Kindergarten Kindergarten

Shapes...Shapes...Everywhere!

Here's a quick PowerPoint I made for 3-D shapes. I use it as a warm-up by showing a few slides per day and having the kids discuss what shapes they see. Super easy!

You can download the slideshow here: Download Shapes, Shapes, Everywhere!

Enjoy!

Math Problem-Solving: 3-D Shapes

So here are some 3-D Shape Problems. Make sure you do lots of exploring with 3-D shapes before you even think about doing these problems! (Click here for ideas). Some of these problems are very challenging. You know your class best! You determine which problems are appropriate and which ones aren't. (And you can always do them whole-group. Just make sure the kids are doing the thinking and you're not telling them how to solve it!)  

Day 1

This is a fun activity that really encourages kids to think about the attributes of 3-D shapes.It also integrates science and makes kids think about how the shape of an object affects how it moves.

It's super easy. Just prop up a flat surface (we used dry erase boards), give the kids a variety of 3-D shapes and let them go!

I encourage the kids to make predictions and explain their thinking before they roll, slide or stack. For example, "I think the sphere will roll because it is round all over," or "I think the cube will slide but not roll because all of its sides are flat."

I also encourage the kids to try all sides of a shape out--i.e. a cylinder will roll on its sides, but slides on its ends. You can stack a cone on top of another shape, but because it has a point on top, you cannot stack another shape on top of it (although they sure try!)

After the kids have had lots of time to explore, they fill out a recording sheet for their journal. 

You can download the recording sheet here: Download 3D Shape Movement

Then we discuss! What different attributes helped or stopped the shapes from rolling/sliding/stacking? Would it be a good idea to make a car with cone-shaped wheels? What about a sphere-shaped soccer ball?

Day 2

Make sure you give kids actual shapes to manipulate when solving these problems. This one is pretty straight forward...

Day 3

This one is 2-steps...count and then compare.

Day 4

This one is fun...there could be multiple answers. A cube and a cylinder? Or a pyramid, a cylinder and a cone?

I love this one...can you read it? SALANDR (cylinder) AN (and) RAGELR RAZAM (rectangular prism...I think!).

Day 5

This one is very challenging. Again...it has more than one possible answer. Is it a cube and a cone? Or a pyramid and a cylinder?

 
Have fun!

Shapes...Shapes....Shapes.... 3D!

My kids love 3-D shapes even more than they love 2-D shapes! They are super excited to learn everything they can about them, so that makes my job very easy. As always, hands-on exploration is essential in order for students to develop a solid understanding of 3-D shapes. So we play and explore a lot! 

I let the kids explore 3-D shapes by building, stacking, rolling, etc. Then, together, we create an achor chart. We describe the shapes using both formal and informal language (so the kids can build on their schema) and record the information on the chart. In the beginning, the kids will call spheres "circles" and cubes "squares," but they learn the correct names very quickly. Although I introduce the vocabulary--face, base, point, edge--I do not require my kids to memorize it. We're just building that foundation. We compare the 3-D shapes to their 2-D counterparts and talk a lot about the 2-D shapes we see in the 3-D versions.

Then we think of examples in real life--and this is where the real fun begins! I challenge the kids to go home and find as many examples of 3-D shapes as they can and bring them into school. We create a Kindergarten Shape Museum! We find a very special place in the room and add to the museum as the week progresses. We talk about the objects the kids bring in--What shape is it? How do you know? What do you see?

Here are just a few examples of objects that make their way into the museum...

And a few others that don't fit...mostly triangular prisms (which the kids mistakenly think are pyramids) and eggs (what shape are eggs, anyway? Google it...it will give you a headache!)

Here is one of my favorites from this year...the kids dubbed it a "Star-angular Prism"!

After a couple of weeks, all the shapes go back home. But the kids never stop looking for 3-D shapes. They point them out all year long! 

We also do 3-D shape recording sheets for our math journals. First, the kids write about the shapes. Some kids use formal mathematical language, and other kids use everyday language. It just depends on where they are in their understanding.

 

You can download these pages here: Download 3-D Shapes

And like so many other things, we compare and contrast different shapes--2D and 3D. Not only does this reinforce concepts and vocabulary, it really promotes critical thinking.

Finally...when all the kids are familiar with all the shapes, we can get down to some problem-solving.

So check back soon to see what we do!

Math Warm-Ups: 2 Dimensional Geometric Shapes

Kindergartners love shapes!

For most children, learning about shapes is one of their earliest learning experiences--their preschool years are filled with shape games, puzzles and sorting toys. Hence, they come to school with a great deal of background knowledge already. As kindergarten teachers, it is our job to build upon and extend that knowledge.

