2nd Grade Math in Focus
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August 2013
We have new curriculum maps that have more information, Common Core Standards on the document, as well as coding to match the PARCC Content Frameworks. The links to the right are the word documents. We will continue to build these maps. |
General Recommendations ·
Specifically for 2nd grade – we worked on a lesson to introduce the making tens strategy using counters and double ten frames. We began by having students tell how many counters were in a single ten frame. We showed 8. One students saw 5 + 3; another 4 + 4; another 10-2. By providing the picture of the number, then asking different students to share the strategy, more “facts” are brought to light and practiced. Students were able to understand the strategy of making tens. We told them, no more counting all or counting on. They have to begin learning these facts with this strategy. By using the counters, they were very successful. Then we moved to a two digit plus 9; 23 + 9. Students were able to tell us to make a 10 by adding one more to 9. If we take 1 away from the 23, they were not sure what they would get. Then adding 10 to 23 was very difficult.
What to do . .
- Provide more opportunities for students to interact with the problems by presenting as open-ended problems (not the teacher demonstrating right away how to solve it) – put up the problem and let students begin to think about how to solve it. Try not to show everything first. Students need to begin developing a sense of learning mathematics by trying different strategies, not just learning steps to get to a right answer.
- Fluency is a problem for students. Teachers can spend some time – about 15 minutes only- building fluency with higher level games, number talks, fluency practice. The focus should be on the strategies. Students need to be able to explain the strategy, show how it works with concrete materials, before applying to “naked” math. Send home some of the fluency practice sheets or the transition guide resources for homework.
- Try to keep the book closed during the teach/learn. Have students work on brainstorming different methods to do the mathematics. Elicit “lots” of student telling and describing.
- Use visuals – concrete, pictorial, abstract – to build understanding of the concepts. Students have to be able to manipulate the concrete, then draw it on their own, before going to abstract. Do not pull the old naked math worksheets. Students need more time with the concrete and describing the processes.
- IEP students or the struggling students – much more time developing the concept of the mathematics (apply fractions to real-life problems), estimation, placing numbers on the number line.
Specifically for 2nd grade – we worked on a lesson to introduce the making tens strategy using counters and double ten frames. We began by having students tell how many counters were in a single ten frame. We showed 8. One students saw 5 + 3; another 4 + 4; another 10-2. By providing the picture of the number, then asking different students to share the strategy, more “facts” are brought to light and practiced. Students were able to understand the strategy of making tens. We told them, no more counting all or counting on. They have to begin learning these facts with this strategy. By using the counters, they were very successful. Then we moved to a two digit plus 9; 23 + 9. Students were able to tell us to make a 10 by adding one more to 9. If we take 1 away from the 23, they were not sure what they would get. Then adding 10 to 23 was very difficult.
What to do . .
- Once the strategy has been introduced, then I would spend about 10-15 minutes a day with the ten-frames and counters doing a few problems each day.
- Students need to show how the strategy works with the counters, then begin writing the fact. Today we only wrote the fact as 9 + 7 = 16. They need to begin writing the fact as 9 + 7 = 9 + 1 + 6 = 10 + 6 = 16. You can use the number bonds to show this also. Students can show these on the whiteboard also.
- 10-15 minutes a day of this will help them develop and practice the strategy.
- Then introduce a problem that may better use doubles as 6 + 5. Remember, it is NOT doubles plus one. Let students describe the strategy using the ten-frames. A student could use 5 + 5 + 1 or 6 + 6 -1. The ten frames provides the visual.
- Lots of practice with the ten frames daily will help build conceptual understanding and then put it into long term memory!
- Remember, that students are not mastering the traditional shortcut algorithm. They can solve the problems using the manipulatives and should master partial sums and then regrouping first. Continuing to see the shortcut algorithm in 3rd will provide students the background to master this in 4th grade!
