Today we measured Nathan. We wondered what to measure him with. Aidan suggested cubes, Angus suggested books, Azi Hedeleen and Leander thought wooden pegs would be good. Leona volunteered to do the measuring. She chose red pencils. Nathan lay down and Leona laid the pencils out in a line. Jaiden pointed out that the pencils didn’t start at the bottom of Nathan’s feet. Leona corrected this and carefully placed the pencils in a line to the top of Nathan’s head. However Scarlett noticed the pencils were not touching, “so there is gaps that didn’t get measured“. Leona made sure the pencils we all touching. Once everyone was satisfied, we all counted the pencils. 14. “That means Nathan is 14.” said Aiden. ”Yeah” agreed Jaiden. “Not 14 like his old, but 14 high.”
Shoei wanted to have a turn. There were only two red pencils left, so he decided to measure Nathan using orange pencils. Nathan was 8 orange pencils long. Now we had a problem- was Nathan 14 or 8?
Lovisa decided to solve the problem by measuring Nathan one last time. She got the yellow pencils and carefully laid them out. Oh oh! Nathan was 11 yellow pencils!
Jaiden noticed that the pencils were different lengths; red pencils were the shortest, the yellow pencils were the next longest and the orange pencils were the longest of all. (We had an interesting conversation about why that might be. A few children figured out that the red pencils must get used more and therefore concluded that red must be most people’s favorite color – a lovely authentic survey and data collection and graphing opportunity that I let go (for now) as I wanted to focus on the measuring.)
I asked the children what answer we should tweet to KinderPals. Some children thought we should tweet all answers. Others thought we should choose the biggest answer. One person thought we should tweet the yellow answer as yellow was her favorite color. After much discussion, the children reached a consensus that we should tweet all three answers and explain that one was short, one was a little bit long and one was the longest. Scarlett suggested that we needed to mention “one what? They need to know what the thing is, like a pencil“. She was out-voted. I decided not to interfere at this stage, but to wait and see how the inquiry unfolds; finding out for oneself is a much more powerful learning experience than being told.
The KC children are delighted with their work. I am wondering what KinderPals will make of this information. I look forward to seeing how KinderPals respond and where this inquiry will go next.
When the children came together to plan what learning they would share with parents this month, someone suggested one of the counting games we play regularly. This gave someone else an idea about a game with a 100 square. This made someone else think of a card game we often play. That reminded someone else of a dice game! Before long, we had a long list of number engagements to share at our monthly parent sharing session.
It is delightful to see the children so deeply engaged in explaining the games to their parents, offering help and sharing strategies when needed. This role reversal, with children as teachers and adults as learners is a powerful experience for both children and parents.
This morning, two children from Grade 1 made an announcement over the school speaker system to tell everyone that today was the one hundredth day of school. The children in KC were quite impressed. We decided to change our usual number of the day inquiry and to conduct an inquiry into “How much is 100?“. Children worked on their own or in pairs to count 100 objects. I asked the children to arrange their objects in such a way that the objects could be quickly and easily counted by someone else.
100 Days of School on PhotoPeach
The children were deeply engaged. They all chose to continue working on their 100 collections during Free Inquiry Time. There was a buzz in the room as the children checked each other’s work, pointing out mistakes and commenting on interesting strategies. A couple of the children suggested drawing their collections so that they woud have a record of their work once everything was tidied away. The other children liked this idea, and everyone made some kind of written record of their collection. Several children have chosen to put this work in their portfolios.
I was able to use some of the ideas we explored last week with visiting Math consultant, Michael Ymer, regarding place value and counting in tens, to help the children deepen their understanding of the decimal counting system.
Playing cards are a wonderful way of developing children’s mathematical skills and thinking, from Kindergarten all the way through to Upper Elementary. This link shows some examples. Personally, I don’t call the games ‘War’, and I find the child in the video is developmentally a bit young for these games, but the link gives some idea of the versatility of playing cards as a mathematical tool.
Today I introduced the children to playing cards for the first time. I was interested to see what the children already knew about the cards -what prior knowledge and experience they were bringing from home. For this engagement, I asked the children to choose their own partners, but to work with someone they had not worked with today. I invited them to play with, organize or sort their cards any way they wished and told them that they should be prepared to share what they had done when we met together at the end of the session.