I really want my kids to explore and think about shapes in ways they never have before. So we spend time manipulating concrete models, and then we talk about them--a lot!

I'm not overly concerned that kids memorize facts about shapes and then regurgitate them on command. I have found that this happens naturally as we explore shapes through hands-on learning and problem-solving.

I'm not afraid to talk about/explore things that are beyond traditional kindergarten expectations--especially if the kids are the driving force behind it. I just try to frame it in a way that kindergartners will understand by connecting it to things they already know.

 I use math vocabulary and everyday language interchangeably. I want my students to have something to relate new knowledge to, but at the same time, I would like them to be exposed to formal math language. A great example of this is corners/vertices. Kindergartners know what corners are and can easily identify them on a shape--but the correct word (and the word they will be using as they move through school) is vertex. Although I may use this language, I don't expect my students to memorize it.

 

 Here is an anchor chart we created in my class this year. It took us several days to create. We talk about what the shapes look like, how many sides/corners they have and where we might see them in the real world.

I also have the kids fill out their own shape table and put it in their math journals for future reference:

Download Shape Table

Here is another anchor chart that my kids helped create (I'm trying to put up more kid-created and less store-bought reference materials. The kids have a greater connection to them, and they save me a lot of money!)

We spend a lot of time comparing shapes--How are they the same? How are they different? We generally do one of these charts per day (it only takes about five minutes and can usually be done at the beginning of math or during calendar).

We also do shape sorts. We usually do these whole group so we can talk about it. But you could also do them in math notebooks. I like to do a triangle/not triangle sort so that kids understand that triangles can look different--they can be long and skinny or short and fat--as long as they have 3 straight sides!

I also do a rectangle/square sort (even though a square is actually a rectangle!)

 

 

Here are a few other activities we do in my classroom to learn about shapes:

• We free explore with pattern blocks and other shape manipulatives. I talk to  the kids and ask lots of questions as they "play." I challenge them to create shapes from the pattern blocks.

• We look for shapes in the real world and record them in our math notebooks. We also make class books about shapes.

• We make shapes. One of the best ways for kids to understand the attributes of shapes is by creating shapes themselves. For example, they are going to need 3 popsicle sticks to make a triangle...or 2 short sides and 2 long sides to make a rectangle. We use popsicle sticks, geoboards and Wikki Stix. I also like to give them a piece of string tied in a loop to see what shapes they can make from it.

• We draw shapes. Again--when drawing shapes, kids really have to think about them. Will they need straight lines or curved lines? Are the sides all the same length or different lengths?

•  We use shapes to make pictures (we like robots!). I keep a good supply of die-cut and punched shapes in the art center for my kids to create masterpieces with. You can extencd this activity by having the kids record how many of each shape they used in a graph.

Download Shape Graph

 And, if you want to spend some money, here are some products I love:

 Learning Resources Shape Stencils

Mighty Mind  

(I love all their stuff!)

 Mighty Mind Tiles

 Mighty Minds Super Mind

 Next up-- Geometric Solids. Check back soon!

Math Problem-Solving Week 7: 2-Dimensional Geometric Shapes

Here is the first week of my Shapes Unit. These are just the problems--I do lots and lots of other activities to get the kids exploring and really thinking about the attributes of shapes. I will detail specific activities tomorrow in a warm-up post.

But for now, here are some problems!

This is a very hands-on unit. I provide my students with lots pattern blocks and other shape tiles so that they can explore and manipulate shapes in a very concrete manner.

Pattern Blocks

Square Color Tiles

Shape Magnets

 

Day 1

For this problem, I give each student a blackline master of a circle and some colored square tiles. I challenge them to fill the circle completely with the square tiles. They cannot overlap the tiles and they must cover the circle completely--no white spaces left. They will try and try and try--but despite their best efforts, they are unable to complete the challenge.

The most important part of this problem is the discussion that occurs during and afterwards. Why can't they fill the circle with the square tiles? They will inevitably come to the conclusion that they cannot fill the circle with squares because squares have straight edges and circles have a round edge.

I then challenge the students to use the square tiles to see what shapes they are able to make. They quickly discover that they can make different sizes of rectangles and squares. And they try and try to make triangles...and some think they actually do.

This leads to some more really good discussion...Can you make a triangle? Why or why not? Of course the answer is no--and the reasons are a little too complicated for kindergartners to understand (the angles of a triangle must equal 180 degrees and the angles of a square are 90 degrees, which means you could only have 2 angles and a triangle needs 3...and even my head is about to explode right now!) The purpose of this activity is for the kids to explore and wonder...they will start to see that the shape of a square's corners do not fit in a triangle's corners (unless it's a right triangle).

