One of my favorite books is the New York Times Bestseller, The Grapes Of Math by Greg Tang. This hilarious and interactive tale invites students to think outside the box to tackle wacky math riddles. Each challenge encourages new ways to see quantities and count objects. It invites kids to think and ask, “How else can I find the total?” or “What is the most efficient way to count or add or multiply?” These are the kinds of problem solving challenges that will develop and deepen number sense in kids. So if you’re excited to dig in, grab a copy of the book and then extend the challenge with these additional problem solving pages!

*Please Note: Some of the links in this post are affiliate links and help support the work of this site. Feel free to read our full disclosure policy here.*

Problem Solving Challenges for Kids:

Although I designed these challenges to be used along with the book, The Grapes of Math, you could use them independently. The key is to encourage creative problem solving and challenge kids to find another way to see the images.

Each page presents a math problem that requires addition. Each could be solved simply by counting the objects one by one, but the point of each puzzle is to try and find a way to solve the problem quicker and easier.

Greg Tang’s picture book, The Grapes of Math, uses silly rhymes and engaging illustrations to help kids learn several helpful problem solving strategies, such as making ten to add more efficiently, looking for groups of numbers to skip count, subtracting to add, and more!

As Greg Tang explains in his introduction,

“The Grapes of Math teaches four important lessons in problem solving. The first is to be open minded. Children will learn to look beyond the obvious in search of smarter solutions. Second, they are encouraged to think strategically by finding convenient sums that make adding easier. Third, kids are taught to save time by using a variety of skills when solving problems, such as subtracting to add. Finally, children learn to organize information by identifying patterns and symmetries.”

This book is great for visual learners, or for students who like a challenge. Even after finding the right answer, I would encourage you to ask your child (or student) how they arrived at their answer (try to figure out how they saw the picture) and then ask them to figure out another way to solve it. This is a great way to have mathematical discussions and get kids used to explaining their thinking.

And if your kids love The Grapes Of Math as much as we do, they won’t want to stop once the book is finished! So I’ve created some problem solving challenges with addition questions similar to the ones in the book!

Want to learn more about engaging students through meaningful problem solving? Check out my professional development course, Problem Solved: Teaching Math through Problem Solving.

This free download includes 8 pages of unique challenges, as well as an answer key for each page. And although it does not include cute rhymes with helpful hints, hopefully your kids will have some good ideas and be ready to tackle these on their own after working through The Grapes Of Math!

And because these will be printouts that your kids can have (rather than a picture book), I hope you will encourage them to write on each page! It’s often helpful to circle groups of five or ten, or to circle the objects to subtract.

Just be sure they are using pencil, so when you ask them to solve another way, they can erase and start again!

I hope this proves to be a great source of FUN and engaging math learning, and gets your kids excited about exploring new problem solving strategies!

If you’re looking for a similar challenge for younger kids, I recommend starting with dot card visuals and asking “how many?”

And if your kids enjoy this book and the practice pages, be sure to check out some of Greg Tang’s other books:

Math For All Seasons: Mind-Stretching Math Riddles

Math-terpieces: The Art of Problem-Solving (I especially love this one, because I love art history!)

Math Potatoes: Mind-stretching Brain Food (a little more challenging than The Grapes of Math)

And if you want to see this kind of problem solving play out with a more challenging question, check out this video of 6 year old Autumn solving a finite series problem!

{Click HERE to go to my shop and download “The Grapes of Math” Problem Solving Pages!}

Enjoy!!

The post {FREE} Problem Solving Challenges based on “The Grapes of Math” appeared first on Math Geek Mama.

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

Lately, my kids have been obsessed with the idea of setting up their own lemonade stand. They are so excited to get out there and try to earn some extra money!

But in all their excitement, I try to help them understand the math side of things and help them think through things like expenses, revenue and profit.

I also told them I could act as the bank and give them a loan to get started-a.k.a I would buy the lemonade mix and cups.

I’m also tempted to purchase this cute lemonade stand tablecloth for them, but I haven’t yet convinced myself that it’s worth the expense, ha!

