How Do Your Students Use REAL Data?

How do your students use data in real and meaningful ways? 

Before you can answer that question, you may need to back up to consider how YOU use data in real and meaningful ways. If you reflect on a typical day, I imagine you may be analyzing and interpreting data more often than you consciously realize. You may notice trends in your spending when you check your bank account online, or you may be interpreting graphs as you read your daily news updates. So then what do you do after you read something that contains data? More than likely, you take a moment to reflect on the patterns you are noticing (or a lack thereof) and consider if you need to take action of some sort. Do I like what I am seeing? Or is there something I can do differently to try to make a change to what the data will show in the future?

Data literacy is becoming an increasingly popular conversation in the world of math education, and for good reason! Jo Boaler and her YouCubed staff have started a data literacy movement, and they are even writing a course for California high schoolers take because they believe it is so critical.  

Being data literate is truly an equity issue. If a person does not have a solid understanding of numbers or does not understand how to interpret and analyze data, they can be taken advantage of in life. 

More importantly, a solid understanding of data allows people to notice patterns and relationships that cause concern so they can take action and change behaviors to improve future outcomes.

So what does this mean for educators, particularly of educators of young children who typically do not have many learning standards devoted to collecting, representing, interpreting, and analyzing data? It means you integrate it into regular class conversations anyway because this is critical to being a savvy citizen and a change agent.

In Early Childhood Education, we begin to formalize mathematical thinking with the idea of grouping and sorting. We can help children start to form ideas related to making data visible if we help them group and sort in more organized ways. Our preschoolers at GEMS World Academy Chicago have begun collecting their own data as they go on community walks to observe the animals they see as a part of their inquiry into how animals, including humans, depend and rely on each other. Notice how they drew the lines themselves to separate their paper into three categories, one for each animal they are looking for, and how they are drawing dots/circles in a category each time they see an animal. While they are not formally creating a bar graph or pictograph, they are developing an understanding of how they can visually keep track of and categorize their observations to help them reflect on what they saw. While some students at this age can quantify, this type of visual representation makes it easy for any child to see when they saw none in a category versus when they saw many in a category. 

Our goal is to continue to build on this momentum started from a very young age to support students in developing their desire to visualize data they collect, and we begin to support them in using the data to analyze the data and then interpret these conclusions. While students still may not be able to create graphs independently, our Kindergarten classes harness the power of creating class graphs to draw conclusions based on the visual of their data so they are learning to read and interpret graphs before they are able to independently make graphs. 

As a part of their inquiry into how humans produce and dispose of waste, our Kindergarten classes decided to collect data on the amount of food waste generated each day from their lunches at school. Using a scale and support from the teachers, a class graph was added to over time, noticing each day how much waste was generated and if it was more or less waste than the day prior. Students began to notice on days when there was more food waste, it was tied to the types of foods they had for lunch! In an effort to take action and combat this problem, our Kindergarten classes drew pictures and wrote letters to the lunch supplier to suggest changes to the menu that they think will result in less food waste. 

In third grade, the students are able to graph data independently and can really take the interpretation step further to focus on creating more detailed action plans. This year, our third graders collected and graphed data related to plastic waste their class generated each day over the course of a week as a part of their inquiry into how humans impact the environment in different ways over time. After creating their bar graphs either by hand or using Apple's Keynote, students noticed there were clearly areas where our school could make improvements. They then created a proposal which they presented to our school leadership team. Using a variety of calculations, they were able to articulate clearly why the ideas were proposing would not only save the school money but also result in less single use plastic trash. They were able to take action in their homes as well, bringing home some of these same ideas so they could produce less single use plastic waste at home. 

Understanding how to interpret data is powerful, but that is only a start. If our students start collecting, visualizing, interpreting, and analyzing data from a very early age, just think of what they will be able to do when they encounter data in various forms as they grown older. They will be the change agents we need to make our world a better place!

What Does Supporting Teachers Look Like?

As of writing this post, it has been 328 days since COVID began to transform the way schools function. For those of us in leadership roles, a critical question this time has been what does it look like to support teachers? 

First and foremost, the mental health and wellbeing of our teachers must be prioritized. Organizations like The Greater Good Science Center out of University of California Berkeley and ASCD have sent out resources with articles to address this. We know that while remaining physically distant for safety purposes is necessary, we must prioritize connectedness through community. Providing moments of joy in Zoom meetings for sharing endearing moments with students and for sharing personal celebrations is a sacred ritual that must be maintained since many of these conversations used to happen in the staff lounge or during hallway conversations. Successful learning moments in the classroom (whether in person or remotely) must continue to be shared to bolster pride in our commitment to our community of learners. Similarly, instructional leaders must continue to provide support related to teaching and learning but must also acknowledge that professional learning, while still important, may not feel like the top priority to those who feel they are in a survival mode. 