Below are some of the observations the children shared at the end of the session
I noticed that some cards have faces and those ones have letters instead of numbers.
All of the faces are different; all the ladies are different and the mans.[sic]
I noticed that as well, some have numbers and some have letters.
Some numbers have more than one.
Because there is four of everything.
There are different shapes like clovers and hearts and aces.
I know these at home.
There’s a A and two Js and K.
K is for king. And there’s a queen with a crown
There are dot shapes the same as the numbers, like on the three is three shapes like hearts.
My observations tell me that many children know quite a bit already about playing cards and how they work. This exploring session has given the children a chance to look closely at the cards, and to observe carefully, compare, question and hypothesize. This will be a good foundation for the number strategizing work we will do with the cards in the following weeks.
Yesterday, at tidying-up time, I overheard the following conversation between Trenton, Nikhil, Hal and Leander as they tidied plastic tiles into the tile tub.
Leander: Here is so many!
Nikhil: Yeah, one hundred!
Leander: I think one thousand.
Nikhil: No, it’s more. It’s ten hundred. And even a hundred hundred.
Hal: A thousand hundred.
Trenton: A million.
Hal: A billion.
Leander: A million hundred.
Nikhil: No, because million is the biggest.
Trenton: But nothing is biggest because numbers never stop. They always not stop counting because always more
Nikhil: But not more than a million.
Leander: I think two hundred 0r one hundred
Hal: But we can’t count because there is too many.
Nikhil: But we can’t count. How we can count? Too many.
Trenton: But we can still count.
As I listend to the conversation it occurred to me that there were several possibilities for further exploration: the infinite nature of numbers; place value; estimation; counting large numbers. I have observed that recently quite a few of the children have shown a particular interest in counting large numbers so I decided to follow that line of inquiry.
At our next meeting, I told the children that I had noticed that many of them seemed interested in counting big numbers, and I wondered if we should make some time to explore this more. The children responded enthusiastically. ”I LOVE to count!”, said Rika. “Me too!”, rang out a chorus from other children. For this engagement I had decided that I would group the children, rather than having them choose their own partners. I paired some children with partners of a similar ability and paired others in mixed ability groups, depending on the children’s social and developmental needs. I decided not to give the children much direction at this stage, and to observe carefully to see what they did. I was particularly interested to see what counting strategies the children would use when faced with a large number of objects (between 100 and 1000). In math circle times, we have been skip counting in twos and tens. I wondered if any of the children would transfer those skills to a hands-on counting task.
Throughout their inquiries the children were engaged and focused. There was a purposeful hum of activity as the children went about their business, trying out strategies, encountering logistical problems and coming up with new strategies to overcome those problems. This will be an ongoing inquiry. The adults in the team have been engaged in conversations about how we can best support the children in their inquiries. We wondered at what point we should intervene and model the strategy of grouping in tens. For now, the children are engaged and motivated and are clearly learning so I see no need to intervene. Finding out for oneself is so much more powerful than being told.
The children have been exploring shape. I begin this session by asking the children what a shape is. They call out their own theories and add to and challenge each other’s theories.
Ryan: It’s lines
Nia: Not only lines, because it’s curves too.
Hal: Yes, lines and curvey shapes
Nikhil: Like circle because circle is shape
Trenton: But they is lines, straight ones and curve one is all lines
Rika: Yes because Mr Welk say that
Trenton: But shape is in the lines
Olivia: When the lines come together and cross over then it makes a shape inside.
The children like Olivia’s definition. I write the definition up on chart paper and display it so that we can revisit it in future sessions.
The children go off to explore the shape materials and continue their own inquiries. I decide to leave the inquiry open, but suggest to the children that they might like to explore ways of sorting the shapes. As I expect, some children prefer to follow their own ideas while others are interested in pursuing my suggestion and set to work sorting and categorizing.
At the end of the session, we gather on the carpet and children share their discoveries. It seems that after a varied start, many children have ended up sorting shapes. As the children explain what they did, a pattern emerges:
Maya: I know this sort! It’s with how many sides
Nia: Yes, I guessed that too. I knowed it is three and four and six (sides)
Olivia: That’s just what we did! That’s how we sorted our shapes too!
