A new puzzle to consider

Recently, a friend introduced me to this game/puzzle, and I wanted to be sure to share it with you.  It might be a great thing to use your PTO money or ask a generous parent to pick up for the class.

The only problem I really have with this game is its name: Genius Star.  I hate for that to cause students to believe they aren't capable of solving it, or vice-versa, that if they are able to solve it, it makes them a genius! 

This puzzle explores spatial relationships which for so many of our students can be a challenge.  It also offers students the opportunity to distinguish pieces they should prioritize as well as a trial in perseverance!

Here's how it works:

Roll the die that come with the game:

Lay the little white triangles onto the corresponding triangles on the board:

Now, I usually solve these on my own, and I don't recommend that it becomes a racing game, but students then take the 11 game pieces and place them on the board to cover in the star.

Students can compare their solutions to see what they did the same or different.

Students can also reflect on what made the puzzle challenging or easy. 

The box comes with two black trays to solve the puzzle on, but you could maybe get more than one game so that more students could work to solve. I find it quite fun, and it highlights the spatial skills of math.  The company makes other similar games that will show up when you follow the above link to this game.

Students can solve the puzzle in pairs and discuss their findings, they can investigate the dice and the regions of the board that each one covers, they could create their own puzzle numbers that they think are unsolvable and ask classmates to prove them wrong, they could create fractional questions about the puzzle or its pieces, or you could use two solutions for the same numbers as a same/different discussion. It seems to me like there are a lot of ways that this little puzzle could be used!

Let me know in the comments if you have found or find other ways to use this puzzle in the classroom!

March is Full of Palindromes this Year!

 As we approach the end of March, we come close to multiple school days which are palindromes. From 3-20-23 to 3-29-23, our dates will be palindromes, and they may offer opportunities for you and your students to explore palindromes!

Students of all ages can look more closely at palindromes! I am going to focus on explorations with numbers, but your students might enjoy finding words that are palindromes, too. Here are a few books you might share with your students:

Some of your students may get caught up in noticing individual words that are palindromes, but some may enjoy the word play involved in sayings and phrases that are palindromes.  At either level, it is word work that many students find FUN!

For math explorations, you might not explain to your young students what a palindrome is, but let them discover!  

• Using your pattern blocks as a visual, you can give students numbers to "create" and allow them to notice what makes these numbers special.  For example:

If you display the pattern blocks to represent different digits, then you can dictate numbers and ask students to create them.  Can they identify the pattern that makes palindromes special?  Can they see with the March dates how they are palindromes?

• Ask your students to find all of the palindromes between 0 and 100.  What do they notice about two-digit palindromes? Is there a pattern in 3 digit palindromes?

• Will there be other palindromes this year?  How about next year--What palindromes will there be?  Is there ever a year without a palindrome date?  What can your students find?

• Finding palindromic numbers Math For Love has a great lesson exploration opportunity where students search for different levels of palindromes. It offers a way for students to add, look for patterns, and have fun with numbers--all in one activity!

I hope you and your students find some time to explore the fascinating patterns and elements of palindromes in our words and numbers!  You might want to consider ending with this Weird Al video, Bob, which is made entirely of palindromes.

Looking at Data

While the post title might lead you to believe that this post is about looking at student data, that is not the case in this situation.  Let's look at some resources for students looking at data!

Last fall, I met with some representatives of a major company in my community to discuss math education in our schools.  The number one take-away:  We want workers who know the answer to the question, "What does the data tell you?"  

It is common for teachers to present math pictures or problems to students and ask them "What do you notice? What do you wonder?"  But this post focuses on true data and how we can get students to look at it more thoughtfully, with the ultimate goal being that they can use the information to be better informed about the world around them.

Jo Boaler and youcubed have come up with data talk images!  Here is a link to their page of images (which I am sure will grow...)  Displaying these data images to students not only is great practice with graphs and infographics, but it also allows them to be better readers and understanders of data.  While these might make a great start to a math lesson, they can also be wonderfully embedded into content areas such as social studies and science--all with the simple questions, "What do you notice?"  "What do you wonder?"

