Mathematical Reasoning and Problem-Solving, Sentence Stems, SentenceStarters, Harkness math seminar discussion and framework, and Sentence Frames…
MATHEMATICIANS Start A Math Dialogue by Asking Questions
Number Talks (3 - 5)Liberty County
Stem Questions to Promote the 8 Mathematical Practices
3. Greetings mathematicians, The math strategy I discovered today was…
4. Greetings mathematicians, I discovered my error because...
5. Greetings mathematicians, I noticed that you solved the problem another way, can you explain your thinking…
6. Greetings mathematicians, another math strategy you could use is…
7. Greetings mathematicians, the first thing …next…then…after that…I do when solving a challenging word problem…
8. Greetings mathematicians, how did you work out your answer, did you use your number sense?
- Counting up counting down
- One-to-one correspondence.(math manipulatives)
- Subitizing.
- Composing and decomposing numbers (part-part-whole)
- Comparing numbers/sets.
- Estimating.
9. Greetings mathematicians, what math guide words "clues" did you use to choose that operation?
Math guide words list:
- Addition: Sum, Add, Plus. More. Total. Increase. Together / Altogether. Combined. Increased by. More Than. Combined, Together. ...
- Subtraction: Difference, Subtract, Take away, How Many More/Less, Decreased by. Minus, Less than. Difference Between/of. ...
- Multiplication: Product, of. Times, Multiplied by. Product of. ...
- Division: Quotient, Per, Out of. the Ratio of, ...
- Equals. is, are, was, were, will be. gives, yields. sold for, cost.
10. Greetings mathematicians, can you explain your thinking to me?
Number Talks are an effective way to build number sense and develop mathematical reasoning skills. They work as an anticipatory set, preparing students' minds for the math lesson ahead.
During a Number Talk, the teacher presents a computation problem such as 23 + 47. Students are given time to think about the problem and come up with strategies to solve it mentally, without paper and pencil. This allows them to tap into their existing number sense and math strategies.
Students then share their strategies with the class. This gives them a chance to explain their thinking and learn from each other. Often there are many different ways to mentally solve the same problem. Listening to others' strategies exposes students to new mathematical ideas and heuristics.
As students practice Number Talks regularly, their flexibility with numbers and ability to think mathematically improves dramatically. They become adept at using strategies like decomposing numbers, using landmark numbers, and more. This builds their confidence in their own math abilities.
Number Talks are designed to keep all students in their Zones of Proximal Development. Problems are scaffolded to stretch students just beyond their current skills. Collaboration expands their ZPDs as students teach and learn from peers. The result is rapid growth in mental math and mathematical thinking.
By front-loading math concepts with Number Talks, teachers can set students up for deeper understanding when formal instruction occurs. The Math Talk environment also provides a safe space to take risks and make mistakes as part of the learning process. Ultimately, Number Talks promote strong mathematical reasoning, flexibility, and problem-solving skills.
Math Talks vs. Number Talks
While both utilize structured student discussions, math talks and number talks are distinct classroom activities.
Math Talks:
- Take place during the main math lesson
- Align with the objectives of the lesson
- Involve conceptual conversations about the topic being taught
- Incorporate math vocabulary and sentence frames
- Encourage students to communicate mathematical thinking and ideas
- Allow students to build on each other's ideas respectfully
Number Talks:
- Are short, standalone activities
- Typically occur at the start of a lesson as anticipatory sets
- Focus specifically on building computational fluency
- Provide practice with mental math strategies
- Give students opportunities to share strategies
- Develop flexibility and number sense
- Target key skills rather than connect to lesson concepts
- Take less time than in-depth math talks
In summary, math talks are structured discussions embedded into math lessons to develop conceptual understanding. Number talks are brief warm-up activities that build foundational skills in isolation. While number talks may be a component of a math talk, they serve distinct purposes in the classroom.
Here are some suggested question stems that can be used to facilitate effective math talks and number talks:
For Math Talks:
- What mathematical ideas are we exploring today?
- What do you notice about this problem/example?
- What math vocabulary helps explain this concept?
- How did you arrive at that solution? Can you explain your thinking?
- Do you agree or disagree with what was just shared? Why?
- Does anyone have a different method for solving this?
- How could we represent this idea visually?
- What connections can we make to previous concepts?
For Number Talks:
- What strategies did you use to solve mentally?
- How did you break apart the numbers?
- What path did you take in your head? Can you describe it step-by-step?
- What landmark numbers did you use? Why?
- How else could we solve this?
- What math rules or properties do you notice?
- How did you know your answer was reasonable?
- What was efficient about that approach? What could be more efficient?
- How did you get your solution? Can you model your thinking?
These types of open-ended questions allow students to explain their thinking, make connections, and learn from each other during math and number talks. The goal is to develop conceptual understanding and fluency through student discourse.
