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I am currently using the ten frames, number lines and hundreds chart.  Until this year, I did not realize how much students need these visual images to reinforce learning.  Subitizing is something that many of my students have difficulty with.  They want to count everything one by one and I have been trying to show them how to be more efficient in seeing the numbers without counting.  These tools definitely fit in a number talk.  I have been trying to implement number talks with my students and I thought it was going to be impossible with such a small group, but the other day we experienced such success with a group of only 3 that I felt like dancing.  I couldn't believe it had finally sunk in and they really thought on their own without me prodding them.

There is great benefit in using the strategies on page 50.  It takes practice and repeated effort, but like I said before, I felt success the other day.  I got some poster board and laminated it so that I could write on it with dry erase markers and I post the strategies on the poster board.

We have been doing all the things you mentioned to try to build number relationships.  Estimating is such a difficult concept for students to master.  We started out by placing a pile of cubes in the table and I asked each student to guess how many cubes there were.  Even though there were only about 25 cubes, they all guessed really large numbers, like 75,150, etc.  After each student made a guess, then we counted the cubes and discussed how we can look at something and estimate how much that is.  After several practices, they got much better with estimating things they looked at.  Then we moved on to numbers and how close they were to the  nearest 10 or the nearest hundred to estimate them.  We solved problems using estimation, then we solved the problem using exact numbers so they could see how they relate.  We talked about when it is reasonable to estimate and when it is not.  We have also been working on breaking numbers apart to make it easier to add or subtract mentally either by using place value or to make tens.

These strategies seem very advanced for primary students, especially if the students are a little slower than average, but if you keep working at it and practicing, they begin to see the sense in it and it is no longer too advanced.  I think because as the teacher, we only facilitate the lesson and allow the students to drive it, that aids the process.  We all know that we learn better from doing and from our own mistakes, so why not allow the students to experience those same successes and failures by doing and explaining their thoughts.  It helps for them to express what they are thinking.

Today we were working on a traditional multi-step story problem in 3rd grade.  I was having the students read the problem and work in pairs to determine how to solve the problem.  They were to discuss what the problem was asking them to do, draw pictures or write a number sentence to work it out and they had to be in agreement before they presented their results.  When the students presented, I asked if everyone in the room agreed with the way the student solved the problem. It worked very well because all the students were engaged, and they discovered one another's mistakes without me having to say a word.  I was excited to see that even some of my lower students were able to see errors that were made and voice what was incorrect and why.

I plan to teach very differently next year as a result of what I have learned from the Number Talks and another book I am reading called It Makes Sense! Grades K-2 by Marilyn Burns.  I realize that many of my 3rd-4th graders lack skills.  We will need to go to a lower level to fill those holes in rather than trying to just tutor them in the skills they are learning in their classroom.  My job is to fill the holes so that eventually they will catch up and be able to understand the skills on their grade level so I think that is my lightbulb moment.......just discovering how to change what I am doing to help the students that I have and not being the answer machine, but allowing them to discover the answers and strategies for themselves.

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Math tols that I am currently using include: dot cards, hunderds charts, number line, and ten frames.  I agree with Deb S. about the level of sophistication for the first graders in reference to the problems on pg. 63.  The example of rounding up for one digit and subtract for the other digit is unlike instruction that the students have been exposed to.  I have some good math students but am afraid to attempt this!

We need ongoing professional development to keep up with the current trends.  We owe it to our students to expose them on all levels of instruction.

The traditional ways of instruction do not seem to be keeping our students competative.

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Number Talks: Chapters 3 & 4

In responsde to math tools: dot images, rekenreks, five frames,ten frames, number lines, and hundreds, I am currently not using any of these tools, but definitely will if/when I have a math class.  After talking to Gina, this sounds like what many of our struggling students need at all grade levels.

The problem on page 50 absolutely opens a door for inventing new strategies.  It breaks away from tradition. Many students of today will learn the algorithm for adding with regrouping, but will have no idea what the process truly means.  This holds true with most traditional ways of solving problems for all operations of math.

As far as helping our students to understand the importance of efficency, we might venture into other domains.  We might want to get our point across by organizing the room for books, math materials, data collecting, and forms of scheduling.

In response to the addition and subtraction strategies I was surprised with the level of sophistication for first grade. For example the problem on page 63 the student changes 18 to the friendly number of 20.  She then subtracts 2 from the addend of 23. Then she totals the addends of 20 and 21 to get a sum of 41.  What reasoning.  I really want our students to reach this level of learning.

Light bulb moments:  We as educators must up our "A" game.   The level of learning is changing rapidly. The time for professional development is imperative and must be ongoing.

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Asking students to estimate an answer before solving a problem and provide evidence that an answer is reasonable... WOW! What a transistion from some current practices of find and solve. Important concepts in in the primary grades are conservation of numbers, one to one correspondence, fluency with small numbers, subitizing, and building tens. Some great tools for developing this number sense are using dot images, rekenreks, five frames, ten frames. number lines, and hudreds charts. Are these tools that you currently use within your math lessons? Are they tools you see fitting within a short number talk on a daily basis?