Since I think this is something most kids get excited about and may try at one point or another in their childhood (I and my friends certainly did!) I decided to create a set of word problems with this theme.

This free downloadable packet uses this main theme (setting up and running a lemonade stand) to look at a whole host of math problems.

Hopefully, by thinking about each question within the related context, students will have a better understanding of the math needed to answer the questions, as well as seeing many different ways we use and apply math in our daily lives.

–>Pssst! Do your kids need help making sense of and solving word problems? You might like this set of editable word problem solving templates! Use these with any grade level, for any type of word problem:

Included in this Word Problems Set:

There are three sets of questions in this download.

The first set of problems are two-step addition and subtraction problems (including 2-3 digits).

The second set includes money related problems, and the third set includes time and elapsed time problems.

The download also includes answer keys, for your convenience.

These problems are appropriate for grades 2-4, or even kids in 5th grade who struggle with word problems or multi-step problems.

{Click HERE to go to my shop and download the complete Lemonade Stand Word Problems Set!}

I hope your students enjoy thinking through these questions, and maybe even feel inspired enough to tackle their own entrepreneurial idea!

Want to make this even more fun? Why not include the book, Lemonade in Winter to your plans! It’s a fantastic and fun math read.

The post {FREE} Lemonade Stand Word Problems for Grades 2-4 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.

I love this post from Christopher at Talking Math with Your Kids. He is writing a completely new and different type of “shapes” book for kids (available soon). His post inspired me to come up with a version using numbers.

I’m sure this is not a new concept, but I had fun creating this and trying it out with my husband and kids.

The beauty of this critical thinking math challenge, is that there are so many possible right answers!

So I hope it encourages you and your kids to come back to them again and again to try and come up with a new solution and supporting reason.

And I hope it challenges any preconceived notions you or your students have about there always being exactly one right answer.

How to Use Which Number Doesn’t Belong?:

The concept is simple enough.

Each page has a set of four numbers.

The object is to determine which number doesn’t belong in the set and provide a true and valid reason for your answer.

What I love is that these are great for kids as young as kindergarten and as old as high school.

I created each set with at least 2 or 3 possible answers in mind, but when writing out the “possible solutions” page, I found even more as I contemplated the sets more deeply.

My challenge to you: find a solution for one of the sets that I didn’t include!

Included in the Which Number Doesn’t Belong? Set:

This download includes ten math challenge sets.

First, are ten full size pages that you can use for a large or small group activity. If you are a classroom teacher, you might turn these into projector slides or use a doc camera and post them at the front of the class.

You could use this as a fun math warm up as kids begin class. It’s also a great way to spark a math conversation (or debate ).

This download also includes ten half sheets which you can use as individual assignments. These include a space for kids to write out their solution and reasoning. Then there’s a second question which challenges kids to find another solution and explain their reasoning.

You could use this as an exit ticket or quiet activity for kids who have finished their assignments.

Please note: though there are two different versions (so you can use it different ways), there are only ten sets. The full page and half page versions are the same, just different formats.

Also included in this download is a “possible solutions” page for teachers and parents. I debated including this, because I wanted to leave it open-ended and encourage math talks.

But I also want to provide support for parents and teachers, so I hope this gives you a good starting point as you discuss with your kids.

Want to download this set for your home or classroom? Click the link below to get it FREE in my shop!

{Click HERE to go to my shop and get a copy of the “Which Number Doesn’t Belong?” math challenge for kids!}

Want more unique challenges for your kids? Try one of these!

• Mental Math Challenges
• System of equations puzzles
• Hands on logic puzzles (with pattern blocks)

And be sure to check out this post: How to Raise Logical Thinkers and Why it Matters

The post Which Number Doesn’t Belong? Math Challenge appeared first on Math Geek Mama.

Obviously, this is an extreme example on a t.v. sitcom, but I think it helps us see the point that learning how to think logically and apply reasoning to real life situations is essential. But how to teach logical reasoning may seem like a daunting task.

For some of us, this may come more naturally than for others. Regardless, it is important that we are diligent and intentional about cultivating logical reasoning skills in our kids.

