Archive for January, 2010
Tens frames are a great tool for teaching guided math lessons. The ten-frame provides a spatial representation that supports children’s visual understanding of “five-referenced, ten-referenced, and doubles-referenced conceptions of numbers up to ten and the development of mental imagery for such numbers. It also supports development of partitions of ten.
Teachers should start off by using 5 frames to make sure that students learn the complements of 5. Then they can move on to using 10 frames. These frames can be used to teach students at the concrete, pictorial and abstract level. Use two color markers (if you don’t have these then just spray paint some lima beans so they are two-colored). See the ideas and links below for resources.
Concrete Level Activities:
1. The markers are tossed and then placed on the board. The children add up how many are red and how many are white. They do this several times, noticing the different ways to name 10.
2. A number is generated with dice, dominos or cards and then the children place that many markers on the board. They have to tell how many more they would need to get to 10.
1. The children actually play the above games, but color in where the markers would go.
2. The children play games with ten frame flash cards. This is a great way to illustrate FACT Families. They get to SEE the FACT FAMILY in this way.
1. At the abstract level, students are bringing together their understandings and actually working with the numbers by writing out the number sentences. At this level I have students make a book and write the number sentence under each representation.
2. I also have the children match the picture of the ten frame with the correct number sentence.
3. Here are free downloadable worksheets using 10 frames for problem solving. http://www.fuelthebrain.com/Printable/boosters.php?p=1&act=tags&val=combine&gr=
DOUBLES TEN FRAMES
Use these to teach complements of 20. Also use these to teach doubles and double +1 facts. So for instance, you have the students illustrate 3 +4 so that they can see this is a doubles +1 fact… have them do the +1 in a different color so it stands out. You would illustrate this at the concrete level and then carry it over to a pictorial level by drawing it and finally by having the children find all the double +1 facts in a stack of flash cards. You want them to easily recognize doubles +1 facts because it helps with their automaticity. You can definitely lay the foundation by illustrating and practicing with the tens frames. Great activity and song for teaching compensation with 9’s using a tens frame http://www.songsforteaching.com/carlsherrill/9bemyfriend.htm
More Ideas and Games:Read Full Post | Make a Comment ( 2 so far )
When teaching a guided math lesson, you always want to think about providing concrete, pictorial and abstract activities. You want to make sure that you are asking questions that make students think mathematically and justify their answers. These are the types of activities that build conceptual understanding but also help build automaticity. When the students are counting the pips they are working on understanding the numbers and how they are represented. But, when they are working on the fact sorts, they begin to build automaticity and fluency because they are thinking about the types of facts. I call fact knowledge, knowing the Dolch words of math. If students can look at a fact and recognize it as a double and then add fast, it gives them automaticity. If they recognize, “oh, that’s a plus 1 fact, I just count up one number” then they are building their fluency. If they can recognize, “oh that’s a doubles +1 fact, I just double and add one more” then they can add fast without using slower strategies such as counting on their fingers or counting up. Once children have conceptual understanding, we want them to have procedural fluency and automaticity. Dominos is a great tool to build that.
Concrete Level Activities: ACTIVITY A: Students match number facts with dominos. The good thing about using dominos is that the children can count the pips. I tend to have a wide assortment of dominos in the classroom. ACTIVITY B: Students create their own dominos with big dots (from Staples). You can either give them a large construction paper template or have them make their own.
Pictorial level: ACTIVITY A: Students pick a domino and draw it on a blank template. They then write the number sentence. ACTIVITY B: Using the fact sheet (which is differentiated by readiness) students paste a paper domino with the correct fact. They also play a domino match game, where the facts are on one side and the dominos on the other and they connect the ones that match with a line.
Abstract level: ACTIVITY A: Domino Fact Sort. Students have differentiated sorting sheets and they sort the facts according to specific criteria. For example, on one sheet students sort doubles dominos from all other dominos. ACTIVITY B: Domino Fact Sort Races. Using a sand timer, students see how long it takes them to find and sort various facts on a template.Read Full Post | Make a Comment ( None so far )
In this activity, students receive a template with number facts. They then have to find the fact domino that matches the number sentence. I do this activity with novice mathematicians so they can begin to sort fact dominos and put the domino representation with the number model. Students enjoy Domino Fact match. I ask them how they know it’s correct. I want them to justify their answers. For the more advanced students we play a different version, where there is a missing addend. Here is great link to domino math ideas and blackline masters:
It is really important that while the teacher is conducting a guided math lesson, that the other students are engaging in activities that provide purposeful practice. These activities should be differentiated so that children are working on the skill sets they need to grow. Here is a great website with some pictures from an early childhood class, that shows the kinds of activities that the other students can be doing. http://www.windham.k12.me.us/wsd_primary/staff/mhalpern/math.cfm
Shaving cream numbers is always a hit because it taps into the bodily-kinesthetic learning style. The block building does too. I would be sure to differentiate these activities. For example, the task card for the novices would say draw different numbers that they should be working on…ones they are having difficulty with, doing reversals or just learning. Whereas with the experts, I would have them writing number sequences and two digit numbers.
