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Number talks were developed for classroom teachers to engage students in "mental math" through grappling with interesting mathematics problems. Educators can use number talks regularly as introductions to the day's mathematical practice, as "warm ups" for other lessons, or as stand-alone extended engagements with mathematical concepts. The teachers in these videos are from schools participating in the Silicon Valley Mathematics Initiative.

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Number talks were developed for classroom teachers to engage students in "mental math" through grappling with interesting mathematics problems. Educators can use number talks regularly as introductions to the day's mathematical practice, as "warm ups" for other lessons, or as stand-alone extended engagements with mathematical concepts.

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Number talks ( Kindergarten, 1st Grade & 2nd Grade) offer a bridge between conceptual understanding and mental math. During mini-lessons and Guided Math, I am ALL about manipulatives. Base 10 pieces, unifix cubes, cuisenaire rods - give me all the math things. Especially in 1st grade, manipulatives offer a concrete way to represent a number and their thinking. At some point, this concrete thinking has to begin to transition into abstract and mental math processes. Number Talks offer a daily, short, structured way for students to talk about math with their peers.

What is a Number Talk?

Number Talks are short (10ish minutes), daily exercises aimed at building number sense. Number sense is the ability to play with numbers meaning students can visualize problem solving, perform calculations quickly, and are flexible in their mathematical strategy. Students who have strong number sense solve problems in more than one way and check that their answers make sense. As a part of this routine, students are thinking, asking their peers questions, and explaining their own thinking all while the teacher records the thinking.

Sherry Parish has written the book Number Talks (Amazon affiliate link) and it offers awesome ideas for Kindergarten to 6th grade. It is definitely an expensive (up to $60 if bought new) but offers great ideas and real-life examples of Number Talks.

What Do Number Talks Look Like?

When possible, I love slipping a number talk ( Kindergarten, 1st Grade & 2nd Grade) in at the beginning of our Guided Math block. If we're running late, I'll slip a Number Talk in during an awkward transition or at the very end of the day. A traditional talk follows this routine -
Present the class with a problem. Students are seated in a common area with no math tools. Number Talks are mental exercises. I store my number talks ( Kindergarten, 1st Grade & 2nd Grade) on binder rings next to my Document Camera for easy access.

Give think time. (When a student raises their hand, it tells other students they were not fast or good enough in their thinking. To account for this, students give me a sly thumbs-up on their chest to signal that they have thinking they want to share. Then, they put up multiple fingers (on the same hand) to indicate they have multiple ways to answer/solve the problem.

3. Call on a student - "_______, what are you thinking?" Have the student explain their thinking and then give their answer. My focus is always on the process not the answer.

4. Offer the strategy to the class. Student will elaborate (if correct) or ask questions (if misguided). If students aren't sure they understand a friend, they will say "I'm a little confused. Could you tell me in a different way?" If students agree with the student sharing they will do sign-language for 'me too' (thumb near chest and pinky pointing at friend). This builds the student's confidence and offers the student sharing positive affirmations.

5. Invite other students to share their strategies.

Scaffolding Students

If students have never been expected to explain their mathematical thinking, students may be very resistant to share their own strategies. So, how do I encourage students to share their own thinking/strategies?

Model, Model, Model - The first 2 days of Number Talks, I do a lot of modeling. After this, I completely release the Number Talks to the students.

Sentence Stems - "In my head I saw..." "My first step was..." "At first, I decided to try..." "I needed to..." "Since I wasn't sure what to do, but I noticed..."

Force It - Awkward silence is your friend. Sometimes I will wait (for extended periods of time) for students to share their thinking. Even if a friend is STRUGGLING with a problem or sharing their thinking, I do not come to the rescue. Growth comes when friends are able to sort out their own thinking and my 1st grade friends are able to do this...even if it is a little painful for me.

Examples of 1st Grade Number Conversations

So, it all sounds great, right?? But what do number talks actually look like? My first talks ( Kindergarten, 1st Grade & 2nd Grade) each year are always subitizing patterns (dot patterns). They are the perfect introduction into composing and decomposing numbers. Slowly that transitions into the 100s chart and eventually into word problems and balancing scales.

