Showing posts with label math junkie. Show all posts
Showing posts with label math junkie. Show all posts
Thanks to almost two weeks in quarantine, we tried out our own "Chalk Your Walk" project earlier this week!  We had seen pictures shared on facebook with ideas and I was even invited to join a local group about this so I knew we had to try it!

Little did I know we would end up with the PERFECT first grade shapes lesson right at the start of Spring Break!  This activity is great for practicing shapes at home during this time of social distancing or in the summer! Here's how we joined the trend and learned quite a bit of math skills all in the name of "Chalk Your Walk" fun!

The designs I had seen online showed coloring in an entire sidewalk with a mosaic, stained glass design.  But before we conquered that, I wanted us to try something smaller on the driveway.  Cooper wanted to do a shark (of course!), so we got busy!

First, we taped off the outline of the shark.  The shared pictures online showed using painters tape.  But we didn't have any one inch painters tape, so we tried out washi tape because I have an ENDLESS supply of it that was given to us.  Washi tape worked just fine (but probably more expensive if you don't already have a ton on hand you need to use up).

Then, we divided his fins and tail with tape.  And then we filled in the large part by dividing the shark into two parts on the diagonal.  From there, we simply started adding taped lines to make shapes!  For preschoolers and kinders, this would be a great time to have them name the shapes you are taping off as you go.  You could even have them touch the "side" of the triangle or a "vertex" of the shape.

And that's when I realized we were hitting some first grade math standards with this!  I taped off a huge triangle in our shark.

Then, I had Cooper grab his washi tape and decompose my big triangle into smaller shapes.  We actually used that language.  I said, "Take your tape and decompose my triangle into smaller shapes...I can't wait to figure out how you decompose it!"  It may be hard to tell, but first he decomposed the bigger triangle into 2 right triangles.  He said, "Look, Mom!  I turned it into 2 smaller triangles."  So, I reinforced our math language and said, "Yes! You decomposed my bigger triangle into two right triangles!"  Within minutes he was using the words compose and decompose too!

Once we finished decomposing, we got to coloring!

We each used a different color and colored five shapes that same color before we switched colors, but obviously, you can color however you want to!

Once we finished coloring, it was time to remove the washi tape!

I just LOVE how our little shark turned out!

This is the perfect quarantine math shape lesson or summer time math lesson!  But you can easily do this in the classroom too!  Just use some washi tape and crayons and do the same thing!  Then, have your first graders write about how they decomposed their shape!  

Find the activity here with 6 shape options!

Math Talks.  Number Talks.  Whatever you call them, they've been around for a while now.

We know that talking about number sense with our classmates leads to a deeper and more meaningful understanding of our base 10 number system.  You can read about Why I do Math Talks here.  Or, you can say...

"But I don't have 30 minutes every day in my math block to dedicate to a Math Talk!"

"But I've been doing Math Talks and it doesn't seem to be making a difference!"

"But I've started Math Talks but I have NO IDEA what in the world I'm doing!"

Don't worry.  I've been there.  I've had many a failed Math Talks over the years.  But I knew in my heart that Math Talks was a best practice because it was best for kids.  So I dug in my heels, put my big girl panties on (sorry, Mom!) and kept on.

And I finally found a rhythm to Math Talks that worked for me and my first graders.  So let's chat about how to make the most of a Math Talk.

Follow A Predictable Routine

There are no surprises in my Math Talk routine.  Oops.  I lied.  The content is a surprise to the kids.  The rest is the. exact. same.  Every time.  Why?  Because predictability is good for kids.  It makes the routine smoother and faster.  Once the kids learn what's coming next, there is no more explaining and it moves along like a well-oiled machine.

So what is the routine?
When it is time for the actual Math Talk, I pull up the digital Math Talk file on my White Board.  I tell the kids what our goal is for the talk.

"Today, we are working on using what we already know to solve a new problem.  Get your thinking caps on because it's time to TALK ABOUT MATH!"

Then, I click on the Math Talk link to pull it up.  If you are using your own Math Talk, this is where you would put that Math Talk on the board.

If it is an image (dots, ten frames, rekenreks, etc), then I only show it for 3 seconds.  After 3 seconds I click to the next (blank) slide and give them 30 seconds of wait time to solve.  The kids know this.  I don't remind them after the 2nd or 3rd time.  If it is an equation or skills (shapes, measurement, etc), I don't time them.  I just leave it up and they get to solving.  Again, they get 30 seconds or so of wait time.

After the wait time, I say, "TURN AND TELL" and they echo, "HOW I GOT MY ANSWER!"  Then, they think-pair-share for a minute or so.  I listen in to a few partners to hear strategies.

