# data[].attributes.attachment_link.readable_text
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.

# data[].attributes.attachment_link.description
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.

# data[].attributes.headline
100 questions that promote Mathematical Discourse

# data[].attributes.subject
100 questions that promote Mathematical Discourse

# data[].attributes.attachment_link.readable_text
Can the questions you're asking in the mathematics classroom be answered with a simple "yes" or "no," or do they invite students to deepen their understanding?
Asking better questions can open new doors for students, promoting mathematical thinking and classroom discourse. To help you encourage deeper discussions, here are 100 questions to incorporate into your instruction by Dr. Gladis Kersaint, mathematics expert and advisor for Ready Mathematics.

# data[].attributes.attachment_link.title
100 Questions that Promote Mathematical Discourse

# data[].attributes.attachment_link.description
Can the questions you're asking in the mathematics classroom be answered with a simple "yes" or "no," or do they invite students to deepen their understanding? Asking better questions can open new doors for students, promoting mathematical thinking and classroom discourse.

# data[].attributes.attachment_link.readable_text
Teacher: Time for our morning Number Talk.
Everyone consider this question. (She writes 9 + 17 on the board).
(A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)
If you get more answers, show me by holding up more fingers. (She waits for 30 seconds. Several students are holding up multiple fingers, though many have just a thumb.
The teacher is noting to see if anyone hasn't solved the problem-this is a great opportunity for formative assessment.
Finally, she begins calling on students for their answers, starting with those who have only one solution.)

Teacher: Lucy?
Lucy: 26. (Teacher writes 26 on the board.)

Teacher: Charles?
Charles: 107 (Teacher writes 107 on the board.)

Teacher: Michelle?
Michelle: 25. (Teacher writes 25 on the board.)

Teacher: Any other answers? (No one has any.)
Who would like to explain how they got their answer? Tyrone?
(The teacher records what the students write as they explain.)

Tyrone: I know that 9 + 7 is 16, and then I added another 10 to get 26.
Sarah: 10 + 17 is 27, and 10 is 1 more than 9, so 9 + 17 must be 26.
Charles: 9 + 1 is 10, and then you put a 7 after, so it's 107.
Lucy: I counted one by one, but I just realized that I miscounted.
I agree with 26
(Teacher crosses out 25 and replaces it with 26.)
Sam: I respectfully disagree with Charles.
You can't add the 9 + 1 because the 1 stands for 10.
Charles: But that's how you add. I did it right.
(Teacher lets conversation continue until class consensus, or near-consensus, is reached.
Meanwhile, she's noting where students are in their understanding of place value and addition.)

# data[].attributes.attachment_link.description
Teacher: Time for our morning Number Talk. Everyone consider this question. (She writes 9 + 17 on the board). (A student starts waving his arm in the air.) When you have the answer, show me with a thumb at your chest. (The student puts his arm down and holds up a thumb.)

# data[].attributes.body
A great resource for open questions to use in a math talk

# data[].attributes.attachment_link.title
You searched for open questions - Rubicon Publishing Inc.

# data[].attributes.attachment_link.readable_text
LIZ O'NEILL: And we're going to be using our base ten...our ten frames again, the ten frames. And...who can remind me, why do we call a ten frame a ten frame? Kaylani?

STUDENT: There are ten blocks.

LIZ O'NEILL: There are ten blocks or ten...? Ten squares. Very good. And when you see that frame with 10 squares, do you even have to count the squares, or do you just know there's 10 already?

STUDENTS: There's ten.

LIZ O'NEILL: Absolutely. Okay. Give me a private thumbs up when you have a number in your head. Private thumbs up. You ready? Our question will be...

STUDENTS: What number did you see? I saw the number, blank. How did you see it?

LIZ O'NEILL: And here again "I saw" or "I counted" blank. Either way is okay. Get to our partner. Let's remind ourselves real quick of our "Four L's." And...here we go. One, look at your partner, lean towards your partner, lower your voice, listen attentively. Tap your shoulder partner. The person with the shortest hair, ask the questions first.

STUDENT: What number did you see?

STUDENT: I saw ten on top, ten in the middle, and three on the bottom.

STUDENT: I saw 23 dots. Ten on the top, ten in the middle, and three on the bottom.

LIZ O'NEILL: I heard some really great thinking going on over here, and I was very pleased with every partner group -- you were all doing exactly what I asked you to do. But what I want to do is get some different ideas, so that we can hear different ways that we came up with our number. What number did you see?

STUDENT: I saw 23.

LIZ O'NEILL: Okay. Okay, so, "I saw the number..." Beautiful! And...how did you see it? I'm going to count by 2's. 2...

STUDENT: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 23.

LIZ O'NEILL: All right, Kaylani, now here's the tough part. Because we have a lot of 2's there, I need you to give me a number model to match that. Oh, let's have Kaylani do it! This is her turn! Okay. Hang on a second. You know what? I'm going to lose track. You know what we're going to do here? We're going to do a little...to help us out, we're going to count how many 2's we have, how many partners we have, so we can keep track here, or else I'm going to totally lose track because my brain cannot keep track of all that. Let's count how many partner groups we have. 1, 2, 3. Okay, now let's count and double check to make sure we agree with this.