I ask the children what we could name the sets. Ryan suggests that we call the sets threesters, foursters, fivesters etc, according to the number of sides. “That’s great idea!” says Hal and the other children agree.
I decide that this is a good time to introduce the children to Greek and Latin prefixes. To start with we focus on tri and quad. We have come up with lists of words that have these prefixes
Perhaps you can think of some more? Over the next weeks, we shall continue with our inquiry into sorting and categorizing shapes, and into shape names. Please join in at home!
We have begun a collaborative inquiry into shape. The central idea is that the paths and boundaries of natural space can be described by shape, which helps us to understand and explain our world. We want the children to develop their understanding that shapes have characteristics that can be described and compared, and to begin to develop a common language to describe paths, boundaries and shapes in their immediate environment.
I begin by explaining that we are going to start a new math inquiry; an inquiry into shape. The children respond enthusiastically, and begin to share the wealth of knowledge that they bring to the inquiry:
That’s a great idea! I know lots about shape!
Me too, because I have shapes in my home, so many.
Diamond is a shape.
And there is even shapes in this class room.
And square and rectangle and egg is shape.
But not egg.
Yes, because my mummy tell me!
I can do all different shapes
I am a shape expert.
And me, I am a shape expert
Yes, we can all be shape experts!
I am delighted that the children are so willing to leap on board the shape inquiry; I constantly struggle to find a balance between child initiated inquiries, driven by the children’s interests and passions, and my inquiries which are driven by curriculum. I am pleased that, once again, we have found overlap.
I am interested to find out more about what the children know already. I set out several tubs containing a variety of 2D and 3D shapes, including logi-blocks, power blocks, pattern blocks, clixi, lego and mini wooden building blocks. I ask the children to explore the materials in any way they like. I do not set parameters or guide-lines, but simply remind the children that we are engaging in a shape inquiry. I observe the children and take notes as they go about their inquiry.
At the end of the session, we come together on the carpet and I ask the children to share their inquiries. Some children have combined shapes to make pictures. Others have combined shapes to make new shapes. Yet others have sorted and categorized the shapes. As the children share their thinking, I listen carefully and gain an insight into both the understandings of individual children and the collective understanding of the group. This will inform my planning for the next session.
The most recent development has been a mathematical inquiry as the children used various materials and strategies to try and work out how much money we will need to buy more fish for our fish tank. We began with a discussion about how many fish and plants we should buy. The children decided that we should have a total of six fish and and six plants. Several children pointed out that since we already have one fish, we would only need to buy five more fish.
I explained to the children that we could estimate the approximate cost of fish and plants based on the information we had gathered from our research. I decided to work in $US rather than Japanese yen, as I thought it would be easier for the children to work with smaller numbers. I estimated that one fish would cost approximately $5 and one plant would cost approximately $3. I wrote the information on the white board so that the children could refer back to it during their inquiry.
I thought about whether I would guide the children’s inquiries at this stage and decided not to give them suggestions, and instead to observe the ideas and strategies the children came up with.
Some children chose to work by themselves and others sought out partners. Although there was a wide range in the level of the children’s mathematical understanding, everyone took the work very seriously. Some children selected materials to help them count, others used fingers, and still others went for paper and pencil. Children used pictures, arrows, tables and letters to show their mathematical thinking. They discussed their findings and puzzled over conflicting answers. The video clip below shows the depth of mathematical thinking and, at times, frustration, as two children compare their answers. The look of delight and satisfaction is evident on both children’s faces as they finally solve the problem! It reminded me once again of the importance of giving children time to find out for themselves, rather than giving them the answers.
Today during free inquiry time, I asked the children to use the time to find out more about numbers or patterns, the two mathematics strands we have been working on this term. Together we brainstormed some of the possibilities, and then the children went off to conduct their investigations. The children purposefully selected materials and got to work. The adults moved about the room observing and recording the children’s discussions.
It was wonderful to see how deeply engaged the children were, and how they were able to come up with investigations all by themselves.
Math Investigations on PhotoPeach
Free inquiry times provide an opportunity for children to practice skills and deepen understanding introduced in guided inquiry times.