Then, I say, "TIME TO SHARE in 3, 2, 1..." and by that time they are turned back to face the Math Talk.  If it was an image, I go back to the slide at this time.  If it was an equation there is no need to change anything.

Now it's time to share as a whole group.  I ask some kids (randomly or intentionally's up to you) to tell me the answer only.  We collect different answers.  Then, I go back and ask those same kids to tell me how they got their answer so we can agree on the correct answer.

Once we agree on the correct answer, we start sharing different strategies.  This part can get long if you let it.  Don't.  Stay focused on your guiding question(s).  In my example, I would say after each strategy is shared, "Did you use something you already knew to solve?  What was it?"

As the kids share, I notate.  They do not come up to the board.  This will take up too much time.  They stay seated and they TALK.  I notate.  I share 2-4 strategies MAX.  I notate each strategy in a new color so we can easily see what goes with what!  Really enough to see different strategies and to reinforce our guiding question.  If I get the strategies I want and can reinforce our guiding question after 2 strategies, I move on.  If not, I may ask for 1 or 2 more.

There are 3 images or equations in most of the Math Talks.  I use the same exact routine for the 2nd round.  I repeat our goal, "Remember, we are working on using what we already know to solve a new problem.  Get your thinking caps back on because it's time to TALK ABOUT MATH!"

During the 3rd round, we do the same thing again with one difference.  This time, after our think-pair-share, we play, "Guess My Way."  We will come back to this in a few!

Picking the Right Math Talk

Once you have the routine down, it's time to learn how to intentionally pick a Math Talk that is best for your students.  This is definitely an art that gets better over time.  If you are new to Math Talks, my suggestion is that you just pick something--anything--and try it out.  Just jump in head first and follow the routine above.

You will find out quickly if you picked well or not.  If you missed the mark, don't be afraid to stop in the middle and tell the kids you'll start over later that day or tomorrow.  My hands up because I've totally done this a few times!  It's okay--no, it's good--for kids to see that adults and teachers mess up too! :)

Here is my thought process for picking out a Math Talk.

What is my base 10 or math skill goal for the day or week?
If I'm working on counting on, I need to choose images with a set that's easy to subitize and count on.

If I'm working on making a ten, I need to choose ten frames to help kids see how many more to ten.  Or I need to choose equations with numbers that can be combined to make ten and some more (3 + 4 + 7) or decomposed to make 10 (5 + 6).

If I'm working on shape attributes, I need to choose a shape talk that asks kids to defend what makes a triangle a triangle.

What do I want kids to demonstrate in the math talk?
If I want them to show FLUENT THINKING, I stick with images and equations that will push kids to do something besides counting all.  Those are images that can easily be subitized.  Or that have the bigger set on the right side so that they add on from the bigger number.  Those are also equations that have a clear bigger number (2+12) or have a 10 in them (5 + 3 + 5).

If I want students to show FLEXIBLE THINKING, I tend to use images or equations with more than 2 numbers.  Images always encourage a wide range of strategies because everyone sees the pictures differently where a basic equation, most kids read left to right and it's harder to push them outside of that box.

What type of Math Talk should I use?
In first grade, I do a mix of images and equations.  At the beginning of the year, the mix is probably about 70% images.  By the end of the year, that is flipped with about 70% of our Math Talks being equations.

In kinder, all Math Talks will be images at the beginning of the year.  And we will move to 30% of them being equations by the end of the year.

In second grade, the mix is mostly equations with a few images here and there as needed!

For my first grade teacher friends that don't want to have to think about all of this, I have the Math Talks I use for each of my weekly goals listed in my Guided Math Workshop Plans.

Engage Kids in Active Listening & Talking

The best way to keep kids engaged in a math talk is to keep it short, laser focused on the guiding question and goal, and move quickly from one part to the clockwork.  Timing really is...everything! :)

The next best thing to keep kids engaged and active in Math Talks is partner talk.  Giving kids a chance to turn and talk gives them a reason to move their body and talk one on one.  Everyone's strategy gets heard by at least their partner...even if they don't get to share with the whole group.

Another strategy I use is writing names next to the strategies as I notate them.  Kids LOVE seeing their names and their friends' names on the board.  And they will want to share more when they see names on the board.  I promise you that!

I'm a believer in TPR (Total Physical Response).  So when I show the image or equation, students put their thumbs to their chest when they have a strategy and are ready to talk.  But then, they continue to think of a different way to solve and add a new finger when they have another way.  So I can see kids who have one way or multiple ways or no way at all.

