This list is not my own, it’s actually from a poster I used to have hanging in my classroom.  But I did not hang this poster simply because it was cute and took up a lot of space on my otherwise bare walls (I was a high school math teacher…not the most creative type…). I hung it because I really and truly believe that these are some of the most helpful things one can do when trying to solve a problem.

10 Things Every Good Mathematician Should Do:

1. Look For Patterns

If you are trying to solve a complex problem, and have no idea where to start, try to find a pattern and see if that pattern tells you anything.  Math (and life) is full of patterns, and often seeing a pattern will either help give you direction in finding a solution, or at least help you to better understand the problem and come up with an idea to solve it.

Related: How to solve problems by finding a pattern

2.  Draw a Picture, Diagram or Chart

As a visual learner, this is almost always my first step in working out a problem.  Simply drawing a diagram of what’s happening, or organizing the information in a chart or table will give you a better understanding of the problem, and possibly help you spot patterns or information that you otherwise would have missed.

Related: How to solve problems by drawing a picture

Related: How to solve problems using an organized list

3.  Estimate

In terms of real life application, this is one of the most overlooked math skills.  Estimation is not just random guessing, but rather careful consideration, and is a very important life skill. Estimating can help you quickly determine if a solution makes sense in context, or give you an idea of what the final solution should look like.

4.  Ask Good Questions

Often, students look at a problem, have no idea where to begin and thus give up before they have even started. However, learn to ask yourself questions about the problem at hand using what you know.  For instance, “What is the question asking?” “What should the solution look like?”

As you get better at thinking through and solving problems you should also learn to ask things like, “Does my answer make sense?” “Does it answer the question being asked?” “Is there another way to solve this problem?” “Is my method of solving going to be true in all cases?” “What happens if I change the numbers in the problem?”

Asking good questions will lead you to a deeper understanding of the problem and give you greater insight for the next problem you solve.

5. Create a Plan

When you first read through a problem, take a moment to think through it.  Ask some questions, organize the information, and then come up with a plan.  Start by thinking about what your solution should look like (Should it be a measurement? Should it be large or small? etc.) and then come up with a plan for how to get there.

Sometimes you need to find a different piece of information in order to find the answer you’re looking for.  Sometimes, you may need to change the plan halfway through because you’re on the wrong track. That’s ok! That’s part of the problem solving process.

Related: Word Problem Solving Templates

6.  Take Your Time 

Often, students are in such a hurry to “get it done” that they don’t take time to stop and think about the problem. This leads to careless mistakes, or simply guessing because they don’t know how to solve it right away.  It’s ok to try something that doesn’t work, and then try something different.

Related: Types of Math Errors & How to Prevent Them

7. Check Your Work

After all that hard work, no one wants to go back and do it all over again.  But thinking about whether your answer makes sense, and then briefly going back over each step to check for mistakes is a vitally important step.  You didn’t work that hard to solve the problem just to end up with the wrong answer because you said “2 + 3 = 6”!

8.  Explain Your Work

Once you have successfully worked through a problem and checked and verified that you have the correct solution, talk through how you went about solving it.  Explain your plan to a partner and see if you came up with the same answer.  See if you each solved it a different way and learn from each other!

Talking through a problem will not only help you better understand what you did and why it worked, but will help you remember for the next time. If you can’t explain what you did, it may be that you don’t actually understand and you need to go back and look at the problem more closely.

9.  Use Math to Solve Everyday Problems

Whether in your classroom, in your home or at the grocery store, there are problems that need to be solved! So put your skills to the test and try to come up with a plan and work out a solution. Using your brain outside of the math classroom will help hone your problem solving skills as well as better understand the math you are learning in school.  Then discuss the problems with your classmates and see if there are other ideas for how to tackle the problem!

10. Seek New Ways to Solve a Problem

One of the beautiful things about mathematics is that there is always more than one way to come up with the right answer. Looking for more than one way to find the solution will stretch your thinking and help you grow into a better math student and problem solver, and that is always the goal, right? And as a bonus, looking for another method of solving will help you check your work because if you use two different methods and get two different answers you know something is wrong somewhere!

And finally, don’t be afraid to make a mistake.  That’s part of the learning process!! Especially when it comes to mathematics.  Sometimes the only way to figure out what works is to first determine what doesn’t. Just don’t give up!

Related: 8 Reasons Making Mistakes in Math is a Good Thing

Happy problem solving!

The post 10 Things Every Good Mathematician Should Do appeared first on Math Geek Mama.

Luckily, if you’re a parent who wants to help your child better understand math, there are several different ways to make the subject more accessible. The more you combine math with things your child loves, such as games or sports, the more relatable and enjoyable it becomes. And it doesn’t have to be hard! In fact, here are five different ways you can help your children get better acquainted with this seemingly foreign language.

*Please Note: This post contains affiliate links which support the work of this site. Read our full disclosure here.*

This is a guest post from Tiffany Young at HeyTutor.

