTacToe

Monday, April 20:

We'll begin this week with a photo prompt. Start by studying the photo below and responding to as many of the questions as you can. Possible extension: What foods have you seen that you could ask math questions about? What are the questions and how would you go about solving them?

Source: IM Talking Math

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Friday, April 17:

Let's wrap up the week with a Fold-and-Cut challenge inspired by Games for Young Minds. This exercise will help strengthen your understanding of symmetry. To get started you'll need several sheets of paper and scissors.

Task: Can you cut the following shapes from a folded sheet of paper?

  • Rectangle

  • Square

  • Circle

  • Heart

  • Triangle

  • Star

  • Plus sign

  • The letter H

  • The letter X

  • The letter M

  • A person

Challenge: Can you take a piece of paper and fold it so that with a single, straight cut you can cut a square out from the middle of the paper? Can fold the paper in a way that would allow you to cut a star with a single cut?

Are there shapes you cannot make/cut from a folded sheet of paper?

 

Thursday, April 16:

Have you inspired your neighbors by adding a math problem to your sidewalk yet? I've added a few in front of my house this week. It has been fun to see neighbors stopping by for a #mathwalk! I'd love to see the problems you have added to your neighborhood. Email me a photo by next Monday, April 20, and I will feature your work on the Daily Math Challenge page next week  (mdonahoe@phillipsbrooks.org).

Here's a photo of the problem I added today, which seems to match the age level of the children who live on my street. 

How many solutions can you come up with for each triangle?

Wednesday, April 15:

Julia Robinson Mathematics Festival shared a new Game of the Week! This is two player game that can be enjoyed by students of all ages. Click on the file to the right. Click again to open the full document (3 pages).

 

As you play, consider the following:

  • What strategies lead to a win?
  • Do your strategies change if you alter the number of dots at the start of a new game?
  • Do you play with more of an offensive or defensive mindset?
First page of the PDF file: GameoftheWeek_9Dots

Tuesday, April 14:

Today I will introduce a photo prompt, which will become a recurring exercise on the Daily Math Challenge page. The task is brought to you by Illustrative Mathematics, a problem based math curriculum that is strongly aligned with Bridges in Mathematics. Moving forward, I plan to share a photo prompt with you about once a week. Start by jotting down what you notice and wonder about the photo, then respond to the prompt for your grade level (and beyond if you'd like more of a challenge).

This is 1 pea pod split open:

Source: IM Talking Math

 

Monday, April 13:

I hope you all enjoyed a relaxing spring break! Are you ready to dig into a good math puzzle? Today's task is inspired by a project called #mathwalks that emerged in the early weeks of Shelter in Place. Math educator, Traci Jackson, has been putting math on her sidewalk and sharing it with anyone who is up for the challenge. 

Below are two sidewalk challenges from the #mathwalks project. Try them out, and then spread the joy by creating your own problem to share on your sidewalk!

Spring Break Math Enrichment

There has never been a more important time for data literacy. Before the school closure began, I was looking forward to teaching a spring enrichment class on data visualization. I've repurposed some of the materials to share with you as a spring break challenge that combines art, personal reflection, and data. The tasks are all inspired by a year-long data drawing project called Dear Data. The project was the brainchild of Giorgia Lupi and Stefanie Posavec, two award winning information designers who lived on different continents (one in New York and one in London). Each week they would select a specific theme, and then collect, organize, classify, and represent their personal data in visually interesting ways. The artists drew their data on one side of a postcard and a detailed legend on the other side before exchanging them by snail mail.

I love this project because the elements of self-reflection encompass all of our core values at PBS: Community, Courage, Kindness, and Love of Learning. Here are a few examples of postcards from the Dear Data Project to get your creative juices flowing:

Day 1:

You'll want to start by organizing your materials. It will be helpful to have the following items on hand:

  • Paper - you can use your math journal or any blank paper you have at your house
  • Writing utensils - Any combination of colored pencils, markers, pens, crayons, or highlighters will work


Task: Experiment with different methods and techniques to determine the best tools for each of the simple drawings. Click on the document to the right to access the assignment page. Click again to view as a printable PDF.

First page of the PDF file: SpringBreak-Day1

Day 2:

Today you'll explore drawing as a form of measurement and you'll collect soundscape data. You will need paper, a pencil, and a clock or a timer for this activity. Click on the document to the right to access the assignment pages. Click again to view as a printable PDF.

