Notice how she used a sign at the bottom of the chart to help the students reflect not only on what to put in an answer, but also on what they can do to improve their answer as well.
Friday, September 23, 2011
Grade 3 Success Criteria
Here is a picture of the Success Criteria that Arpine created with her Grade 3 class after they solved a problem on their own.
Notice how she used a sign at the bottom of the chart to help the students reflect not only on what to put in an answer, but also on what they can do to improve their answer as well.
Notice how she used a sign at the bottom of the chart to help the students reflect not only on what to put in an answer, but also on what they can do to improve their answer as well.
Using The Walls To Improve Students Strategies
Arpine's Grade 3 class was about a week into their unit on Patterning and Algebra. She was finding that the students were always using pictures as a way to communicate their thinking. They had been exposed to different strategies (like using a number line) but were always going back to drawing a picture. Not only is the strategy not varied, it also was taking them a lot of time to complete their work!
As she headed to her class one day she noticed the work of Brian's Grade 6 class posted on the wall. She stopped and had a look at what they were doing. They too were doing Patterning but had shown different strategies in their answers. So she decided to take her class down the hall to look at the wall before she gave them their next problem. This is what they saw:
Here are samples of some of the different strategies that she go after the walk:
To consolidate this lesson, they then created an anchor chart with the strategies that they could now use to help them when they solve a problem. Even though they choose not to use some of these strategies, they remembered seeing them done by the Grade 6's and wanted to include them for future use.
As she headed to her class one day she noticed the work of Brian's Grade 6 class posted on the wall. She stopped and had a look at what they were doing. They too were doing Patterning but had shown different strategies in their answers. So she decided to take her class down the hall to look at the wall before she gave them their next problem. This is what they saw:
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The "Wall" of student work.   |
When the students went back to their class something happened. They wanted to do what the Grade 6 students did. They now had seen different ways to find patterns, and wanted to demonstrate their thinking in a different way. Here is a sample of the work Arpine was getting before looking at the "wall"
Here are samples of some of the different strategies that she go after the walk:
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| These students decided to try a number line. |
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| This student attempted to use tally marks to help show their thinking. |
Why Minds on Matters
Part of Sarika's Annual Learning Plan this year is to become more familiar with, and use more regularly, the three part lesson in her math class; and to become more comfortable with (and consistent with) teaching through problem solving. Her Grade 5's are currently learning how to make a table of values and how to recognize patterns.
She has modified problems from her text to use as the "action" part of her lessons for a week. She was able to break down the problem into multiple parts so that the problem is not only extended, but the students can use information they already know from a previous problem and apply it to the problem they are working on.
In this lesson her minds on activity was having the students identify the pattern and extend it on a table of values. The first table was a simple growing pattern that increased by 5 each time. The class talked about what the pattern rule would look like in words and recorded that beside the table.
For the second table of values the students were only given two terms then they were asked to talk to their partner about what thought the next term value would be.
When the students were done they gave us a "thumbs up" sign, and when the majority of the class was showing "thumbs up" the students shared what they thought the next term value would be. One student said it would be "93" and another justified that by saying that "the pattern rule would be start at 31 and add 31 each time". This was recorded on the board. (We used initials and a chart to record their answers and thinking). The students were asked if this could be the only possible number. They were then shown 124 and asked to discuss if they thought it was possible or not to be used as the next term number.
At first there were a few puzzled looks. The majority of the class could not see that multiplication was also a way to extend patterns. A few then began to think of "doubling" and then one student put up his hand and said that it could be the next term because if we "multiplied 31 x 2 we would get 62...62X2 we would get 124..We could then do 124x2 and get 248 for the next term." The light bulbs went on.
Why this Minds on was important for Sarika is that it gave her a lot of information about her class. She knows that they are able to identify and express in words what a pattern rule is, they can extend a numeric pattern, and are working on making predictions about growing patterns. She knows that for her next few lessons, she will have to include problems and activities that involve using multiplication and addition in the patterns, and encourage the students to use these tools to help them solve problems.
