Here's a math warm-up I will be doing with my kids when we start our Attributes and Sorting unit.
It's really great for eliciting discussion and teaching kids how to express differing opinions respectfully. What's the right answer? Well, clearly, the milk does not belong because it is not a school supply. But wait--it must be the scissors, because they are not a liquid. Hmmm...
There are 5 problems included--all with multiple possibilities for answers!
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This is a continuation of my Attributes and Sorting unit. You can see the introduction here.
I am lucky enough to have a class set of attribute blocks. They are great because they can be sorted 4 different ways: by color, size, shape and thickness.
The kids record the different ways they sorted in their notebooks with either pictures or words. During mathematician's chair, I point out journals that were well-organized and clearly showed how the blocks were sorted.
While the kids are busy sorting, I walk around and take lots of anecdotal notes. This is an excellent opportunity for me to see who can sort the blocks quickly and in multiple ways. I also take time to talk with the kids about their thinking. I get so much more information about them this way than with a formal assessment.
Day 2
With this problem, students get a chance to apply their sorting skills to an actual "problem." I divide the kids up into groups of 3-4 and give them each a set of cookies and 4 paper plates. (I prepare the cookies ahead of time by coloring and cutting them out. I laminate them and use them from year to year).
The challenge is to sort the cookies so that each plate will have 3 cookies on it.
Is it by color? No...
Is it by size? No...
Is it by shape? Yes!
We do not record anything in our notebooks for this problem. During mathematician's chair, we simply discuss the strategies we used to solve the problem.
Here is the cookie problem if you want to try it:
Download Cookie Sorting Problem
And here is a similar problem I send home for families to try together:
Download Flower Sorting Problem
Day 3
It's another lonely day for our problem-solving notebooks. We will not get them out today. But we are still problem solving! Remember --problem solving is about the process, not the product!
The kids love making attribute trains. We use the mixed-up math manipulatives from last week. Start by putting one manipulative down. The next manipulative in the train must share some attribute with the first one...
Here, I could choose another button, or something else that is red...
I chose the button. Now, I can choose another button, or something else that is blue...
I chose the button, Now, I could choose yet another button, or something else that is green...
I chose a green cube. Now I could choose another cube, or something else that is green. And so on and so on...
At first, the kids might just make long runs of manipulatives that are the same color and then change to a new color without any common attribute to link the 2 colors. Instead of just showing them their mistake, question them until they figure it out themselves. ("How is this green button connected to this blue cube?")
But remember--there is no wrong answer as long as the students can justify their "link." They might say "The blue button and green cube are connected because they both have holes."
At first, I just let the students practice building long trains. But once they become competent at that, we make it a little harder by turning it into a game. Each player starts off with 10 random manipulatives. Player #1 puts down 1 manipulative. Player #2 puts down a manipulative that shares an attribute. If they do not have one, they must close their eyes and draw another manipulative from the tub. If they can make a match, they put it down. If they cannot, the next player gets to go. Play continues until someone runs put of manipulatives!
There is a lot of strategic thinking in this game. Let's say a player has a choice between putting down a yellow cube or a yellow button. He sees that the next player has a blue cube, but nothing that would match the yellow button. He can make the strategic move to put down the yellow button and force the next player to draw. So even though it is a game, and the math notebooks are tucked away for the day, there is still excellent problem-solving going on!
Day 4
In order to introduce Venn Diagrams, I sit the children in a big circle on the floor and get out 2 hula hoops. At first, I DO NOT overlap the hula hoops. I simply place them next to each other. I tell the children that we are going to put green things in one "circle," or group, and fruit manipulatives in the other. I hand manipulatives to several children to place in the correct group.
After we have placed 5 or 6 manipulatives in the correct group, I give a green apple to one of the kids. They will usually stick it in one of the circles with great confidence. And almost always, somebody else will immediately object.It is green, it goes in the green group. NO--it is an apple, it goes in the fruit group. And almost always, some brilliant kid will suggest that we overlap the circles so that the green apple can be in both groups at once. But, if nobody does suggest that, you can question and guide them in that direction. "Boy--I sure wish we could figure out a way that this green apple could be in both circles at one time!" They'll figure it out!
