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Multiplication Strategy and Model Matchup for 45 x 16. 

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Multiplication Strategy and Model Matchup for 45 x 16. 

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Multiplication Strategy and Models Matchup

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Here is an activity to matchup various multiplication strategies and models.

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Dr Nicki's Math Fact Fluency Playground site chock full of resources

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Dr Nicki's Math Fact Fluency Playground site chock full of resources

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WorldWall.Net SO many games and activities!

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WorldWall.Net SO many games and activities!

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Wordwall - Create better lessons quicker

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Need a fresh teaching resource that fits your class and teaching style? Create a customized pack of interactive and printable activities in just one minute.

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Subtraction Strategy and Model Matching Activity

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Subtraction Strategy and Model Matching Activity

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Procedural Fluency in Mathematics - National Council of Teachers of Mathematics

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Procedural fluency is a critical component mathematical proficiency and is more than memorizing facts and procedures.

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Pam Harris' Major Strategies beyond the algorithms packet

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Pam Harris' Major Strategies beyond the algorithms packet

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Want to know all the major strategies students need to know to build powerful numeracy? This free booklet tells all, including examples with models.

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Use code 25EFLY1  on the Routledge site for a 20% discount!

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Use code 25EFLY1  on the Routledge site for a 20% discount!

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Biography

Dr. Nicki Newton has been an educator for 35 years, working both nationally and internationally with students of all ages. She has worked on developing Math Workshop and Guided Math Institutes around the country; visit her website at www.drnickinewton.com.

Ann Elise Record has been an educator for over 22 years as a teacher, math coach and specialist, adjunct faculty member for Plymouth State University, and, currently, as a national speaker and independent elementary math consultant. She can be found on Facebook (www.facebook.com/groups/2022849141262766) facilitating the Math Running Records group. Visit her website at www.anneliserecord.com.

Dr. Alison J. Mello has been in education for nearly 30 years as a classroom teacher, math specialist, director of curriculum, and assistant superintendent. Alison now enjoys serving teachers through her work as a math consultant, graduate instructor, and national speaker. You can find her at alisonmellomathconsulting.com.

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Fluency Doesn't Just Happen in Multiplication and Division: Strategies and Models for Teaching the Basic Facts

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Fluency in math doesn't just happen; it is a well-planned journey. In this book, you'll find practical strategies and activities for teaching your elementary students basic multiplication and division. The authors lay out the basic framework for building math fluency using a cycle of engagement (concrete, pictorial, abstract) and provide a multitude of examples illustrating the strategies in action.

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NHASCD's podcast with me discussing Building Thinking Classrooms  October, 2023

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NHASCD's podcast with me discussing Building Thinking Classrooms  October, 2023

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Building Thinking Math Classrooms with Ann Elise Record by NHASCD Spotlight: A Podcast

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ABOUT
Ann Elise Record is a well-known New Hampshire math educator, writer, and consultant. She has been in the field for 22 years as a K-5 Math Coach, adjunct faculty member for Plymouth State University, Bureau of Education and Research presenter, and currently an independent elementary math consu…

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NHASCD's podcast with me discussing Building Thinking Classrooms  October, 2023

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NHASCD's podcast with me discussing Building Thinking Classrooms  October, 2023

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Building Thinking Math Classrooms with Ann Elise Record by NHASCD Spotlight: A Podcast

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ABOUT
Ann Elise Record is a well-known New Hampshire math educator, writer, and consultant. She has been in the field for 22 years as a K-5 Math Coach, adjunct faculty member for Plymouth State University, Bureau of Education and Research presenter, and currently an independent elementary math consu…

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My interview with Laura and Karina on the Learning Through Math podcast debriefing the Building Thinking Classrooms 1st Annual Conference (Pt1)

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My interview with Laura and Karina on the Learning Through Math podcast debriefing the Building Thinking Classrooms 1st Annual Conference (Pt1)

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‎Learning Through Math: A Conversation with Ann Elise Record on Apple Podcasts

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In this episode, Laura and Karina have a conversation with Ann Elise Record. CHALLENGE: Share anything you know about Building Thinking Classrooms!