Another resource that I often lead teachers to is numberless graphs.  Much like numberless word problems, numberless graphs force students to think and make relationships about the things they know from the graph while still missing key information.  Also much like a numberless word problem, the data is slowly revealed to them to help them make sense of it all in a thoughtful way.

No matter the grade you teach, what are you doing to engage your students in reading and understanding data?  Consider trying some of the links above, and watch the lightbulbs go off!

Cutting the holiday pie

A good opportunity for exploration and problem-solving for your students.

With one straight cut, you can cut a pie into two pieces. Cutting it again and having the second cut cross the first cut gives you four pieces. With three cuts, you might get up to seven pieces.  What is the maximum number of pieces you can get with 6 straight cuts?

Your cuts do not need to produce equal pieces.  Once students identify the solution, can they keep going with more cuts?  Is there a pattern that begins to emerge?

Photo by Alex Loup on Unsplash

What Does the Data Tell Us?

In a recent conversation with some representatives from a major nationwide business company, we were discussing the needs in elementary math education to help lead students to be productive workers in tomorrow's business world.

The big question they said that students need to learn to answer is, "What does the data tell us?"  We also discussed the importance of probability and statistics,  but in the end, they said that they are looking for workers who can answer this question.

What would this look like in an elementary classroom?   I think it just reframes our questioning.  In many of our activities, we already expose students to real-world information.  We just need to be sure to be more intentional in our questioning in order to get them to look at data.

For example, look at this picture.  I took it thinking that it would be a good one for students to determine what was the best deal. What does it tell us?  What are some possible reasons a person would be willing to pay more for 3 Peep trees when they can get 9 for such a better deal?  

Noticing and wondering is a classroom routine that really benefits our students.  When they notice and wonder, you can ask them what the picture tells them.  Make them infer from the data that they have.  Numberless graphs are a good method of providing data that the students have to make sense of.  Here is a good example of a 2nd grade lesson regarding them.  You can find lots of examples and ideas for using them by reading some of the posts listed here.

What do you notice about this data?  What do you wonder?

We want our students to be able to compute and do basic math, but not at the expense of good math thinking and discussion.  These are the skills that will carry them into the future--not only in their career, but also in their roles as consumers and citizens.

How can you incorporate statistics and probability into your classroom (whether it is a K classroom or a 5th classroom) by framing your questions and your students' thinking around the question, "What does the data tell us?"

Using Puzzles to Create Persevering Problem Solvers

Helping our students to grow through productive struggle is often a challenge for us.  One way to consider as you work to build your students' problem solving skills is through the use of puzzles.  Here are some ideas for you to consider:

Yes--it can be as simple as having a jigsaw puzzle in the back of your classroom.  The visual acuity needed to solve jigsaw puzzles is important for students to build, and who doesn't love to finish a jigsaw puzzle?  Oftentimes, students do not have this opportunity at home, so having one set up in your classroom could help them to develop a new skill or hobby.

Besides jigsaw puzzles, tangram puzzles and pattern block puzzles also help students to build visual and geometric skills.  Allowing students time to explore with tangrams and pattern blocks is important, too, and it allows them to find the creativity in math as well as in themselves.  You can find other resources to help with tangrams in this post as well.

Kenken puzzles are an awesome tool to help build logic, fact fluency and number sense in all students.  The website also has an education portion, and you can sign up to have new sets of these puzzles sent to you weekly.  These puzzles are one of my favorites, but you do need to take a little time being sure your students understand how to do them and reminding them to explain how they know where numbers go in the puzzle.  Too often, students will guess where numbers go.  This method will work for a short time, but as the puzzles become more difficult, guessing will not lead to success.   While Kenkens have some similarities to Sudoku, I think they are better in the classroom because of the decomposition of numbers that is involved.  Many students are familiar with Sudokus, and they are a great type of logic puzzle that can be easily found. More information about Kenkens can be found here.