1. Make Your Home a Math-Rich Environment

Children of every age find it easier to connect with the relevance of math when it is part of their everyday environments. When they can see, touch, and play with mathematical ideas at home, classroom activities will make much more sense and won’t seem quite as intimidating.

The first things we might think of are counting books on the bookshelf, counting mats on the wall, and times tables posters on the back of the bathroom door.

While these resources can be helpful for reinforcement, children first need to develop a strong concept of what these numbers actually represent. We refer to this as “number sense,” and according to research from Stanford University, this is the foundation of all learning in math.

How to Develop Number Sense at Home

Children develop a good grasp of number sense when it is connected to something real, like weights, lengths, time, quantities of cooking ingredients, the number of people, and so on. To encourage your child to start counting and measuring at home, make the following tools accessible:

• Rulers, measuring tapes, pedometers, and family height charts
• Kitchen and bathroom scales
• Clocks (digital and analog), stopwatches, calendars, and timetables
• Measuring cups, spoons, and containers

You can also give them toys and games that provide visual pictures of math, including:

• An abacus
• Sticker charts
• Playing cards
• Building blocks
• Connecting shapes (such as Magnatiles or Geometiles)
• Dot flashcards and puzzles

Once you have created a math-rich environment with everyday items, some magnetic numbers on the fridge or a colorful counting poster on the wall will be the icing on the cake!

2. Talk about Math in Your Everyday Activities

If your child is surrounded by math and measuring tools, it will become much easier to make mathematical learning part of everyday life. How do you connect their toys with learning? By talking about it and asking questions.

Count Everything

Children who are still learning to count can benefit from counting anything and everything in their environment. You can ask them to find out how many steps from the house to the park, how many stairs to reach the top of the staircase, how many blocks they have of each color and shape in their building-block collection, and so on.

Measuring with Height Charts

The family height chart is an easy starting point for talking about lengths, addition, subtraction, multiplication, and division.

You can use this visual tool to discuss with your child:

• How much they have grown in the past year
• How much taller/shorter they are than other family members
• How many times taller they are now than when they were a baby

Fractions with Food

When cooking together, talk about fractions of pounds, ounces, and pints.

When baking something round like a pizza or cake, calculate the fractions of the finished slices and enjoy the result!

3. Focus on Problem-Solving Strategies

When it comes time to solve equations or word problems, help your child focus on the strategies rather than the answers.

It is helpful to emphasize that there are many different ways to solve a problem, as this encourages the child to really understand what they are doing rather than focusing only on the memorization of answers.

Visual Aids

To help with this understanding, you can help your child draw a picture of the problem.

For example, for the problem 5+7, your child could draw this as one row of 5 in one color and another row of 5 with a “partial” row of 2 underneath in another color.

Alternatively, they could start with a row of 5 in one color and add the 7 in another color, completing the row of 10 and continuing onto the next line with the 2 over.

The more they arrange numbers in rows of 5 (for smaller numbers) and rows of 10 (for larger numbers), the more quickly they will be able to recognize numbers as combinations 10s and 1s (and later adding in 100s, 0.1s, and so on).

Once your child is ready to use mental strategies, they might suggest these two main strategies for solving 5+7:

• 5 plus 5 is 10, plus two more equals 12
• 5 plus 10 is 15, minus three equals 12

Encourage a “Growth Mindset”

When children start to realize that they have the tools they need to solve each problem, the fear of “getting it wrong” starts to disappear.

Praise your child for their effort and strategies in solving the problem rather than rewarding them for pages of correct sums.

This will boost their confidence and encourage them to keep attempting harder problems. There are even specific math tasks that promote a growth mindset – seek those out to empower your little learner.

4. Have a Homework Routine

In addition to the spontaneous, everyday math conversations, it’s helpful to set aside a time for math every day and have a dedicated place where this happens.

It could be a desk or on the couch, or even in the car. In your daily “math spot,” your child can explain their math homework to you, do some work with flashcards, or you can take turns giving each other written and verbal problems to solve.

Their teacher will be able to tell you what they are learning in math and which aspects need more practice at home. There are lots of cheap and free math resources that your child can print out or use online, such as these Pre-K Math Activities and Corbett Maths.

The publishing company of your child’s math textbook might also have activities on their website that you can use.

5. Seek Outside Support

If you have done all you can and your child is still struggling with math, it may be time to get additional help.

Start by speaking with your child’s teacher about their strengths and weaknesses, and consider hiring a 1-on-1 tutor to work on the areas that need strengthening.

Related: How to Find a Math Tutor for Your Child

You might even like to take a math class yourself to learn the current teaching methods and refresh your skills.

Above all, make math an activity that your child enjoys and have fun learning together!

Tiffany Young is a freelance writer, content strategist, and former graduate assistant. She frequently writes about the latest developments in teaching, public policy, testing, and educational technology for sites like HeyTutor.

The post 5 Simple Ways to Help Your Child Succeed in Math appeared first on Math Geek Mama.