Another sign we use is "Me too."

The last thing I use to keep kids engaged during our 3rd "round" of Math Talks is "Guess My Way."  We basically do the same think time, partner talk time, and whole group share.  But I have a specific strategy in mind that matches our goal.  After each strategy, I say, "That was a great strategy, but...THAT'S NOT MY WAY!" and the kids learn to say that with me.  Once kids guess my way, I say, "That's a great strategy, and...YOU GUESSED MY WAY!"  If no one has guess my way after a few tries, I do tell them, just to keep things moving.   It doesn't matter that we play this every time.  This is their favorite. Every hand goes up during this game.

Notate, Notate, Notate

Notation is what takes a Math Talk from good to great.  Notation is writing exactly what we say in mathematical language.

And it's MY job to notate kids thinking in a Math Talk.  It's my chance to model how mathematicians write their thinking.  It's not unlike writer's workshop where I model how to write what kids are saying.

So if a kid says, "I started at 9 and counted 1 more," I'll say, "So you got 9 in your head" and write the 9 with a circle around it.  Then say, "and then counted 1 more" and write 1 more tally mark with a 10 in the green strategy below.  Then, I'll write the equation the same way--as I talk.

For kinders, my notation may just look like recording how I counted (either all or counting on) and with or without an equation depending on your kids.  That's an important piece too.

It's important for kids to see lots of ways to write equations and notations.  And it's MOST important that you talk as you write so they can connect their language to the written math language.

You may be tempted to have kids come up and write their equation.  Please, please, please do your best to refrain from this.  Not only does it take more time, it's not the goal of a Math Talk.  It's the time to model.  Just like in Writer's Workshop our mini-lesson is where we model write and then we send kids back to independently write and try out what we modeled.

During math problem solving, students will try out notations you model for them.  I've had first graders accurately use parentheses in their problem solving notation because I modeled it in Math Talks.   That would've never happened if I let kids notate their own thinking in Math Talks.  You model it, they will try it out on their own when they are ready!

Try out the Digital Math Talks for FREE here or find the bundle here.

You know that math kid.  That one who draws pictures to solve his math problem.

Every. Single Day.

And no matter what you say, she keeps drawing bubbles.

Do you have that math kid in your room too?  Cause some years I've had like 10 of them!

Maybe your kids aren't counting all anymore, but you can't get them to quit counting on, or drawing tens and ones...the concept is still the same...and still as frustrating!

How do we get kids to quit direct modeling or drawing pictures, or whatever we want them to quit doing and move on to more appropriate math strategies?  Let's talk about how I use the word EFFICIENT to help kids move beyond drawing bubbles!

What Does It Mean To Be Efficient?

An efficient math strategy is the quickest way to solve a problem that I understand.  In first grade, we start off by generating strategies.

Throughout the year, we chart strategies as they are shared during math talks or during story problems.  We learn from the very beginning how to identify and name a strategy. (Note this chart is one from several years ago and we had not added strategies like tens and ones yet.)

We start the second half of the year practicing using multiple strategies.  I encourage kids to have more than one strategy ready to share during math talks.  And during our story problem time, I have them show me two ways to solve the same problem instead of showing one strategy for 4 different problems.

The next week, our focus is on picking the best strategy for each story problem and number set.  We read a digital book called Finding Bingo.  (The dog is lost and we are generating ways to find him and deciding which way is the best.)  Then, we introduce the word EFFICIENT.  We talk about what it means and chart some synonyms.

What Are Efficient Math Strategies?

Once we understand what efficient means, we go back to our "Model With Math" chart and evaluate our strategies.

Is this strategy efficient? Why or why not?

Then, we color code our strategies.  This works best if you add strategies to your "Model With Math" chart on index cards from the beginning of the year.  Then, use tape to add them to your chart.

Once you are ready to categorize them into efficient and inefficient, it will be easy to move and you won't have to rewrite them!

In first grade, at the beginning of the year, all strategies are welcome as long as it fits the story.  Any strategies you share that result in the correct answer are "green strategies."

Any strategy that doesn't fit the story, is inefficient and we call a "red strategy."  A red strategy is a strategy that will not ever result in the correct answer.  That could be doing nothing.  Or subtracting on an addition story, etc.

In upper grades, move strategies to red when students are "not allowed" to use these anymore.  And if you see a red strategy as you conference, you simply mark through it with a red crayon and have them choose another strategy.  Be careful not to move strategies to red too quickly.  We don't want to take away strategies that build understanding for kids who need them too soon!