In terms of the blocks, I would give different groups, depending on their readiness levels, different amounts to build. So, the novices might be building block structures with amounts from 5-15 and the experts might be using 25–30 blocks. I would also have the children draw and or write about what they built, using their math words. This could be done on scaffolded graphic organizers, so for some students they would check off what they used, while for others, they would draw what they used and name it.Read Full Post | Make a Comment ( None so far )
It is really important that students have ways to talk about math. We need to teach them how to have accountable conversations in math. We have to teach them how to justify their mathematical thinking, question each other and question themselves. We should definitely make accountable talk charts for math so that students have ways of talking with each other. A sample chart might look like:
|Accountable Talk in Math Class|
|When Explaining I can say||When asking questions I can say||When needing help|
|I got my answer by….This is the strategy that I used….First I, then I….finally I….
I think I am right because
I got a different answer. This is what I did….
|How did you get that answer?How do you know it’s true?||I don’t quite understandI’m not sure aboutCan someone explain that again to me please?
Who gets it, cause I’m still confused?
Who can help me?
This book by David A. Carter is great for teaching Plus 1 facts. It is this fantastic pop-up book, that counts all these amazing things that pop off the pages, plus one red dot. We follow up with a 3 level lesson.
Concrete level: Students roll the dice and count out the unifix cubes and build a tower. They then add 1 red unifix cube.
Pictorial level: Students then draw a picture of their tower.
Abstract level: Students add the number sentence.
Follow- Up: Get red dots from Staples. Students roll the dice and then draw that many squares. Then they add one red dot. We also make our individual and class versions of One Red Dot.Read Full Post | Make a Comment ( None so far )
Picture Books are great springboards for guided math lessons. They allow you to immediately engage the students through storytelling and then to follow up with appropriate intervention or extension activities. I will be sure to discuss my favorite books on this blog. I buy most of my books used from Amazon and Barnes and Nobles online. I get them for really inexpensive amounts, ranging from 2 cents to $10 and then I pay for shipping. I belong to Amazon Prime so I get shipping for free sometimes and usually within 2 days.Read Full Post | Make a Comment ( None so far )
It is really important to remember that math is a language. So for students who speak English as their first language, it is then a second language. For our ELL students it is the third or fourth language. So we have to teach it like we would teach any foreign language. Let the students act out math. Let them sing math. Let them role play math. Let them live math in a way that makes it come alive! Be sure to read the latest books on teaching math to ELL learners! Here are some resources:Read Full Post | Make a Comment ( None so far )
|Framework for a Guided Math Lesson|
|Mini- Lesson||Present the student activity||Share/Debrief|
|A. Hook the students||A. Children try problem, strategy or skill (often done with a partner initially; done as a game, on a graphic organizer; manipulatives are often used as part of learning)||A. Start Conversation with a Question stressing Focus of Lesson|
|B. Explain Focus of Lesson (1 or 2 teaching points)||B. Children engage in guided practice as the teacher constantly checks in with each student for understanding||B. Facilitate discussion about the math practice|
|C. Present the concept, strategy or skill for the day||C. Teacher takes notes, fills out checklist, asks questions||C. Ask for points of clarification, confusion, comments. * Make sure to touch base with each student throughout this period. Each child should be doing some independent math work and reflect on this during the debrief|
|D. Model, check for understanding, do with children,||*(Interact with the students while they are doing the math; provide necessary scaffolds and interventions throughout the lesson; ask thought-provoking questions)|
|*(Give overview of content, strategy or skill; Review)|
|Further Practice: Center Work and Homework|
Teacher engages in focused talk, utilizing various “talk moves” throughout the guided math discussion. Chapin, O’connor and Anderson (2003) propose 5 talk moves. The first talk move involves “revoicing” repeating what the student has said. The second talk move involves asking students to “restate” what one of the peers has said. The third talk move requires that students consider each others’ reasoning by “agreeing or disagreeing” with a bodily gesture- such as thumbs up or down. The fourth talk move asks students to “add on” or contribute, extend or expand upon what has already been said. The fifth talk move requires teachers to use wait time so that students have time to process their own thinking and prepare to talk. Throughout the Guided Math lesson, teachers should employ these talk moves in order to better facilitate the discussion and hold the children accountable to the ongoing conversation.Read Full Post | Make a Comment ( 1 so far )
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