As the Math Coordinator and Specialist for my school, I created a weekly PDF which I sent out to staff each Friday morning for perusal at the teacher's convenience over the weekend. Through the Weekly Math Update, I have offered a consistent place for weekly professional development that can be used as a "take some" or "take all" model based on the needs of the teacher. This weekly PDF contains a "Best Practices" quote for a bite-sized reminder of what we value as good teaching. The "Article of the Week" allows for a more in-depth look into an area of instructional practice through a hyperlinked podcast, blog post, video clip, or article. In the "Check This Out" section, there is a math-related resource with specific images, tools, and/or tasks for use with students, while the "Integrate Tech" section provides a suggestion for leveraging the capabilities of our students' 1:1 iPads as a way to make student thinking visible, to allow for increased mathematical discourse, and to amplify student voices in and outside of the classroom context.  Finally, the "Tweet of the Week" section is an opportunity to highlight some of the exciting math moments that have happened recently in our school. 

The goal is for the common theme of the Weekly Math Update to reflect a recent conversation had with a teacher(s) that may be worth sharing more broadly or to reflect a need in the school community as it relates to teaching and learning math. There is always a link included to the "archives" of past weeks resources as well so teachers can go back at their leisure to dig in more deeply, particularly if there were times when other areas of life took precedence over looking at the math PD resources that were emailed that week.  In reality, I know every teacher does not open this email every week. But it is my hope that those who do get varying levels of professional growth, affirmation, and encouragement from the resources therein. 

So as I say in the Weekly Math Update, "take a moment, and take a look" at some of the Weekly Math Update slides. If you have feedback on how to make this more useful to teachers, I would love to hear it! If you are an instructional leader, how have you adapted to support your staff with professional development and instructional resources during this time? Let's broaden our community of learners to support each other as we continue to navigate this transformational time in education.

Dear Parents, From Your Child's Teacher

Dear Parents,

Well, we are five weeks into remote learning. Those of us in Illinois recently got official word from the governor that we will not be returning to school this spring, which is the reality for so many states. Although we knew it was a possibility, the finality of this decision has been heartbreaking to hear. Our glimmer of hope has been extinguished, and now we know remote learning, which we all hoped would be temporary for a few weeks, is more permanent.

So has it become easier? Has remote teaching become easier for us educators? Has remote learning become easier for our students, your children? Has this arrangement become easier for you, as parents? Well...perhaps in some regards, but overall, no. This is still really, really hard.

As educators, many of us are working from home while also parenting our children, and the balancing act (or lack of balancing) is becoming exhausting. I know you feel us since many of you are working parents, too. While the immediate shock to our systems may have passed, we are now in the phase where we must come to terms with the fact that we are in this for the long haul, "a marathon and not a sprint" as some people say.

You, as parents, always want what is best for your children, and we, as educators, desperately want to provide what is best for our students. But how can we do that when we know what is best is face-to-face interaction, conversation, collaboration, and care? How can we do what is best when we cannot be with our students to respond to their individual needs in the moment, in person?

We want to make everyone happy. But the reality is each family has its own story of what is happening in their homes, and so everyone's vision of what they hope remote learning will look like is different. Some parents want more academic work; some parents want less. Some parents want more screen time on Zoom; some parents want less. We want you to be happy with how we are handling remote learning, parents, but do you know what we want even more? We want our students to be happy.

Like you, we are doing the best we can each day to adapt to our current reality. Of course we are providing some academic content since there is concern about the lost instructional time, but we are seeing with every passing day just how much the social-emotional well-being of our students matters. Yes, we always prioritize building relationships with our students, but never have these relationships with our students been more critical. To be honest, the vast majority of teachers do not care about the academics if we know our students are struggling with being happy, struggling with feeling safe, and struggling with life overall right now. This is an anxiety-inducing time for everyone, children included, and we cannot ignore that. It is because we want what is best for our students that we cannot ignore that. As a result, we may ease back on some of the academic rigor, or we may reassure you that some of the activities we share are optional. This is not because we do not care about educating your children; rather it is because we care so deeply about educating your children that we know their social-emotional health and wellbeing must come first.

If you are a parent who wants more learning activities, we cannot emphasize enough that play is learning. The International Baccalaureate's Inquiry Through Play provides valuable research and insights as to why and how play is essential for learning with concrete ideas for how parents can support children in their play. For parents with more independent children, this is also the perfect time for your child to dive into a passion project.

If you are a parent who is feeling their child is overwhelmed, and heck, perhaps you are overwhelmed yourself, just take a step back. The most important thing is to first make sure your child is feeling your love during this time of uncertainty. Denaye Barahona, who is a clinical social worker and has a PhD in Child Development, hosts the Simple Families podcast. The podcast episodes provide helpful parenting advice which are now catered to our current reality with COVID-19. She reaffirms that the most critical thing right now is for parents to be present for their children; you are enough.