By January (at the latest), we don't want students counting all anymore.  So, once we discuss why counting all is inefficient, we move that strategy from green to yellow.

"Yellow strategies" result in the correct answer, but are a much SLOWER way to solve.  When I am assessing story problems, these would be a "2" on my rubric or below basic.  Notice that yellow strategies include drawing and counting all AND drawing all, but counting on.

If you are in second grade, you may start out with these as yellow strategies at the beginning of the year, and move more over as your year progresses.  This is super easy to differentiate between grade levels, but keep the same language for kids throughout the school!

"Green strategies" are the ones that quickly get us the correct answer.  But they also are strategies that we understand and could teach to a friend.  For example, decomposing 10s and 1s is efficient for the kid who understands it, but for a kiddo who doesn't understand 10s and 1s, it is not an efficient strategy.

This is where it gets tricky.  Not all green strategies are appropriate for every kid.  They have to be able to find a strategy that makes sense to them, and makes sense with the problem or number set.

These strategies are posted with our Model With Math chart so that we can use them during share time.

How Can I Use This With Small Groups?

If you follow my Guided Math Workshop Curriculum, you share during your small group time.  This makes it very easy to differentiate and only add green strategies that each group is ready for.

And it makes total sense to have a different green chart for each group!

As you share your strategies, have kids color a yellow, red or green bubble next to each of their strategies to determine if it is efficient or not.

For the yellow strategies that we find, we talk as a group about how to improve the strategy to make it efficient.

What is inefficient about this? (Reference the efficient chart)
How can we make it more efficient?

Make the word efficient part of your sharing routine helps move our kids beyond those strategies we need them to "drop."

You can find this lesson and materials in my Guided Math Workshop Plans.

It's no secret that I LOOOOVE a good anchor chart.

That's probably why I have an entire Pinterest board called "Anchor Chart Addiction."  It's definitely a legit problem!

Here's a look back at some of my favorite Math anchor charts we've made over the years.

Math Practices Charts

I use the Standards for Math Practices as our goals for each week in math.  You can read about that routine in detail here. When we introduce it we start the anchor chart and then add to the anchor charts throughout the year as we learn more and understand more about that math practice standard.

Here are a few examples from most of our standards for math practice using our old chart printouts! #throwbackpics Find the updated charts here!

Number Sense Charts

In addition to our Standards for Math Practices charts, sometimes we need specific charts to help us understand a bigger number understanding in math!

Our fractions chart from when we discovered how to equally divide shapes. Read more about the activity with this chart here.

When we learned about relationships between numbers and equations, we learned about related facts with this fun jingle that we charted together.  Read about that activity in detail here.

One of my all-time favorite math charts is one of the simplest too!  When my kids discover commutative property during math talks or our math wall time, we chart it.

I'm a big believer in calling a spade a spade.  So, equations that use the commutative property are not "flip flop facts," because that's not what real mathematician's call it.  They call it commutative property.  And so do my first graders! #steppingoffsoapbox

BUT, I love using the flip flop as a visual anchor chart reminder of what the commutative property is!

During our Counting Collections routine (read more here), we chart our expectations for building number sense during this weekly time.

Math Skills Charts

While about 80-90% of my yearly math instruction is spent on building number sense and algebraic thinking, we do spend some time on math skills too!

But since we don't spend much time with them, we need fabulous charts to help these skills stick!  Here are a few of my favorites!

When we work on our data investigations, we use this chart throughout that week to add to our ideas about what data displays need.  Read about that engaging investigation here.

We did a similar investigation on measurement using these digital math talks slides on measurement.

And more measurement with our pumpkin investigation.  Can you tell I like to make anchor charts into shapes! #easytofind

And, of course, our clock investigations and crafts which you can read more about here!
Number sense puzzles are one of my favorite ways to challenge my first graders' math thinking skills...especially my early finishers.  They are quick, low prep and engaging for kids.  My five year old begs to try them at home when I print them out!  Read on to see how to use number sense puzzles in the primary classroom and how I differentiate them for my highest thinkers and scaffold them so that even my 5 year old can successfully finish a puzzle on his own!

What Are Number Sense Puzzles?

Number Sense Puzzles are cut up pieces of a hundreds chart that students use to put back together using what they know about number order.

Why Should I Be Doing Number Sense Puzzles?

Number Sense Puzzles are important in the primary classroom for a lot of reasons.  At the simplest level, they are great for giving kinder babies practice identifying and matching numbers.

At the highest level, number sense puzzles force kids to think about number order and place value and compare 2 and 3-digit numbers.

They are also fantastic at quickly exposing misconceptions that kids have with counting, number order, or place value.