STUDENTS: 2, 4, 6, 8, 10.

LIZ O'NEILL: What number did you see?

STUDENT: I saw 23 dots.

LIZ O'NEILL: Oops! I saw the number...

STUDENT: I saw the number 23.

LIZ O'NEILL: Okay. And how did you see it?

STUDENT: I saw 10 on the top, and 10 in the middle, and 3 on the bottom.

LIZ O'NEILL: Okay! And remember how you told me that? How did you describe that for me when you saw this 10 on the top? What did you call that?

STUDENT: Two tens and three ones.

LIZ O'NEILL: Oh! So you saw two tens and three ones. Okay. Two tens and three ones. Can you make a number model for me? What would we say for two tens? What would we call that? What number would we say?

STUDENT: 20...

LIZ O'NEILL: 20.

STUDENT: Plus...three equals 23.

LIZ O'NEILL: What number did you see?

STUDENT: I saw the number 23.

LIZ O'NEILL: How did you see 23?

STUDENT: I saw ten on the top, ten in the middle, and three on the bottom.

LIZ O'NEILL: Okay. So you saw 10 on the top, 10 in the middle, and 3 on the bottom. 10 on top, and 10 in middle, and...did I spell that right? Yes. And 3 on bottom. Give me a number model, please.

STUDENT: 10 plus 10 plus 3 equals 23.

LIZ O'NEILL: Okay. Let's double check on that.

STUDENT: 10, 20, 23.

LIZ O'NEILL: 23. Okay. Katherine, do you still see 40? Or, what number do you see now, Katherine.

STUDENT: I see the number 23.

LIZ O'NEILL: Okay, so you're good? You see 23 now? You're good? All right. If Katherine's good, it's all good.

# data[].attributes.attachment_link.title
classroom videos /number talks /1st grade math - quick look with ten frames /number talk /

# data[].attributes.attachment_link.description
LIZ O'NEILL: And we're going to be using our base ten...our ten frames again, the ten frames. And...who can remind me, why do we call a ten frame a ten frame? Kaylani? STUDENT: There are ten blocks. LIZ O'NEILL: There are ten blocks or ten...? Ten squares. Very good.

# data[].attributes.headline
Developing a Classroom Community Where Students Feel Safe to Talk

# data[].attributes.subject
Developing a Classroom Community Where Students Feel Safe to Talk

# data[].attributes.attachment_link.description
No longer just a numbers game, math class is increasingly centered on conceptual understanding and reasoning. Students need to be able to use language to formulate, synthesize, and communicate their mathematical thinking.

# data[].attributes.headline
Getting Started with Effective Math Talk in the Classroom

# data[].attributes.subject
Getting Started with Effective Math Talk in the Classroom

# data[].attributes.attachment_link.readable_text
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.

# data[].attributes.attachment_link.description
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.

# data[].attributes.attachment_link.title
Teaching Tools | Resources for Teachers from Scholastic

# data[].attributes.body
http://wodb.ca/

# data[].attributes.attachment_link.provider_name
Steve Wyborney's Blog: I'm on a Learning Mission.

# data[].attributes.attachment_link.readable_text
Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

This post includes 50 (fifty!) free, downloadable PowerPoint math lessons!

Watch the video, download some (or all) of the lessons, and experience what happens when you unleash this resource in your classroom!

I've been excited to click the Publish button on this post for several weeks! It's time!
UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

Splat Through 10
How many dots are under the Splat?

Splat Through 20
How many dots are under the Splat?

Multiple Splats
(Note: Splats that are the same color must cover the same number.)
Splat 3.1 - multiple splats Splat 3.2 - multiple splats Splat 3.3 - multiple splats Splat 3.4 - multiple splats Splat 3.5 - multiple splats
Instant Multiple Splat
(Note: An additional feature of this level is the opportunity to ask, "What could the total be?")

Splat 4.1 - Instant Multiple Splats Splat 4.2 - Instant Multiple Splats Splat 4.3 - Instant Multiple Splats Splat 4.4 - Instant Multiple Splats Splat 4.5 - Instant Multiple Splats
2-Color Splat
(Splats of different colors must have different values.)

Splat 5.1 2-color Splat Splat 5.2 2-color Splat Splat 5.3 2-color Splat Splat 5.4 2-color Splat Splat 5.5 2-color Splat Splat 6.2 Instant 2-color Splat Splat 6.3 Instant 2-color Splat Splat 6.4 Instant 2-color Splat Splat 6.5 Instant 2-color Splat
Instant 2-Variable Splat
(Splats of different colors must have different values. Splats of the same color must have the same value.)
Splat 7.1 Instant 2-variable Splat Splat 7.2 Instant 2-variable Splat Splat 7.3 Instant 2-variable Splat Splat 7.4 Instant 2-variable Splat Splat 7.5 Instant 2-variable Splat
Number Splat
(Note: Only the numbers circled on the screen may be used.)
Splat 8.1 - Number Splat Splat 8.2 - Number Splat Splat 8.3 - Number Splat Splat 8.4 - Number Splat Splat 8.5 - Number Splat Splat 9.1 - Instant Number Splat Splat 9.2 - Instant Number Splat Splat 9.3 - Instant Number Splat Splat 9.4 - Instant Number Splat Splat 9.5 - Instant Number Splat
Instant Number Splat with 2 Variables
(Note: Only the numbers circled on the screen may be used, and Splats of different colors must have different values.)
Splat 10.1 - Instant 2-Variable Number Splat Splat 10.2 - Instant 2-Variable Number Splat Splat 10.3 - Instant 2-Variable Number Splat Splat 10.4 - Instant 2-Variable Number Splat Splat 10.5 - Instant 2-Variable Number Splat
NOTE: I wrote each of these lessons using PowerPoint, so I recommend playing them in PowerPoint. If you do not have PowerPoint, you may want to download the PowerPoint viewer so that you can play the lessons.

UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Other Posts and Resources Which May Be of Interest Tiled Area Questions The Maze Hundreds Chart
Introducing Cube Connectors
Provide Massive Space to Notice
Primary Tile Questions
3 Powerful Tile Strategies (and 40 new downloadable pages)
Please take a moment to subscribe to the blog so you'll be notified each time new resources are posted!

I would treasure hearing about your experiences using Splat! to promote number sense in your classroom!

All my best,
Steve

# data[].attributes.attachment_link.title
Splat! - Steve Wyborney's Blog: I'm on a Learning Mission.

# data[].attributes.attachment_link.description
Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

# data[].attributes.attachment_link.readable_text
To engage students in productive mathematical conversations , teachers can orchestrate discourse and structure learning environments to deepen engagement and support learning. Using effective strategies will support students as they learn to participate in mathematical discourse.

Below are six strategies from mathematics expert Dr. Gladis Kersaint to help you address these core areas and promote mathematical thinking and discourse in the classroom. For more, please download Dr. Kersaint's new whitepaper: Orchestrating Mathematical Discourse to Enhance Student Learning.
Dr. Gladis Kersaint
Strategy 1: Help students work with and rely on one another.

Rules such as "Ask three before you ask me" can help establish classroom expectations by encouraging students to seek assistance from peers before defaulting to the teacher.

The teacher can also designate student experts (students who have demonstrated depth of understanding about a particular problem, concept or procedure) whom other students can consult before approaching the teacher.

Strategy 2: Allow students to work independently before sharing in small or large groups.

Students need time to gather their thoughts and identify what they know or do not know before they are exposed to the influence of other students. Then they can compare and contrast their approaches and solutions with those shared by others during the mathematics discussion.

Strategy 3: Use questions strategically to engage students in mathematical discourse.

Teachers can engage students in mathematical discourse by posing questions that encourage discussion and debate. Strategic prompts and questions require students to attend to particular aspects of the learning process, explain and justify their thinking, and deepen their understanding in the process.

For strategic question examples, see Talking Math: 100 Questions That Help Promote Mathematical Discourse .

Strategy 4: Acknowledge the importance of mistakes in learning and understanding by:

Learning mathematics is not just about getting the right answer. It is also about learning from previous mistakes. Encourage students to take risks in mathematics by:

Recognizing that students will make errors because they are exploring and making conjectures.

Reminding students constantly that errors are expected and natural and that they can be a good thing because they lead to enhanced learning.

Helping students recognize what they have learned by analyzing their mistakes and identifying misunderstandings.

Encouraging students to ask questions to clarify and critique the reasoning of their peers and establish the correctness of solutions.

Empowering students to reach and justify conclusions based on their own mathematics knowledge without relying on the authority of the teacher.

Strategy 5: Use collaborative learning strategies.

When students work with peers or in small groups, they are able to take risks and build confidence on a small scale before they present solutions to the whole class. Strategies include:

Think-pair-share . This approach can be used in a variety of instructional circumstances to encourage students to engage in mathematics independently and then share their results with a partner.

Numbered heads . When students are working in groups of three or four, each can be assigned a number. Students know that any member of the group may be called on to provide a response, so everyone must have the same level of understanding.

Strategy 6: Take a creative approach to engaging all students in whole class discussion.

Teachers can use a variety of methods to gather information from the whole class or individuals that simultaneously allow them to assess individual and collective student understanding:

Thumbs up/thumbs down . Teachers pose a question or problem that has a dichotomous answer (yes/no, true/false, X or Y) and ask students to respond, using thumbs up to represent one choice and thumbs down to represent the other.

Response sticks . Teachers write each student's name on a Popsicle stick or similar item, place the sticks in a container, and randomly select students by choosing a stick.

Classroom response systems or other digital tools . Teachers can use classroom response systems to gather immediate feedback from students by asking them to respond using a clicker, website or text message and display results as a chart or graph.

We hope you've enjoyed our Mathematical Discourse blog series and are ready to begin this journey in your classroom. We strongly feel everyone benefits from mathematical discourse in the classroom: teachers are better able to access, monitor and evaluate students' mathematical understanding and development; and students can reflect on their own understanding while making sense of and critiquing the ideas of others in a collaborative and supportive learning environment.
This blog is part of a three post series on the importance of mathematical discourse from For more on mathematical discourse and Curriculum Associates, check out: Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of South Florida. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update Curriculum Associates , a Getting Smart Advocacy Partner, and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy

# data[].attributes.attachment_link.title
Talking Math: 6 Strategies for Getting Students to Engage in Mathematical Discourse

# data[].attributes.attachment_link.description
To engage students in productive mathematical conversations , teachers can orchestrate discourse and structure learning environments to deepen engagement and support learning. Using effective strategies will support students as they learn to participate in mathematical discourse. Below are six strategies from mathematics expert Dr. Gladis Kersaint to help you address these core areas and promote mathematical thinking and discourse in the classroom.

