Ditch the flashcards: play these fun games instead!

There’s only one word to describe Alissa’s math workshop last week: ENLIGHTENING! It certainly provided us with a lens into today’s math teaching and methodology. The content was illuminating and the Q&A session covered thought-provoking topics. 

As promised, Alissa is sharing some of her top number fluency games to keep the math conversation going at home. Although it’s only April, we know that many of you are already thinking about the summer and how to keep your children engaged while they are out of the classroom. We all want to avoid the summer slide and even more so, the dreaded summer math packet! So grab a deck of cards, read her easy-to-follow instructions, and get ready for some fun quality time with the family! Remember, keeping your children engaged is half the battle when trying to instill a love of learning… 

One last thing: Alissa is available for group and one-on-one tutoring sessions, so email us any time to connect. And lastly…a HUGE thanks to Alissa’s kids for being such good sports and exemplary math game models!

how to Develop number fluency through fun exploration

Developing fluency with numbers starts with exploration. Leave the flashcards behind and give your children opportunities to play around with numbers in order to build confidence and strategy. Give them the option to use their fingers, number lines, hundreds charts, and tangible manipulatives. The more a child can visualize a number and its relation to other numbers, the more connections they can make. 

A deck of playing cards might be the best tool for practicing number fluency. Below are three games that can be used with children as an alternative to flashcards. Have fun!

Head to Head

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This game can be used to practice sums, differences, quotients, and products. It’s a game that not only encourages number fluency but allows students to practice communicating like mathematicians using the appropriate vocabulary. Additionally, students need to think flexibly about the operations in order to solve the mystery of the number on their heads.

Players : 3

Set up:

• Remove the face cards from the deck. You can add them back in when the children are ready. (J = 11, Q = 12, K = 13)

• Two players take a card from the deck and place it facing out on their forehead without looking at it. 

• The third player says the sum, product, difference, or quotient of the two cards. The first two players try to solve for the number value that is on their head. 

Example:

• Player A has a 3 card on their head. 

• Player B has a 6 card on their head.

• Player C might say, “The sum is equal to 9!” Player A would see the 6 on Player B’s head and deduce that they must have a 3 on their own head. 

War

This game is a fun way to practice all four operations.

Players: 2 or more

Set up: 

• Remove the face cards from the deck. You can add them back in when the children are ready. (J = 11, Q = 12, K = 13)

• Deal out all the cards equally to each player. All players turn over 2 of their cards and determine the sum. The person with the highest sum gets to keep all the cards. Play continues until one player has all the cards. 

Variation: This game can be played using sums, differences, and products. 

Target Number

I love this game because it can be played in pairs, small groups, or independently. It's a game that allows children to use any combination of all 4 operations if they are comfortable, or just addition and subtraction if they prefer. Later on, it can be played with older students using the order of operations and introducing parentheses. This is a game that can be adaptable as children’s skillsets grow. 

Players: 1 to 4

Set up:

• Remove the face cards from the deck. You can add them back in when children ready (J = 11, Q = 12, K = 13)

• Deal 5 cards to each player and leave them face up in front of the player. 

• Turn over one card and place it in the center. This is your Target Number. 

• Each player uses the 5 cards in front of them to create an equation that equals the target number. The goal is to use as many cards as possible. If playing against other people, the person who uses the most cards in their equation wins that round. If playing solo, the child should challenge themselves to use as many cards as possible. 

• For the next round, each player sets aside the cards they used and collects new cards from the center pile so that they again have 5 cards in front of them. Turn over a new Target Number. Play continues until all the cards are used up. 

Example:

• Target Number: 5

• Cards drawn: 7, 4, 2, 3, 1

• Child could play:  

  • 2 points:  4 + 1

  • 2 points:  7 – 2

  • 3 points:  (7 + 3) ÷ 2

  • 5 points:  [(7 + 3) × 2] ÷ (4 × 1)

Raising Fluent Mathematicians

In my last post, I introduced the notion of developing number fluency for our young mathematicians in order to help them be flexible, accurate, and efficient in their numerical problem solving. But what does it actually mean to be fluent in mathematics? And how do we support the growth of a fluent mathematician?