After we have placed even more manipulatives, including green apples, in the Venn Diagram correctly, I give somebody a manipulative that is neither green or a fruit. Here is another dilemma--where should we put the purple butterfly? It can't go in the green group, and it can't go in the fruit group, but it has to go somewhere! Again, somebody will figure out that you can put it outside the diagram.
This is a great problem-solving activity in itself, but you can follow up by having the kids do a Venn Diagram in their notebooks. Here, I had them sort colored heart, star and happy face stickers into a Venn Diagram.
Day 5
We end our Attributes and Sorting Unit with a special treat--a Snack Mix Sort!
I make a tasty mix that has all sorts of snacks--different types, colors and sizes! Here's what I put in my snack mix:
As you can see the kids have many options for sorting. I have them sort into 2 groups, for example:
And many more!
If you want a record in the problem-solving notebook, you can use this:
And finally...the kids get to eat their manipulatives!
And with that--we are DONE with attributes and sorting (but we will, of course, revisit it during he course of the year.
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So now that my kindergartners have been introduced to the whole concept of math problem-solving notebooks, it's time to start tackling the math curriculum. Week 3 introduces sorting and classifying by attributes. This is one of the easiest units to convert to the problem-solving model. I really just do the same activities I did before, I just pose them in the form of a problem.
Day 1
This purpose of this first problem is to get the kids thinking and talking about attributes. To do this, I have collected a big basket of balls--yes, balls! I have all different colors and sizes--big balls, little balls, glittery balls, bouncy balls, squishy balls..
OK...are you laughing yet? Because I can hardly keep a straight face typing this. Seriously, though--can you think of a better way to get kids engaged? The balls are perfect, because they come in all different colors and sizes.
I have collected these balls over the years. I get them at the dollar store, party stores, Target, Walmart, kids even give them to me! If you don't have, or particularly want a giant collection of balls in your room, you can just have the kids each bring in a ball from home. Make sure you keep them all week--there are all sorts of sorting activities you can do with them.
So, I have each child draw and write words about their balls. The drawings are usually pretty easy--most kinders can draw a circle at this point (another reason I love the balls!) Encourage them to add the details--like the color, or pattern of their ball. Because most kindergartners will have very rudimentary spelling skills at this point, you will probably have to do a lot of dictation. But don't stress if you cannot get to everyone--it is much more important to talk about the attributes at this point.
When everyone has finished, bring the kids to the rug for mathematician's chair. Have them bring their journals. Ask the children to tell you the words they used to describe their balls and write them on a chart paper.
Once you have completed a good list of words, introduce the word attribute--a characteristic used to describe an object. Choose one word from the list. Decide as a class what attribute that word describes. Here, we started by choosing the word small, and decided it described size. Then we circled all of the other words that described size.
We then transferred those words to a separate chart. Originally, I would not have had the other attributes (like color, texture...) listed on the chart. We would come up with those words and add them together as a class.
For example, we would have chosen another word from the list, like red, and decided it described color. Then we would have circled all the other color words and made a column for them on the attribute chart.
As we transfer words over to the attribute chart, we may think of other words we had not initially thought of, i.e. more color or size words. We add those words as we think of them. We also leave the chart up all week so we can add to it or refer back to it when needed. Color, size and shape are definitely the most common attributes (shape is a given for balls--most are round), but your class can add the categories that are appropriate for your balls (or for whatever you're working with).
We revisit the basket of balls throughout the week during Math Warm-Ups. We compare the balls and sort the balls into different groups.
Even though my class uses balls for this initial lesson, you could use anything that has a variety of attributes to explore--buttons, toys, etc.
Day 2
My mystery box is simply a collection of small objects from around the room--pencils, erasers, small toys, blocks, Lego's, etc. Again, you are focusing on getting the kids to recognize and verbalize the attributes of the objects. But this time, you are taking it a bit further by having the kids compare 2 objects.