She has modified problems from her text to use as the "action" part of her lessons for a week. She was able to break down the problem into multiple parts so that the problem is not only extended, but the students can use information they already know from a previous problem and apply it to the problem they are working on.
In this lesson her minds on activity was having the students identify the pattern and extend it on a table of values. The first table was a simple growing pattern that increased by 5 each time. The class talked about what the pattern rule would look like in words and recorded that beside the table.
For the second table of values the students were only given two terms then they were asked to talk to their partner about what thought the next term value would be.
When the students were done they gave us a "thumbs up" sign, and when the majority of the class was showing "thumbs up" the students shared what they thought the next term value would be. One student said it would be "93" and another justified that by saying that "the pattern rule would be start at 31 and add 31 each time". This was recorded on the board. (We used initials and a chart to record their answers and thinking). The students were asked if this could be the only possible number. They were then shown 124 and asked to discuss if they thought it was possible or not to be used as the next term number.
At first there were a few puzzled looks. The majority of the class could not see that multiplication was also a way to extend patterns. A few then began to think of "doubling" and then one student put up his hand and said that it could be the next term because if we "multiplied 31 x 2 we would get 62...62X2 we would get 124..We could then do 124x2 and get 248 for the next term." The light bulbs went on.
Why this Minds on was important for Sarika is that it gave her a lot of information about her class. She knows that they are able to identify and express in words what a pattern rule is, they can extend a numeric pattern, and are working on making predictions about growing patterns. She knows that for her next few lessons, she will have to include problems and activities that involve using multiplication and addition in the patterns, and encourage the students to use these tools to help them solve problems.
Wednesday, September 21, 2011
But they only have one strategy. Now what?
Vicky gave her Grade 4 class a question relating to their upcoming Curriculum night BBQ. The students completed a K-W-C chart to help them decode the information from the problem. Her group of students is very comfortable with problem solving, and was not only able to quickly complete the chart, but also infer things that were in the problem (e.g., we need to remember the number of students in our class - 19).
When the students completed the problem, she noticed that almost everyone used the same strategy - Drawing a picture. So she wondered how to get them to do things in a different way, perhaps one that is a little more quicker, and shows a bit more understanding of patterns.
She got them to talk a little bit about their work in a congress. As the pairs began to talk, probing questions were asked and that helped them pull out ideas, make connections between their thoughts and their work, and have their thinking challenged. As the congress was going on, a chart was created to show the different ways that they could have solved the problem.
When the students completed the problem, she noticed that almost everyone used the same strategy - Drawing a picture. So she wondered how to get them to do things in a different way, perhaps one that is a little more quicker, and shows a bit more understanding of patterns.
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| Drawings of Tables |
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| These students started to use numbers and pictures |
Vicky also included the statement "The pattern rule is" because she knew from her ONAP pre-assessment that the students were having difficulty in writing out the pattern rule in full using words. After the chart was made, the students then were posed the question "If you were to do this problem again, what strategy would you use and why?" There responses were very insightful and meaningful. The best one was that the student commented on the fact that they would use the number line because then they would be done their work a lot quicker. :)
Getting Ideas for Problems
Arpine teaches Grade 3 and wants to incorporate more problem solving into her math program. She found some problems at www.mathwire.com but wanted to open them up a little bit more so that there were more points of entry for her students. She also wanted to introduce the K-W-C to her class to help them get started at solving problems. In creating a few problems all at once it not only helps her with planning, but also helps her to allow her students the time to build on their new learning, and try different strategies out.
Here are a few of the problems that she modified to meet her needs. She used the names of teacher in the building to help make the problems more "real" to the students. As well, she began to incorporate multi answer questions for her students to answer so they become accustom to completing mult-step questions.
Here are a few of the problems that she modified to meet her needs. She used the names of teacher in the building to help make the problems more "real" to the students. As well, she began to incorporate multi answer questions for her students to answer so they become accustom to completing mult-step questions.
One Expectation, Three Ways
Jenine, Michelle and Janice all teach Grade 3 at three different schools. They are all working on the first overall patterning expectation of describe, extend and create a variety of numeric patterns and geometric patterns. Here are some of the ways that they started their units.