In the 2nd grade number talks, the focus is on building fluency within 20 and 100, as well as, layering skills in different ways. From missing addends, to algebraic thinking, over 400 prompts offer students dozens of chances to spiral review math skills each month.

Subitizing Quick Images

Subitizing ( Kindergarten, 1st Grade & 2nd Grade) is the ability to quickly identify the number in a group of objects without individually counting the objects. It is a concrete way to explore composing and decomposing numbers. Students will see dot patterns in different ways, and that is a great thing. When showing students 6, made from a pyramid students might see 3 and 3, 5 and 1, or 3 and 2 and 1. These are all ways to build 6 and lead students to understand that numbers can be composed and decomposed in many different ways.

Composing Numbers

Flexibility in number thinking is a critical skills in beginning mathematicians. Students must understand that 7 can be made from 4 and 3, 2 and 5, 6 and 1, or 7 and 0. Below students are provided with a "Target Number" and ask students to use some of the provided numbers to hit the target. Students then have to decide how many numbers to use, which operation to use (addition or subtraction), and then, decide if number order matters. ( 1st Grade Prompts, 2nd Grade Prompts)

Flexibly Composing AND Decomposing Numbers

An important part of teaching primary students is to build number fluency and flexibility. Students should be able to encounter numbers in a variety of formats and engage with them in a variety of ways. During our Representing Numbers conversations ( 1st Grade & 2nd Grade), I encourage students to branch outside of the typical ten frame, plus one, etc. These are great strategies when we first start, but after the first few days students can build on these basic representations to develop different relationships and understanding.

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Number Talks: How and Why? - The Brown Bag Teacher

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Number talks ( Kindergarten, 1st Grade & 2nd Grade) offer a bridge between conceptual understanding and mental math. During mini-lessons and Guided Math, I am ALL about manipulatives. Base 10 pieces, unifix cubes, cuisenaire rods - give me all the math things. Especially in 1st grade, manipulatives offer a concrete way to represent a number and their thinking.

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Notice & Wonder Math Routine: Third Grade

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Teacher and students engage in a Notice and Wonder Math Routine. Using text without numbers, the class tries to make meaning of the content. Aligns with Common Core Standard Math.3.OA.A.3, Math.Practice.MP1.

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By Patty Reed
What is noticing and Wondering?
Noticing and wondering is a powerful tool. My favorite part about noticing and wondering is that every single student can participate mathematically. Everyone can notice something, and everyone has something they can wonder about. It's a great way to get students thinking about a problem. No matter what your background, language, gender, or family, everyone has something to wonder and notice.
Why notice and wonder?
Noticing and wondering is a routine that encourages students to make careful observations while clarifying a problem or situation. It also helps stimulate curiosity and sets the stage for inquiry.
How can this help students?

1. It levels the playing field.

2. It gets students thinking and talking early in the lesson.

3. There is no wrong answer so teachers can affirm ideas their students share.

4. It directs students' attention to the things that are mathematically important in the question or picture.

5. It gives students time to make sense of the problem without any pressure to solve it.

6. Teachers can build on what students have shared- often borrowing their exact language- to ease into the next part of the lesson and building confidence at the same time.

7. It's a life skill.

How to Implement Notice and Wondering

1. Students can identify important information in a story problem.

2. It connects their own thinking to the math they are doing.

3. It helps students notice the details in their math problem.

4. It helps students feel safe.

5. It helps students think about the problem before they start solving it.

6. It encourages the process of thinking about math and connecting ideas and wondering about it.

There are many ways to implement, but this is what I like to do:

Step 1: Put up a story problem or a picture and ask students what they notice.

Step 2:Students think then pair share their noticing with their team.

The group's recorder writes down all noticing of group members. Groups pick favorite noticing to share out to the class.