*Please Note: This post contains affiliate links which help support the work of this site. Read our full disclosure here.*

The Role of Calculators in Math Education:

I would like to argue that there is a balance to be found. The calculator can be a wonderful tool in the math classroom, if used in an appropriate setting and in an appropriate way.

For example, there are ways to incorporate calculators into the elementary classroom without using them for computation, but rather, to explore and discover.

If you are trying to teach students their multiplication facts, it won’t help them to let the calculator do all the work.

If you use a calculator, however, to show them the pattern of addition in multiplication, it can help enhance their number sense and build a stronger foundation for their multiplication facts.

While working out 9+9+9+9+9+9+9+9+9+9+9 would be long and tedious by hand, students can see the patterns quickly with a calculator.

Similarly, playing with the calculator to explore other patterns or create their own patterns can lead to excellent mathematical discussions and discovery.

In addition, students can explore the number Pi or the Fibonacci sequence with a calculator. This allows them to focus on the concept and discover new ideas rather than getting bogged down with computations.

Again, calculators should not be used to compute and solve problems in elementary school, or take the place of mental math exercises. But they can certainly enhance learning and allow for great discoveries if used in that way.

Calculators in High School Math Classes:

As students get older, the role of the calculator changes. There are times in high school math courses where the use of a calculator is helpful and effective.

For instance, graphing equations is an important skill in Algebra, but once students have mastered it, it won’t always be necessary to graph everything by hand. Letting the calculator do the heavy lifting can help students make observations about graphs and form connections between the equation, table and graph.

But a word of caution: I have definitely seen students who were too dependent on the calculator. It is incredibly easy to make careless mistakes by punching something incorrectly into the calculator.

If high school students don’t know how to do the basic computations by hand, or don’t have a good understanding of estimation, they may not even realize that the calculator got it wrong.

Whatever the context, balance is key! For more great ideas for using a calculator for exploration, see this NCTM article, or this article from Homeschool Math.

And stay tuned for my newest blog series, Math+Technology! I’ll be sharing even more ideas for using a graphing calculator to explore math concepts in middle and high school.

Happy learning and exploring!

How do you use a calculator or other technology in the classroom? Share in the comments!

The post The Great Debate: The Role of Calculators in Math Education appeared first on Math Geek Mama.

My son is now learning about division, and I wanted to make sure he is developing an understanding of these vocabulary words too. My son needed to focus on the vocabulary, so this is what I created to help him succeed.

*Please Note: This post contains affiliate links which help support the work of this site. Read our full disclosure policy here.*

This is a guest post from Rachel at You’ve Got This.

Division Vocabulary Book

The division vocabulary book helps children become familiar with six vocabulary words. Here is what your kiddos will be learning about as they work through this book:

1. Division is when you share or split something into equal groups.
2. The dividend is the number that is being divided up.
3. The divisor is the number you are dividing by or how many equal groups you will create.
4. The quotient is the answer to a division problem. It is how many objects are in one of the equal groups.
5. The remainder is the amount that is left over or can be put into groups because the groups will not be equal.
6. Finally, the inverse operation basically states that multiplication reverses division.

The children will not just be reading about the definitions, they will be required to find pictures that illustrate that word.

For example, for each way a division problem may be written, there are cards that have arrows pointing to each part of the division problem.

If the students are looking for examples of a dividend they would find a card that has an arrow pointing to the numerator in a fraction, or the first number in a problem like 24 ÷ 8.

Materials Needed:

• Division booklet for each student (link to the download is at the end of the post)
• Scissors
• Glue

Division Book Prep – Work

Prep-work for this book can be incredibly simple. But if you want this activity to take up less of your math time, you may want to do some prep-work ahead of time.

Simple (This will take students time to complete):

1. To begin, print off enough books for each student that will be putting it together
2. Provide your students with scissors and glue
3. Have students cut out the book, assemble them, and staple.
4. Finally, have students cut out the illustrations

More Prep on your part:

1. First, print off book
2. Assemble book by cutting out the pages, putting them in order, and stapling them together.
3. Next, allow students to cut out illustrations, or you could cut out illustrations for them.
4. Provide glue for students

Put the Division Vocabulary Book Together

Now comes the fun part: figuring out which illustrations go on the pages! Some children may be able to figure this out quickly, and others may need a little more support. I constantly used the definition as my son searched for his illustrations.

“What number do you think is going to be divided up in this problem?”

“How many is in each group in this problem?”

“How many groups would I need to make to solve this problem?”

After each question, I would use the vocabulary word and confirm my son’s choice.

He learned a lot, and as we have moved on to division word problems and creating division arrays, I have loved seeing him continue to use the vocabulary he has learned.

You’ve Got This

{Click HERE to go to my shop and grab this fun interactive division vocabulary book!}

Want more fun ideas for exploring division? Try one of these:

• • Multiplication and division roll and write activity
  • Books to explore division
  • Division BINGO game

Rachel is a homeschool mom to four little ones, ages 2 to 6. She is a former public elementary teacher, and has recently begun blogging at her page You’ve Got This. You can also find her on Facebook and Pinterest.