So dear parents, we know this is hard. We wish just as much as you do that we could be learning in person with your child at school. But since we cannot be, please know that we are all doing the best we can remotely. Take comfort in knowing that we are people who care deeply about your child, just like you, and we are constantly striving to do what is best for your child, just like you. Be kind to yourselves, and be kind to us. Share your respectful feedback—we do want to hear it—and always remember that we are on the same team supporting your child.

In the meantime, please give your child a big hug. You are your child's first and greatest teacher, and this is a unique moment in time when you get to embrace this amidst the chaos of our current reality.

Stay safe, and be well.

Sincerely,
Your Child's Teacher

Reflection: A Powerful Tool in a Math Classroom

"Self-reflection is one of the most underused yet powerful tools for success."
—Richard Carlson

One of the most influential lessons I have learned throughout the course of my career as an educator is how critical self-reflection is to growth.  In reflecting on classroom lessons, we deepen our understanding of students' needs and how we can better support them in their learning journey.  As leaders, we reflect on interactions with colleagues to consider how we can better support others in their growth as they strive to reach their own goals.  We reflect on how we can communicate more clearly, how we can utilize and share resources more effectively, and how we can better manage our time.  But how often do we intentionally provide similar opportunities for reflection for our students related to their math learning?  How do we empower our students to pause, self-assess, and think about how they will propel their own growth?

A student reflects in her
journal about her math thinking.

Reflection in a math classroom is a powerful tool for deepening student understanding, developing flexible thinking, and coming to realize the interconnectedness that embodies the world of mathematics.  Often times, writing in a mathematics classroom is a foreign concept, but it shouldn't be.  Written reflection is one of the most critical ways we can empower our students to take ownership of their learning. 

At a professional development event I attended this past fall, Dr. Yeap Ban Har also emphasized the importance of writing as a critical routine in math classes.  He shared that there are four types of math journaling: 

• Descriptive: "Show and tell me the best method, in your opinion."  This is open-ended, and students have the opportunity to describe any method they think will allow them to solve the problem.  How are students using academic vocabulary?  Is their method viable?  Is it efficient?  Does it build on relevant prior knowledge?
• Evaluative: "Out of these two methods, tell me which is better and why."  This is more structured, and the teacher provides two targeted problem-solving methods to compare.  Do students understand the similarities and differences between the methods?  Can they articulate why one method may be more efficient or precise than another given the problem-solving situation?
• Creative: "What is a story to go with 300 - 125?"  This type of journaling allows our students to put context with computation.  Do students understand a scenario in which the given computation is useful?  If given a similar computation on another occasion, do they understand multiple contexts, or do they continue to go back to the same context for a given type of computation?
• Investigative: "Which method works because the value in the problem is 125?  Which method will work for any value?"  Do students understand the nuances of the different strategies compared in class?  Will they be able to select a viable strategy in a variety of situations?

In addition to the types of journaling above, I also think it is critical to add self-reflection to the list.

• Self-Reflection: "What did you try already?  Was it successful?  Why or why not?  What will you do differently next time?"  Are students able to perceive the most successful aspects of their problem-solving attempt?  More importantly, are they able to identify why unsuccessful attempts did not result in the desired outcome and come up with a revised plan of attack?

Self-reflection can, and should, occur on a regular basis throughout the learning process.  It gives the teacher great insights into how students perceive themselves as mathematicians, what they are taking away from class conversations about what is most important, and if they are able to plan for what they will change as a result of the experience.  Recently after what I thought was a successful debrief of sharing strategies and consolidating learning following a rich task related to capacity, I noticed in some student self-reflections that a few students still did not grasp the key takeaway.  What valuable information for me, as a teacher, so I can revisit the conversation in a different way and plan the next steps for those children according to their actual needs, not what I originally thought they needed.

A student reflects using Seesaw.

Self-reflection can also be a valuable tool for further growth after a summative assessment.  Some of our Lower School teachers have begun using Seesaw as a means for students to reflect on an area of their summative assessment (whether it is a project, presentation, performance task, or test) of which they are particularly proud, as well as an area where they want to continue working to improve in the future.  If it is something like a test, students may explain an error that was made the first time around and what they have since done to re-attempt the problem.  Students are able to do this as a written reflection or as a recorded audio reflection to accompany the photographs of their summative assessment product.  By using a tool like Seesaw or another learning management system, both teachers and parents are able to share in the students' learning journey and self-assessment of their progress.  

A kindergartener shares his
mathematical thinking.

For our youngest learners who may still be learning to write, it is also helpful to encourage an audio component with the self-reflection as well.  After the student "writes" their reflection, an interview where a teacher transcribes the student reflection or an audio recording on a device like an iPad can ensure teachers and parents alike understand what the student is thinking.