Task 1: Drawing Shapes

Task 2: Recording Soundscapes

First page of the PDF file: SpringBreak-Day2

Day 3:

Today you'll practice following a set of rules while analyzing personal data. You will need to have writing and coloring materials handy. Click on the document to the right to access the assignment pages. Click again to view as a printable PDF.

Task: Representing your family

Task: Following drawing rules

First page of the PDF file: SpringBreak-Day3

Day 4:

Today you'll demonstrate your love of learning by creating a data visual about your book collection at home. What do your books reveal about you?

Task: 

  1. Start by taking an inventory of your bookshelves (you can choose to include physical, digital, and audio if you'd like). Jot notes if it's helpful.
  2. Think about how you will classify your books. Below are a few suggested guidelines if you're feeling stuck. Feel free to come up with your own!
  • Choose shape to represent the books (perhaps a rectangle?)
  • Use color to represent the book's genre
  • Use height or shape to indicate whether the book is physical or digital
  • Shade in the books you've read cover to cover, outline the books you haven't finished
  • Add small details in pen to add extra information (someone has read it to you, you've read it more than once, you dislike it, it's a library book)

3. Create a postcard that illustrates your data. Don't forget to include a legend! Perhaps you'll want to mail the postcard to someone special when you're done?

Below are the postcards Georgia and Stefanie's created to represent their book collections. Feel free to use them as inspiration!

Postcard Photo Source: http://www.dear-data.com/by-week#/week-46-a-week-of-books/
Inspiration for this enrichment project: http://www.dear-data.com/theproject and Observe, Collect, Draw! A Visual Journal by Giorgia Lupi and Stefanie Posavec

 

 

Thursday, April 2:

Exciting news for math game enthusiasts! Our friends at Julia Robinson Math Festival announce that they will be publishing a game of the week. This week's game is accessible to mathematicians of all ages. Click on the image to the right for details. Click once to access, then click again to open the full document (5 pages total). Play a few times and consider the following questions:

  • What happens when you change the number of dots in the triangle?
  • Does it matter who goes first?
  • What strategies do you notice?

 

First page of the PDF file: Criss-Cross

Wednesday, April 1:

While I love a good April Fools Day joke, I promise there are no pranks involved in today's math challenge! 

Each letter in the puzzle below maps to one and only number (0-9). There are no leading zeros. There are multiple solutions. How many can you find?

     A  P  R  I   L
+   F  O  O  L  S 
     P  R  A  N  K

Puzzle source: Manan Shah

 

Tuesday, March 31:

There are tons of fun ways to improve our mental math skills. Today I will share a few web based games that provide a great workout for your brain. 

Kindergarten: Math Limbo

  • This game is a great way for young students to practice simple addition and to think flexibly about number combinations. It also exposes students to multiple visual representations of numerical values (numerals, ten frames, fingers).
  • Click "learn" for a brief explanation

 

1st Grade and Up: Kakooma

  • Click "practice" to select operation, puzzle size, and level of difficulty
  • When you click "start game" it will briefly walk you through the instructions
  • Addition puzzles will be most accessible to 1st and 2nd graders, 3rd-5th graders should select multiplication

 

3rd Grade and Up: Mathjong

  • Based on the ancient Chinese tile game, Mahjong, this game allows you to exercise mental math in a fun an strategic game. There are multiple levels of difficulty, and various game formats to choose from. 
  • There are detailed instructions at the bottom of the page (you need to scroll to see them). Don't be intimidated by the instructions - the game is pretty simple once you get the hang of it.

 

Monday, March 30:

Let's kick off the week with a geometry puzzle! I came across this puzzle on the website theothermath.com. Instructions are listed on the printable PDF document. You can also check out the video below for a brief tutorial on how to get started. 

First page of the PDF file: JonsPuzzle_1

Friday, March 27:

Today's challenge is a series of puzzles designed to develop algebraic reasoning. I love that they are accessible to students of all ages and allow children to solve in many ways depending on their age and stage.

The puzzles come from bovinemath.com, which was designed by high school math educator, Pete Harrison. To access the puzzles, click on the document and then click again to open the PDF in a separate window. Each file contains multiple puzzle pages.

First page of the PDF file: BovineMathSumPuzzles
First page of the PDF file: BovineMathDifferencePuzzles

Thursday, March 26:

Today I will share one of my favorite mathematical meditations: The New York Times Tiles Puzzle. I find it very relaxing to work on these puzzles. I hope it brings you a sense of calm as well! The puzzles are visually interesting and they change often. There is no subscription necessary, although you will only have access to two puzzles per day without a subscription. Click on the "Rules" link to learn more about how to play.

https://www.nytimes.com/puzzles/tiles

 

Wednesday, March 25:

Today's challenge is a paper and pencil strategy game game. The game commonly gets played at Julia Robinson Math Festivals. It's appropriate for all ages, so it makes a great game for siblings to play together. Click here to access the instructions and game sheets.