The post Simple, Interactive Division Vocabulary Booklet {FREE} appeared first on Math Geek Mama.

Or at least, that’s what my husband said when he asked what I was writing about. “Unit rate, huh. What’s that?”

I was a little surprised that my math savvy husband didn’t know about this crucial math skill he probably uses nearly every day. Once I told him what it was he said, “Oh. I use that all the time.”

So, don’t feel bad if you don’t know the term. It really is something people use frequently, but if you aren’t familiar, you probably will be after reading this post.

And if you’re a teacher or homeschooling parent, I have some suggestions on how to teach unit rate to your students.

*Please Note: This post includes affiliate links which help support the work of this site. Read our full disclosure policy here.*

What is a Rate?

According to Math at Hand (a super useful reference book every home should have):

a rate is a special ratio that involves quantities that aren’t measured the same way, like miles and hours.”

Example, if you rode your bike 40 miles in 2 hours, the rate would be 40 miles/2 hours. Or if you’re me-passed out on the side of the road from exhaustion.

Think about all of the ways to measure things and you can see we have a lot of options for rate: weight/time, volume/mass, distance/time, etc.

As useful as rate is, there’s a specific kind of rate that’s even more useful. It’s called unit rate.

A unit rate has a denominator of 1. You remember denominators, yes? The bottom of a fraction (in this case, ratio).

In our bicycling problem, the unit rate would be 20 miles/hour (read, 20 miles per hour).

How are Unit Rates Useful

There are 2 reasons you might want to find unit rate. To compare two or more events/items and as a jumping off point to solve other, more challenging problems.

Using Unit Rate to Compare:

Let’s say you want a bag of chips. After all, who doesn’t?

You’ve chosen the brand. But should you buy the big bag or the smaller one? You decide to save yourself some money and buy the smaller bag. But did you really save yourself money?

Assuming a large bag of chips would last longer than the smaller (not always a safe assumption in my house), the smaller bag probably costs more. But how to know for sure?

The problem is, each bag weighs and costs a different amount. In order to compare them, we need either price or weight to be the same. Let’s use weight.

Let’s find the unit price, the price for 1 unit. To find the unit price, divide the price by the weight.

Let’s pretend an 8 oz bag costs $2.50 and a 16 oz bag costs $4.00.

$2.50/8 oz = $0.31/1 oz

$4/16 oz = $0.25/1 oz

You would save 6 cents an oz if you buy the bigger bag for a total of 50 cents saved.

Shopper beware, buying in bulk is not always cheaper. In fact, I used real numbers to make this example and the first brand I looked at, the bigger bag was more expensive than the smaller.

Using Unit Rates As a Starting Point:

Another reason to use unit rate is as a place to build off of.

For example: If I have $20 spending money a month, how long will it take until I can afford that $100 dress I want?

$20/month is my starting point. Each month I add another $20 until, after 5 months, I am at $100.

Ideas For Introducing Unit Rate to Students

The examples I gave are near and dear to my heart. With 5 children on one income, saving money on groceries is an important life skill I use regularly. Planning spending money is fun and something else I do frequently.

So the question is, what makes your students interested? The perfect topic would interest them, be easy to collect data on, and offer many opportunities to ask questions. If you’re not sure where to start, I have found students are often interested in themselves and what they can do.

I once took my 8th graders outside to the track to time how long it took them to complete a mile. There might have been some incentives for this lesson, like it was spring and I really wanted to be outside!

Once back in the classroom, they answered questions like:

• How fast do they run one lap?
• How many miles could they run in 1 hour?
• How long would it take them to run to a town nearby, how about a town further off, or to the next state…etc.

I would avoid comparing students. But you could compare students to animals like cheetahs or turtles. (Biggest, Strongest, Fastest by Steve Jenkins would be a great book to read along with this lesson).

Some other things students can measure about themselves: number of jumping jacks/minute, words written or typed/minute, words read/minute.

I would encourage you to find something students can be a part of. But sometimes that’s not feasible.

If that’s the case, pick something they can see (how fast does the ball roll down the track) or something they’ve seen so many times they can easily imagine it (bike riding). A very easy unit rate problem to demonstrate would be cost/item. All you would need is a bag of candy to get them both the visual and the interest.

Suggested Order to Teach Unit Rate

Once they can see unit rate (cost of one candy, jumping jacks in one minute), solve simple problems starting with unit rate. If one candy costs 5 cents, how much is 10 candies, 20, 100, x? Introduce a wide variety of measurements, sometimes length, sometimes weight, sometimes time, but always the same concept.

Next, have students find unit rate. It’s a little harder to find unit rate because division is harder than multiplication. That’s why this step is second. An example problem would be: 12 sodas cost $3, how much does one cost? Again, introduce them to a wide variety of measurements.