The website Math Pickle also has a large puzzle bank for you to choose from.  This site offers students the opportunity to play with their work in a way that allows them to better develop math concepts.

These puzzles from the Julia Robinson Mathematics Festival also allow students an opportunity to persevere through problem solving in  a fun way.  Although developed for a building-wide math night, many of the puzzles could be used in the classroom.

Let students decide how they want to do their puzzles.  Sometimes students prefer to solve them alone.  Others need to talk it over and think it through with a classmate.  Neither way is wrong.  Let students build their puzzle-solving skills in the way that feels best to them!

Math is fun.  It is puzzles.  It is visual. It is cooperative.  Sometimes, we get so caught up in teaching a curriculum or a standard, that we forget these important pieces of math.  There are so many good puzzles and problems out there for students; this is not even the tip off of the iceberg.  In what ways can you work to incorporate some of these ideas/resources into your classroom.  How can you help your students to not only become more persevering, but to ENJOY doing math?  

Countdown to the Holidays!

You know how I love nrich.maths.org for rich problems to solve.  Well--today I saw that they have an advent calendar for elementary students.  Each day has a rich task that accompanies it.  The problems are not holiday based; only the design of the calendar is.

You might just refer to it as a holiday countdown calendar, but no matter what you call it, it should lead to some good student thinking!

https://nrich.maths.org/14060

3 Act Tasks: Have you tried them yet?

3 Act Tasks offer our students such an engaging opportunity to make sense of math! However, as teachers, sometimes we are afraid to try something new not knowing where it might take us and scared that something bad might happen.  I just heard an analogy recently about this being like being at the top of a rollercoaster:









via ytCropper
And, while it might have twists and turns and dropoffs, not to mention bugs in the face, it also brings an excitement and thrill that we rarely find doing a traditional math lesson. We need to think about putting ourselves in that precarious position at the top of the rollercoaster; it's what we ask our students to do on a regular basis so that they can grow.  We should try it, too!

3 Act Tasks are real-world problem-solving scenarios which require students to make sense of what to do.  During Act 1, they use the reading skills of visualizing, predicting, and inferring in a math context.  They figure out what they need to know to solve the problem. In Act 2, students work to solve the math question in a way that makes sense to them. They discuss their thinking with a friend and compare their answer to their estimate.  Act 3 is exciting because that is when they find out if they were on the right track!  

While they are working during Act 2, you are monitoring (and asking questions that help them understand--not helping too much).  You are monitoring to see the methods that students used in order to solve the problem.  During Act 3, it is your job to have students share ways that they solved the problem.  These should be sequenced so that you can show connections between different methods. Be clear on what your math target for the lesson was and be sure that your models and discussion help that math target to be evident to everyone.  You synthesize the learning at the end of the lesson.

3 Acts are very visual and often use videos to help students better understand the situation. They follow more of the format of "you do, we do, I do" rather than the traditional layout of "I do, we do, you do."

Typically, a 3 Act Task in K-2  about 20-30 minutes.  In 3-5, a task usually takes about 4o minutes.  As students get stronger and more comfortable, the time needed for a 3 Act might decrease.

I am happy to come and model a 3 Act Task for you and your class, but I know that many of you can do them without my support.  You just need to put yourself on the rollercoaster!

At the top of this blog, you will find a tab labeled 3 Act Tasks.  This will take you to a large number of standards-aligned tasks that I have organized using SMART Notebook (and sometimes Google slides).  They are by a variety of mathematicians; I just put all of the pieces together into one format.  You can also find more great tasks by clicking here or here or even by Googling 3 Act Tasks.

As always, share with me your questions, struggles, or successes and let me know how I can help!

