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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

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Marian Small's Open Questions (WNCP) - Rubicon Publishing Inc.

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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.

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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.

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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.

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Dot Talks to Build Computational Fluency 

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Dot Talks to Build Computational Fluency 

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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)

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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

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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

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Dot Talks: Building Fluency with Numbers

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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.

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Mental Math: Number Strings (Mr. Shonk's Math Virtual File Cabinet)

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Number Talks in Grade 2 to Build Computational Fluency 

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Number Talks in Grade 2 to Build Computational Fluency 

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Adapted from - Number Talks: Helping Children Build Mental Math and Computation Strategies

Addition and Subtraction Number Talks

Second Grade Number Talks

A number talk is a short (10-15 minute), ongoing daily routine that provides students with meaningful practice with computation. Tools should be used during second grade number talks to provide a context for reasoning with numbers. Some examples of tools appropriate for second grade are rekenreks, ten-frames, double ten-frames, open number lines, and hundred charts. When using these tools it is helpful to record number sentences to match the students' thinking.

Note: During a number talk, the teacher only serves as a recorder and facilitator, not as a teacher.

for the Second Grade Year

Number talks in August should focus on facts within 10. The following addition strategies should be practiced: "Counting All" and "Counting On". The following subtraction strategies should be practiced: "Removal" and "Adding Up".

Use "Counting All" and "Counting On" strategies for addition. Use "Adding Up" or "Removal" strategies for Subtraction.

Show students 6 on top and 3 on bottom. Have them tell you how many beads are shown. Talk about how to use the "Counting On" strategy. I knew there was 6 on top (five red and one white). Then I started with the number 6 in my head and added on 3 more....7,8,9.

Use these visuals to practice counting on for a couple of weeks, then transition to the number sentences. Use any number sentence that has a sum equal or less than ten and write on board. Allow students to find the answer using the counting on or counting all strategy.

Show students 9 beads on rekenrek. Remove 4. How many are left?

Show students 8 beads on rekenrek. Tell them the fact is 8 - 3. Have students start at the 3 on the rekenrek and count up to the 8.

(and review any strategies previously learned for addition and subtraction facts)

Number talks in September will continue working on the combinations to ten and bring in problems within 20. Introduce the strategy "Doubles/Near Doubles". When using the doubles / near-doubles strategy, students adjust one or both of the numbers to create a double or near double combination. When students use doubles / near doubles, they are creating equivalent but easier or known sums.

Begin the month by using using rekenreks, or double ten-frames to provide a context as students begin to reason with numbers. When using these tools it is helpful to record number sentences to match the students' thinking.

Use these visuals to practice Doubles/Near Doubles for a couple of weeks, then transition to the number sentences. Use any number sentence that has a sum equal or less than ten and write on board. Allow students to find the answer using the Doubles/Near Doubles strategy. In second grade students need to be fluent in facts to 20! Take away the ten frames and rekenreks as soon as possible.

(and review any previously learned strategy for addition/subtraction facts)

Show students 4 on top and 7 on bottom. That makes the problem 4 + 7. Show students it's easier to make a ten in your mind. Move 3 from the 4 on the top to the bottom so now the problem is 10 + 1.

Focus on Addition within 100 using the strategy "Breaking Into Place Value" and "Sketching".

and "Sketching" Strategies.

During the month ofJanuary, students will practice using the "Friendly Number", "Breaking Into Place Value" Strategy, and "Sketching" to add within 100.

Here are some sample problems that can be used throughout the month of January.

These problems lend themselves well to "Friendly Numbers".

Subtraction within 100 using sketching or adding up with blank numberline.

During the month of February, students need to practice solving subtraction problems using the strategies of "sketching" or "adding up with blank numberlines".

(students choose strategy- encourage students to solve the problem more than one way)

Practice subtraction or addition problems within 100 on the board everyday. Allow students to solve the problem. Then share the strategies they used. Have a discussion about what strategies might have been more efficient than others.

Math Number Talks are a wonderful resource and activity to use during Math Teaching time as well as calendar times. View Videos and Activities on how to do a Math Talk at Math Solutions.

and the breakdown of how to implement

More Number Talk resources HERE

Inside Mathematics also has some great resources for

Or....you could check out the book by Sherry Parrish and get it from the writer's mind...

Quarterly Suggestions for Topics.

Great resources for Number Talks can be found on the

More Resources for Number Talks to help you

implement them in your classroom daily:

PDF of ch1 from book by Sherry Parrish

using the Math Solutions Book "Number Talks"

PDF of number talk topics for second grade based on book "Number Talks"

PPTs created to go with number talks from book "Number Talks" by Peggy Parrish

downloadable resources for Number Talks

Pinterest Board of Number Talks for 2nd Grade

Greg Tang Math Books are FABULOUS for helping with both math number talks as well as a form of Math Task practices with literature...and BONUS....most all of them are ONLINE!!

Need a cool way to integrate place value into daily calendar time?

Check out these calendar cards for a free download from "Travel Teach and Love".

Bridges in Math has some free resources from their program you can download HERE

Need practices and reviews for the SAT10?

You can find a pdf to download a file with some practice pages... HERE

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Adapted from - Number Talks: Helping Children Build Mental Math and Computation Strategies Addition and Subtraction Number Talks Second Grade Number Talks A number talk is a short (10-15 minute), ongoing daily routine that provides students with meaningful practice with computation. Tools should be used during second grade number talks to provide a context for reasoning with numbers.