Once those two steps are easy, introduce multi-step problems. Multi-step problems could use either of the above skills and are not always as obvious what you are supposed to do.

Example: 12 pack of soda costs $3, how much do you save buying the 12 pack instead of the $0.75 soda from the vending machine?

Just How Useful is Unit Rate?

Whether you are a teacher, a homeschooling student or a parent helping their kid with homework, unit rate is something we all use. I hope this post has taught you something you didn’t know and given you fun ideas for how to teach unit rate.

And if you’re interested, there’s a fun and engaging lesson on unit rate included in the Math Geek Mama Membership site: Passing Snowballs. Click here to learn more about membership.

And please share in the comments how you have used or taught unit rate, either in the classroom or in real life!

Danielle is a homeschooling mamma of 5.  She is committed to making life with young children easier and sharing her passion for math.  If you would like to learn more about teaching math to multiple age groups visit Blessedly Busy or follow her on:  Facebook, Instagram, Pinterest  or Twitter.

The post How to Introduce and Teach Unit Rate: Practical Tips appeared first on Math Geek Mama.

Maybe your student struggles with multi-digit addition or multiplication. Maybe it’s division that’s got them hung up. Or perhaps, it’s subtraction with (gasp!) regrouping. In all likelihood all of these struggles can be boiled down to one issue:

Place value.

*Please Note: Some of the links in this post are affiliate links which help support the work of this site. Read our full disclosure policy here.*

This is a guest post from Danielle at Blessedly Busy.

Place value is the foundation for our number system. All operations (multiplication, addition, etc…) build on top of it.

We don’t want our math house to have a weak foundation and risk it coming down on us when we get to a tricky math concept. We want a firm foundation. So what does a solid foundation look like?

What Students Need to Know:

Place value is understanding how much a digit is worth. The value changes depending on its position in a number.

For the number 983, the 9 really means 900. In 91, the 9 means 90.

Our system is really efficient, but it can be confusing for students first learning.

There are also concepts that support an understanding of place value.

I looked at all of the Common Core Standards for grades K-5th. There are 5 big concepts students learn that support place value: Counting, reading and writing numbers, comparing numbers, understanding multiples of 10 and rounding.

Here is a brief list to give you an idea what a firm foundation looks like:

• Count by 1’s, 2’s, 5’s, 10’s, and 100’s up to 1000.
• Read and write numbers as: a numeral, written word and expanded form (it’s also useful to use base ten blocks)
• Compare numbers using <,> or =
• Understand that our system is a base 10 system. To move place values, multiply or divide by 10.
• Round to the nearest 10 or 100

Why Place Value Matters–The Tale of a Struggling Math Student

Charles is in 5th grade. Next year, he will be in middle school. He’s very excited about moving on to middle school next year, but there’s a problem.

He hates math!

He is terrible at it (so he believes). It started around 2nd grade, double digit addition. He dutifully wrote his numbers vertically and added down the columns. 23 + 34 is 57. Easy. He didn’t know why he had to line them up the way he did, but it worked so he didn’t worry about it.

Then he gets to the problem 55+36. His answer 811. Why is this wrong? He did what he always did, add down the columns.

Next comes subtraction. 55-36=21. Apparently you are supposed to borrow. What’s borrowing? The teacher explains it again, for what feels like the 50th time. He can solve the problem, most of the time. Again, he is just following steps, he doesn’t know why they work.

Now he is being introduced to multiplication. At first it’s easy. Memorizing things has always been easy for Charles. And now, we are into double digit multiplication. After many explanations and many failed attempts he finally has all of the steps memorized. He is starting to think that math is not really his thing and maybe he is stupid at math or maybe just stupid.

And now, the nail on the coffin, division. Multi-digit division. There’s no way! He gives up.

Hope For the Struggling Math Student

Charles’ story is sad. The saddest part is that all of his struggles could have been avoided if he understood place value and was able to use that knowledge to solve problems.

If your student is struggling in operations (addition, subtraction, etc…) I encourage you to start over and make sure their foundation is firm. Even if they are in 5th grade.

You can also find lessons that show students how to solve problems using place value. Like this post on multi-digit multiplication, for example.

For more ideas on how to teach place value visit: 100 Activities, Games, and Lessons to Teach Place Value to the Elementary Student.

More FREE Place Value Resources:

• Place value puzzles
• Build a Snowman place value activity
• “Sir Cumference” place value board game
• Equal or not equal place value sort
• Books to teach and explore place value and large numbers

Danielle is a homeschooling mamma of 5.  She is committed to making life with young children easier and sharing her passion for math.  If you would like to learn more about teaching math to multiple age groups visit Blessedly Busy or follow her on:  Facebook, Instagram, Pinterest  or Twitter.

The post How to Build a Solid Mathematics Foundation appeared first on Math Geek Mama.