Would You Rather? -- Holiday Edition

If you are looking for some problem solving to get your students thinking and proving themselves while mixing in some holiday cheer, maybe these Would You Rather problems will work for you!

Would You Rathers are something that students are very familiar with, and these just include a mathematical twist.  Students can choose whichever option they want, but they need to have a mathematical explanation of why that is what they chose or didn't choose.  They can be used with students of all ages and offer great opportunities for collaboration.

If you like these, you can find more like them at this site, but I am betting you can come up with some good ones of your own!

Holiday Would You Rather 1

Holiday Would You Rather 2

Holiday Would You Rather 3

Holiday Would You Rather 4

Holiday Would You Rather 5

A Stepping Stone to a More Student-Driven Workshop

If you are still looking for ways to make your math workshop more about collaboration and problem-solving rather than about independent work and computation, a Week of Inspirational Math by Jo Boaler/Youcubed might just be the ticket!  If you have done any of these lessons before, you know how awesome they can be!  Well--she has recently posted her WIM #4!  That's right--4 weeks of math explorations and engaging lessons that you can use to build your mathematicians.

These engaging lessons are organized by grade level strands and are grouped into a week's worth of lessons.  They are great to use a week at a time, but you certainly could use them independently if you needed to.  They embody the paradigm shift in math education with a focus on growth mindset, visual math, patterns, and collaboration.

Besides that, each lesson will really engage your students for at least math period.  (Oftentimes, students keep working on the problem after class...) Each lesson begins with a video that you can show if you wish.  It helps to build the growth mindset in your students and presents them with mathematical thinking that helps them to see math is all around them.  After the video, there is a lesson (with full lesson-plan) that you can have students work on in small groups and share out with the class.  You can learn so much about your students as you circulate the room listening to their thinking, and they will learn so much about themselves as mathematicians!

With the craziness of the holidays, you might find a few days where some WIM activities are just the ticket, and they might cause you to begin rethinking your workshop!  They might be a good way to spend your math time during those days right before holiday break, but they might also be an awesome way to set the tone for 2019!

I have blogged about WIM before, but I can't tell you enough how much they can invigorate and change your classroom, your student's thinking, and your own thinking!  Time well spent!

Building Collaborative Thinkers

Are you giving your students enough time to work with each other to solve problems?  This is an area of growth for many of us.  Consider the following problem.  How could you build it into your math workshop?  In what ways would you anticipate that your students would be able to prove their answer?

Thanksgiving in the US has been declared to be the fourth Thursday in November.  This year, Thanksgiving is the earliest date it can possibly be.  What is the latest date Thanksgiving can possibly be? Be prepared to prove your answer.

I'd love to hear your results!

The Last Number--an exploration

Just found this problem recently, and thought about what a great exploration it would be--for nearly any age!

Consider the string 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Cross out any two numbers in this list and add the difference to the end of the list. This new number is now part of the list. Continue the process of crossing out two number on the list and adding the difference until there remains only one number. What can you say about the last number? Explore. [from Richard Hoshino]

This problem offers a rich exploration of number while practicing basic subtraction facts. (Making it great for 2nd grade!).  

Once your students have a conjecture about the final number, can they try that conjecture out on a different string of numbers?  What happens when your string goes from 1-15?  How about a string from 3-12?  Can they figure out what the pattern is and why the difference ends up like it does?  Even if they can't, they should have some rich time practicing subtraction, working together, and looking for patterns!

Can you figure out what is happening?  If you are like me, you might spend a lot of your free time working on this problem to see if you can make sense of it!

Does it look right? Does it sound right? Does it make sense?

These words were always such a big part of my instruction of reading workshop.  Students used hand signals to help them remember the three questions as they reviewed what they had just read.  Many times, they realized the word they had just read did not sound right or make sense in the context they had just read.  So---they worked to figure out what the new word was that they were struggling to read.

