Oh What Fun...Math Games!

With winter break approaching, I cannot help but reflect on the, "How do I keep my students engaged?" question that would run through my mind the first couple of years when I was teaching my own class.  I wanted to make the time the last day before break meaningful (and also ensure my classroom did not turn into a madhouse).  I came to realize over time that the days before winter break, spring break, and summer break were the perfect times for focused, yet fun, math games.  As Mark Chubb so eloquently lays out in this blog post, the purposeful use of math games can be a great way for students to practice computational skills, increase conceptual understanding, and build fluency in an enjoyable way.

Teachers can also support families by passing along any math-related games they have played in class.  While there are many math-related games families can enjoy together, I have compiled a list below of some of my favorite math-related games as a starting point which can be used both in the classroom and at home.  Zeno Math also has a great list of games for early math learning, and check out Kent Haine's website Games for Young Minds with tons of math-related games (he even has a newsletter you can sign up for which delivers a new math game idea to your inbox each week).

Paper/Pencil Games

Four Strikes and You're Out - This Marilyn Burns game is a mathematical twist on hangman and can easily be adapted to use lesser or greater values.  One person generates an addition/subtraction/multiplication/division equation and writes out blanks for each of the digits. For example, __ __ + __ __ = __ __.  The other players get to guess digits, one at a time, and similar to hangman the blanks are filled in if the digit is a part of the equation.  As the name of the game implies, the other players must use their understanding of computation and place value to strategically avoid getting four strikes.

The Product Game - This game from NCTM is a combination of tic-tac-toe and multiplication.  Players take turns selecting a factor from the digits 1 - 9, and then players color in the corresponding product for those factors on the game board.  The player to get four products colored in a row/column/diagonally first is the winner.  It can be played with paper and pencil by printing out this game sheet.

Strike It Out - This game from Nrich, a University of Cambridge resource, requires players to use their understanding of addition and subtraction to strategically stop their opponent from being able to take a turn.  The first player selects two numbers to cross out and then circles the sum or difference of those two numbers.  The next player must use the number just circled as a part of the next addition or subtraction problem and select one additional number to cross off before circling the sum or difference of these new numbers.  Gameplay continues until one player stops the other from making a move.

Dice Games

Sum Dice - One of the most straightforward dice games, this is accessible to our early math learners who know how to add numbers through 12 and understand the concept of even and odd numbers.  Two dice are rolled. If the sum is even player 1 gets the point, and if the sum is odd, player 2 gets the point.  To adapt this game and increase the difficulty, roll more than two dice or use dice with 10, 12, or 20 sides.  You can also find the difference or product instead (though this would change the name of the game...).  Take it to the next level after gameplay by figuring out if Sum Dice is a fair game (see Kent Haine's post about this here).

Race to 100 - This is a game that can be adapted depending on math readiness.  Players roll two dice and then find the sum/difference/product/quotient of the two numbers rolled.  The game piece is moved along the game board based on the answer to the rolled dice, and the first person to reach exactly 100 is the winner.

How Close to 100? - I love this YouCubed game because it couples computational fluency with conceptual understanding.  Players roll two dice and shade in the corresponding array on the grid (i.e. a 6 and 4 are rolled, so a 6 by 4 rectangle is shaded in).  The player also writes down the corresponding multiplication equation (6x4=24).  Gameplay alternates between players, and the goal is to fill up as much of the grid as possible.  The game ends when both players have rolled the dice and cannot fit any more arrays onto their grid.  This can easily be adapted to use larger grids or dice with 10, 12, or 20 sides to increase the complexity.

Farkle - Roll six 6-sided dice, and use the scoring guide to determine how many points each player gets during each turn.  The winner is the person who reaches 10,000 points first.  The game can also be purchased here.

Card Games

War - This can be adapted for many different levels of math readiness.  The typical War card game is perfect for younger learners who are comparing numbers, and the numeric cards even have the pictures that allow students to use 1-1 correspondence to count.  As students grow older, this can become Addition/Subtraction/Multiplication War where each player lays down two cards, and the person with the greatest sum/difference/product of the cards gets to keep both pairs.  This can be played by assigning additional numeric values to face cards (Jack=11, Queen=12, King=13, Ace=1), or the face cards can be removed.  When students are ready to work with integers, Integer War can be played with red cards representing negative numbers and black cards representing positive numbers.

5x5 - This game shared by Sara Van Der Werf requires multiple players (ideally 4 or more).  Each player has a 5x5 grid, which can easily be made by drawing it on a sheet of paper.  One person draws cards from a deck (face cards removed), and the players have to put the number drawn in one of the spaces on the grid (no erasing to move numbers around or "saving" numbers to place later).  After the 25 numbers have been drawn, each player calculates his/her score by adding any adjacent numbers that are the same in each row and column (i.e. if a 10 and a 10 are next to each other in the same row, the score for that row is 10+10=20).  The total score is calculated from adding all the sums from each row and column, and the highest score wins.

