Today we played a great game to practice place value exchanges when adding.
I started with a template of ten leaves, each with a digit 0-9. (You can find it at here) I cut the leaves out, and then placed them in a pile. Students drew four digits, and arranged them to create two two-digit numbers.
Next, students lined the two numbers up to practice double-digit addition.
Differentiation, anyone?My students--even my highest math kids-- are shaky on the concept of regrouping. Some don't "carry" at all...some do it at random...others do it, but don't have a strong conceptual understanding of what they're really doing when they "carry" a digit.
To combat the confusion, and to make more visible the need for regrouping, I took a file folder (dual purpose: use for storage afterward), opened it up, and drew a grid with boxes that would the leaves.
Another support strategy: Draw the grid on your students' personal whiteboards with Sharpie or other permanent markers. This can be removed later, and quite easily, with either bleach cloths (think Clorox or Lysol) or by simply wiping a regular dry erase marker over your Sharpie lines.
I did both, using the folder myself for demo and modeling and giving each student a whiteboard and marker to actually write out each problem (since the ultimate goal is for them to be able to line up and correctly add multi-digit numbers independently). For some of my learners, writing what they know is a critical part of committing it to memory.
In order to really make the need for regrouping more apparent, I also wrote the digits 0-9 onto post-it notes. This way, when we added digits to a sum larger than nine, I could say, "whoa! problem!" and demonstrate that I couldn't fit 2 digits into one place value position. (Eventually one of my students remarked, "Wow, Miss. You got so much problems!")
Enter the base-10 manipulatives:
Once it was obvious that all of the ones we had wouldn't fit into the ones place, I asked my students, "What can we do now? Is there any way you can get some of those ones exchanged?" After looking at the 10s-strips and 100s-flats in front of them, eventually each group figured out that I would trade them a 10s-strip for 10 of their ones. And once that exchange took place, they were able to select which of the two digits from their original answer went in the 1s place, and which went into the 10s place.
One more note of differentiation: I modified the activity even farther so that the addition was one-digit. Even students who are only adding one digit numbers can practice exchanging ones for tens, which provides them with background experience for adding double-digits later on.
...That's the long version. The short of it is that this activity was SO effective for practicing all of the skills and concepts necessary for successful double-digit addition!
Showing posts with label lesson. Show all posts
Showing posts with label lesson. Show all posts
Monday, October 24, 2011
Thursday, October 20, 2011
Helping your student understand Tracks of Thinking
So your child just brought home a clear bag filled with books, post-it notes, and a letter from their ever-zealous teacher declaring how important it is that they read and leave tracks of their thinking.
What?
This week, I introduced the children to the idea that good readers leave tracks of their thinking. For several days, I have modeled how I think as I read. I am constantly thinking. In fact, I told students, the most important thing about your reading is your THINKING about the text.
Here's a simple representation:
Think about a salad. Not a complicated salad, just a run of the mill lettuce-and-tomato deal. A big bowl full to overflowing with lettuce and tomatoes. Yum.
Now-- what is there more of in that typical bowl of salad. Lettuce? or tomatoes?
Generally the answer is lettuce.
When we think as we read, we do two major kinds of thinking.
Right There
Some of the thinking we do as we read is recalling or remembering. The information right there in what the text says or the pictures show us is important. But recalling or remembering is only a small part of really comprehending what we read. That's why our recalling and remembering are like the tomatoes of the salad-- they aren't a salad all alone, but a salad isn't a salad without them, either. (Whew! How's that for circular reasoning?) Right there thinking is important, but we also need connections, predictions, and inferences to really deepen our understanding to comprehension.
In Your Head
Those connections, predictions, and inferences you make as you read often take place In Your Head. You might never say them out loud at all, but that doesn't make them unimportant! Helping students become aware that they think as they read can be a tricky task. That's why we've taken the sticky notes in hand, in hopes of becoming more metacognitive learners-- thinking about our thinking!
If your child is having trouble identifying thinking in their head, and are stuck on telling what is happening just like the text says or the pictures show, you might point out that In Your Head thinking might sound like one of these things:
-- "I wonder if..."-- "Because.........., I think ................... will happen next..."
-- "Oh, I get it now...!"
-- "At first I thought................., but now I think....................... ."