Do we teach our students to do this same kind of thinking when solving a math problem?  In my experience, it is a less common practice.  Sometimes, a teacher will ask the students if the answer makes sense, but really, shouldn't we be teaching our students to ask themselves that question?

Tying our math instruction to real world situations allows for the students to better make sense of their answer.  We need to be intentional in our plans to teach students to make sense of situations and solutions. One of our biggest goals during math instruction is for our students to EXPECT that their answer will make sense.

Algebraic Thinking Puzzles

I am often asked about ways to challenge our students during math workshop.  I believe it is important that we have a variety of problems that we use.  I also don't think we should spend much of our time accelerating content to teach our students things beyond our grade level.  There are many ways we can build their thinking and logic skills by having them look at numbers more flexibly. Building deeper thinking skills will enable them to persevere as they move into more challenging problems in the future. 

I recently came upon this site.  I think it could have many uses in classrooms as low at 1st grade.  Teachers could use some of the puzzles for a whole class think aloud.  They might also choose to have students work in partners to solve the puzzles.  They might print out a few of the puzzles and have students work on them on paper.  They might introduce some individual students to them.

These puzzles offer students opportunities to think algebraically about numbers and to better explore the meaning of equality and balance.  

Solveme puzzles has three levels of problems:  Explorer, Puzzler, and Master.  Problems become progressively more difficult as students move through the levels.  There are some that involve fractions and negative numbers.   I solved all of my problems as a guest, but you might find it beneficial to create accounts for students.

Let me know what you think of this site.  Feel free to share it with a colleague.  Try some of the puzzles yourself--you might find that you enjoy them, too!

Extension Activities for Unit 6

Below are a variety of games, problems, and tools that you might use to help meet your students' needs in Unit 6 of Everyday Math.

1st Grade:
Two-Digit Targets:  This challenging place-value activity has an interactive version, but would be easy to print out for your classroom, too.
What is the Time:  Some extra practice with time
Coded Hundred Square:  Can your students crack the code for the hundred square?
Making Sticks:  This activity has a hands-on component that allows students to manipulate blocks to answer the questions.
Make those Bracelets:  Students are challenged to find as many solutions to the problem as possible.
GregTang books:  Use any of these books to reinforce problem solving and/or to introduce arrays.  This link takes you to the books in case you don't have the physical copy on hand!
Cookie Monster Puzzle:  Video that explains how puzzle works.  Great puzzle to promote perseverance.

2nd Grade:
Create a Bar Graph Online: This site allows students to input data to create a bar graph.Bar Graph examples:  Sample bar graphs to use in whole class or small group
Learn Zillion:  This site is good for introducing or reteaching the partial sums method of addition.
GregTangMath:  This site offers another way for students to look at partial sums.  Most of these problems are laid out vertically, so they may be for your students who have developed a strong conceptual understanding.
GregTang books:  Use any of these books to reinforce problem solving and/or to introduce arrays.  This link takes you to the books in case you don't have the physical copy on hand!
Sweets in a Box:  Great problem solving problem involving arrays layered in a box.
Thinking Blocks:  This visual model helps students to make sense of the story problem they are trying to solve.
Valentine 3 Act Task:  This 3 Act Task works on basic addition/subtraction.  Good for making sense of a story problem.

3rd Grade:
Make 100:  This problem asks students to use flexible thinking to reach 100 in as many ways as possible.
25th Wedding Anniversary: A 3 Act task using subtraction (and my grandparents!)
Would you Rather:  Students must make a choice and defend it mathematically.  This one deals with fractions.
Nim-7:  Not only do students learn how to play this game, they must think about the strategy needed to win.
Tables without Tens:  This problem asks students to find patterns in the multiplication table.
Carrying Cards:  Nrich problem in which students must look for patterns and do basic computation.
Is My Son Going to Win...Again?: Real world problem solving activity where students have a number of details to determine who will win the game of Monopoly Jr.