*Please Note: This post was sponsored by Grids for Kids Logic Books and contains affiliate links, but all thoughts and opinions are my own. Read our full disclosure policy here.*

Why Teach Kids Logical Reasoning:

1. It will provide them with critical thinking skills

When kids grow up and face real world problems, they will be better equipped to solve them if they have strong critical thinking and problem solving skills. They will be ready to think outside the box.

We should be teaching our kids to think for themselves, and not always accept everything they hear at face value.

Rather than facing a task that’s hard by immediately asking for help or assuming someone else will do it for them, they should be ready and prepared to tackle the problem themselves.

Related: The Importance of Logic and Critical Thinking

2. It’s good exercise for the brain

In addition to providing kids the necessary tools to function in life (and not drive their car into a lake), learning to apply logical reasoning through logic puzzles and brain teasers can stimulate the brain, as well as aid in memory and concentration.

Working through a challenging brain teaser or logic puzzle requires patience and concentration as the logic is teased out and the final solution verified.

Practice with these types of puzzles helps the brain make connections and get used to focused concentration on a single problem.

3. It will help in their math studies

Logic puzzles and brain teasers may seem like simply a fun way to pass the time, but I believe they will help your child be a more successful mathematician.

Math is logical. There’s no denying it. And yes, some kids are brilliant at memorizing facts in the early years. And they may do well in math for a time.

But at some point, they will no longer be able to simply regurgitate facts. They will have to use and apply logic to work out math problems successfully.

In a high school geometry class, there is a large emphasis on reasoning and proof. When writing a proof for any given geometry theorem, however, there is no “one size fits all” solution or algorithm. You have to understand the structure of proofs, and then you have to write out a solid mathematical argument for why it is in fact true.

And you simply can’t write a valid mathematical proof that is devoid of logical reasoning.

In Algebra, kids will be given countless real world examples of math and word problems which will all require logic to solve.

So if you’re feeling overwhelmed right now, don’t worry! I have some helpful and simple tips to share so that you can raise logical thinkers and problem solvers!

How to Teach Logical Reasoning:

1. Ask “Why?” frequently

Try to get your kids used to hearing the question, “Why?”

For instance, ask things like, “Why is the answer 15?” or “Why did you multiply in step 2?” Answering questions like this will help kids think through the logic they used to solve a problem or come to a certain conclusion.

They should be so used to having to justify their methods or their answers that when they go to solve a new problem, they think through the why on their own.

2. Play board games that encourage strategy and logical thinking

There are tons of fun games out there (beyond Sudoku or crosswords) that will help kids develop their logical reasoning skills.

Try Apples to Apples, Blokus, or Quirkle, just to name a few.

Or play with a Rubik’s Cube.

3. Use a structured approach

Another resource that my kids and I have loved is this set of Grids for Kids logic puzzle books. This set of books is specifically designed to teach kids logical reasoning, and progresses in a way that builds on what kids have already learned.

My daughter has been going through the first book now that we’re done with school for the summer, and she has really enjoyed the challenge.

After completing the first two puzzles, she began to notice patterns in the problems and showed a greater confidence in her own ability to solve the next puzzle on her own.

And although I helped significantly with the first puzzle, she is determined to try to solve the rest of the puzzles on her own.

If you’re not familiar with this type of logic puzzle, you may find them challenging at first, but the books include 30 puzzles and worked examples with very detailed explanations of how the grids are completed and then logically solved.

I will note that while they suggest starting at age 8, my daughter is 7 and has been able to work through these puzzles with a little help from me.

One of the thing I did to help her was write out sentences with fill in the blanks to make sure she knew what she was trying to figure out once she had filled in the grid.

For instance, in Puzzle 1C, the goal is to determine who wears what type of shoe and what color shirt. So I would write out sentences such as, “Fred wears _____ and a _____ shirt.”

She then filled in the sentences on her own and we would check it together.

The creators of Grids for Kids shared the following,

“Our daughter loves puzzles and games of all types.  We wanted to use this love of puzzles to develop her reasoning ability in a non-formal way.  Obviously, her concentration is engaged when working the puzzles.  But it has also helped her ability to pay attention to the little verbal “nuances” that can change a sentence’s meaning, or make it more exact.”