Here are additional question stems for math talks and number talks based on the 13 problem-solving heuristics:
- What information is given in this problem? What are we trying to figure out? (Understand the problem)
- Can you restate the problem in your own words? What are the key parts? (Paraphrase)
- What does this problem remind you of? Have we solved anything like this before? (Analogies)
- Can we break this down into smaller steps or parts? (Break it down)
- What assumptions do we need clarify before solving? (Assumptions)
- What tools or models could help represent this scenario? (Models)
- Can we estimate or predict a reasonable solution first? (Predict)
- How can we verify our solution makes sense? What's a quick check? (Check)
- What math concepts connect to this problem? Can we think conceptually? (Conceptualize)
- If we're stuck, what's another way we could approach this? (Alternate routes)
- How can we learn from mistakes here? What would we improve next time? (Learn from mistakes)
- What patterns or relationships do you notice in the information? (Patterns/Relationships)
- Can you visualize this scenario? Make a sketch to clarify. (Visualize)
- What are the key mathematical takeaways? How would we summarize this? (Summarize/Takeaways)
Gersten and Chard say number sense "refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons."13 Heuristic Math Strategies: Singapore Math Method
[PDF]Number Talks
Developing Number Sense and Math. Vocabulary through. Number Talks. Jane Osborne jane.osborne@hoodriver.k12.or.us.
[PDF]Making Number Talks Matter—Resources by Chapter
Number Talks Build Numerical Reasoning ..... talks on first grade students' number sense.
[PDF]What is a Number Talk? - Rhodes University
Number Talks Build Numerical Reasoning” (Sherry Parrish, 2011). How can educators make shifts in their instructional practices that foster sense making ...
[PDF]Silent Signals - Wisconsin Mathematics Council
Number Talks: Helping Children Build Mental Math and Computation Strategies. ... http://www.svmimac.org/images/Cristo_Rey_-_Middle_Level_Bank.pdf .... Number sense is the foundation for all higher-level mathematics (Feikes ...
[PDF]Number Talks - Liberty County School System
Building Mental Math and Computation Strategies while ... How can I use Number Talks to build student mathematical fluency and number sense while.
[PDF]What is a Number Talk.pdf
ability to reason about quantitative information, possess number sense, ... ing efficient, flexible, and accurate computation strategies that build upon the key ...
[PDF]What Are Number Talks?
[PDF]Middle Level Routines
Sense of the relative size and value of very large and very small numbers .... Routines are an excellent opportunity to build on-going rich practice into the ... Number Strings. Number. Talks. Concepts of. Equality. Thinking. Relationally. Math.
[PDF]Improving Number Sense Using Number Talks - Digital Collections ...
classroom on number sense/critical thinking in mathematics. ... the teaching of math through number talks, in addition to their regular math instruction. ..... their students with ample opportunities to engage in number sense building activities.
[PDF]Participant Guide for Number Talks - CESA #4
Building Number Sense First. Understanding the Progression of Skills. Number Talksand Mental Math. Sharing Best Practices from ...
[PDF]KINDERGARTEN Number and Number Sense - Virginia Department ...
Number and Number Sense Module – Kindergarten ... and use linking cubes to build a tower to represent their numbers. After the towers are built, the ..... Come back together as a class and talkabout how students might know that they found.
[PDF]Developing Number Sense and Conceptual Understanding through ...
Developing Number Sense and Conceptual Understanding through Number Talks and Manipulatives is a new endeavor of the Columbus Regional ...
[PDF]Number Talks Grades 3-5 Resources - BPS.solutions
with two or multi-digit numbers. In addition to developing efficient computation strategies, Number Talks encourages students to make sense of mathematics, ...
Developing Number Sense and Math. Vocabulary through. Number Talks. Jane Osborne jane.osborne@hoodriver.k12.or.us.
[PDF]Making Number Talks Matter—Resources by Chapter
Number Talks Build Numerical Reasoning ..... talks on first grade students' number sense.
[PDF]What is a Number Talk? - Rhodes University
Number Talks Build Numerical Reasoning” (Sherry Parrish, 2011). How can educators make shifts in their instructional practices that foster sense making ...
[PDF]Silent Signals - Wisconsin Mathematics Council
Number Talks: Helping Children Build Mental Math and Computation Strategies. ... http://www.svmimac.org/images/Cristo_Rey_-_Middle_Level_Bank.pdf .... Number sense is the foundation for all higher-level mathematics (Feikes ...
[PDF]Number Talks - Liberty County School System
Building Mental Math and Computation Strategies while ... How can I use Number Talks to build student mathematical fluency and number sense while.
[PDF]What is a Number Talk.pdf
ability to reason about quantitative information, possess number sense, ... ing efficient, flexible, and accurate computation strategies that build upon the key ...
[PDF]What Are Number Talks?
[PDF]Middle Level Routines
Sense of the relative size and value of very large and very small numbers .... Routines are an excellent opportunity to build on-going rich practice into the ... Number Strings. Number. Talks. Concepts of. Equality. Thinking. Relationally. Math.
[PDF]Improving Number Sense Using Number Talks - Digital Collections ...
classroom on number sense/critical thinking in mathematics. ... the teaching of math through number talks, in addition to their regular math instruction. ..... their students with ample opportunities to engage in number sense building activities.
[PDF]Participant Guide for Number Talks - CESA #4
Building Number Sense First. Understanding the Progression of Skills. Number Talksand Mental Math. Sharing Best Practices from ...
[PDF]KINDERGARTEN Number and Number Sense - Virginia Department ...
Number and Number Sense Module – Kindergarten ... and use linking cubes to build a tower to represent their numbers. After the towers are built, the ..... Come back together as a class and talkabout how students might know that they found.
[PDF]Developing Number Sense and Conceptual Understanding through ...
Developing Number Sense and Conceptual Understanding through Number Talks and Manipulatives is a new endeavor of the Columbus Regional ...
[PDF]Number Talks Grades 3-5 Resources - BPS.solutions
with two or multi-digit numbers. In addition to developing efficient computation strategies, Number Talks encourages students to make sense of mathematics, ...