4th Grade:
Pebbles:  Students look to continue a pattern using as few pebbles as possible.
Massive Mosaic:  This 3 Act Task looks at area and division.
What's My Angle?: Extra practice measuring angles using a digital protractor
Would you Rather?:  This problem asks students to pick a side and defend their choice.  This problem deals with money.
Area and Perimeter:  These problems ask students to look more closely at area and perimeter.
Star Polygon:  An angle exploration from nrich.  Students investigate their hypothesis.
Alison's Quilt: Story problem with putting square pieces together to form a rectangular quilt.
The Quotient Cafe: App from NCTM that helps students visualize division

5th Grade:
Spiraling Decimals: Students practice knowledge of decimal value in this partner game.
Jumping:  Story problems that involve computations with decimals
Sugar Cubes:  3 Act Task that focuses on 5.NBT.6 and 5.NBT.7
Round the Dice Decimals: This nrich activity lets students think through the value of decimals.
Pick a Path:  This game from NCTM has students use all operations to move the octopus through the maze. Numbers include whole, exponents, and decimals.
Star Wars Phenomena:  This lesson involves a lot of number manipulation on a topic that many students are interested in:  Star Wars!
Carl's Aquarium:  Illustrative Mathematics task that gives real world exposure to volume
Your Number Was:  This machine can guess the number you are thinking of.  Try it with decimals!  
Would you Rather:  Students must make a choice and defend it mathematically.

One step at a time....

Many of us are looking for baby steps to begin our changes in math instruction.

Robert Kaplinsky just wrote an awesome post called, "I Hope You're Embarrassed."  In this post, he discusses how we should be looking back on our math instruction, embarrassed by the methods we used to teach our students in the past.  If we are embarrassed, we know that we have improved!  We might be embarrassed by methods we used in our first years in the classroom, a few years ago, or just last week!  No matter, noting that we can do better is a huge step towards more improvement.

In my talks with teachers, I try to expose them to a number of routines, problems, and best practices that I find in my own professional development, hoping that something I share will spark an idea for teachers to integrate into their own classroom.

Today, my spark is pretty straight forward: My Favorite No.  Watch this video from Teaching Channel and consider ways that you can use it in your classroom.  Ms. Alcala uses this routine daily; maybe for you, it is enough to try it once a week to start?  How can you take this practice and use it to help you transform your learners (and yourself) into better mathematicians?  

Have you tried this routine in your class already?  What were the results?  

Real World Math

Math@Work offers upper grade teachers some great resources to use in the classroom.  The website offers webisodes and downloadable lesson plans and resources which will help yo ur students begin to understand the connection between math and their future careers!

I watched the webisode with Ty Pennington in New Orleans building a sustainable house.  The connections and the math were real and would be great stepping stones for our students as they begin to think about the future.  In the video, a math "expert" talks through solving the problems, but I think it would be worthwhile to stop the video and have the students see if they can work together to solve the problem before revealing the expert's solution.

Goal for 2018: Modeling a Growth Mindset in Math

Jo Boaler is an educator at Stanford who has done much research and writing about math education.  She has worked closely with Carol Dweck to provide us with books, videos, activities and resources to help us encourage a growth mindset for our students. If you are looking for some professional reading, I would recommend looking at some of her books.

Her website is youcubed.org.  I use it a lot when searching for rich problem-solving activities.  When speaking about growth in math, she stresses the importance of visualization.  From her site, you can download some posters that show students the value of training our brains as mathematicians.  

 


If you are interested in books to use during your workshop that encourage growth mindset, you might be able to find one here or here.

Do you have any tools that you use to build growth mindset?  Share in the comments below!

Math Maven's Mysteries

It always amazes me the free things that I find out there on the internet...

Link to Scholastic's Math Maven's index page

This site from Scholastic offers interactive math mysteries of all levels and on a variety of math topics.  They would be great to use as a small group activity or a problem-solving station during workshop.  It offers many great resources.  Many of the problems are ready for the SMARTBoard, there is the opportunity for the story problem to be read to the students, the teacher's resource has many supplemental activities, and you can print out paper copies for students as well!  The main page provides links to all of these options.  I hope you can find something that will fit your classroom!