Step 3: I make a public record of noticing and keep them on display throughout the problem-solving process. Collect additional noticing that students would like represented but aren't on the class poster. Students should add noticing they like to their own recording sheets.

Step 4: Repeat the same process with wondering.

Step 5: Reflect. Looking over our list I give students a chance to reflect on their noticing and wondering. What leads to mathematical discoveries?

Step 6: Proceed with the problem.

Step 7: Check back on your noticing and wondering when you are stuck during a problem. ( If students have noticed and wondered their way into a problem, those noticing and wondering can serve as reminders for different ideas that can help students get unstuck).

Question Stems " Look at your work and your partner's work. Is there anything that jumps out at you that looks different?"

"What would be worth a try?"

"What would happen if ...?"

"Would it help to ...?"

" Would ___ work?"
Beginning to Problem Solve with "I Notice, I Wonder"from NCTM Annie Fetter video

As I guide my students in noticing and wondering their problem solving abilities increase. They are better able to noticing and wondering mathematically. This begins as a practice strategy, then a skill , that soon becomes natural to them. Students are also fulfilling mathematical practice #1 which states- Make sense of problems and persevere in solving them. And who doesn't need this skill in their life?

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By Patty Reed What is noticing and Wondering? Noticing and wondering is a powerful tool. My favorite part about noticing and wondering is that every single student can participate mathematically. Everyone can notice something, and everyone has something they can wonder about. It's a great way to get students thinking about a problem.

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This week I'm going to link-up for "Book Talk Tuesday" with Mrs. Jump's Class and a new one - "Tried it Tuesday" with Fourth Grade Flipper.

I love teaching math! I've mentioned this before, but I really do! It's hands on, full of problem solving, and there are so many great pieces of literature that connect to math lessons!

Last year we had some professional development on using the "Notice and Wonder" strategy with our students. I was immediately hooked and wanted to try run back to my classroom and use this with my students!

If you haven't heard of this strategy before it is a great way of getting your students to problem solve in math and have all students participate in the discussion. Basically you do the following:

1. Pose the problem to your students.

2. Ask them to share what they notice.

3. Ask them to share what they wonder.

4. Have students solve the problem.

5. Share!

The biggest difference is that you are not really asking them a question in the problem. I'll show you one that I plan to use with my students so you understand a little better...

If you notice, I don't actually ask them a question. However, students can still solve this problem based on the information they are given. The best part...there are SO MANY DIFFERENT ANSWERS!! This alone is a great discussion point for your students when they are sharing and you discuss why two friends came up with different answers, but are both correct!

For this problem I would write the problem on chart paper for students to see and then have them share what they notice and record what they say. Then I have them share what they wonder and record what they say. The best part about using the word notice and wonder is that students are able to naturally notice and wonder about things.

The picture that I have shared above has two copies of the same problem. A great way to differentiate is give some students the copy where they write what they notice and wonder and give some students the copy with just the jar. My plan is to have students use candy corn candy and candy pumpkins as manipulatives to solve this problem, but you could also have students use orange and yellow unifix cubes.

If you have 5 minutes, this is a great video to watch for "Notice and Wonder."

And since I'm also linking up for "Book Talk Tuesday...here is a book I like to use in math during October!

This is a cute counting book with pumpkins. The numbers double throughout the book so it's great for teaching doubling numbers and counting. The kids love it!

Hope I've been able to teach you something new!!

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This week I'm going to link-up for "Book Talk Tuesday" with Mrs. Jump's Class and a new one - "Tried it Tuesday" with Fourth Grade Flipper. I love teaching math! I've mentioned this before, but I really do! It's hands on, full of problem solving, and there are so many great pieces of literature that connect to math lessons!

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First, let me tell you how much I love Twitter for the #MTBoS. This connection has allowed me to collaborate with the great, Kristin Gray, all the way in Delaware from California! That in itself is pretty awesome!

Kristin Gray (A.K.A. @mathminds) recently tweeted that she was going to begin working on planning a first grade lesson and posted a blog a few days ago about 1st Grade Story Problems.