Krypto - This game from the National Council of Teachers of Mathematics can be played online or by dealing out five normal playing cards.  Players must use all 5 numbers and any combination of addition/subtraction/multiplication/division to reach the target number as the final answer.

Other Math-Related Games

24 - Use each of the four numbers show on the card once with any operations to come to an answer of 24.  This classic math game can also be played online at 4nums.com.

Battleship -Battleship is a great introduction to the coordinate plane.  By understanding how to name a location based on its horizontal and vertical coordinates, students will be ready to transfer this to the x, y coordinate plane.  For students in grades 5+, you can try playing Coordinate Graphing Battleship from MIT by printing out this template.

Mancala - This is a game of counting and strategy.  A game of counting strategy, the goal is to capture more stones than your opponent into your mancala (area of your game board).  This game also has a fascinating history if you care to read about it!

Quirkle - This game can be enjoyed by young and old math learners!  Players build lines by matching either color or shape and score points based on these matches.

Shut the Box - Players roll two dice and put down the tiles that have the same value as the sum.  For example, if a 5 and a 3 are rolled, the player can put down the 8 or the 5 and 3 or the 6 and 2 or the 7 and 1.  This is a great game for practicing addition coupled with strategy.  This game can also be played using dice and this paper game board.

Sumoku - This is a crossword-style game with numbers where players use repeated addition or multiples to determine the tiles laid down and then the corresponding score. 

Yahtzee - This classic game has players striving to get the most points possible by rolling five dice each turn.  Points are scored for rolling a straight, full house, and three/four/five of a kind.  Probability and addition are ripe opportunities for math conversations with this game.  (As long as you know how to score, you can also play Yahtzee without the formal game set as long as you have five dice.)

Scorekeeping

Any time there is any game that involves keeping score, a young mathematician in the group should serve as scorekeeper.  At the most basic level, tally marks can be used to keep score for some games, and addition/subtraction of increasingly complex numbers will be relevant for other games.  Scorekeeping is a great way to build fluency, and it can also be a valuable opportunity to talk about computational strategies.  For example, if I am playing a game with a child, and a player has 18 points with 8 more to be added, I would ask the child how she would find the score.  After the child shares her strategy (like using knowledge of doubles like 8 + 8 to do 18 + 8), I could share that I have another strategy (like adding 10 and then taking away 2).

What are some of your favorite math-related gams?  Please comment below so we can add to our list!

Helping Your Child Understand Our World Through Math

One of the questions classroom teachers and I are asked on a regular basis by parents is, "How can I support my child's math learning at home?"  It is so wonderful when parents want to support their child's growth and understanding of how mathematics is relevant outside of school!  Plus, there is a significant body of research that shows how beneficial it is when parents support the learning efforts started at school.

While some people may think of activities like practicing math facts with flashcards or purchasing math workbooks, I would like to offer some alternatives that are arguably more meaningful since these ideas allow students to make sense of our world through the lens of math.  Through counting, comparing, and composing or decomposing numbers and/or shapes, children learn how to understand mathematical relationships in authentic contexts.  Here are some of the ideas I recently provided for parents of kindergarteners, though these ideas can certainly be adapted for a variety of age levels to include more complex math concepts like fractions, decimals, percentages, ratios, multiplication, and division.  

• Have your child make math stories from book illustrations when reading together by counting, comparing, or adding/subtracting.  

• Ask your child to count the number of coins or dollar bills in your wallet.  See if your child can skip count by 5s, 10s, or 20s if you have multiple of the same bills!

• Involve your child in cooking.  Measuring the number of Tbs, tsp, cups, etc. provides both measurement and counting practice.

• Ask your child questions related to comparisons of number and size using words like most, least, bigger, smaller, more, fewer.  For example, “Who has more broccoli on their dinner plate, you or your brother?”  Then see if your child can tell you how many more/less pieces each person has when compared to the other or how many pieces will be left if your child eats a certain number.

• Count the number of pages you read after you finish a book.  To take this to the next level, see if your child can find the total number of pages read if you read multiple books.

• When checking out at a store, ask your child to tell you how many people are in each line, and then determine the best line to stand in (and remember, it may not always be the line with the fewest people based on how many items each person purchases).

• When you are out shopping, use whole number costs to have your child tell you which item is the better deal/costs less.

• Build something together!  Using blocks or Legos are great opportunities for counting, measurement, and conversations about shapes and spatial awareness.

• If you are taking a family trip, use a map to show your child where you are going compared to where you live.  Compare the distances to other locations you have visited.  For example, “We live in Chicago, and here is New York City where we will go next week.  We visited your grandmother in Indianapolis last month, which is here.  Which city is farther away?”

• Try exercising together at home!  Have your child count the number of jumping jacks/sit-ups/squats, and you can make it more competitive by comparing the number each of you can do.

• Ask your child to help you put items into equal group items.  For example, if you are plating dinner, ask your child to put an equal number of carrot sticks on each plate.  Then have your child tell you how many total carrot sticks were used.

• Look for opportunities when you can ask your child how many are missing.  For example, how many eggs are missing from the carton or how many ice cubes have been taken from the tray.