*Please Note: I received this game free and was compensated for my time in writing this review. All opinions, however, are my own and I was not required to give a positive review. Read our full disclosure here.*

Holimaths X- A Multiplication Card Game:

I love to play math card games. I’ve shared a large list here, covering a variety of math concepts from Kindergarten to high school.

But with a standard deck of cards, there are some limitations to the games you can play. And if you’re working on the multiplication tables, playing over and over again with a deck of cards can get boring and repetitive.

That’s why I love playing Holimaths X with my daughter!

This unique multiplication card game is designed specifically for learning the times tables.

The fun, color-coded cards make it super easy to focus on specific facts.

For example, my daughter (second grade) has only been exposed to the beginning facts (0-3). She understands the concept, but has not yet begun to learn and memorize the upper tables.

But that hasn’t stopped us from playing and learning together!

I simply pull out the cards for 1s, 2s, and 3s and let her play the “Solitaire” version using facts she is comfortable with.

This version of the game is also perfect for her because, as the oldest, none of my other kids are ready for multiplication yet.

This gives her a chance to practice and explore the facts by playing, even when she doesn’t have anyone to play with her.

A Game for the Whole Family:

And when my husband and I are available to play with her? It’s even more fun!

So far, we’ve been playing the original Holimaths X version.

To play, players have to match multiplication problems to the solution cards.

If you don’t have a match, you can swap out your problem cards, solution cards, or a combination to try and find a match.

When you solve a problem, you get a designated amount of points (which varies depending on the problem).

Once someone runs out of cards, you tally up the points and the player with the most points wins.

I love that in addition to  practicing multiplication facts, there’s an element of strategy involved.

Because you win by gaining the most points, you have to think about which cards you choose to swap out.

For example, my husband always kept the cards with the highest point values and continued swapping solution cards until he found the right solution.

You could, however, try for problems with slightly lower points but higher chance of choosing the solution. Solve more problems, earn more points.

It takes some thought and planning. It also makes it more fun and challenging than a simple and straightforward matching game.

In addition, there are help cards for kids who are younger to find the solutions to the cards they have. So even if younger family members don’t have the facts memorized, they can still join in the fun!

10 Ways to Play:

As I mentioned, playing a game such as “Once Through the Deck” can get boring if you play over and over again.

With Holimaths X multiplication card game, however, there are 10 different ways to play with just one deck of cards.

I will admit, we have yet to try out all ten games. But with four kids, and many years of learning the times tables ahead of us, I am sure we will get through all ten eventually!

Want to Learn More?

This game is currently available separately with the 1-6 times tables as a set and the 7-12 times tables as a set. Or you can purchase both sets together to work on the complete times tables from 1-12.

The post Multiplication Card Game the Whole Family Will Love appeared first on Math Geek Mama.

3 Types of Math Errors:

As I’ve thought about the different mistakes students of all ages make as they solve math problems, I’ve narrowed them down to 3 categories:

• Careless Errors
• Computational Errors
• Conceptual Errors

(You may have different classifications, or think I’ve missed something. If so, be sure to share in the comments!)

Careless Errors:

Careless errors occur simply because they are not paying attention, or are working too fast. Some examples might be:

• Copying the problem wrong to begin with
• Writing a wrong number
• Dropping a negative sign
• Sloppy handwriting
• Not following the directions
• Typing it wrong into their calculator

Here are some simple ways to help kids prevent making careless mistakes:

• Slow down
  • This seems obvious, but students are often in a rush to finish so that they can move on to something else. Rushing is the easiest way to ensure careless mistakes. Encourage kids to take it slow and pay attention to what they’re doing.
• Circle important information
  • Whether it’s a worksheet or word problems, circling important information will help students know what to do. Circling something in the directions will help them follow them correctly. Circling key information in a word problem will help them think through their strategy and make sure they don’t forget anything
• Use graph paper
  • Using a sheet of graph paper to work out problems can be a really simple fix for kids who struggle with neatness. Graph paper allows kids to line up the numbers correctly and prevent sloppy mix ups.

Computational Errors:

The second type of mistake is computational. This means somewhere in the process they incorrectly added, subtracted, multiplied or divided.

Making one computational mistake in a multi-step problem means the rest of their work will be wrong and the final solution wrong.

As a classroom teacher, I always required students to show all their steps because if they used the correct procedure and showed me that they understood the concept, I was not too concerned about a small computational error.

Yes, that may have meant the “whole problem” was wrong, but to me, the final solution is not as important as understanding the concept and the process.

Still, we never want to encourage carelessness in computation.

Here are some ways to help students prevent computational errors:

• Slow down
  • Again, simply slowing down and working more carefully on a problem will cut down on the computational errors.
• Check the answer after solving
  • After working hard to complete tedious computations or multiple steps, kids are reluctant to go back and check their work. However, checking the solution for accuracy shows whether or not the work has been done correctly. If the final solution is wrong, students should go back through their work and check for computational errors.
• Use a calculator
  • If you teach older students who are working on long and difficult concepts, you may want to encourage them to use their calculator for computational parts. I realize this is entirely a matter of preference, but to me, it’s much more important that I can see students understand the concepts. I hate for them to get bogged down in tedious and long computations. This tends to lead to frustration and removes any joy or excitement about the math we’re studying.