# data[].attributes.attachment_link.title
Search results for talking math - Getting Smart

# data[].attributes.attachment_link.readable_text
L'idée de ce site a pris naissance grâce à une conversation avec Tracy Zager et Chris Hunter. De plus, d'autres personnes en dehors de la conversation initiale ont inspiré, d'une façon ou d'une autre, ce site.
The idea for this site was born out of a conversation with Tracy Zager and Chris Hunter. Furthermore, other people, in one way or another, have inspired the creation of this site. ​

# data[].attributes.attachment_link.description
Custom Number Talk Images Créer vos propres images! Voici une ressource de Berkeley Everett . Offert en format PowerPoint ou Google Slides, vous n'avez qu'à modifier les diapositives afin de...

# data[].attributes.attachment_link.readable_text
Same and Different Images

Lots of images to support students in developing the habit of comparing and connecting representations. Thanks Brian Bushart for pulling them together!

# data[].attributes.attachment_link.description
Great tasks you can do in 10-15 minutes every day...click the image and they're yours.

# data[].attributes.attachment_link.readable_text
Wondering what a number string looks like in a classroom? Curious about the details of the routine? The following video features site co-founder Rachel Lambert teaching a group of 4th grade students at the Citizens of the World Charter School in Mar Vista, CA. These students have a wonderful classroom teacher, Hayley Roberts, who does number strings regularly with the students as part of a rigorous, inquiry-based mathematics curriculum. Hayley is off camera in Part 1 leading the students in a mathematics mindfulness exercise.

Students in this class had done lots of number strings with the open number line for addition and subtraction, as well as the array as a model for multiplication. On the previous day, the number string had been a multiplication doubling and halving string on the open number line. Today's number string was designed to help students understand division on the open number line, focused on using equivalence as a strategy. Before you watch, you might want to anticipate how 4th graders might solve these problems, and how Rachel will represent strategies on the open number line.

Make sure to click on captions if that is useful. For info on how I finally figured out captions, go to a new post on my other blog mathematizing4all.com

In the first segment, Rachel reminds the students of the strategies they used the day before (giving students credit), and gives the first (2 x 50) and second (4 x 25) problems.

Notice the way the classroom teacher leads her students to be mindful mathematically before they begin. This is a beautiful way to help students orient themselves to the mathematics.

In the second segment, Rachel takes more strategies for 4 x 25, and then presents the third problem, 100 ÷ 2.

In Part 3, Rachel begins by asking students if they can find an open number line that represents 100 ÷ 2. Throughout this segment, she asks students to visualize representations before she models them. This segment continues, moving fairly quickly through 100 ÷ 4 and 200 ÷ 4, before moving more slowly through 400 ÷ 8 and 800 ÷ 16. It ends with one student beginning to generalize a strategy for understanding the relationship between the dividend and the divisor in division.

In Part 3, Rachel also adds another support to the number string: context. She asks the students to imagine that the division problems represent a lottery winning beings shared by students equally. She wants this context to support them in in thinking about the relationships between the dividend, the divisor and the quotient. What happens when the amount of money in the lottery is doubled? What happens when the number of students sharing the money doubles?

Part 4 continues with another student sharing their thinking about that generalizable relationship. Like the first student, this generalization is supported by the context of the lottery.

Rachel then tries to wrap up the number string, but a student offers what they think will be the next problem: 1600 ÷ 32. Students love to predict the next problem in a number string! Although she is over her time limit, Rachel throws out what would have been the last problem if she had time: 800/16 as a fraction.

In the final part, Rachel asks students, not to solve this problem, but if they can think of any equivalent fractions for 800/16.

A couple of small points. Students use the sign for "agree" in American Sign Language to indicate that they used the same strategy as a classmate. Rachel stops the class several times for a turn and talk, particularly at moments in which they were unsure, or she was unsure how much students understood. The turn and talk gives students a chance to talk through their thinking, helping them make sense of still emerging understandings.

Finally, we present this number string not as an example of perfect practice, by any means, but as a sample of practice that can be analyzed. What did you notice? What are your questions?

# data[].attributes.attachment_link.title
Video: Division on the open number line in fourth grade

# data[].attributes.attachment_link.description
Wondering what a number string looks like in a classroom? Curious about the details of the routine? The following video features site co-founder Rachel Lambert teaching a group of 4th grade students at the Citizens of the World Charter School in Mar Vista, CA. These students have a wonderful classroom teacher, Hayley Roberts, who does number...

# data[].attributes.attachment_link.readable_text
"...that ability to 'just see it' without counting is called Not surprisingly, subitizing." (Van de Walle)
There's no doubt about it...subitizing is all the rage! It's not a new concept, though. According to Wikipedia the phrase was first used in 1949. So why are we just hearing about it now? My theory is that the popularity of subitizing is directly related to the implementation of the Common Core State Standards for Mathematics, which stress conceptual understanding and number sense over rote memorization of mathematical procedures and facts.
John Van de Walle's books have featured activities related to subitizing for many years. I enlarged some of Van de Walle's cards (shown below) so they would be easier to use, and you can grab them .