- Set up stations with different activities for students to engage in building understanding of the strategies to operate! Students need lots of practice with counting and hands-on activities. This link provides hands-on activities with dot patterns and ten-frames to build fluency. http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf
2012-2013 School Year Notes
February 2013
We discussed the pacing for the program and what are the major clusters in each level. This year, we need to make sure to teach Chapter 10, 11, 13, 14, 15. Then at the end, if time permits, go back to Chapter 12. This will ensure the major clusters for the Common Core State Standards. For the assessments, let students find their mistakes and work to build understanding of why they
missed the problem. The teacher can model how to think through one, and then let students work on their own to find their mistakes.
We worked on an addition table to help students see how many facts they need to memorize. We strategically color-coded the table
to show where are the facts that deal with the 0 rules, counting on strategy (1 and 2 facts), ten facts, double facts. Then using commutative property, there are not many to memorize. Teachers can work on number talks that focus on these strategies. We will also be working on math sprints.
For the strategies with computation – focus on the left to right process for addition called partial sums as well as the traditional method of beginning in the ones place. To help students, we may need to write the expanded form out to the side.
271 = 200 + 70 + 1 Make sure students understand this is 2 hundreds + 7 tens + 1 one.
+27 = 0 + 20 + 7 Again, emphasize this is 2 tens + 7 ones
200 200 + 90 + 1
90
8
298
We can do that with the subtraction also. Please look at the Let's Stick to Math link above for the algorithms and explanations.
Student can benefit with extra practice with number bonds. We used an example of 125 to have students show different ways to make 125. Show how the number bond can show more than two parts.
Model drawing - Keep the focus on reading and understanding the problem (not on key words).
Have students read the problem. What do we have to answer? (You can write this in a sentence with a blank.) Then, to understand the problem, they have to re-read each sentence to create their diagram. They put down the who/what, draw the bars to represent the problem. The bars show the quantity and relationships of the quantities. Adjust these as the problem is re-read. Placing the question mark or marks is very important.
From the drawing, students should plan their solutions and write equations to represent the problem. After solving, don't forget the checking! Plug the value back into the drawing. Does this answer make sense?
We discussed the pacing for the program and what are the major clusters in each level. This year, we need to make sure to teach Chapter 10, 11, 13, 14, 15. Then at the end, if time permits, go back to Chapter 12. This will ensure the major clusters for the Common Core State Standards. For the assessments, let students find their mistakes and work to build understanding of why they
missed the problem. The teacher can model how to think through one, and then let students work on their own to find their mistakes.
We worked on an addition table to help students see how many facts they need to memorize. We strategically color-coded the table
to show where are the facts that deal with the 0 rules, counting on strategy (1 and 2 facts), ten facts, double facts. Then using commutative property, there are not many to memorize. Teachers can work on number talks that focus on these strategies. We will also be working on math sprints.
For the strategies with computation – focus on the left to right process for addition called partial sums as well as the traditional method of beginning in the ones place. To help students, we may need to write the expanded form out to the side.
271 = 200 + 70 + 1 Make sure students understand this is 2 hundreds + 7 tens + 1 one.
+27 = 0 + 20 + 7 Again, emphasize this is 2 tens + 7 ones
200 200 + 90 + 1
90
8
298
We can do that with the subtraction also. Please look at the Let's Stick to Math link above for the algorithms and explanations.
Student can benefit with extra practice with number bonds. We used an example of 125 to have students show different ways to make 125. Show how the number bond can show more than two parts.
Model drawing - Keep the focus on reading and understanding the problem (not on key words).
Have students read the problem. What do we have to answer? (You can write this in a sentence with a blank.) Then, to understand the problem, they have to re-read each sentence to create their diagram. They put down the who/what, draw the bars to represent the problem. The bars show the quantity and relationships of the quantities. Adjust these as the problem is re-read. Placing the question mark or marks is very important.
From the drawing, students should plan their solutions and write equations to represent the problem. After solving, don't forget the checking! Plug the value back into the drawing. Does this answer make sense?