Conceptual Errors:

Conceptual errors occur because kids have misunderstood the underlying concepts or have used incorrect logic. This is the most difficult type of error to identify at first glance. This is also the most difficult type of error for students to recognize, but it is the most important to catch and correct.

When students make conceptual errors, it’s possible that all the math computations are correct. If they’ve misunderstood a concept and thus used an incorrect method to solve, they can work out each step meticulously and correctly but still get the wrong answer.

For example, say your kids are given the following word problem:

Sally and her friends have a bag of candy with 24 pieces of candy. They decide to share the bag equally. If they each get 6 pieces, how many friends are there altogether?

If a student solves this by multiplying 6×24, it shows that they do not actually understand the problem or the concept of division, even if they work out 6×24 correctly.

Here’s another example:

When learning how to calculate surface area and volume of 3D shapes, students are often given a list of formulas without any explanation of the formulas. So when given the following problem,

Find the total volume of a rectangular prism with base side lengths of 6 inches and whose height is 8 inches.

Knowing the formula is V=Bxh, students will often solve this by simply multiplying 6×8. Even if they multiply correctly, this shows that they do not understand what volume is measuring, or that they have to find the area of the base.

Ways to prevent and correct conceptual errors:

Obviously preventing conceptual errors is not as easy or straightforward as careless or computational errors. And of course, all students will have varying degrees of understanding, and will struggle with different concepts.

But here are a few things you can do to try and encourage conceptual understanding and prevent future conceptual mistakes.

• Introduce concepts in hands-on, conceptual ways
  • Give your kids lots of time to explore and discover new math concepts in a way that helps them to see and understand the why. This is not always easy, but showing the why behind math properties or formulas will help students understand, form connections and retain.
  • For example, My Hands On Skittles Math bundle provides lots of hands-on visual practice for early math skills, and Algebra Essentials includes lessons to help kids make sense of challenging concepts.
• Teach a concept more than one way
  • There is always more than one way to solve a math problem. By teaching or exploring a concept in multiple ways and from multiple angles, you provide students a richer math environment and allow for deeper understanding. Plus, some students may find one method easier, while other students prefer a different method.
  • For example, My Introduction to Multiplication bundle includes a variety of ways to see and understand multiplication (as well as hands on practice)
• Have math talks
  • Provide your kids with open-ended questions to allow for discussion. This will reveal students’ understandings as well as misconceptions. These talks can also allow students to explain things in their own words which may provide a light bulb moment for another student.
  • Learn more about simple ways to have math talks with your kids
• Use math journals
  • Give kids a chance to write about math in a math journal. This will give them time to think about concepts, as well as explain things in their own words. By reading their explanations, you can gain insight into their understanding (or misconceptions).
  • Another math journal idea is this Notice & Wonder Journal. Great way to get kids thinking about math in an open ended way!

And if you’re a classroom teacher and you notice the same conceptual error from multiple students, stop and take time to go back and reteach. If most students have missed something somewhere, there’s no point in moving on.

Analyzing Errors:

In the early elementary years, it can be difficult to analyze errors, because so much of what they’re learning is computational. It can be easy then to dismiss mistakes as simply computational mistakes and move on.

Take some time to dig deeper, though. Talk through the steps and require kids to show their thinking when they solve. For young kids, this can be as simple as drawing a picture. As they get older, explanations will hopefully be more sophisticated, such as writing equations.

By middle or high school, students you should able to recognize and classify their mistakes themselves. Have them think through what types of mistakes they’re making so that they can in fact learn from them.

Want some helpful templates & classroom posters to explore these types of math errors & analyze mistakes together? Grab my new Error Analysis Pack!

This collection includes teaching tips, blank templates to help kids analyze and learn from their mistakes + a classroom poster set to provide a visual for kids.

Buy Error Analysis Here!

Did you find this helpful? Were there any new ideas you’re going to implement? Anything else you would add? Share in the comments!

Looking for more tips for teaching math in a way that makes sense? Check out the following articles:

• Using Literacy Strategies to Teach Math
• Teaching Math with Story Books
• 4 Reasons Teaching Math Vocabulary is Vital
• Math is a Foreign Language
• How to Raise Logical Thinkers and Why it Matters

The post 3 Types of Math Errors and How to Prevent Them appeared first on Math Geek Mama.

*Please Note: This post contains affiliate links which help support the work of this site. Read our full disclosure policy here.*

To assemble this set of foldable 3D shapes: 

I highly recommend printing the nets on stock paper rather than regular paper. I have tried it both ways, and regular paper is just too flimsy.

After printing, simply cut out the 3d shape nets on the solid lines.

If you’ve printed on white card stock as I have, take some time to get creative and color or decorate the shapes before assembling them! This could make a great math art project!