Real life contexts... the benefits include relativity, attached meaning to numbers, and it makes mathematics accessible. What benefit do you see using the samle problem on page 50 of the text? Do agree that this opens a door for inventing strategies?

Keeping the students' strategies up where you can see them is important when discussing efficiency. By numbering the strategy, you can have students use their finger signs to let you know which strategy would be most efficient... this takes learning to an even deeper level. Discussing efficiency is very important. How else might we address efficiency with our students?

Building number relationships is vital in this process. Different ways to build number relationships include asking students to estimate first, which gives them a sense of reasonabless of their answer. Locating numbers on the hundreds chart and talking about their distance from the nearest ten is also another way to build number relationships. Also, have students think about equivalencies. How numbers can be broke apart and put back together.

There are some common strategies that your students will probably use when solving their problems at hand. Some common addition strategies include: counting all (counting every number), counting on (start from one and move on), doubles (adjusting number to make a double), making tens (breaking numbers apart to make 10), friendly numbers (using easy to get to numbers), compensation (manipulating numbers into a friendly number), breaking each number into its place value (expanding each number), and adding up chunks (same as breaking each number into its place value except focusing on keeping one number whole).

There are also some common subtraction strategies. These include: Adding up (add up from number being subtracted) and counting back (starting with the whole and taking away).

Do any of these strategies stand out as most common? Surprising? Too advanced for primary?

Kindergarten Number talks: designed to provide opportunities for counting, building fluency, one-to-one correspondence, and conversation of numbers. Important things to keep in mind when creating a K level talk, arrangements of figures being discussed and viewing time.

What difference do you notice in tradtional questioning and number talks prompting? (i.e. How many do you see? How do you see them?)

First Grade Number Talks: designed to provide students with opportunities to continue to build fluency with numbers up to 10 and develop beginning addition strategies.  What transition do you see from kindergarten to first grade in dot design? What patterns do you notice in the Rekenrek problems on pg. 102?

Second grade Number Talks: desinged to elicit and foster specific computation strategies. Start with small numbers so students can focus on the nuances of the strategy and build their confidence in their mathematical abilities. Do you see purpose in the problems according to the strategy that it promotes?

Light bulb moments within your readings up to this point?

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I was able to use the ten frames to try to help students understand rounding.  That is a really hard concept for them to understand especially when they don't understand place value.  For instance, to round 79 to the nearest 10, we counted out 7 ten frames to represent the 70.  Then I put down 9 individual squares to represent the ones.  I asked them to count by 10's and I wrote those numbers on the white board.  I asked them which one of the numbers on the white board was closest to 79.  We then added one more square to show that now we had 80 and another full 10 frame.  This seemed to help a little.  We shall see when we revisit the subject this week.

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Double click anywhere in the clouds and a response box will appear. Type your name and the title of your post (i.e. Chapter 2 response). Then type your post! Click anywhere in the clouds again, and your response will be posted! Check back weekly for new responses and discussion posts! Happy posting!

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Chapter 2 thoughts: Preparing for Number Talks...

Preparing for your first Number Talks session may make the teacher a little uneasy. I know I get uncomfortable when I have to do something that I have never done before, and especially when I put the pressure of being a pro at it on my own shoulders! Selecting a special location to encourage transitional thought into a Number Talks session is a great place to start! How could you transition into a Number Talks session?

Wait time is so hard for teachers to give sometimes. We all have to practice appropriate wait time from time to time. Do you think the thumb signal is a good way to develop wait time? Do you have any other wait time strategies that could work in a Number Talks session?

Accepting all answers right or wrong is also a big transition for teachers. Remember to use that "blank face" when students call out their answers! How else can we encourage an accepting environment free from fear to share answers?

Asking students to use a new strategy used during a Number Talks is a great way to add to your students' mathematical toolbox... remember, we only remember a small percentage of what we hear, but when we add action to it, we remember far far more!

What were your feelings on Classroom Clip 3.1? Did this clip help you in anticipating and recording student responses?

This chapter shared six ways to develop accountability with students. I really liked the exit question suggestion. Once again, I think it is important that students use what they hear in order to retain it. What accountability recommendations stood out to you?

I am going to end with the 5 small steps towards teaching for understanding.  I think all five of these steps are important to follow. Start out small, offer another students' strategy when in a "no-response" situation, put a strategy on the backburner to give yourself think time, limit your Number talks to five to fifteen minutes to keep engagement, and be patient (change takes time)!

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Chapter 1 thoughts...

The first important piece of information that I found with Number Talks is that it prepares students to be "mathematically proficient and compute accurately, efficiently, and flexibly". We want our students to be accurate, but how much do we focus on the efficient and flexible components?

I teach math readiness courses for a local university and the majority of the reason I have students taking the course is because they fall short in the ability to decompose numbers, they do not understand the tens system, and they have no understanding of the math properties. How do we encourage these basic yet absolutely necessary skills to be addressed in the classrooms?

Another key piece that I noticed in the reading... MATH is making sense of numerical relationships... very similar to what we focus on in reading... comprehending the relationships in the words we read... thoughts?

There are five key components of Number Talks: environment, discussions, the teacher, mental math, and purposeful problems... how do you see yourself creating a number talks environment in your own classroom realizing these five necessities?