Let’s take a step back and first look at fluency in a more traditional context. A fluent reader is able to decode symbols on a page in a way that brings the meaning behind those words to life. They use appropriate phrasing and intonation to convey a character’s feelings, an intended message, or an author’s purpose.

A fluent language learner not only repeats the words they have learned, but understands the meaning behind the words in order to respond in a variety of ways to questions and comments given the overall situation.

It is widely accepted that we would not consider a reader fluent even if they could read 150 words per minute, but could not comprehend or explain what they read. Likewise, we would not consider a person fluent in a language if they rapidly repeated words and phrases, but did not use them appropriately in a given situation.

However, in mathematics we often equate speed with success rather than fluency. What is it about mathematics that drives us to be the fastest? We all grew up with the “mad minute” striving to answer 60 multiplication problems in less than a minute. We played games like “Around the World'' where the quickest student was deemed the winner, otherwise known as the smartest math student in the room. We spent hours each day with those relentless flashcards trying to beat our time and struggling to get through the deck. These days, not much has changed. Every iPad app that claims it will help your child master their math facts comes with a built-in timer, flashcards are still the go-to resource for many families, and those “mad minutes” are still causing anxiety for students.

When we speak about math fluency, our focus should be on the meaning behind the numbers and the connections they have to each other just like it is with language learning. However, with the emphasis placed on speed it really means we’re valuing memorization over understanding.

How often do you perform your job based solely on memorization? My guess would be not very often. As adults we rely on critical thinking skills, logical reasoning, analysis, and reflection to make the choices we do, both at home and at work. We should be focused on raising a generation of critical thinkers and problem solvers so that they can use these skills as adults in the workforce. Children who can reason abstractly and think logically are demonstrating that they truly understand numbers and do not just rely on memorization.

Memorization versus Understanding

The key difference between memorization and understanding is strategy. When a child memorizes something, it requires little to no strategy. Maybe they learn a cute rhyme (8 and 8 went through the door, 8 times 8 is 64!) or a mnemonic device (Who remembers SOHCAHTOA?) to boost their memory, but those aren’t connected to deep understanding. There’s nothing about 8 and 8 walking through a door that relates to that fact that 8 groups of 8 is a total of 64. This is not to say that memorization isn’t useful. It is good for things when the information doesn’t connect to something else - a street address, a phone number, a series of keystrokes on the Xbox controller, etc. When a student learns mathematics through memorization, that is the only thing they have to fall back on. If they can’t remember the answer, the rhyme, or the mnemonic, they get stuck.

However, when a student learns numerical operations through strategy, they can apply the strategy in a multitude of situations because strategies are flexible. Strategies connect concepts together. Strategies lead to numerical fluency.

The ultimate goal for students is to be flexible, accurate, and efficient in their numerical operations. And yes, at some point we do want them to be able to recall their facts in a relatively quick manner. At some point, students will need to begin using higher level thinking for things like factoring polynomials and graphing functions. If at that point they are still struggling with their basic math facts, this will just add to the complexity of the new concept and can cause frustration. But, for now, in elementary school, let’s give them the time to explore, to discover the relationships between numbers and operations, to test out different strategies, and to create a true understanding of number sense. Eventually, if students strategize enough they can get to the point where they use a strategy (or strategies) so often that it can become automatic and quick or efficient. By slowing down now and developing a true conceptual understanding, we have the option to speed up later because there will be fewer gaps to fill in.

So, if I’m saying throw away the flashcards, and get rid of the “mad minutes”, how then are you supposed to help your children develop numerical fluency? Join me on April 1, 2021 at 7:30 pm to discuss this and learn some practical strategies to help

Join us for a New KQ Workshop:

What is a Mathematician?
with Alissa Helgesen

Thursday, April 1
7:30 pm

Click here to register

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Written By Alissa Helgesen
Math & Workshop Specialist at Keating Quigley

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Offered by Keating Quigley Educational Advisors

Keating Quigley Educational Advisors is a Greenwich-based educational advising practice that partners with domestic and international families to provide highly personalized educational consulting services for Nursery through Grade 12 students. Services include school search support, essay guidance, social-emotional mentoring, relocation support, and enrichment workshops.

“My teacher doesn’t explain it that way!” Sound Familiar?