If your students are older, have them label the different parts of the shape (face, edge, base) before assembling to use as a reference throughout their study of shapes!

This will help them see and learn math vocabulary.

Then, carefully fold each tab so that it can be used to glue the shape together, and fold each side of the shape.

Finally, glue each side together. I suggest adding a few dabs of glue to each tab and then hold it in place for a few seconds before gluing the next tab. This will help make sure it stays together.

You can also use tape if that’s easier for you (or you don’t have glue).

Once all the shapes are assembled, you can use them however you like, depending on the age of your kids!

Learning ideas for foldable 3D shapes:

• Discuss math vocabulary such as polyhedron, face, edge, prism, etc.
• Compare the shapes by counting number of faces and edges or other characteristics
• Use them to go on a 3D shape hunt: find the shapes in real life
• Compare the different pyramids and then compare them to the great pyramids of Egypt (combining math and history!)
• Use the nets to learn about surface area and volume
• Use them along with the book, Sir Cumference and the Sword in the Cone to learn about Euler’s formula (see more free resources to use with the book here!)
• Or simply as a fun math art project!

This set of geometric nets is FREE to download and contains the following three dimensional shapes:

• Cube
• Rectangular Prism
• Triangular Prism
• Cylinder
• Triangle Based Pyramid
• Square Based Pyramid
• Pentagon Based Pyramid
• Cone

In addition, this set includes a foldable copy (with tabs) to allow students as young as preschool build their own models, as well as geometric nets without tabs to be used for any other purpose in the geometry classroom!

For instance, let students measure the nets to explore surface area with these FREE surface area lessons (surface area of prisms and cylinders and surface area of pyramids and cones)!

{Click HERE to go to my shop to get the foldable 3D shapes Printable Pack!}

Hope you find these helpful and FUN as you explore three dimensional shapes!

Looking for more 3D shapes fun? Try one of these resources:

• 3D shapes games printable pack
• Exploring 3D shapes with a 3D drawing pen
• 3D shapes and their nets worksheets

The post Foldable 3D Shapes {FREE Printable Pack!} appeared first on Math Geek Mama.

*If you want a fun resource for seeing math in nature, scroll to the bottom of this article for a FREE poster set!*

6 Benefits of Taking Math Outside:

1. The fresh air and sun is good for their health.

Being outside can increase the levels of serotonin and dopamine in the brain, helping your kids be happier and less stressed. In addition, getting out for a walk or hands on math activity can provide exercise and a chance to get up and move.

Read more: Improving Your Child’s Mental Health Through Easy Everyday Activities.

2. A change of scenery can be motivating.

Sometimes just a change from the normal, everyday can be exciting and fun for kids. A 2008 study of Kindergarteners found “a significant amount” showed enhanced enthusiasm about learning by taking it outside. In addition, I personally saw greater engagement and participation from high school seniors when we worked outside.

3. Kids can learn outdoor skills at the same time.

Incorporating math learning into outdoor skills can help kids learn math and life skills at the same time. Gardening or using a compass, for example, can be a means of exploring math in the real world.

4. Kids can look for patterns and shapes.

Our world is made up of mathematical structures, whether it is in nature or the buildings around us. Going outside gives kids a chance to see patterns (such as Fibonacci numbers or fractals) in nature, as well as all kinds of shapes that make up our world.

5. It can help them retain more.

By working on math in a context or within a particular experience, kids are more likely to remember what they learn and practice. Creating fun memories can help kids build a foundation on which to build later learning.

6. It’s an opportunity to see and use math in real life.

Making math relevant is an incredibly important component of math education. If kids don’t see how and why it is necessary, they will not be as motivated to learn and succeed. Going outside and exploring math problems in real life can help make math meaningful. Using measurement and estimation skills, for instance, is one way kids can apply what they’re learning to the real world.

Steve Humble, regional coordinator for NCETM, is a proponent of learning math outside of the classroom and states, “I like the idea of young people gaining ‘mathematical eyes.”

Being outside helps kids develop mathematical eyes, and see all the ways that math is around us.

Read More: The Value of Outdoor Learning: Evidence From Research in the UK and Elsewhere.

It’s also important to note that while my focus is on the benefits of taking math outside, many of these are really benefits of taking any kind of learning outside.

Photo Credit: Kazz.0 via Compfight cc {text added}

Fun Ideas for Taking Math Outside:

• Go on a shape scavenger hunt
• Have an even and odd number bean bag toss game
• Take out some cards and play a math card game
• Go on a “math walk”
• Play sidewalk chalk number line race
• Make a life size hundreds chart
• Measure nature
• Learn about circle measurements with trees
• Play with bubbles
• Go on a leaf hunt
• Do math in the snow

These are just a handful of ideas, but hopefully it gives you some places to start!

What would you add? What would you say are the benefits of taking math outside? What other fun ideas do you have?

The post 6 Little Known Benefits of Taking Math Outside appeared first on Math Geek Mama.