They are building a schema upon which they will add to in the coming years as they learn more and more about geometry!

Download Fill a Circle

Day 2 

This is another activity similar to Day 1. I provide the kids with a blackline master of a triangle and pattern blocks. I challenge them to fill the triangle. The same rules apply--you cannot overlap shapes and there can be no white spaces remaining.

I give them all the pattern blocks--even the orange squares and the skinny white parallelograms that won't fit. I let them try and try until they figure out that, because of the shape of the corners (the angles), they won't fit. Again--they are building that schema!

I give the kids paper pattern blocks and have them glue them into their math journals. I also have them fill out a chart with the number of each shape they used. For share time, we take a gallery walk around the room to see the different combinations of shapes the kids used.

 

Download Fill the Triangle

Download Fill the Triangle Table

Day 3

This activity is based on the Investigations Fill the Hexagon game. I give the students a blackline master with several hexagons on it and pattern blocks. I challenge them to fill the hexagons in as many different ways as they can. Again--I let them figure out that the orange square and skinny white parallelogram aren't going to fit.

 
This is a challenging activity, because the kids must find different ways to fill the hexagons. They get 2 or 3 quickly, but then they get stuck. It pushes them to really think!

For share time, we make a class chart that shows all the different ways the kids were able to fill the hexagons...

Download Fill a hexagon

Day 4

Here's a fun problem that the kids love. I actually hide 2 shapes in a basket and they get to guess what shapes they are. It is essential that kids have actual shapes to manipulate and count the sides when solving this problem. Most will not use an addition strategy at this point in the year...they will simply guess and check. They will choose 2 shapes and count the sides. If they do not equal 7, they will try again. It is interesting to see which kids will put both shapes back and start all over again from scratch, and which will keep one shape. Watch for the kids that figure out that they have too many or too few sides and choose their second shape accordingly.

(a rhombus, a triangle) Gotta love that kindergarten spelling!

When the kids have found a combination of shapes that equals 7 sides, I say, "That might be it...but it might not be. Can you find 2 more shapes that have 7 sides?"

I have the kids record their answers in their math journals. For share time, we make a class chart recording the different combinations of shapes that have 7 sides. This year, one of my kids figured out that "the triangle always stays the same." He has very good computational fluency, and figured out that it was going to have to be a combination of 3 and 4 sides, and that a triangle is the only shape that has 3 sides!

When we are all done, I open up the basket and reveal the shapes inside--the kids love to see whether or not they were right!

Day 5


So this is the same as yesterday's problem, but taking it a bit further--this time I do not tell them how many shapes I have--just that it's "some."  So there are even more possible combinations.

(a hexagon, a square) (a hexagon, a rectangle)

(I love the early attempt at writing equations!)


(square, hexagon) (hexagon, rhombus) (hexagon rectangle) (trapezoid, hexagon)   We still haven't mastered organization when recording at this point!

Again, during share time, we make a chart with the different combinations the kids thought of. During the big reveal, the kids discovered that I had included an oval, which added zero sides--they loved that!

Check back tomorrow for some 2-D Shape Warm-up activities!

Math Problem-Solving Week 6: More Patterns

Kindergartners love patterns. Or should I say "pat-ter-ens." They're super fun! But what they don't know is that they are an essential building block in their understanding about numbers. What starts out in kindergarten as making pretty designs with pattern blocks eventually leads to skip counting, repeated addition (and therefore multiplication and division), algebraic reasoning, and beyond! So it's important that we provide them with a solid foundation.

Day 1

I want my students to recognize patterns in many different contexts. I want them to understand that red...red..green is the same as orange...orange...blue...is the same as big...big...little.

For this activity, I make several patterns on large pieces of chart paper and place them on tables around the room. I divide the students into pairs and give them different math tools. Their challenge is to go around the room and create the different patterns with their own math tools.

 
I try to make sure the math tools I provide are different sizes and shapes so that they cannot just place their own tools on top of my pattern. I want them to find the pattern core and then recreate it on their own.

You can extend this activity by having the students create their own patterns in their math journals and then seeing how many different ways they can make the same pattern...different colors, shapes, etc.

 

Day 2

 

I debate every year over whether or not to teach my students how to name patterns using letters. My concern is that they will come to associate patterns with letters and not see their connection to numbers. But it is an easy way to identify patterns, especially when I'm pushing them to create different patterns. Some kids will create LOTS of AAB patterns...red-red-orange...green-green-blue...circle-circle-square. When I ask them to create a different pattern--they say, "But they ARE different!" If we can name them with letters, they eventually see that they are actually the same.