Jenine started her unit with looking at number patterns. The students completed a problem about a classmate. They also did a K-W-C chart to help them comprehend what the problem was asking of them.
The students then got to work solving the problem in similar ability pairs. When they had completed the activity, we did a congress to consolidate their learning.
The students who shared their work were chosen because their work showed strategies that were different. One group re-created a hundreds chart to show what they thought the pattern might be. This opportunity was then used to show the class how you could also use a number line to show the same thinking (and with doing a little less writing!)
At the end of the lesson, a highlights sheet was created to show the students the different strategies that they used to solve the problem. This will then help them complete problems later on in the unit.
Michelle used a different approach to start her unit. She began by having the students orally share what they knew about patterns. She then had them create a pattern of their own. When they were done making their pattern, they talked about the pattern that they had made. Michelle recorded these words on a chart under two headings "Words" and "Attributes"
The students then went back to their desks and used the vocabulary to write about their pattern.
(Click on the picture to see what the student wrote clearer). The students now have a good understanding of what attributes are, and how to use words to describe patterns. From this activity they were able to demonstrate if they can create, extend and describe patterns.
Janice used technology and art to help her class get a grasp of patterns. She gave them a digital camera and they went around their school looking for patterns that they saw in the world around them. Not only did they capture that pattern in a photo, they then wrote about and extended their pattern the next day. Here are a few examples of their real life patterns.
Janice also has her learning goals and success criteria posted for her class to see.
Three different ways, but three great starts to the Patterning unit!
Jenine started her unit with looking at number patterns. The students completed a problem about a classmate. They also did a K-W-C chart to help them comprehend what the problem was asking of them.
Michelle used a different approach to start her unit. She began by having the students orally share what they knew about patterns. She then had them create a pattern of their own. When they were done making their pattern, they talked about the pattern that they had made. Michelle recorded these words on a chart under two headings "Words" and "Attributes"
The students then went back to their desks and used the vocabulary to write about their pattern.
Janice used technology and art to help her class get a grasp of patterns. She gave them a digital camera and they went around their school looking for patterns that they saw in the world around them. Not only did they capture that pattern in a photo, they then wrote about and extended their pattern the next day. Here are a few examples of their real life patterns.
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| This student noticed two patterns - the colours of the desk tops and also the tiles in the floor. |
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| A very observant student noticed that the Principal's tie and shirt had patterns in them. |
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| Even the heater proved to have patterns in it! |
Janice also has her learning goals and success criteria posted for her class to see.
Three different ways, but three great starts to the Patterning unit!
Saturday, September 10, 2011
Starting A Unit - What Do They Know: Part Two
As a follow up to the previous lesson, Brian turned to the ONAP 6 package he has (available through Nelson Canada) to help him get some ideas on where to go next. They have a pattern matching game that he decided to use with the students to get them looking more in depth at what a pattern is, and the different ways you can represent a pattern. Using his ELMO, Brian demonstrated how to play the game, but also had the students talk about what they were seeing on each card and what knowledge they could use to determine if it was a match. (The cards represent patterns in four ways: Table of values, in a model, a pattern rule (in words) and in number pattern form).
After the student's did that, he had each student select a pair that they had successfully found. His question to them was "How do you know your cards match? Justify your answer." He then modeled for them how to write an answer that involves them justifying their answer. He then had the students re-read the answer and point out what key math vocabulary words were that should be in a good answer.
He differentiated the lesson by having students do this for either one or two pairs (so the struggling students could focus more on the quality of their work than the quantity of their work) and also had students who were finished quickly then make another representation of the pattern.
For students who finished one answer fairly quickly, descriptive feedback was given to them so that they could use it on the next answer. The pictures below show the different responses and the different descriptive feedback that was given: (My apologies for the upside down photo, just click on it and then rotate it on your desktop. A new camera is coming!)