Again--week 3 notebooks are probably going to be a mess. Encourage them to do as well as they can on their pictures and to include as many details as possible. If they can write words, super! If they can't, take dictation. If you can't get to everyone, again--no worries. It's the discussion that's important!
For mathematician's chair, bring them to the rug. Call on several children to explain how their objects are the same and how they are different. It might sound a little like this:
My pencil and ruler are the same because they are both long. But they are different because the pencil is yellow and the ruler is green.
My objects are the same, because they are both blue. But this one is a pencil and this one is a button.
My objects are the same because they are both rectangles. But the eraser is big and the lego is small.
Take this opportunity to add any additional words to the attribute chart!
Day 3
So, today, the actual sorting begins. I make a big scene and say that somebody snuck in the room overnight and mixed up all the math tools, or manipulatives (me!) And then I simply ask them to help me organize them.
I do not model how to sort the manipulatives, and I do not give them any rules. I don't necessarily want to just see all the like manipulatives grouped together. However, that is what the kids will naturally do (and I do want to know that they can do it).
In order to encourage some more divergent thinking, I might say, "Now that the math manipulatives are all messed up anyway, I was thinking of organizing them a different way. Does anyone have any good ideas?" Here, you can see this little girl sorted by color.
You can learn so much about kids and their mathematical thinking through this problem. How do they organize the manipulatives--in lines, in groups? Do they make sub-groups, i.e. sort their bugs into specific kinds--butterflies, caterpillars, etc. Really talk to the kids while they are sorting and get them to verbalize their thinking!
Notice the papers the kids are sorting on. I use these mats a lot--they are laminated with their names. I take a picture when they are done sorting, print them and glue the picture in their math notebooks!
For mathematician's chair, I have the kids take a gallery walk. Half the class circulates around the room and the other half explains how they sorted. Then we switch. Easy-Peasy!
Day 4
Today is a replay of Day 3 with buttons instead of manipulatives. Remember--do not model how to sort the buttons. If they get stuck, ask them to show you a button they like. Ask why they like it and then see if they can find more like it. Challenge the kids by asking if they can find a way to sort their buttons that is different from anyone else at their table. They love a challenge!
Again--I take pictures of their sorts to glue in their math notebooks. For mathematician's chair, we take another gallery walk.
Day 5
On Day 5, I want to see if the kids can sort objects by one attribute, and then mix the same group of objects up and sort them by a different attribute. I take 2 pictures for each kid and glue them both in their math notebooks, and we take another gallery walk for mathematician's chair.
At the end of this lesson, I read The Button Box by Margarette S. Reid. I used to read it before we sorted buttons, but that gives the kids ideas on how to sort, and I want them to think of idea themselves. They can try the ideas in the book when we sort buttons again during math warm-ups.
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When most of the children have completed their solutions, bring them to Mathematician's Chair to share/discuss their answers. (See tips here.)
Day 1
You will be amazed with the variety of answers kids will come up with for this question. Of course, there is The fish--because it lives in the water. But then again, it might be The cat--because it can't swim. Or The fish--because it doesn't have legs. Or The cat--because the dog will chase the cat and the cat will eat the fish, but the dog and the fish will get along just fine!
Day 2
Seems simple--3 tails, 3 cats, right? But wait--maybe it's 10 cats, but only 3 are sticking out their tails. Or maybe its Zero cats--there are puppies in the box. Here's a great question for Mathematician's Chair: Can there be just 2 cats in the box?
Day 3
Again--let them come up with creative answers, as long as they can explain their thinking... 
I actually have a box that I hide things in. I give the kids clues and see if they can guess what is hidden inside. You can change the object and clues. The answer is a button, but one year, some guessed: An apple with worm holes. This is a great way to start working with attributes.
Again--there are multiple answers to this problem. Let the kids explain why their answer is the best answer. This introduces TEK K.2A Use language such as, including before or after, to describe relative position in a sequence of events or objects.