So my compromise is to teach them how to do it, but to make it very clear that this is just ONE way that they can name patterns. I start by having a student create a pattern in the pocket chart. Then I have different students recreate that same pattern using different math tools. Eventually, I will give a student a set of letter cards and have them recreate the pattern with those.

 
Next I challenge the students to find the core of the patterns.

I explain that a simple way to give a pattern a name is to just refer to the core, because if we know that, then we can make that pattern as long as we want. We could name the pattern any of these options: green-yellow; square-circle; hexagon-square. But a very simple, and popular way to name a pattern is with letters: A-B.

We make some more challenging patterns and name them in the same way. But I make sure to stress that we could just as easily name this pattern chicka-boom-boom-splat. ABBC is just a convenient way that they may be asked to use throughout their school years.

 

Day 3

 
As much fun as we have making patterns out of pattern blocks and macaroni and stamps and shapes--we cannot forget numbers! I start this lesson by simply asking the kids to make patterns with numbers. Some kids use actual numbers, some kids make repeating groups of objects (and, of course, some kids don't know where to begin). We share and discuss the different ideas the kids have and base our discussion on them.

I eventually make a simple pattern like the AAAB pattern below. Then I ask the kids what would happen if I counted how many of each color were in each "group." We recreate the same pattern using connecting cubes and place them vertically in the pocket chart.

 
Then we count the cubes and put the corresponding number under each tower.

 
And then we discuss it--Is it a pattern? Does it repeat? Is it easy to tell what comes next? What is the core?

I give the kids connecting cubes and challenge them to create their own number patterns. Then I have them record them on a grid paper for their math journals.

Download Can you make a number pattern Grid 

Day 4

 
Here, I challenge the kids to apply what they have learned about patterns to solve a problem. Remember--resist the urge to show the kids how to solve the problem. Read the problem, discuss it, provide them with a varity of tools and see what happens. Make sure to circulate among your students and guide them with questioning and gentle nudges. And then come together during mathematician's chair to have the kids explain the different ways they solved it.

 

Day 5

 
Here is similar problem. You can, of course, adjust the numbers or difficulty of the pattern to fit the needs of your own class (the example below is actually different than the one on the label). You can also solve these problems together as a group (although you need to sit back and let the kids take the lead!)

 

Bonus Activity

I always like to reward my kids at the end of a unit with something fun. In this case, I let them make bracelets out of pony beads and chenille stems. The beads are our school colors. Of course, the bracelet MUST be a pattern.

 
 
You can also have them record it in their math journals by drawing the pattern and naming the core.

We are not done with patterns, yet. We will continue to revist them throughout the year in many contexts. And we will explore number patterns (specifically growing and shrinking patterns) in a few weeks.

Have fun!

Math Warm-Ups: Patterns

Here are a few warm-ups/mini-lessons I do during my patterns unit...

After I have introduced patterns, and we have discussed what makes a "pattern" a pattern...we work on creating an anchor chart describing patterns. Hopefully, the kids will determine things like Patterns repeat themselves; It's easy to tell what comes next in a pattern, etc. This is an excellent opportunity to discuss and debunk any misconceptions the kids may have about patterns.

 

We talk about different places in the room, school and world that we find patterns. We go on a pattern hunt and see what we can find. They might be visual, like the stripes on a shirt or the tiles on the floor. They might be auditory, like the ticking of a clock or sound of a fan oscillating. They might even be events, like day/night or our specials rotation (music, art, PE).

 
Warm-ups are an excellent time to do some "traditional" pattern activities...

 

 

 

 

This is always a fun activity...we "translate" visual patterns into sound patterns by assigning each symbol or color a different sound action. For example, the first pattern might be clap...snap...clap...snap...or pat...stomp...pat...stomp...
Have Fun!

Math Problem-Solving Week 5: Patterns

Day 1

I introduce my patterns unit by doing sound patterns with my kids...you know...clap, pat, clap, pat. I don't say a whole lot, I just do the patterns and let the kids join in. Then I let them make up their own sound patterns. I say, "Wow--you guys are really good at this! How do you know what comes next?" and we discuss. I want them to come to the conclusion that the patterns repeat--over and over again. Like everything else math-related, I do not directly tell them. I let them figure it out on their own--with a little pushing in the right direction from me. Then I ask, "Does anybody know what that's called--when something repeats over and over again?" They might say pattern--they might not. If they don't, I tell them.

When they hear the word pattern--they will be dying to tell you that they know how to make patterns (most will have previous experience with patterns). So I ask them to tell me everything they know about patterns and I record it on a chart paper.