For years, families across the US have been hearing cries like this from their children as they try to support math schooling at home. This has only been amplified since COVID-19 became our new reality. One day our students were in school learning from trained math teachers, and the next day it was suddenly our responsibility to continue the process. As a math educator with three school-age children of my own, even I was not immune to these battles.

Cue the social media memes. “These homeschool children are about to learn how to carry the 1!” is my personal favorite. Another one that makes me chuckle is, “Why did they change math? There wasn’t anything wrong with it!” I’ve seen posts like these floating around for years, but now that we are all expected to support our children through distance learning, it’s become even more prevalent.

So, why can’t we do math the old fashioned way?

The short answer is, you can! There is no such thing as old math and new math. Math is the same as it has always been. Numbers still add up to the same sums, multiplication facts are still important, geometry is still about spatial reasoning, and word problems still use extraneous information. The main difference in today’s classrooms, from the ones we grew up in, is that teachers today are actively seeking ways to develop an understanding of mathematical concepts and not just memorization of algorithms.

Take for example, the above problem. The student who worked on this had clearly memorized a series of steps, or an algorithm to achieve success, but you can see that there is a lack of understanding of the concept behind the algorithm. If the student had understood how the numbers related to each other, he would have no need for the standard algorithm of "going next door to borrow" or regrouping in order to solve it. We are now focused on moving beyond memorizing such algorithms and moving toward a deeper understanding of mathematical concepts so that students understand how numbers relate to each other.

One way that we can build number sense is by making sure students can solve problems in multiple ways. If students have a true understanding of how numbers relate to each other, they should ultimately be able to utilize several strategies to arrive at an answer. It’s true that some strategies will be more efficient and some will take a more circuitous route to the answer, but that’s part of the learning process. Developing number fluency means that students are accurate, flexible, and efficient in their problem solving. Could you build an entire house with a hammer? Probably, if you were open to new methods and were flexible with your plans. Would it be efficient and easy? Definitely not. As educators, we help guide students towards choosing the best tool for the job.

Teachers have spent countless hours in professional development workshops, reading literature on best practice, and learning from experts how to develop a strong number sense in their students. Now all of a sudden, parents and caregivers are being challenged to navigate this type of learning at home with little to no instruction. Let’s be clear, this is not an easy task! Nor is it fair to expect the new homeschool teachers to know how to guide students through multiple strategies in order to develop flexible and efficient thinking. However, if our goal is truly to help students see multiple paths to solving a problem, then why not teach them the way we learned? It’s just another strategy after all.

But, before you jump into showing your children the standard algorithm, think about the words you choose and how you present the information. By declaring that your way is better, or faster, or easier, you automatically undermine all the other strategies that they may have already learned. The truth is, nobody’s brain works in exactly the same way and for some kids, using number bonds, place value charts, or visual representations are going to be the most beneficial methods at this moment in time. Knowing that there is another strategy out there, one that involves regrouping (please don’t call it carrying! You’re not taking it anywhere!) is, however, still beneficial.

When working with your child, first, take a deep breath. This is going to take some patience! Begin by offering to show them the strategy that works best for you. Take some time to explain the process you use when adding/subtracting/multiplying/dividing numbers. These students are used to being told WHY they are doing something, so they’ll likely have questions. Have them try your method out a few times and then they can try out their current favorite method as well. Giving students the opportunity to see the similarities and differences in the methods will help to solidify the concept for them. Older students will likely start to make the connection that the standard algorithm that we recall so easily is simply a shorthand version of the place value method they are using.

Let’s be honest, none of us have a lot of time to devote to this right now, so don’t panic: there are some fantastic free resources available like Khan Academy, that can help you through this with digestible how-to videos for grades K-12 covering all topics imaginable. And don’t forget that you can always reach out to your child’s teachers for advice: they will want to support you because they know that their students (fingers crossed!) are returning to their classrooms and so they have a vested interest in supporting continuity of learning.