I think these puzzles would be great for kids who love brain teasers and puzzles, or gifted kids who are looking for a challenge, but I will also add that this is a fantastic tool for anyone wanting to strengthen logical reasoning skills in their kids or themselves.

The Grids for Kids books are written by fellow math geeks who are much smarter than I am. And they have put their knowledge of math and logic to great use by providing such a valuable resource for parents, teachers and homeschooling families! I highly encourage you to check them out!

Want more fun grid and sudoku puzzles for your kids? Check out these sets:

Buy Pattern Block Logic Puzzles | Buy A Year of Logic Puzzles

What do you think? What are some of your favorite ways to develop logical reasoning skills in your kids? Share in the comments!

The post How to Raise Logical Thinkers and Why it Matters appeared first on Math Geek Mama.

One of the most important concepts introduced in pre-algebra (or algebra) is integer operations. I can distinctly remember learning “the rules” and fun little tricks to remember them. But I also remember wondering why in the world subtracting a negative means you add! So when I saw this method to introduce adding and subtracting integers, I knew I had to try it.

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

Understanding integers and especially how to correctly add, subtract, multiply and divide integers is a skill that is essential to higher level math. Unfortunately, in my experience, adding and subtracting integers is something many students struggle with all the way through high school.

When I was teaching juniors and seniors, even if they used their calculator for computations, they would still struggle and get wrong answers because they didn’t understand the concepts (or how to correctly type them into the calculator).

Whether students never actually understand the concept in the first place, or they simply forget or confuse the “rules,” by the time they are in high school level classes, they are relying on their calculator.

Now you might be thinking, “Who cares? Just let them use a calculator!” Well, the problem with that is that the calculator is not as smart as we are! If you input something incorrectly or don’t use the correct parentheses, the calculator will get it wrong (especially when multiplying or dividing).

Therefore, I think it’s incredibly important that students master these skills early on in middle school, without learning “tricks” or “rules” so that they will be more successful down the road.

And that is why I have put together this lesson on adding and subtracting integers and exploring what happens when you combine positive and negative numbers!

Adding and Subtracting Integers with Credit/Debit Tables:

The basis of this lesson is on representing numbers using a +1, -1 table. In other words, each +1, -1 pair will equal zero, and then the value of the table will be the ones that remain.

This will likely be a new way of thinking about and representing numbers, so spend time teaching and exploring the tables first. Step 1 of the lesson gives students a chance to practice “reading” them, but if it seems like there is still confusion, stop and work out more examples and have kids make up their own examples before moving on.

Step 3 begins to guide kids through what happens when you add positive or negative ones to the table.

This is the real “meat” of the lesson. The goal is to help them see that adding negatives is the same as subtracting, and subtracting negatives is the same as adding (because your +1 column will now be bigger).

I would also combine each of these examples with a number line to really help students see how the number changes as you add or subtract negative and positive numbers.

This lesson includes teaching tips, a student hand-out and complete answer key.

Hopefully after looking at integers this way, students will have a solid understanding and tools to use to solve problems, even if they forget the “rules.”

If you enjoy this lesson, become a Math Geek Mama+ member and gain access to the entire library of engaging math lessons like this one, hundreds of math games and low-prep practice worksheets for grades 5-8!

Learn more about Math Geek Mama+ right HERE.

I hope you and your students find this helpful!

{Click HERE to go to my shop and get the Adding and Subtracting Integers lesson!}

Add if you need more practice, grab this free integer operations game!

And if you like this lesson, try one of my other Algebra lessons:

• Introducing Absolute Value
• Exploring Exponent Properties
• Understanding the Distributive Property

The post Adding and Subtracting Integers {FREE Lesson!} appeared first on Math Geek Mama.

Materials Needed for the Cut and Paste Logic Puzzles: 

• Cut and Paste Puzzles (available free in my shop)
• Scissors
• Glue

How to Use the Cut and Paste Logic Puzzles: 

First have your kids cut out the shape cards at the bottom of the puzzle. Depending on the age of your kids, they may need some help with this.