• Patterns can be found in so many places, from clothing and jewelry to floor tiles and artwork.  Ask your child to look for patterns wherever you are, and then have your child explain why it is an example of a pattern and what the sequence of the pattern is.

• Do number or shape scavenger hunts around the house or out and about, and then use the opportunities to make mathematical comparisons between numbers or shapes.
• Whenever you play a game with moving a piece on a game board, have your child count the number of spaces to be moved for each player.  If scoring is involved, ask your child to use tally marks or addition/subtraction to be the game's official scorekeeper.

The websites Math Before Bed and Bedtime Math also provide prompts for families to use to facilitate math conversations at home, and Bedtime Math has developed two free apps as well, MiniMath (ages 3 - 5) and Bedtime Math (ages 3 - 9).  Games are another great way to engage the whole family in math-related activities and conversation, so stay tuned for a future blog post on that!  What are additional ideas you give to parents to help support their child's math development at home?

Creating a Community of Mathematicians through Number Talks

One of the primary goals of a math educator is to support the growth of mathematicians who are strong thinkers and problem solvers.  In order to do this, the math classroom needs to become a community of thinkers, where students feel safe and welcome sharing their ideas and different methods of problem-solving and where students regularly learn from each other.  A great way to build a culture of problem-solving in a classroom is through Number Talks (also called Math Talks).  I have been inspired by so many wonderful math talk scenarios that I have seen in the first few weeks at of school at GEMS World Academy Chicago, so I want to take some time to share some resources and best practices for number talks in the classroom.

What is a Number Talk?
A Number Talk is a brief (5-15 minute) discussions about a single, strategically chosen mental math problem or situation.

• Students are presented with the mental math problem and are provided adequate wait time to think to themselves about the math problem.  Giving a silent thumbs-up hand signal on their chests notifies the teacher when they are ready to share.  Placing the thumbs-up on the chest is more discrete rather than raising a hand so others are not made to feel self-conscious if they are taking longer to think.
• In a non-judgemental way, the teacher allows all willing members of the class to share their answers only. 
• The teacher then follows up by asking students to share their problem-solving strategies orally, which the teacher charts on the board to compile a visual representation of the various strategies the students share.  
• The teacher invites students to ask questions of each other and make connections between the various strategies.  The teacher may also ask strategic questions to prompt thinking and help students compare/contrast strategies.

Why use Number Talks?
Through independent thinking and then communicating and comparing/contrasting various strategies, Number Talks are one way teachers can engage students in the Five Strands of Mathematical Proficiency as explained in the National Research Council's book Adding It Up: Helping Children Learn Mathematics.

Image from Adding It Up: Helping Children Learn Mathematics

Jo Boaler, Standford Professor of Mathematics Education and faculty director of YouCubed, also argues that Number Talks are one of the best ways to build number sense.  The focus of a Number Talk is not necessarily on the answer, but on how you arrived at the answer since problems can be seen in many different ways.  When students verbally share their thinking, the role of the teacher is to visually model/record the multiple strategies with the purpose of making connections among the students' many different methods for thinking mathematically.  (You can hear from Boaler herself about how routines are established and what these number talks look and sound like in this 15-minute video, which is an excerpt from her Stanford online course.)

Where can I find ideas for Number Talk prompts?

• The book Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom by Marian Small provides ideas for open questions that are accessible to a variety of learners and allow for mathematical debate and conversation.
• Fractiontalks.com provide images that can be great prompts for fraction-related number talks.
• VisualPatterns.org provides images that can be used as prompts for number talks.
• MathTalks.net provides math talk prompts used with 6-8th grade students.
• Which One Doesn't Belong? is a "website dedicated to providing thought-provoking puzzles" which allow for rich mathematical conversation. You can also follow the #WoDB hashtag on Twitter for more ideas.
• Use any mathematical problem that allows for multiple ways of thinking!  This graphic organizer from SFUSD may be helpful to use as you start to plan your own.

What if I want to read more about Number Talks?
Check out the following resources for more information about how to implement number talks in your classroom with students!

• The article Number Talks: Building Numerical Reasoning from NCTM's Teaching Children Mathematic's provides a wonderfully detailed overview of a Number Talk's key components. "The heart of number talks is classroom conversations focused on making sense of mathematics."
• Inside Mathematics, an education non-profit focused on supporting high-quality math education, has a series of number talk video clips which allow you to see number talks in action in a variety of classrooms with a debrief afterward.
• Number Talks: Whole Number Computation Grades K - 5 is a fabulous (but pricey) resource that details how to start doing number talks, ask strategic questions to follow and prompt students' thinking, and advice for developing grade-specific number talk prompts.
• The Teaching Channel (Tch) also has created a page called "Dig Into Math Talks" with links to many additional resources.

Spread the Number Talk Love!
What are some of your favorite resources for number talks?  What have been some of your most successful number talk prompts?  Do you have any advice for someone new to doing number talks?

Thank you for growing our community of learners by sharing in the comments section!