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Written by Alissa Helgesen | Math & Workshop Specialist at Keating Quigley

5 simple ways to get your kids thinking mathematically

Let’s face it, very few children get excited to do math work out of school. And who can blame them? They need a break from work just as much as we do. But the fact is, math doesn’t just exist inside the four walls of a classroom or the pages of a workbook. Children need to be able to apply the math skills and knowledge that they have learned to the real world in order to solidify the concepts and avoid the academic slide. But don’t go rushing out to buy more workbooks or print more worksheets for the kids. There are many ways to work math into your everyday routine - the same way you sneak vegetables into their meals!

Here are five of my favorite ways to keep kids thinking mathematically each day:

Schedules. Children thrive on routines. They need to be able to anticipate how their day will unfold, even if it just means playing all day. Give your children some power over their schedules and routines by co-creating them together.

• How much time is allotted for each activity?

• How much time do you have to complete all of your chores? Can you get them all done in time?

• How much longer until you can start something? By when do you need to finish?

• How will you fit in your daily reading, chores, screentime, outdoor play, etc. before dinner?

Concepts covered: telling time, elapsed time, addition, subtraction, division

Allowance. Giving children an age appropriate allowance for doing chores is a great way to introduce your child to money management. Paying your younger children in cash will help them recognize different coin and bill combinations so they can practice counting money. Older children can be exposed to decimals depending on the amount you choose.

• If your allowance is x dollars each week, how long will it take to save for that item?

• If you buy that item, how much money will you have left in your bank account?

• If you save all your allowance for a month how much will you have? What about after six months? A year?

• Ask for different coin and bill combinations. Can you pay me all in quarters? What about dimes?

Concepts covered: addition, subtraction, multiplication, division, decimals, skip counting by 5s, 10s, and 25s

Budgeting. Learning how to balance a budget is a life skill that all children should learn, and modeling how you use your budget is a perfect way to include children in this real life application.

• Give your child your grocery list, the weekly circular or access to the store website, and a budget. How can you make sure that you can get all the items we need?

• If the item is on sale, calculate the new cost.

• Look at unit prices versus retail prices. Calculate the better value.

• Have your younger children round up the prices and estimate how much the total will be. Older students can calculate the exact total.

• When ordering takeout food, calculate the bill. Older students can include the appropriate tip percentage. Encourage them to find different ways to calculate 5%, 10%, and 20% of the total.

• How will the state tax affect the bill? Estimate or figure out the exact figure.

Concepts covered: estimation, rounding, addition, subtraction, percentages, decimals

Travel. Most of us are traveling less than we’d like to currently, but having your children be a part of the conversation around travel (even if it’s just down the street) allows for great mathematical conversations.

• Have your child figure out what time to leave to get to your destination on time. If we need to be there at x time, and it takes y minutes to get there, what time should we leave?

• Calculate the total mileage for the trip.

• Calculate the total time for the trip taking into account speed, pit stops, and traffic.

• Calculate the amount of gas that will be needed for the trip. Have your child research the gas prices and calculate the estimated cost of the trip.

Concepts covered: time, elapsed time, rate, money, decimals, addition, subtraction, division, multiplication

Baking and Cooking. I don’t know about you, but at the start of this quarantine, I started baking ALL THE TIME. We made bread, cupcakes, cookies, muffins - all the baked goods. Baking is a phenomenal way to incorporate math.

• Don’t just take the recipe as given. Look at how many people you want to feed and then plan on doubling, tripling, or halving the recipe as needed.

• Remove some of the measuring tools from your cabinet. If you need ¾ cup of flour, but don’t have a ¾ cup, what are the other ways you can measure ¾ cup? Don’t have a ⅓ of a cup? How can you use tablespoons instead?

• Grocery stores are out of a lot of ingredients! Look up substitutions if necessary. Some substitutions are a 1:1 ratio, but others have different ratios that will need to be calculated.

• When cutting out cookies you can incorporate geometry! How can we get the most cookies out of this dough? Use flips, turns, and translations to fit the cookie cutter in the most efficient pattern.

Concepts covered: fractions, operations with fractions, addition, subtraction, multiplication, division, spatial reasoning, geometry

Encouraging mathematical thinking with real world connections is a very powerful way to give children a purpose and context for the skills and concepts they learned in their classroom. But most importantly, it answers the essential question - when are we ever going to use this?

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Written by Alissa Helgesen | Math & Workshop Specialist at Keating Quigley