You can also take some time to review the shapes and have a discussion about where they see these shapes around them. For instance, ask them to point out a square in the room or name something that is a circle.

Then, explain that each row and each column must have one of each shape, without repeating.

While it may be tempting to also point out the row or column that already has two of the shapes and lead them to figure out which one must be missing, step back and let them try first!

The point of these puzzles is to help kids learn to think and problem solve and use logic. So give them the space to think through it on their own.

If they complete the puzzle and have repeating shapes in a row, simply show them WHY that’s not right (“I see there are two circles in this row. You need to have one of each shape. How can you fix it?”) rather than explaining how to solve it.

I guarantee they will catch on quickly and be able to solve the first and the rest of the puzzles independently.

Once they have correctly solved the puzzle, allow them to glue the pieces down in the correct squares. Try to be careful that they solve the puzzle first, before glueing, so that they aren’t trying to pull up and move around pieces that have already been glued.

And once they’ve got the hang of these puzzles, try these pattern block logic puzzles! These fun, hands on challenges will keep kids busy and get their brains thinking!

{Click HERE to go to my shop and grab the Cut and Paste Logic Puzzles!}

LOVE this idea? Grab my ebook packed with fun, hands on puzzles for kids ages 4-9!

Want more fun puzzles for kids? Try one of these:

• Pattern block logic puzzles
• Find the cost logic puzzles
• Mental math challenges
• Spring themed logic puzzles
• Addition and subtraction equation search (like a word search)

The post Cut and Paste Logic Puzzles for Preschoolers appeared first on Math Geek Mama.

Ahhh, summer.

A time for vacations and catching fireflies, trips to the pool and firing up the grill. While there are probably endless images and activities that come to mind when you think of summer, I’m willing to bet that doing math just isn’t one of them.

But the truth is, for most students, summer is a time when all the important math skills they worked so hard to learn throughout the year are completely lost. So here are some SUPER simple summer math activities that will keep your kids from being bored (and keep them learning!).

*Please note: Some of the links in this post are affiliate links and help support the work of this site. Thanks for understanding! Feel free to read our full disclosure here.*

Fun and Simple Summer Math Activities:

Read through the different types of ideas below to find some summer math activities that are right for your kids. There are ideas for games and puzzles that won’t even feel like learning, along with outdoor games, hands on activities, simple printable pages and more!

Play with Math Puzzles:

• Work on Sudoku puzzles. Kids too young for them? Check out Kidoku Puzzles | Krazy Dad
• Try Magic Squares or a Magic Triangle | What Do We Do All Day
• Play with these Pattern Block Logic Puzzles
• Challenge each other to Mental Math Races
• Create Jumping Mazes (inside or outside!)
• Put together these Fraction Puzzles, Telling Time Puzzles or Money Puzzles

Take Math Outside:

• Have an even and odd number beanbag toss
• Practice important skills with Water Balloon Math | No Time for Flash Cards
• Make a hula hoop clock to review time related problems | Creekside Learning
• Build 3D shapes with sticks | Creative Star Learning
• Play Marshmallow Shoot and Measure | No Time for Flash Cards
• Have a shapes scavenger hunt (Want more of a challenge? Look for 3D shapes instead!)
• Play Sidewalk Chalk Number Line Race
• Practice measurement in your flower bed or garden | The Educator’s Spin On It
• Heading to the beach? Use sea shells for counting, sorting or a fun memory game | No Time for Flash Cards
• Try a fun twist on a classic: Skip Counting Hopscotch
• Play Puddle Jump, a simple, easily adaptable game

Related: 6 Little Known Benefits of Taking Math Outside

Learn Math with LEGO:

• Work on place value with LEGO | The Science Kiddo
• Explore addition & subtraction with LEGO
• Explore multiplication & division with LEGO
• Build a rocket powered Lego car | Frugal Fun 4 Boys
• Play LEGO Baseball (and discuss statistics!) | Teach Mama
• Practice double digit addition and subtraction | Real Life at Home
• Create LEGO Duplo Puzzles for your kids to put together
• Prove the Pythagorean Theorem with LEGO bricks

**Looking for more LEGO math ideas? Check out 30+ easy ways to learn with LEGO Math!

Play Math Games:

• Incorporate math into family game night with  Sum Swamp , Hi Ho Cherry-O, Monopoly Junior, or if you have older ones, here’s another list of games | Planet Smarty Pants
• Play with a Calculator (hint: NOT to do math calculations) or try these fun calculator riddles | And Next Comes L
• Play Strike it Out for adding and subtracting fun | Teach Mama
• Play Math Twister to review any and all math facts
• Use this simple game to review any math facts (all you need is a piece of paper!)
• Let the kids “play store” with their favorite books or toys to practice adding money and making change (Here’s a great Play Money Set)
• Use a Hundred’s Chart to play Euclid’s Game or Hundred Chart Nim | Let’s Play Math
• Play this “Jack and the Beanstalk” multiplication game | Relentlessly Fun, Deceptively Educational
• Play Multiplication Dash, another printable multiplication game
• Play a math card game
• Make a DIY Mancala Game and play together

Read Math Story Books:

• Learn with the “Sir Cumference” math story books
• Read Bedtime Math (or Bedtime Math 2) together each day and discuss (it doesn’t have to be a bedtime! We are currently reading a little each day at lunch! Read my full review here.)
• Read and play with Ten Apples Up On Top
• Learn about money with Pigs will Be Pigs
• See math in real life with Math Curse
• Explore fractions and patterns with The Lion’s Share
• Learn about triangles with The Greedy Triangle
• Practice problem solving with The Grapes of Math
• Tell time with The Grouchy Ladybug

Looking for math books by topic? Check out the math read aloud lists below:

• Math books about counting
• Math books to explore place value and large numbers
• Math books to learn about addition & subtraction
• Math books to understand multiplication & division
• Math picture books to make sense of fractions
• Money math picture books
• Picture books about time and telling time

Math Around the House Ideas:

• Create a STEAM Bored Jar for activities throughout the summer |  Left Brain Craft Brain
• Explore summer STEM Ideas specifically for middle school
• Practice counting with watermelon seeds (or other fruits)
• Have a weekly estimation jar challenge using small toys, balls or household items (encourage your kids to make educated guesses and work on estimating techniques)
• Get in the kitchen for fun with math and cooking
• Explore math with Q-Tips
• Play with math and Skittles in PreK-1 or math with Skittles in 3-5

Printable Summer Math Games & Practice:

Looking for some summer-themed worksheets? The activities below are a fun way to easily work on targeted math skills as kids work their way through the maze, solve the riddles or cut and paste numbers. The best part? Just print and play!

• Ice Cream Counting Mats: Play Dough Math Play | Numbers 1-20
• Summer Counting Cut & Paste | Count to 20
• Summer Math Mazes for Grades 3-4 | Addition, Subtraction, Multiplication & Division
• Camping themed Ratio & Proportion Challenges
• Summer Algebra: Solve Equations Riddle Pages

Reviewing important math skills doesn’t have to be boring, time-consuming or expensive! Use items you already have on hand, grab some books at the library or make up fun games to play outside to encourage young learners to keep thinking and problem solving all summer long!

Got any other FUN and simple summer math ideas to prevent learning loss and still have a fantastic summer?? Share in the comments!

The post Engaging Summer Math: Easy, Hands On & FUN Ideas appeared first on Math Geek Mama.

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

It’s incredibly important that math concepts not be taught in isolation. Mathematics is a rich, interconnected subject, and we should take every opportunity to help kids see and form those connections.

Multiplication and division are what are called inverse operations. This means they are opposite each other and “undo” one another.

For instance, if take the number 3 and multiply it by 5, you get 15. To “undo” that and get back to your original value, you would simply divide by 5.

Related: Solving Problems by Working Backwards (using inverse operations).

Multiplication and Division Fact Families:

A fact family is a set of three numbers that can be related to each other using multiplication and division. (Or as in this post, with addition and subtraction).

For example, the fact family above includes the numbers 3, 5, and 15. This creates 4 different equations:

• 3 x 5 = 15
• 5 x 3 = 15
• 15 / 3 = 5
• 15 / 5 = 3

This Roll and Write multiplication and division game gives kids the opportunity to write out the fact families.