-- "What would happen if...?"
-- "Why?"
-- "This is good because..."
-- "This is like the time that..."
-- "This reminds me of..."
Because thinking about thinking is tricky, it can be a slow process acquiring the skills to identify thinking as it's happening. Leaving tracks of your thinking is important to young readers as they learn to value their thoughts as the other critical element of comprehension.
It's unlikely, at first, that students will really be able to identify more "lettuce" than "tomato" in their thinking. That's okay. But feel free to ask your child, "Is that tomato-text or lettuce-thinking?" Encourage them to use the sticky notes to write down the thinking that is happening in their head, then attach it to the page where that thinking took place.
The Real World Connection
Very rarely do adults read text simply for the sake of recalling it later. Most often, we read to gain information that will help us make a decision or complete a process (like putting together new furniture or filing our taxes). Being able to read for information involves taking what we read and personalizing it for use ("Oh. I need to turn this board around before I screw it to the other one."; "My husband's email says we're out of milk. That means I need to buy more on the way home."). In order to do that, students need to get comfortable with the idea of actively engaging text, and learning what it means to dig in and understand.
Clearly, we are at the very early stages of this process with our young readers. Thank you so much for engaging with your child as he or she reads at home, and for supporting their learning with your time and energy resources! And thank you for supporting our class!
What?
This week, I introduced the children to the idea that good readers leave tracks of their thinking. For several days, I have modeled how I think as I read. I am constantly thinking. In fact, I told students, the most important thing about your reading is your THINKING about the text.
Here's a simple representation:
Think about a salad. Not a complicated salad, just a run of the mill lettuce-and-tomato deal. A big bowl full to overflowing with lettuce and tomatoes. Yum.
Now-- what is there more of in that typical bowl of salad. Lettuce? or tomatoes?
Generally the answer is lettuce.
When we think as we read, we do two major kinds of thinking.
Right There
Some of the thinking we do as we read is recalling or remembering. The information right there in what the text says or the pictures show us is important. But recalling or remembering is only a small part of really comprehending what we read. That's why our recalling and remembering are like the tomatoes of the salad-- they aren't a salad all alone, but a salad isn't a salad without them, either. (Whew! How's that for circular reasoning?) Right there thinking is important, but we also need connections, predictions, and inferences to really deepen our understanding to comprehension.
In Your Head
Those connections, predictions, and inferences you make as you read often take place In Your Head. You might never say them out loud at all, but that doesn't make them unimportant! Helping students become aware that they think as they read can be a tricky task. That's why we've taken the sticky notes in hand, in hopes of becoming more metacognitive learners-- thinking about our thinking!
If your child is having trouble identifying thinking in their head, and are stuck on telling what is happening just like the text says or the pictures show, you might point out that In Your Head thinking might sound like one of these things:
-- "I wonder if..."-- "Because.........., I think ................... will happen next..."
-- "Oh, I get it now...!"
-- "At first I thought................., but now I think....................... ."
-- "What would happen if...?"
-- "Why?"
-- "This is good because..."
-- "This is like the time that..."
-- "This reminds me of..."
Because thinking about thinking is tricky, it can be a slow process acquiring the skills to identify thinking as it's happening. Leaving tracks of your thinking is important to young readers as they learn to value their thoughts as the other critical element of comprehension.
It's unlikely, at first, that students will really be able to identify more "lettuce" than "tomato" in their thinking. That's okay. But feel free to ask your child, "Is that tomato-text or lettuce-thinking?" Encourage them to use the sticky notes to write down the thinking that is happening in their head, then attach it to the page where that thinking took place.
The Real World Connection
Very rarely do adults read text simply for the sake of recalling it later. Most often, we read to gain information that will help us make a decision or complete a process (like putting together new furniture or filing our taxes). Being able to read for information involves taking what we read and personalizing it for use ("Oh. I need to turn this board around before I screw it to the other one."; "My husband's email says we're out of milk. That means I need to buy more on the way home."). In order to do that, students need to get comfortable with the idea of actively engaging text, and learning what it means to dig in and understand.
Clearly, we are at the very early stages of this process with our young readers. Thank you so much for engaging with your child as he or she reads at home, and for supporting their learning with your time and energy resources! And thank you for supporting our class!
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