Math Talk: Another way to encourage it!

I am always looking for new ways to engage students in math talk.  Math talk is such a powerful tool for building student understanding!

A website I recently found offers some great discussion starters that could be used in a variety of ways in your classroom.  Same but Different Math offers your students images to compare and contrast. These images are categorized to improve your search for what you need.

Let me know what you think about this site or if you would like my help in implementing its images in your classroom!

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!

Holiday Math Online Games

Here some holiday/winter based online math games you might want to try:

Christmas Math:  (K-2)  This site works on identification of numbers, counting, as well as facts within 20.

Math Mosaics: (K-2)  Children solve problems under 10 to color in the squares of the winter mosaic.

Holiday Fun:  (3-5) A multiplication practice game.  Students can choose fact family they want to practice.  Correct answers create a holiday scene.

Blocky Christmas:  (3-5) Logic puzzle from ABCya

Christmas Lights:  (K-5)--Students select the difficulty of basic facts to practice.  They are rewarded at the end with lights to decorate the holiday scene. Students love ABCya!

Super Santa Kicker: (K-5) Students use their knowledge of angles and simple machines to help the reindeer kick the stuffed Santas into the goal.

Winter Math MunchMan: (K-5) Students can choose what level of problems that they want to solve.  Then they move through the Pacman maze to capture the answers and beat the ghosts.

Create your Own Snowflake:  (K-5) Students use digital scissors and paper to create a symmetrical snowflake.

Snowline:  (K-5) Students use angles to direct Santa to the finish line.

Winter Jigsaw Puzzles:  Students put together digital jigsaw puzzles.

DIfferentiating with Fractions

Differentiation can be a challenge. And a lot of work.  Over time, however, I have learned that it doesn't mean that I have to have 3 or 4 different lessons over different content.  In fact, we are encouraged to extend the lesson rather than teach a different lesson.  Below is an example of what I did with Mrs. Bainbridge's fraction kite idea.

I love to color and have lots of those cool design books. I took those design books and used them to design my kites.  The simpler kite ( top design) is made up of 100 equal pieces, and the students had to use 6 different colors.  The more complicated kite did not have equal pieces.  Using the smaller size as a unit, the kite had 650 pieces.  Students then had to use at least 4 different colors for their design, and then had to count and convert the big pieces into small pieces.

Here are examples of what the grids looked like:

The students received a kite shape already made out of these patterns, and they were told how many equal parts there were.  The kids had fun, and it was an appropriate challenge for those kids who needed it.  When the students were done writing their fractions under the kite, they had to check their work by adding the numerators of each fraction to be sure it equaled the appropriate denominator (100 or 650).  Maybe you make kites, or maybe you decide to make holiday ornaments or something else that matters to your class--the idea stays the same.

I have also used Mary from Pitner's Potpourri idea.  We looked at Ed Emberley's Picture Pie and created our own picture pie.  Differentiation was natural on this one.  Certain kids were told they must use 4ths and 8ths in a certain number of colors while others just used 4ths.  The artwork created was fun and beautiful!



Place Value People

As part of a study of place value, I often do a kinesthetic activity which seems to help everyone "get it" a little better.  

I have digits written on construction paper and laminated:  One number per piece of construction paper.  I also have a piece with a comma that says thousand, a comma that says million, and a decimal point that says and.  

I pass out the digits, commas, and decimal point randomly to students.  Then I make up a number and tell the class.  As I say the number, students with corresponding digits go to the front of the room to make the number. They line up and form the number for us by holding the card in front of their chest so we can see it.  I usually let them collaborate some, but I really want them to do some independent thinking.  It helps me to see who is still struggling with the concept.  Once they think they are set, I have another student who didn't have a digit, read us the number. This is good practice for them as well.

After we are done with that number, students hand out their digits to classmates who don't have one, and we start the whole process all over again.

Sometimes, when they have the number made,  I will say "Let's reduce this number by 20,000."  (or something like that)  Then students have to figure out who is affected by this change and who would come take their place.  I begin this in our beginning stages of place value, but it is a great go-to throughout the year for review. Something to think about trying that gets kids up and moving!

Holiday Goodies

Every year the holidays seem to approach more quickly....it must be a sign of my age.  😏

I know how hectic the classroom can be as you prepare for the holidays...you are trying to finish up units, students are distracted, special events and assemblies get in the way, students leave for break a day or two early....

With that in mind, I prepared something for each grade level that I think can be used as independent work, partner work, or in another way that works best for you.  The 3rd, 4th, and 5th grade activities involve story problems which mostly align with the spring PARCC testing.  You should find that some of the pages are things that your students have already studied this year.  Of course, you might decide to look through one of the other grade level's sets of problems--as some of those pages might better fit the needs of your students.