Not only will these reflections provide you as the teacher with valuable insights, but it will also begin to build reflective habits of mind within your students to help them grow as mathematicians and overall learners.  What other ideas do you have for building student journaling and reflection into your math classroom?

Differentiating for Productive Struggle

In my current role as the math specialist and curriculum coordinator in a preK through 10th-grade school, one of the questions I am frequently asked by teachers is how to appropriately challenge strong math students.  We want all our learners to grow in their curiosity, understanding, and love for math, so how do we do this without simply accelerating through content for students who seem to "get it" more quickly than others?

“Student success occurs when you create an instructional environment that sets high expectations for each student and provides scaffolding without offering excessive help. 

The key is to incorporate productive struggle.” 

—Barbara R. Blackburn

As Blackburn states in her article “Productive Struggle Is a Learner's Sweet Spot”, student success is optimized when we set high expectations for our students by incorporating opportunities for all learners to experience productive struggle.  At our recent school-wide professional development day, we focused on how using parallel tasks, open-middle tasks, and open-ended tasks can provide all students with the opportunity to be engaged in similar tasks while providing productive struggle at differing levels based on students' readiness.

With parallel tasks, two (or more) different questions are posed that are related to the same mathematical big idea and context.  This allows various entry points to meet the needs of students while providing a common experience so everyone can participate in a rich mathematical discussion about the tasks.  For example, students may be asked to create a real-world situation that requires counting to 100 or a real-world situation that requires counting to 1000.  After having some time to consider scenarios and decide on one they would like to share, the teacher can facilitate a discussion focused on comparing the scenarios students came up with for 100 versus those for 1000 by asking questions like "What do you notice about the difference in these scenarios?" and "Could this scenario for 100 ever require counting to 1000?  If so, when?  If not, how do you know?"  Mark Chubb also wrote a blog post on parallel tasks where he gives an example related to algebraic reasoning involving pattern blocks.  The most critical component of making parallel tasks valuable learning experiences is that everyone comes together to share and discuss their problem-solving ideas so we can learn from each other, even if we have different entry points to access the math concepts.

Open-middle tasks are those which have one correct answer but have multiple entry points and possible strategies that can be used to solve.  Many problems can be open-middle problems, as long as you prioritize the time for students to share and compare the different strategies they used to find their solution.  When students share their ideas and explain why they have a viable strategy, it is then their peers that should be providing feedback and critiquing their reasoning (CCSS.MP3) rather than the teacher serving as the judge.  For some concrete examples of open-middle tasks, check out Robert Kaplinsky's Open Middle website or his problem-based lessons that allow for rich mathematical conversations about problem-solving strategies.  Andrew Stadel's Estimation 180 and 3-Act Tasks like the ones from Andrew Stadel, Graham Fletcher, Dan Meyer, Kyle Pearce, and Dane Ehlert can also be perfect resources for open-middle problems.

Image made with the
Public Math Sticker app

Open-ended tasks, on the other hand, have many possible solutions and are further opportunities brimming with potential for students to articulate and justify their mathematical thinking.  Number talks, or math talks, allow for "low entry, high ceiling" so all students can access the mathematics, but it is possible to extend the concepts to accelerated levels as well.  Which One Doesn't Belong and Fraction Talks have helpful images that can be used for math talks, and you can always use your own images as well.  The Public Math Sticker App is a fun way to add questions like "What do you notice?"  "What do you wonder?"  "How many?" and "What repeats?" to your images like I did with the gummy bear example on the right.  Brian Bushart explains in this post how numberless word problems can be another way to promote mathematical thinking through open-ended tasks.  When the numbers are removed from a word problem, the context remains.  Asking students questions like "What do you wish the numbers were (what numbers will make it easy)?  Why?" and "What numbers will make it challenging?  Why?" build students' number sense.  Asking in follow-up, "what is another question you could ask about this scenario?" allows students to challenge themselves by thinking about other ways numbers in this context can be manipulated to provide further information.  Marian Small's book Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom is also a wonderful resource to see examples of both parallel tasks and open-ended tasks in different grade bands (K - 2, 3 - 5, 6 - 8) in different math strands (Counting & Cardinality and Operations in Base Tens, Number & Operations with Fractions, Ratios & Proportional Relationships, the Number System, Operations & Algebraic Thinking, Expressions & Equations and Functions, Measurement & Data, Geometry, Statistics & Probability).

In closing, I want to share one quote from a recent professional development experience with Dr. Yeap Ban Har that I continue to keep in mind.  He said, "when enrichment is done well, it leads to natural acceleration."  Our goal is to open our students' minds to multiple ways of thinking through incorporating opportunities for all students to experience productive struggle, thus allowing them to make connections among mathematical concepts and think flexibly about math.  In what other ways do you do this for your students?  I would love to hear from you in the comments!

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?