 
Then I give them 2 colors of a math manipulative and ask them to create a pattern using 2 colors. I really like Unifix cubes for this, because then the patterns are portable, and they can be brought to the rug for mathematician's chair. But you could use anything you have. This is the only direction I give them--

 I do not show them how to make a pattern; I do not tell them what kind of pattern to make (most will make a simple AB pattern, but do not be surprised to see something more complex).

You can have the kids record their patterns in their notebooks, either free-hand or with a pre-made strip they can color in.

 

During mathematician's chair, discuss again how they know something is a pattern and how they knew what color to use next. If anyone did make make an ABB or AAB pattern (or anything else)--use that opportunity to discuss whether or not that is actually a pattern, and how the AB pattern and AAB (etc.) could both be patterns.

Day 2

 

I find that when making patterns, most kids love to make AB patterns, but have a difficulty challenging themselves beyond that. In the past, I would have just shown them how to make ABB, AAB, or AABB patterns. But, now, I let them figure it out themselves. (I know, I know--I sound like a broken record!) I simply give them the challenge and push them through questioning, i.e. Can you only have 1 blue? What would happen if you used more?

 

I have the kids record their patterns in their notebooks and bring them to the rug to share during mathematician's chair.

Day 3

 
 

Today is the same as yesterday--but with 3 colors, not just 2--which opens up a whole new realm of possibilities.

 

Day 4

I feel like children exhibit a true understanding that patterns repeat over and over again if they are able to break apart a pattern into the parts that repeat--or its core units. I have them start by creating a pattern out of core units...(Investigations relates these core units to cars on a train...I think that is a helpful analogy). I have the kids create a core unit with 2 or 3 colors. Then I ask what they need to do to turn that one unit into a pattern (repeat it over and over again). I have them build a pattern using that core unit, then I have them break it apart again.

 

 

You can have the kids record their core units and patterns in their notebooks. For Mathematician's Chair, you can have them show their core units, build a pattern and break it apart in front of the group.

Day 5

 

This activity is inspired by the Investigations activity Break the Train. For this activity, I have the kids make any pattern of their choice out of Unifix Cubes (I encourage them to make a "challenging" pattern--something beyond a simple AB pattern).  Then I have them trade patterns with a partner. I instruct them to find the part of the pattern that repeats and then break the pattern into those parts. 

 

 

 

 

You can have the kids record their partners' patterns and the core units they broke it into in their notebooks. For Mathematician's Chair, you can have them show the pattern and break it apart in front of the group. Discuss with the children: How do you know that's the core unit? (Hopefully, they will see that all of the core units will match!)

 

I will post Week 6: More Patterns! later this week--Stay Tuned!

Math Problem Solving Week 5: Position Words

Ahh...position words. This is a hard week to plan, because, in general, kindergartners' oral language and understanding of the concept is much more advanced than their reading ability and writing skills. I also never know, from year to year, how easy or hard this will be for them. (This is very easy for kids who have had a lot of exposure to the English language--MUCH harder for our ESL learners!)

So--as you will probably guess--I read these problems to the kids--slowly and several times, repeating parts when necessary. Often, we don't even get out our individual notebooks. We just do these problems together in our Big Class Notebook. I can always give them more problems to do individually later in the year, when they're reading skills have improved.

I start everyday with the Position Word Warm-ups found here.

Day 1

 

 

Day 2

Day 3

Day 4

Day 5

 

Of course, you know your own class and can make the problems harder/easier according to their previous knowledge and experience. And this will be a concept you will practice all throughout the year in informal settings--doing art projects or playing games, even cleaning up (I like that one! Please put the frog puzzle underneath the farm puzzle!)

Math Warm-Up: Position Words

So here is a fun activity I do to start my math unit on position words. I made a PowerPoint that has some of the scrapbook layouts I have created in it. We look at the pictures together as a class and I have the kids tell me everything they can about it. I am looking specifically for descriptions that contain position words--i.e. "The apples are in the basket." If somebody gives me a description that is not position-related, I guide them with questions, most obviously, "Where is it?"  

I record all of their position-related responses on a chart paper.

Then I tell kids that I am looking for words that describe position--or where things are. We work together to find them and underline them.

And then we transfer them to a chart we can keep up in the room for future reference. When we think of new position words, we add them to the chart. This activity works well with any picture that is engaging to kids and has a lot of details. Art posters work well, as do big floor puzzles, like the ones from Melissa and Doug.

Here is my PowerPoint if you would like to try it in your own classroom. There are 5 different pictures. I do one a day and just keep adding to the same charts.

Download Position Words Powerpoint

I'll be back later today with my Position Word problems and a few more warm-ups. Happy Friday!