Play a few rounds and consider the following:

  • What strategies can you find to increase your likelihood of winning? 
  • Is there a more advantageous starting position?
  • Do you consider your approach offensive or defensive?
  • Where is the math in this game?

 

Tuesday, March 24:

Today I'll share a game that children of any age can play. It's inspired by the book How Many: A Counting Book by Christopher Danielson, which happens to be one of my favorite math picture books of all time. Earlier this winter, our ELC students created their own version, which includes images from the ELC classrooms and outdoor spaces. We'll use their version for today's activity.


How to play:

  • Select an image from the How Many? book:  ELCHowManyBook.pdf
  • Examine the photograph and determine a numerical value that fits with the image. Tell your partner the number you are thinking of.
  • Your partner's job is to guess which objects you quantified and how.
  • Feel free to add any rules you'd like to keep track of the score. Perhaps you assign points based on the number of guesses before guessing correctly?


Let's practice! (Look at the image of colored pencils to the right) 

  • My number is 27. Can you guess how I got 27?
  • What if my number is 3?
  • How about if my number is 6? Are there multiple correct answers?

Tip: Now that you know how to play, you can play using any picture book, photo, jigsaw puzzle, cereal box, etc. 

Photo credit: Kyela (Preschool)

Monday, March 23:

Dice games are a great way to improve fluency. They are also convenient to play at home because they require very few materials. Check out the games below from Math4Love. 

Kindergarten: Number Races.

1st Grade: Fill the Stairs

2nd Grade: Save Twenty

3rd Grade: Blockout

4th Grade: Blockout (Damult Dice Variation), or just Damult Dice

5th Grade and up: Damult Dice Division Allplay; Horseshoes

 

Friday, March 20:

Today's challenge is brought to you by Annie Perkins, a teacher and mathematical artist from Minnesota. She has been posting a daily #mathartchallenge on Twitter and Instagram this week.

Here is a prompt that can be completed by artists of any age:
Draw a single loopy line that crosses itself as many times as your want, but don't pick up your pencil. Make sure your line meets back at its start. Then, color alternating sections with two different colors making sure that no adjacent regions are the same color.

Try a few! Can you do it? You should be able to. Is there a mathematical reason?

Thursday, March 19:

Try one of the paper folding challenges below. I've included three levels of difficulty to match your level of origami expertise: Tulip (beginner), Frog (intermediate), Dragon (advanced). You will need a perfectly square piece of paper for each of these projects. Some of the instructions contain more than one page. Click on the icon below, then click again to open the instructions in a separate window.

First page of the PDF file: OrigamiChallenges-1
First page of the PDF file: OrigamiChallenges-2
First page of the PDF file: OrigamiChallenges-3

Wednesday, March 18:

The challenge today is to work on SolveMe Puzzles, which appeal to mathematicians of all ages. They start out easy and increase in difficulty. The mobile puzzles build computational skills through logical reasoning and algebraic thinking. You might even enjoy building mobile puzzles of your own.

SolveMe Mobiles: Explore, Deduce, Create

The puzzles are somewhat intuitive. If you need help getting started, follow the steps below:

  • Click on PLAY
  • Select any puzzle
  • Click on the questions mark (?) icon on the bottom left of your screen

Tuesday, March 17:

Below are a series of paper and pencil games recommended by Dan Finkel at Math4Love (one of my favorite math sites). Don't be afraid to play a game for younger students with older children - they are all great opportunities for sibling math play if you have more than one child at home.

Kindergarten & Up:
Dots and Boxes
Don't Make a Triangle
Guess My Number

2nd Grade & Up
Pico Fermi Bagels
Territory 
Hex

3rd Grade & Up
Multiplication Tic-Tac-Toe
Angels & Demons

Monday, March 16:

Did you know Saturday was pi day (3.14)? While pi is typically a middle school concept, there are plenty of fun ways to explore and learn about pi as elementary students! Check out the links below to learn more. 

What is pi? What is pi day?
https://www.exploratorium.edu/pi

Exploring pi (K-2):
https://layers-of-learning.com/pi-day/

Exploring pi (3-5):
https://www.exploratorium.edu/snacks/pi-toss
https://www.exploratorium.edu/snacks/cutting-pi