EM4 Unit 5 Extension possiblities

Here are some links that might help you as you plan Unit 5 in Everyday Math 4.

1st grade:
Equality 2:  Open middle problem which will require some perseverance in problem solving and knowledge of the equal sign.
Coin Bubble:  Good game for all students to gain understanding of coins and their place in base ten.
Adding two-digits numbers: Open middle problem where students are given an addend but must determine the other addend and sum given some parameters.  Challenging.
Two-digit targets:  Students strive to make the numbers that match the clues without reusing any digits.
Pennies:  A 3 Act task that your class can complete.  Helps students to gain practice with pennies.  This task is in SMART Notebook.
Interactive Place Value Mat:  This interactive mat is similar to the one in your ConnectEd etoolkit.  Choose the one you like better as a great way to model problems concretely.

2nd grade:
Two-digit targets:  Students follow parameters to find a sum that matches the description.  Open Middle 
Snail One-hundred:  game in which students use working knowledge of 10s and 1s.
Open Number Line:  This LearnZillion lesson can be used for independent practice or reteaching.  Get a LearnZillion account for full access to their resources.
Interactive Number Line:  This number line can be formatted with or without numbers and gives students a good way to see how adding on a number line can work.
Whopper Jar:  This Notebook 3 Act Task has students add 2-digit numbers.
Would you Rather?:  Students choose a side in this place value problem and defend it.

3rd grade:
Interactive Fraction Pieces:  This app from MathLearningCenter is similar to the one you can find in your ConnectEd etoolkit.  Choose the one you like best.
Distributive Property:  Direct instruction from LearnZillion can be used for reteaching or independent learning.  Get a LearnZillion account for full access to their resources.
Sweettart Hearts:  A 3-Act Task that builds basic fraction understanding. This task is in SMART Notebook.
Fractional Triangles:  This task from nrich asks students to look at ways to break apart a square into triangles.
Matching Fractions:  Online matching game for finding equivalent fractions.
Buzzy Bee:  Students look for and make sense of patterns.
Ordering Cards:  This task helps students gain a better understanding of x2 and x3.
Grapes:  Would you Rather activity where students must justify their choice.

4th grade:
Chocolate:  This task is really at grade-level, but it is a rich version of problem-solving.
Ribbon Lengths:  This LearnZillion lesson can be used for independent learning or reteaching of adding/subtracting mixed numbers.
What's the Secret Code?: This lesson from Youcubed offers students clues to see if they can determine the number.
The Apple:  This 3-Act Task focuses on adding fractions to get a total.  Introduces the idea of multiplying fractions, but gives good practice of addition strategies, too. SMART Notebook.
Fractions:  These Open Middle tasks are varied, but challenging for students.
Blueberry Surprise:  A problem that asks students to convert fractions to solve the problem. 
Brownies:  This problem asks students to make a fraction choice and defend it.

5th grade:
Fractions:  So many Open Middle fraction problems to choose from!  What a great challenge for your students. 
Andy's Marbles:  This work-backwards problem is a good challenge for students to figure out.
Egyptian Fractions:  A rich task to challenge your students' perseverance
Investigation:  This LearnZillion investigation looks at the commutative property and fraction division.
SnowSprint Fractions:  Fun online game to practice multiplying fractions independently.
Who Wants to be a Hundredaire?  This online asks progressively difficult multiplication of fractions problems. Format will be fun for students!
Peaches Today, Peaches Tomorrow:  This is a great problem-solving activity for gaining a better understanding for fractions!
Ben's Game: Great problem solving activity about fractions.  How many ways can your students find?  What if the box held more than 40 counters?

If you have other resources you think would benefit others, please share in the comments below!