Who Are Number Sense Puzzles For?

Kids from kindergarten to second grade can benefit from Number Sense Puzzles.  Because these puzzles build number sense, any kiddo lacking these skills will benefit.

They are especially perfect for early finishers as a challenge, or RTI small group practice with scaffolds.  There is definitely a wide range of options and differentiation with these puzzles!

How Can I Do Number Sense Puzzles In My Classroom?

Before my Mommy leave, I made my own Number Sense Puzzles in my first grade classroom.  I simply copied a 120's chart on colored cardstock and laminated it.  Then, I cut the chart into random puzzle pieces.

BAM! Number Puzzles!  I simply put the pieces in a bag and I was ready to go!  I made multiple puzzles, each on a different color of paper to keep the puzzles separate and we used them as partner practice for math game day and in our math centers.

How Can I Differentiate Number Puzzles?

Number Sense Puzzles are one of the easiest games to differentiate and it does not take much additional prep! #winning

For my pre-made Number Sense Puzzles, I already have 2 different levels of numbers for each puzzle.  If you are making your own like I talked about earlier, you can simply just cut apart 1-50 for your lower babies...

...use the whole 120's chart for your on grade level kiddos, and cut apart a 200s chart for your higher kids.

Another way to differentiate Number Sense Puzzles is with scaffolds.  For kindergartners or RTI first or second graders, give them a completed hundreds chart to either use as a reference, or as a puzzle mat to place the pieces on top of the chart.

Just be aware that with this scaffold, students are working on recognizing and matching numbers, not number sense and number order.  This is not a scaffold I use with my first graders.  They can refer to the hundreds chart we have in our room, but I encourage them not to unless necessary to challenge and grow their math brains!

However, I do use this scaffold with my RTI math groups and lower counters and then slowly take the scaffold away as they improve.

For example, we may start with the chart as a mat to lay pieces down on...

And then move to having the reference chart beside the puzzle pieces...

And then just keep moving that chart farther and farther away from the puzzle until they don't need it anymore!

Where Can I Find Pre-Made Number Sense Puzzles?

If you're like I was in the classroom and just want the puzzles made already, then I have a year's worth of puzzles already made up for you!

There are two puzzle shapes for each month.  And each puzzle comes with two differentiated number levels for 4 total puzzles each month.  Find the bundle here which also has links to each of the 11 months that are also available individually!

By now you know that I'm a big fan of board games in the classroom. {If you don't know that, read this blog post.}

And we've talked about how to work in games in our already busy schedule here.

But not any old game will do.  There are some games that really fabulous and classics, but they just don't lend themselves to any sort of strategy building.  Those are not the games you will find in this blog.  Those are games like Candyland, Hi Ho Cherry-o, Chutes and Ladders and more.  While they are fun, and build people skills, they are more fit for inside recess than during instructional time.

So let's chat about strategies and skill sets we want to develop in primary kids and my favorite no-fluff board games to do just that in the primary classroom {and kids of all ages}!
{affiliate links are included in this post, which means I get a very small commission to add to my chocolate fund! Thanks for supporting me!}

Games That Build Logic

Games that build logic are games that make us think in "If...then..." statements.  Remember those logic grid puzzles?  It's the same sort of thing, but they are built into games to make it friendlier for our littles.

Guess Who
Clue Junior

Games That Build Planning Ahead

These games are ones that make us account for our opponents next step.  "I think they will do _____, so I need to do ______."  Or, "If they do ____, I'll do ____, but if not, I'll do ______."  They help us practice flexibility and adapting our plans to unexpected changes.  And they help us learn that there are multiple ways to win a game or solve a problem...or in Arkansas language: There's more than one way to skin a cat! :)

Connect 4
Chinese Checkers

Games That Build Comparing and Contrasting

These are games where we have to look at similarities and differences, and decide on important information between two objects or cards.  We also need to be able to see how things are connected in order to win the game.  Again, many of the other games also work on these skills, but these games are especially good for this.

Apples to Apples Junior

Apples to Apples Junior is more for kids who can read as they will need to be able to read the words independently.  I would suggest it for 2nd grade and maybe some first graders.

Games That Build Stamina

These games are not won in 5 minutes or less.  They take time.  They help us focus and practice building stamina.  If I can engage in a game for 20-30 minutes, then that can help me engage in other areas of learning during other parts of the day.  Focus and stamina is a learned skill that good problem solvers have.  There are plenty of the other games that are longer and build stamina, but these are the best fit for this skill!

Monopoly Junior

What are your favorite strategy games for the classroom?
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