After all of the discussion about the lesson that she was going to do (and a little peer pressure) I decided to scrap my lesson on time for the day and give the lesson a shot. It was the last day of school before Thanksgiving break anyway. ;) (I told my student teacher that this was a "Do as I say, not as I do" situation.)

I had an hour and twenty minutes for math... which wasn't enough.
We began with a number talk. We rotate number talks and estimation routines daily in class. I planned the dots purposefully hoping a few strategies/properties might surface. There was a lot that could happen here: associative property, commutative property, making tens strategy, doubles strategy, or at least counting on. In Student Centered Mathematics, Van de Walle said that the making tens strategy is perhaps the most important addition strategy, it builds a foundation for working with larger numbers. What I was hoping for most was that the students would see the 2, 6 and 8 and make a ten with the two and the eight. This strategy would be very helpful in the following math lesson.

The number talk helped set the stage for the following math lesson.
We began with the same very open "Notice/Wonder" as Kristin Gray.

My kids are familiar with "Notice/Wonder" and I can tell that they know where we are headed before we even begin. Not sure if I really like that or not... I really liked how open Kristin's class was during the "Notice/Wonder."

We did one more notice/wonder.
What I love most about what came out here is the discussion about the word "some" lead by Carson.
After some rich discussion, we moved on to the task.

I projected the question for the class and left it up for them to refer back to while they were working. What I was hoping for was that they would use some of the strategies they have been learning in number talks and apply it on their own. Here are a few samples.

Many kids were showing the making ten strategy in some way in their work. I noticed that the kids who used 120 chart were marking the digits 4, 6 and 13. They still got to 23, but they weren't marking 6 more from 4 or 13 more from 4 or 6, they were just circling the numbers that were associated with the problem. We had mentioned once in a missing addend problem that we could put a box for a missing number, or maybe we could write "n" because it's the first letter in number and that would represent the missing number. I see River playing with that idea here. She said she had all n's first because when we did the first "notice/wonder" sessions we didn't know what any of the numbers were. I can see in her work that she is also trying to prove that she went back into the context of the story problem. We talk about this often. Some of my typical questions I ask kids when they are finishing up their work are, "Does it make sense? If someone else sits down and looks at your work will they be able to understand it? Did you go back into the context? Where is the proof? Can you show your thinking another way? What equation could you write that would represent your work?"
After students were finished, we did an "Around the World." I asked students to stand up behind their chair with their white board marker. When I said, "Around the World" students switched seats with anyone in the room. Then they had about 2 minutes of quiet time to look at the work where they were sitting. Then, they table talked about the work where they were sitting. They had to explain the work of their classmate. If it was wrong, they had to explain why. They had to explain how/if it connected to the story problem. Then, they left a little star, happy face or a question mark before I called out "Boomerang" and they went back to their seats. I had many representations to choose from for the "Connect" (5 Practices) portion of the lesson. We moved from concrete to representational to abstract. Something else I was happy about in this lesson was that it exposed a limitation of the part-part-whole mat. First graders, at least mine, are overly reliant on this tool. This was a good time to talk about why this tool might not be the best one to use and how a tape diagram or number line might work better. I noticed that a couple kids were off by one on their answer to the problem. In talking to each of them it was due to a counting error on the 120 chart. While students were working with their tools I had a decent amount of time to walk around and talk to them about what they were doing and take a quick inventory of which students got the correct answer and who was using strategies. I have an inclusive class this year. I highlighted my identified special needs students.

We ran out of time for an exit ticket before recess, but I had them do it when they returned. These were a few that I found interesting.

Thank you, Kristin, for a wonderful lesson that showed so much student thinking! It was so fun working with you! Click the link to read how Kristin's lesson went: https://mathmindsblog.wordpress.com

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Notice Wonder Meets Numberless Word Problem

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First, let me tell you how much I love Twitter for the #MTBoS. This connection has allowed me to collaborate with the great, Kristin Gray, all the way in Delaware from California! That in itself is pretty awesome! Kristin Gray (A.K.A.

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.