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Over the next week or so, I plan to post all of my problems for the first nine weeks of school. These problems are just a guide. Every class is different! Some classes need more time to develop basic skills--others are ready to move on more quickly. No matter what problems you choose, be ready to adjust them as you finish your beginning-of-year assessments and get to know your kiddos a little better.
I start problem-solving on the very first day of school. I purposely choose easy problems so that I'm able to teach routines and expectations alongside with them. This first week focuses on the expectations for using our problem-solving notebooks. Before we begin, we go over all of the Problem-Solving Expectations and glue them in our notebooks.
Day 1 
This problem serves several purposes. First, it's very easy, so it will let the children experience success and gain confidence early on. (We want them to love--not dread--problem solving!) Second, it gives them a chance to practice the expectations they just learned (especially the One page at a time and Do your best work!) During Mathematicians' Chair, focus on notebooks that have neat, organized work (i.e.the eyes are clearly present). Look for children who wrote the number 2, but look for other ways that children may have represented the number 2 (for example--did anyone make two dots?) If nobody did, ask the kids for ideas about how they could represent the number 2. Call for volunteers to show different ways to represent the number 2 in the Big Class Notebook.
Day 2
Day 2 is another fairly easy problem. The focus should be on How can you show your answer? Some children might draw a literal picture. Others might draw symbols. Many may write the actual number. During Mathematicians' Chair, ask the children how they found their answer. Get them to use the word count... "I counted!" Ask for several volunteers to demonstrate how they counted. Also, point out the variety of ways that children showed their answers. Point out children that used more than one way to show their answer.
Day 3 
This is a good problem, because there is such a variety of answers. During Mathematicians' Chair, call on several volunteers to write their names in the Big Class Notebook and demonstrate how they counted. Begin to point out good counting strategies! Showcase journals that are neat and organized. Look for alternative ways to represent numbers.
Day 4 
This problem introduces pattern blocks. It also allows children to practice counting and representing number in a neat/organized way. I introduce the pattern blocks in warm-up, and go over all expectations for using them (i.e. do not throw them or stick them in your nose...) Then I let them have at it and "play" all they want. When we are ready to problem-solve, I give each student a baggie that has 20 pattern blocks that they can choose from so that they do not get carried away and create a monster that has 72 green triangles! They still have freedom to create what they want, but are limited in number. During Mathematicians' Chair, have children demonstrate how they counted their blocks. Did they leave them in their design, or did they mess up their design and line them up, or push them away as they counted? Did they touch each block as they counted? Have the children discuss what they think the best counting strategies are and record them in the Big Class Notebook.
This problem introduces unifix (or linker) cubes. I introduce them during warm-up--going over all the expectations (see pattern blocks above) and then letting them play.
When it is time to problem-solve, I demonstrate how to use one hand to grab as many cubes as I can. (This is a great problem to use throughout the year. Differentiate by using smaller manipulatives to produce bigger numbers and bigger manipulatives to produce smaller numbers!) Again--look for good counting strategies. If a child is unorganized and mis-counting, ask, "Can you think of an easier way to count the cubes? How can we make sure that we count all of the cubes? How can we make sure that we don't count a cube twice?"
During mathematicians' chair, call on several children to demonstrate how they counted their cubes. Add to the list of Good Counting Strategies. Hang it somewhere very visible so the children can reference it later.
(For all of the Investigations fans out there, this is a variation of the classic Grab and Count!)
This is not the only time we practice counting in my class! We spend the majority of our time in math warm-ups the first few weeks doing counting and number identification activities--I'll do a post about that soon. But by all means, if your class needs more time counting, give them some more counting problems!
And remember--do not worry so much right now about how the notebooks look--it won't be pretty! Most of the children are brand-new to all of this! Just reinforce the expectations, and praise the children who are neat and organized. You'll start seeing a big difference soon!
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Mathematician’s Chair is an opportunity for children to learn from each other. They learn new strategies by listening to someone else’s strategy. They reinforce their own skills by explaining them to others. They work through mistakes and misconceptions during quality discussions with their peers.