Kindergarten Subitizing Knock it Off! game

1st grade--+1/-1 Knock it Off! game

2nd grade Money Pickup game

3rd grade Story Problems

4th grade Story Problems

5th grade Story Problems

All grades--Holiday Thinking Puzzles

If you are looking for other activities that might be good for your classroom during December, you might check out these previous posts:

Only 8 Fridays 'til Christmas!

For the Holidays

Building Thinkers Through Open-Ended Tasks

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!

Rekenreks--Ideas for use

The rekenrek is showing up more and more in our classrooms.  Hurrah!  They are great tools for us to use to help our students build number sense.  It is also a nice concrete way for students to model what they are thinking.

Christina Tondevold is an educator who provides great professional development for teachers.  She calls herself the Recovering Traditionalist and often discusses her transformation as a math educator.  She recently did a vlog post about her top 5 ways to use the rekenrek.  You can find it here.  It is only about 12 minutes and totally worth your while.

Here are her Top Five Ways to Use the Rekenrek:

5.  PLAY--Just let the students play and discover on the rekenrek independently.

4.  NUMBER STRINGS--Build student understanding through number strings talks.

3.  QUICK LOOKS--Grow students' subitizing skills through quick looks on the rekenrek and discussion afterwards.

2.  SHOW ME--Giving the students prompts and seeing the different ways that they "show me eight."

1.  MODELING STORY PROBLEMS--Having students use this concrete tool to help them make sense of story problems they encounter.

I have shared with many of you an online version that works well on the SMARTBoard.   Here is a link to that site.  You might even want to make it a tab in Chrome so that it is always handy!

It is a good idea to try to build in times when students take their concrete representation on the rekenrek and make it pictorial.  You can find many examples of rekenrek recording sheets online.  Beware, however!  This is much more difficult for young students to do than expected, but a great way to build their understanding.

Finally--I'll end with another great video about the rekenrek by Graham Fletcher.




Let me know if I can help in any way!

Building Thinkers through Open-Ended Tasks

Open-ended tasks offer great opportunities for our students to grow as problem solvers. They also offer students a non-threatening way to show their work, and develop good vocabulary and justification skills.  

These open-ended problems I created are perfect for December or early January because they are holiday-based.  There are 15 different problems in this document, and I think there is something for every grade level.  Please feel free to download and use whatever pages best fit the needs of your students.  

OPEN-ENDED PROBLEMS

More Real World Math Errors

Kids love to find mistakes that others have made.  The attached file is full of errors found in the real world.  Can your students figure out what is wrong?  

Some of these are geared for older students, but there are some in here for the littles, too!

You can use these as a number talk, an opening activity, a collaborative problem solving activity...just be sure to get the best thinking, can they figure out how to correct it?

If your students like these, here are some from an earlier post.

Click for new file

Building Fraction Understanding

In a recent webinar by Graham Fletcher, he discussed the enigma of fractions for a student.  He had what I believed to be a great perception. Just like we teach kids to subitize whole numbers, we could dispel the notion that fractions are difficult by having kids learn to subitize fractions.   And, just as we have students subitize whole numbers in many different ways--through dominoes, fingers, dice, tally marks...we should present fractions in many different ways in order for them to be able to better understand their meaning.

The SMART document that I made stems from Graham's idea, but I also made it with Number Talks in mind.  I think these images could bring up some good math discussions and justifications of fractions.  It is made with images that are easy enough for 1st grade, and some that would be relevant in a 5th grade class.

If you decide not to use the image as a number talk, you might print out a page of the SMART document and have it be a collaborative activity for kids to decide.  

No matter how you use the pages in this doc, it would probably be good to print out the image so that students could cut the pieces apart so that they could prove their thinking to themselves and others by manipulating the pieces of the image.

Sample image from Fractions SMART doc. Click to download document.

Do you have other ideas on how you could use the pages in this document?  Feel free to share below.

Toying with Tangrams

Do you enjoy the challenge of a good puzzle?  Sometimes, people really like them, and sometimes--not so much.  However, most people believe that puzzles are a necessary component to child development.  They help children to build spatial relationships as well as problem-solving skills.  Besides that, the hands-on component of puzzles is an important form of learning for some of our students.

Tangrams are the puzzles that especially seem to connect with math because of their geometric shapes.  If you want to introduce  your students to tangrams, this book is a great start!

You might decide to read and discuss this book as part of reading workshop, or it might be part of your listen to reading activities when you send students to this Youtube video of the book.  No matter how you decide to use this book, it is one that students are sure to enjoy!