You can also easily make dot cards using large index cards and colored labels. Van de Walle suggests using paper plates, but I find index cards or cardstock cut in half are easier to store and use. I hole punch them and put them on an O-ring. Make multiple configurations of each number. In the picture below, you see four different cards showing the number 3. Using different colors of dots helps students see how smaller numbers combine to make larger ones.

So, now that you've made your dot cards, how exactly do you use them? First off, you want to develop routines for using your dot cards. You don't want to flash a card and just have students shout out the number. Start out, obviously, with smaller numbers. Even if you are subitizing in 1st or 2nd grade, if your kiddos haven't subitized before, you need to start with smaller numbers. I like to have kiddos seated on the floor in front of me. I use a strategy I saw on the DVD that accompanies Sherry Parrish's book, Number Talks: Helping Children Build Mental Math and Computation Strategies. Flash a card briefly. When a child thinks they know the number shown on the card, they put a thumbs-up against their chest. Totally silent! You want to be able to look for those kiddos who are counting the dots one-by-one and also see how quickly each student determines the number. Call on "thumbs" one by one and ask what number they saw. Don't be surprised if you get different responses! Avoid the temptation to comment on responses. Use a good poker face and just accept all answers. Next, show the card again and call on several students to tell you how they knew what number was on the card. There is no "right" answer. Looking at the cards above, you might have kids say:

Notice how each of those responses tells you something very important about the child's understanding of numbers. Repeat for different cards. This is a quick, whole-class daily routine that has a huge payout! You also want to use the dot cards, however, in small group instruction to differentiate your instruction. For example, the first kiddo in the example above is probably ready to work with larger numbers and combinations while the third kiddo is not subitizing at all.

5- and 10-frames are powerful tools for building those all-important benchmarks of 5 and 10, and they should also be part of your subitizing routines. They can be used in much the same way as random-pattern dot cards. A great resource for using 10-frames in your classroom is It Makes Sense!: Using Ten-Frames to Build Number Sense. Click to download blank ten-frames (3 to a page) to make your dot cards.

Go forth and subitize!!

You might also want to check out these posts on DIY rekenreks and number bracelets.

You might also like these posts:

# data[].attributes.attachment_link.title
Using Dot Cards to Build Number Sense - Math Coach's Corner

# data[].attributes.attachment_link.description
"...that ability to 'just see it' without counting is called subitizing." (Van de Walle) There's no doubt about it...subitizing is all the rage! It's not a new concept, though. According to Wikipedia the phrase was first used in 1949. So why are we just hearing about it now?

# data[].attributes.body
The most awesome bank of hundreds of estimation tasks for 3rd to 12th graders by Andrew Stadel at

# data[].attributes.attachment_link.readable_text
ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together.

Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.

# data[].attributes.attachment_link.description
How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

# data[].attributes.attachment_link.description
What is the first question that comes to your mind?

# data[].attributes.body
added websites

# data[].attributes.attachment_link.title
Number Talks: The First 10 Minutes (Mr. Shonk's Math Virtual File Cabinet)

# data[].attributes.attachment_link.readable_text
Talking about math helps elementary students deepen their understanding. Use these three tips to get the conversation started.

©Shutterstock.com/Monkey Business Images

Walk into a classroom in the middle of a math talk and you'll see the students gathered in a circle, taking turns showing each other math strategies and questioning each other about the accuracy and efficiency of their solutions. The students are sharing thoughts about a single high-quality math problem they worked on solving earlier in the period without teacher guidance. They are processing the math in a different way than when they worked with paper and pencils, manipulatives, and drawings.

This opportunity to connect math and language benefits all the students and deepens their understanding of math concepts. The teacher listens as students converse about their problem-solving process. This gives her a view into the depth of understanding her students have, and alerts her to any misconceptions that should be addressed in later lessons.

After the students exchange ideas, the teacher will ask them to summarize important takeaways about today's math concepts and strategies. Only then will she chime in with points she wants to emphasize. Here are three tips for guiding math talks.

1. Spend Time Discussing Just One Math Problem

Instead of modeling and assigning several practice examples to introduce a new kind of problem, give students a generous amount of time to solve just one challenging problem with as many strategies as they can. Requiring at least two strategies builds independence in verifying their own solutions and jump-starts students' ideas for discussion. Once students have had ample time to work on the problem, bring the class together for a conversation.

2. Use the Power of Think, Pair, Share

Before students share with the whole group, teachers first give them a moment to think on their own and then talk to a partner. Their understanding develops at each stage of Think, Pair, Share. This is also a time when the teacher can gather important information from students, by circulating and hearing the thinking behind their problem-solving strategies.

Think: Students take a quiet moment to ready themselves to describe their process in words. Think time allows students who wouldn't otherwise participate aloud (shy students, introverts, slower processors, and English language learners) to gather their thoughts and build courage to express them.

Pair: The teacher asks students to turn to a partner and take turns exchanging math strategies and observations. Pair time holds all students accountable for participating, and it allows students a practice run for sharing with the whole group. During this time, students connect math and language. Light bulbs go off as kids verbalize their mathematical thinking. Students who hesitate to share out to the whole group are given a chance to process and participate.