Please note, though, that when you are dealing with doubles, there will only be two equations, not four (i.e. 5 x 5 = 25 and 25 / 5 = 5). 

By creating and comparing fact families with multiplication and division, kids learn (or reinforce) several important math concepts:

1. The commutative property of multiplication
2. That multiplication and division are inverse operations
3. How to correctly write equations involving multiplication and division
4. That knowing multiplication facts means they also know division facts

Plus, they’re able to connect a new math concept (division) with a known math concept (multiplication).

How to use the Number Sentence Roll and Write Activity:

As I’ve said, this activity is SUPER simple. All you need is the student handout (free in my shop) and a set of dice (or just one die, rolled twice)!

Personally, whenever I create or use an activity involving dice, I like to get out our giant foam dice. My kids just love these, and it seems to make it even more fun (but regular dice will totally do the trick, too!)

Once your kids are ready, they start by rolling the dice and recording the numbers on the answer sheet.

They then use those two values to write two multiplication problems (thus demonstrating the commutative property).

After finding the solution to those equations, they can then start with the solution to write two division equations.

They then complete the chart by rolling to get two new values.

And that’s it! Simple, right? And yet, so many important math concepts are being explored and connections made!

UPDATE: This download has been updated to include a page that focuses only on multiplication. Students roll two numbers and write a multiplication sentence, then rewrite it using the commutative property.

If your students are not quite ready to work on the complete fact family, hopefully this will provide a helpful bridge to get there!

I hope you’re able to use this multiplication and division game with your child or in your classroom. It will reinforce known facts or start to form connections between the math they’re learning.

And most of all, have fun forming multiplication and division fact families!

{Click HERE to go to my shop and grab the Roll and Write Multiplication and Division Game!}

Looking for more multiplication and division ideas? Try one of these!

• Printable Multiplication Games
• Summer Math Camp: All About Multiplication
• Learning Multiplication with Arrays

Looking for a fun and hands on way to teach multiplication to your kids? This huge lesson bundle covers 5 different representations of multiplication, as well as the commutative property, printable games, word problems and more!

{Click HERE to see the Introduction to Multiplication Lesson Bundle!}

The post Number Sentence Roll and Write: Multiplication and Division appeared first on Math Geek Mama.

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To Use this Problem of the Day Calendar:

This calendar is set up like a regular March calendar, but does not show the date on each day. Instead, there is a math problem for each day in March.

The secret? The solution to the math problem gives that day’s date.

As I’ve mentioned before, this is a helpful way for kids to self check, because if they know what the answer is supposed to be, but they get something else, they know to go back and try again.

Be sure to ask questions such as, “How did you get that solution?” or “Can you prove that the answer is 5?” to get them talking and showing their mathematical thinking (and to make sure they actually did the math, and didn’t just write the date down )

Included in this download:

This month I have created two different levels of calendars, so if you have older kids they can participate as well!

The first calendar is appropriate for grades K-2 and includes problems involving:

• Place value
• Addition and subtraction within 20
• Word problems (addition and subtraction)
• Sequences (counting on, counting backwards and skip counting)

The second calendar is appropriate for grades 3-5 and includes problems involving:

• Place value
• Addition and subtraction with 2 and 3-digit numbers
• Multiplication and division
• Word problems (addition, subtraction, multiplication and division)

Both calendars are black and white for easy printing, and each calendar is labeled with the age range as well, so you can know which is which.

I hope you enjoy using this March math problem of the day calendar!

It can be somewhat challenging to find age appropriate problems that have solutions to fit into the calendar and cover a variety of problems (so that it’s not the same thing everyday). But as long as readers are enjoying and using them, I am happy to continue to make them!

Have fun playing with math this March!

{Click HERE to go to my shop to get a copy of the March Math Problem of the Day Calendar!}

Looking for more Spring themed fun? Try one of these!

• Spring themed logic puzzles
• Time for Spring: Telling Time Practice
• Easter Peeps Game: Integer Operations

The post March Math Problem of the Day Calendar appeared first on Math Geek Mama.