Another great book to use with younger kiddos is this one:

If your students are older, you might be able to review the legend of the tangram, and then have them move into building with tangrams.  You might have them as a recess activity, an activity that they can choose when they have completed their work, or a math station.

Here are some resources that might help you put tangrams in your students' hands:

Tangram pattern cards

More Tangram pattern sheets

Interactive Tangram puzzles

A web unit for students in grades 4-5

Online Tangram puzzles

More online Tangram puzzles

A friend of mine used to make each of her students a tangram set for the holidays each year.  She would then print out a couple of patterns that they could do at home, too. What a great idea!

Once your students become used to tangrams, you might try a literacy activity I used to use as an option for my kiddos:

After reading a book, they would make a tangram picture that represented the beginning of the book and then write a sentence or two about the beginning.  They would do the same for the middle and the end.  It was a fun option for some of the kids!

Do you have other ideas for Tangrams?  I'd love to hear them. Please comment below if you do.

Area Model Thoughts

I 💗 the area model!  I think it is worth your while to watch this video if you teach this method! (and even if you don't)





 Thoughts?

Looking for Extension Activities for Unit 4?

If you have some students who pretest out of Unit 4 in Everyday Math, you may find some of these activities will help meet their needs.  Even if you don't have students who test out of the unit, these activities will take some of your grade level's unit skills and look at them at a higher level.

1st grade:
Game of Totals --whole day lesson from Youcubed
Snap It--great small group activity that could be used for combinations of 10
Eggs in Baskets--problem solving problem with conditions that make kids make sense
The Brown Family--problem solving activity
Make Ten blog post--this blog post from last year focuses on resources to help teach making ten
Popping Balloons--A 3-Act task that focuses on combos to 10

2nd grade:
How many Times?--problem solving activity about time
Wonky Watches--another problem solving activity about timeWhich is faster?--problem solving about place value and giving supporting evidence for your thinking
That number square--problem solving about numbers to 100
Fruit Shoot--online place value game where students match base ten blocks to numbers. FUN!
Place Values Shapes game--another fun online game for kiddos to think about place value differently.  Challenging!
Place Value Pirates--online place value game
Would you rather--scenario where students choose what they think is the better choice

3rd grade:
Area Shapes game--good review interactive game for students to practice area
Perimeter Shapes game--online review game that practices perimeter
Quadrilateral Shapes game-- interactive game that has student practice with different types of quadrilaterals
Rectangle Interactive--this interactive activity helps kids connect area to the length of the sides of the rectangle
Paper Cut--3 Act Task that explores area
Numerically Equal--problem solving that asks students to look at area and perimeter
Quadrilaterals--problem solving that looks at different attributes of quadrilaterals

4th grade:
All the Digits--problem solving involving multiplication
Shape Times Shape--multiplication problem solving with an introduction to algebra
Table Patterns Gone Wild!--looking for patterns in multiplication tables
Multiplying two-digit numbers--Open Middle activity for finding a product
Massive Mosaic--3 Act Task which focuses on multiplication of two 2-digit numbers
Would you Rather--scenario where students have to choose and defend the better choice

5th grade:
Scooter Quest--online game to practice decimal place value
Rounding Decimals--Open Middle rounding decimals problem
Meteor Coordinates--This onlinegame gives students a chance to explore coordinate pairs.
Place Value Pirates--online game to practice decimal place value
Hungry Puppies--online game where students choose decimal values to combine to make the target
Matching--this online game has students match decimals, fractions, and percentages
Round the dice--an investigation about rounding decimals
Spiralling Decimals--a game of strategy and knowledge of decimal size

If you have other resources to share, please add them in the comments below!

Halloween and Logic

Construct viable arguments and critique the reasoning of others.

This mathematical practice standard is one that needs to be practiced often with our students.  However, some of them get so flustered by the math that they can't explain their reasoning to others let alone listen to other students' ideas.

Consider trying these logic puzzles with your students.  Logic is a great way for students to practice their thinking, and it is often easier for some of our kiddos who struggle with some of our grade level content.

These logic puzzles are October/Halloween themed and vary in difficulty. They are good practice at thinking skills but also in relational words.  I have also created a document for you that has the images for the puzzles.  Often, it helps the students to have something to move around on their desk.  You can just give them a strip of pictures that matches the puzzle you are doing, they can cut the images apart, and then move them as necessary to solve the problem.

If your students like these, consider an activity where groups try to make up their own.  It is more challenging than it looks.

Please share with a colleague.  Comment below if you find other ways to use them in your classroom.