Share: The teacher asks students to share ideas with the whole group. Many teachers are surprised at how drastically participation increases when students have first had a chance to think to themselves and then practice sharing with a partner. Student shares are more eloquent, and the listeners are alert, making comparisons to how they and their partner solved the problem.

3. Take Advantage of Discussion Aids

Anyone who has taught math knows that it isn't always easy to put math strategies into words. Kids need practice with the essential skill of communicating mathematical thinking, and there are several ways teachers can support them.

Math tools: Pattern blocks, grid paper, and base 10 blocks are examples of math tools that provide entry points for solving challenging math problems. These hands-on tools also give students something to describe as they show how they solved a problem step by step.

Visuals: Teachers can spark a math discussion with a teacher-made visual, like the math talk discussion card for kindergarten and first grade above. Or they can encourage students to show and explain a visual (a drawing or table, for example) that helped them solve a math problem.

Language support: During a math discussion, the teacher tries to talk as little as possible, setting an expectation that everyone is to be ready with a question or comment for the sharer. Sentence stems and vocabulary lists support students who struggle to put their thoughts into words and those who are learning English. Using "accountable talk" sentence starters like these turns one-at-a-time sharing into a class conversation:

I see that you used Math Practice _____ when you _____.
I think it would be more efficient to _____.
I will use your strategy next time because _____.
The part of your strategy I do/don't understand is _____.
When I was stuck I _____.
The most challenging part for me was _____.

Teachers are often surprised at how well their students can question and support each other in describing a problem-solving process with some help from these language aids.

Providing lots of time for talking about and showing math strategies for just one problem may sound scary given teachers' limited teaching time, but the payoff from a math talk is great. Students are exposed to multiple ways to approach the same problem. They hear various explanations of math concepts. As they listen, watch, and talk to each other, students begin to see patterns and make connections.

# data[].attributes.attachment_link.description
Talking about math helps elementary students deepen their understanding. Use these three tips to get the conversation started. ©Shutterstock.com/Monkey Business Images Walk into a classroom in the middle of a math talk and you'll see the students gathered in a circle, taking turns showing each other math strategies and questioning each other about the accuracy and efficiency of their solutions.

# data[].attributes.body
http://mrorr-isageek.com/games-in-math/

# data[].attributes.body
http://mrorr-isageek.com/better-questions-two-truths-one-lie/

# data[].attributes.body
http://www.fractiontalks.com/

# data[].attributes.attachment_link.readable_text
If you are a Laney Sammons fan, then you probably already know about Math Stretches. Part of the Guided Math framework is Morning Math Warm-Ups and Calendar Activities. Sammons explains that just like athletes warm up before a strenuous workout, mathematicians need to have a warm-up to get their brains focused on math. Here's how she describes the Warm-Up in her Guided Math: Menu of Instruction:
This daily appetizer prepares the palate for the "Your Choice" entrees below with Math Stretches, Calendar Board activities, problems of the day, math-related classroom responsibilities, data work, incredible equations, reviews of skills to be maintained, and previews of skills to come.
In 2010 and 2011, Sammons published the books you see pictured above. They are a terrific resource! Each book contains detailed descriptions of about 30 Math Stretches and includes a Teacher Resource CD. Click on either of the pictures for more information.

Like many teachers, I like to tweek things just a bit, so the stretches you see pictured below are my versions. I wanted to show my teachers how easily the stretches can be differentiated for different grade levels. For example, I created versions of the How Many More to 100? stretch for 20 and 50.

I also wanted to make the stretches manageable for my teachers. All these files print on 11 x 17 paper, so they can post them on the wall for kiddos to access and they are big enough for the kids to write on. They can be easily adjusted (they are Word documents), so the teachers can use them over and over, but change them up. For the Number of the Day and You Write the Story stretches, I suggest using sticky notes so the kiddos can write their response to the stretch at their desk and then post it on the class chart.

Click on each of the pictures below to download the files, and have a great weekend!!

Note: When you preview the files in Google Docs, they may not look correct (one row spilling over to a second page, boxes not showing up right, etc.). But when you download them as a Word document, the formatting will all be fine.

# data[].attributes.attachment_link.title
Using Math Stretches for a Daily Warm-Up - Math Coach's Corner

# data[].attributes.attachment_link.description
If you are a Laney Sammons fan, then you probably already know about Math Stretches. Part of the Guided Math framework is Morning Math Warm-Ups and Calendar Activities. Sammons explains that just like athletes warm up before a strenuous workout, mathematicians need to have a warm-up to get their brains focused on math.

# data[].attributes.body
Using images to stimulate classroom math conversation and reasoning.
http://www.nelson.com/eyesonmath/download.html

# data[].attributes.body
A collaborative project that has several images that can be used as a launching point for Number Talks. http://ntimages.weebly.com/

# data[].attributes.body
Using mathematical reasoning to decide between two situations or paths.

# data[].attributes.attachment_link.readable_text
Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don't go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

# data[].attributes.attachment_link.description
Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don't go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

# data[].attributes.attachment_link.title
Engaging All Students in Mathematical Discussions.pdf

# data[].attributes.body
Jo Boaler

# data[].attributes.attachment_link.readable_text
One of the most challenging things in my elementary classroom is to move students away from getting an answer in math to talking about and discussing strategies. When students learn mathematical strategies in depth and apply these strategies to unique situations, they have learned how transfer the strategy between problems. I love watching light bulbs go off in students' minds as they realize that they can just [insert a strategy] to solve a problem. It moves them toward efficiency, which is a major goal in math.