After the student's did that, he had each student select a pair that they had successfully found. His question to them was "How do you know your cards match? Justify your answer." He then modeled for them how to write an answer that involves them justifying their answer. He then had the students re-read the answer and point out what key math vocabulary words were that should be in a good answer.
He differentiated the lesson by having students do this for either one or two pairs (so the struggling students could focus more on the quality of their work than the quantity of their work) and also had students who were finished quickly then make another representation of the pattern.
For students who finished one answer fairly quickly, descriptive feedback was given to them so that they could use it on the next answer. The pictures below show the different responses and the different descriptive feedback that was given: (My apologies for the upside down photo, just click on it and then rotate it on your desktop. A new camera is coming!)
Brian also used the Assessment for Learning Tool (A4L) to help him as he read over the student's work to keep track of the vocabulary words they were using, and to see if anyone was incorrectly using a word or a term. His next lesson will be to administer the ONAP questions to his students to then help give him a more concrete idea of where they have a lot of content knowledge, and where they are still struggling.
Starting A Unit - What Do They Know: Part One
In Brian's Grade 6 class this week he began to pre-assess his students' knowledge around patterning. The first strand he is doing is Patterning and Algebra and the expectation he is reporting on this term is Overall #1: Describe and represent relationships in growing and shrinking patterns (where the terms are whole numbers), and investigate repeating patterns involving rotations.
He began the lesson by having the students brainstorm all that they knew about patterns. At first they did some thinking on their own and then moved into "think-pair-share" with a partner and then their table groups.
Once they could not think of anything else, he then had them sort their words into three categories: Attributes, Strategies/Tools, and Vocabulary. This is now an anchor chart that they have up in the room for the students to not only refer to, but also to add onto it as new ideas and understandings come up.
Now that their schema had been activated, the students then got a chance to look at a pattern and then figure out what the pattern rule was, and also make predictions as to what the next term number would be if the pattern continued. Here is the pattern they were given: (my apologies as it should show as being a horizontal pattern and not a vertical pattern).
Many of them quickly picked up on that the pattern rule was "Start at 2 and increase by 2 each time." As well, they had a discussion as to if it mattered that the colour chips were turned over or not, and if in addition to the pattern rule, if the model of the pattern was something to consider as well. At this point one student put up her hand and said that she thought the pattern could also be "Term number x 2 = Term Value" The students set off to explore if this theory worked for different term numbers in this pattern.
When they came back they decided that yes, for this pattern that pattern rule worked and they could now be given any term number and find out any term value they needed to. They then added to the anchor chart by adding the number from this pattern to the table of values so they could refer to it at a later time.
From this lesson, Brian decided to continue on to see what else the students knew about different representations about patterns. That will be his next lesson.
He began the lesson by having the students brainstorm all that they knew about patterns. At first they did some thinking on their own and then moved into "think-pair-share" with a partner and then their table groups.
Once they could not think of anything else, he then had them sort their words into three categories: Attributes, Strategies/Tools, and Vocabulary. This is now an anchor chart that they have up in the room for the students to not only refer to, but also to add onto it as new ideas and understandings come up.
Now that their schema had been activated, the students then got a chance to look at a pattern and then figure out what the pattern rule was, and also make predictions as to what the next term number would be if the pattern continued. Here is the pattern they were given: (my apologies as it should show as being a horizontal pattern and not a vertical pattern).
Many of them quickly picked up on that the pattern rule was "Start at 2 and increase by 2 each time." As well, they had a discussion as to if it mattered that the colour chips were turned over or not, and if in addition to the pattern rule, if the model of the pattern was something to consider as well. At this point one student put up her hand and said that she thought the pattern could also be "Term number x 2 = Term Value" The students set off to explore if this theory worked for different term numbers in this pattern.
From this lesson, Brian decided to continue on to see what else the students knew about different representations about patterns. That will be his next lesson.
Monday, September 5, 2011
Back To School 2011
To all the Teachers, Principal's, ECE's, EA's, Superintendents, Coaches, IL's, and everyone else involved in educating our students, have a great first day!
Looking forward to making "Math magic" happen with you for your students.
Lesley :)
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