Before you begin Mathematician’s Chair, talk with the children about what it means to be a good listener. I always tell them I want them to listen with their eyes (look at the speaker), their ears (listen to the speaker), their brains (think about what the speaker is saying) and their hearts (care about what the speaker is saying).
Then teach the kids how to respond appropriately to someone else’s solution. I often ask, “Do you agree?” and then, without talking, all the kids give me the sign for either yes or no (we use the American Sign Language signs, but you could also use thumbs-up/thumbs down). I will then call on specific children, “Joey—tell me why you agree.” “Alex—tell me why you disagree.” In either case, the students MUST be respectful. 
We talk a lot about hurtful words vs. helpful words (not just in mathematician’s chair—but in every part of our day!) We also talk a lot about mistakes—and how wonderful they are!
So it is OK to make them. (I also point out all the mistakes I make. But before long, I don’t have to—the kids are more than happy to point them out for me!) Bottom line—I want the kids to feel comfortable sharing, whether their answer is “correct” or not. Once the kids are sharing, your job is to guide them. In the beginning, you’ll have to do A LOT of guiding. Tell me what you did. Why did you do that? What did you do next? What did you do next? Expect a lot of one-word answers. Ask them questions that might get them to think of something they hadn’t before…What would happen if…?What else could you have…? If there is a particular strategy you would like them to use that they just don’t seem to be discovering on their own, guide them in that direction by asking questions. But make them think they thought of it all by themselves! Always end Mathematician's Chair with a big round of APPLAUSE for the kids who shared!
Remember… as with everything problem-solving, Mathematician’s Chair gets easier as the kids gain confidence and experience!
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We do math problem solving in my kindergarten class everyday! I will probably write a lot about it this year, so stay tuned! So I thought I would start off showing how I set up my Problem-Solving Notebooks (some people call them math journals). I use a notebook so I can keep all of the kids' problem-solving together in one place. I find that when I use loose papers, they just end up stuffed in backpacks and crumpled on the bottom of backpacks. Besides, It's amazing to look through them and see the kids' growth over the course of a year!
So how, you ask, do parents know what we're doing in math? I send the journals home once or twice a quarter so parents can flip through them. I constantly communicate with my parents through e-mails, my classroom blog and even Twitter to let them know what we're doing and how they can reinforce what we're learning at home. And I use the journals during conferences to show parents evidence of how their child is performing in math.
So, where to start...
1. Choose your notebook. It's really up to your own personal preferences (and what's on your school supply list!) I prefer marble composition books, because those things can take a beating and never fall apart! Pages are sewn in, so they don't fall out. The cover is nice and sturdy. There are plenty of pages. (I do wish they came in a regular 8 1/2 x 11" size). 
You could also use blank copy paper in a 3-brad folder.
2. Label the notebooks. We use composition notebooks for everything in my room--science notebooks, writing journals, reading workshop notebooks--so I have to make each one unique somehow. This year, I was able to get different colors of notebooks at Walmart, 4/$1.00 (What a deal!). I use mailing labels to put the kids' names on their journals. I print out a full sheet for each kid at the beginning of the year and then pull one off anytime I need to label something with their name. Super easy! If you want this label, you can download the PDF here: 
4. Glue in the Problem-Solving Notebook Expectations. I actually do this as a whole lesson with the kids. We go over each expectation. We learn how to find the next blank page (so the kids won't flip to the middle of their notebook to do a problem). We learn how to use the glue properly (both glue stick and bottle) to glue problems and activities in our notebooks. I continue to revisit these expectations throughout the year. You can download this PDF here:
Download Math Journal Expectations
5. Now you're all ready. Please remember that the first few days weeks of problem solving might be a little ugly. Despite your best efforts, kids will still glue their pages together. They will still flip to the middle of the notebook to do a problem. Their drawing/fine-motor/writing skills are still developing, so the journals will be messy (messy...messy!) And I promise you at least a couple of kids will flip their journals completely upside down and start in the back--happens every year! But everyday, it gets a little better. You'll be amazed at how different their notebooks look in a month or two. Don't give up!
OK...off to check the next thing off my list! Bye!
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