*** This post contains affiliate links. What this means is that by clicking on the link and purchasing products from that web site, I receive a small commission from that web site. Receiving this commission in no way influences my thoughts on the value of the product. Read my Disclosure Policy for more information.***

One of the key ways students learn mathematical strategies is by talking about them. I love doing number talks and problem solving in my classroom, but it is so difficult to get students to express their thinking about the problems. Most of my students are English learners who don't have many of the words and sentence structures they need to talk about the math going on in the problems.

I've written a couple blog posts about giving students sentence frames and vocabulary cards to talk about specific mathematical concepts. These posts were geared toward skills and concepts in one area in math, for instance fractions.

Today, I want to share with you another resource that bridges all mathematical problems because it focused on the Mathematical Practice Standards. I developed these Mathematical Practice Discussion Cards several years ago as we were getting started with the new Common Core Math Standards. These cards are designed to be used in partner or small group discussions about math problems. The cards are formatted so that when printed back to back, the question or prompt is on one side and the other side has a sentence frame that goes with the question.

Not only do you have a variety of questions that students can ask each other related to each Mathematical Practice Standard, you also focus students on answering questions in complete sentences.

With my second graders, we start out with only a couple of the cards at the beginning of the year and use them repeatedly for a couple weeks before adding a few more cards to the ring. I'm very explicit about how students hold the cards so that one student reads the question and the other student responds to the question. I want to be sure that both students are participating equally. We generally start with MP 1 & 6 toward the beginning of the year.

By the end of the year, we have quite a few cards on our ring. I simply tell students that they need to discuss a question from a certain color, which corresponds to a Mathematical Practice standard. Students choose the question that best fits their problem and discuss it, using the sentence frames on the back as a guide, if needed.

These cards have been perfect for my English learners who often don't know where to start when I've said, "Turn to your partner an tell them xyz." These cards give student a starting place and add a little bit more specificity to the task.

Are you interested in these cards for your own classroom? They're available on my web site and in my TpT store.

When printing them, I print them back to pack on colored paper. I started with MP1 and printed all the question / prompt cards on red paper. Then, I reinserted the paper back into the printer to print on the opposite side and print all the response / sentence frame cards.

You may need to play around with your printer to figure out how to print back to back, unless you have a setting for it. It is well worth the effort to have a set of these to use with students every year. One more hint, if you hole punch it in the bottom right, students can hold up one card easily without the whole ring of cards falling in front of the one that needs to be seen.

# data[].attributes.attachment_link.title
Get Students Talking with Mathematical Practice Discussion Cards

# data[].attributes.attachment_link.description
One of the most challenging things in my elementary classroom is to move students away from getting an answer in math to talking about and discussing strategies.

# data[].attributes.body
Grade 2 number talk

# data[].attributes.attachment_link.description
Create and publish a book, magazine or ebook with Blurb's self-publishing platform. Sell & distribute globally with print on demand or offset printing

# data[].attributes.headline
Dot Talks: Building Fluency with Numbers (Primary) 

# data[].attributes.subject
Dot Talks: Building Fluency with Numbers (Primary) 

# data[].attributes.attachment_link.readable_text
Math.Practice.MP4

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP4: Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.1.OA.C.5

Common core State Standards

Math: Math

1: Grade 1

OA: Operations & Algebraic Thinking

C: Add and subtract within 20

5:
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Download Common Core State Standards (PDF 1.2 MB)

|

Math.1.OA.C.6

Common core State Standards

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. How does Ms. Gelormino create an environment where students are comfortable sharing their thinking?

2. How does Ms. Gelormino use questioning to encourage the use of academic language?

3. What strategies does Ms. Gelormino use to support her English Language Learners?

School Details

Think College Now School
2825 International Boulevard
Oakland CA 94601

Data Provided By:

Teachers

# data[].attributes.attachment_link.title
Dot Talks: Building Fluency with Numbers

# data[].attributes.attachment_link.description
Students in Julia Gelormino's first grade class engage in a dot talk in order to build fluency with numbers. Students look at a set of dots and share how many dots they see and how the see them. They share strategies for adding within twenty.

# data[].attributes.attachment_link.description
Write something about yourself. No need to be fancy, just an overview.

# data[].attributes.headline
Addressing Diversity in Math with Open Ended Questions

# data[].attributes.subject
Addressing Diversity in Math with Open Ended Questions

# data[].attributes.attachment_link.readable_text
Our math classrooms are more and more diverse each year. Learners come to us with a range of different experiences and levels of understanding of the mathematics that's important to know. Meeting the needs can prove challenging. Dr. Marian Small's book called Good Questions: Great Ways to Differentiate Mathematics Instruction is an excellent resource for learning how to craft questions to make the math accessible to all - challenging for those who need it, and simplified for others. Check it out for more rich and open tasks to engage children in thinking mathematically across the grades!

This is an incredibly useful teacher resource book. In it, Dr. Small poses open-ended questions across the strands as well as what she terms "parallel tasks", which present the same math concept at 2 different levels of complexity. It's a very clever way to include everyone in the mathematical discussion, and can really help when we're planning for instruction in a combined grade setting. Oh - and did I mention that Marian Small is Canadian?? 🙂 Her work is in line with the WNCP math curriculum and so makes a great match for anyone teaching math here in Canada.

This selection of questions from Dr. Marian Small's book are ideal for combined grades settings, since they address big math ideas that are common to side-by-side curricula. Invite your students to represent their thinking with models, pictures and words, and to share what they know with a peer, a small group and/or the class. These questions lend themselves to rich classroom discussions, and can give you as a teacher important assessment data to inform your planning.
Enjoy!
Carole

PS - Marian Small has also authored a companion book for secondary math that's well worth checking out: MORE Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction.

Hello all!

Last week I gave a session for teachers in Coquitlam looking to teach - and assess - problem-solving. We talked about what made a good problem, both in terms of content and wording, then worked through some samples across the grades. I have posted a selection of problems for you here, which I invite you to download and use with your students.

Remember that it's important to collect students' thinking in a variety of forms - numbers, pictures and words, to have them engage with models or manipulatives, and wherever possible to have students communicate their understandings about a concept by translating them to a problem of their own. The latter is no small task! :o) John Van de Walle's diagram outlines the importance of not only including these representations but also connecting and bridging between them. Students learn deeply when they transform their learning from numbers to models, from words to pictures, from problems to numbers and back again...

Carole

# data[].attributes.attachment_link.description
Our math classrooms are more and more diverse each year. Learners come to us with a range of different experiences and levels of understanding of the mathematics that's important to know. Meeting the needs can prove challenging.

# data[].attributes.attachment_link.title
Rich Math Problems - Balanced Numeracy Links & Resources

# data[].attributes.attachment_link.readable_text
Get ready to unleash student math success with this collection of hundreds of open questions from Marian Small. An essential tool for every K-9 math classroom, the Open Questions for Rich Math Lessons: Number Strand books are organized around outcomes from the WNCP Common Curriculum Framework for K-9 Mathematics. These teacher resource books use a highly visual format to present easy-to-use questions with sample responses for all parts of problem-solving lessons. These resources can be used on their own or as a supplement to a core program such as .
These books will:

Prompt discussion of mathematical concepts and lead to deeper understanding

Show connections among the specific outcomes in the WNCP curriculum

Offer models to help teachers develop their own open questions

Add to the teacher's repertoire of engaging tasks for students

Provide opportunities for thoughtful practice of concepts and skills

# data[].attributes.attachment_link.title
Marian Small's Open Questions (WNCP) - Rubicon Publishing Inc.

# data[].attributes.attachment_link.description
Get ready to unleash student math success with this collection of hundreds of open questions from Marian Small. An essential tool for every K-9 math classroom, the Open Questions for Rich Math Lessons: Number Strand books are organized around outcomes from the WNCP Common Curriculum Framework for K-9 Mathematics.

# data[].attributes.body
Jo Boaler

# data[].attributes.body
Parallel and Open Task Problems (K-5)

# data[].attributes.attachment_link.readable_text
Practical-Ready To Use differentiated math word problems inspired by the teachings of Dr. Marion Small, a long-time Canadian professor of education. Covering all five math strands, EACH word problem will engage ALL students at levels 1,2,3,4 from Kindergarten to Grade 5. Included are a generic math rubric for problem solving and a daily tracking sheet for a problem based classroom.

# data[].attributes.attachment_link.title
Parallel and Open Task Problem-Solving Math Bank | Ontario Teachers' Federation

# data[].attributes.attachment_link.description
Practical-Ready To Use differentiated math word problems inspired by the teachings of Dr. Marion Small, a long-time Canadian professor of education. Covering all five math strands, EACH word problem will engage ALL students at levels 1,2,3,4 from Kindergarten to Grade 5.

# data[].attributes.body
Open Questions for Primary Teachers (Gr 1-3)

# data[].attributes.attachment_link.readable_text
This project explores using open-ended questions in math in the primary division as a strategy to assist students in developing number concepts. The teachers had observed that a 'show and tell' method of teaching math resulted in the students being able to perform a task in a familiar context but when presented with a problem in another context, the students struggled with applying what they had appeared to know. Although word problems have always been a part of math work, they are often used as a means for students to apply a learned skill directly after the skill has been practiced. In these situations, the students don't need to sort out how to solve the problem; they just need to apply an operation to some numbers. In this project, we wanted word problems to be a chance for exploration and solidification of number concepts, as the students responded to the problem in different ways.

# data[].attributes.attachment_link.title
Using Open-ended Questions in Primary Math | Ontario Teachers' Federation

# data[].attributes.attachment_link.description
This project explores using open-ended questions in math in the primary division as a strategy to assist students in developing number concepts. The teachers had observed that a 'show and tell' method of teaching math resulted in the students being able to perform a task in a familiar context but when presented with a problem in another context, the students struggled with applying what they had appeared to know.