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NHASCD's podcast with me discussing Building Thinking Classrooms  October, 2023

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NHASCD's podcast with me discussing Building Thinking Classrooms  October, 2023

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Building Thinking Math Classrooms with Ann Elise Record by NHASCD Spotlight: A Podcast

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ABOUT
Ann Elise Record is a well-known New Hampshire math educator, writer, and consultant. She has been in the field for 22 years as a K-5 Math Coach, adjunct faculty member for Plymouth State University, Bureau of Education and Research presenter, and currently an independent elementary math consu…

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All of Ann Elise's favorite games for all operations

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All of Ann Elise's favorite games for all operations

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Here is a collection of games that are my favorite for elementary math! Enjoy!

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NCTM Fluency Position Statement April, 2023 

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NCTM Fluency Position Statement April, 2023 

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Procedural Fluency in Mathematics - National Council of Teachers of Mathematics

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Procedural fluency is a critical component mathematical proficiency and is more than memorizing facts and procedures.

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Teaching Like Ted Lasso!  This episode is my favorite quote - Be Curious, Not Judgmental! 

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Teaching Like Ted Lasso!  This episode is my favorite quote - Be Curious, Not Judgmental! 

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Description
Dr. Amanda Jansen joins John and Dave on the Teaching Like Ted Lasso Podcast to discuss what it means to BE CURIOUS: in the show and in the classroom. And Dave and John do a play-by-play commentary on an assessment interview featuring a first-grader.
Video: https://youtu.be/5TCTYxCQdaw

Show Notes for Episode 2 on Be Curious
IMDB "The Diamond Dogs" episode: https://www.imdb.com/title/tt11193418/?ref_=ttep_ep8
John's Problem Solving graphic: http://mathhombre.blogspot.com/2009/06/polyas-army.html
George Polya's How to solve it: https://math.hawaii.edu/home/pdf/putnam/PolyaHowToSolveIt.pdf
The Literacy Network's parent company - Richard C. Owen Publishers, Inc: https://rcowen.com
Dave's What's your paradigm? post: http://deltascape.blogspot.com/2011/03/whose-job-is-it-anyway.html
IMDB "Inverting the Pyramid of Success" episode: https://www.imdb.com/title/tt14968664/?ref_=ttep_ep12
Innovators' Compass website: https://innovatorscompass.org
John Hattie's Visible Learning for Teachers: https://www.google.com/books/edition/Visible_Learning_for_Teachers/xY-6MyDgks8C?hl=en&gbpv=0
Clements and Sarama (2000) Young Children's Ideas about Geometric Shapes: https://www.researchgate.net/publication/258933238_Young_Children%27s_Ideas_about_Geometric_Shapes
Target Measure from Illustrative Mathematics, Grade 2: https://curriculum.illustrativemathematics.org/k5/teachers/grade-2/unit-3/lesson-13/lesson.html
Amanda Jansen on Twitter: @MandyMathEd
Amanda Jansen's website: https://jansenamanda.wixsite.com/professional
IMDB Ratatouille: https://www.imdb.com/title/tt0382932/
IMDB Stranger than Fiction: https://www.imdb.com/title/tt0420223/
Mandy's article with Denise McCunney: https://democracyeducationjournal.org/cgi/viewcontent.cgi?article=1557&context=home
Association of Mathematics Teacher Educators website: https://amte.net
Frances Harper on Twitter: @WorldMathProblems
Three-read protocol: https://www.sfusdmath.org/3-read-protocol.html
Ewan McIntosh TED Talk: https://www.youtube.com/watch?v=JUnhyyw8_kY
Sara Van Der Werf blog on Name Tents: https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/
Jack Smith's Misconceptions Reconceived: https://faculty.weber.edu/eamsel/Classes/Practicum/TA%20Practicum/papers/Smith,%20DiSessa,%20&%20Roschelle%20(1993-4).pdf
Three-Act Math Tasks: https://www.sfusdmath.org/3-act-tasks.html
Joshua Davis Music: https://joshuadavismusic.com
Other Resources:
Dylan Wiliam on Eliciting evidence of learning: https://youtu.be/jPo1fFQshUY
John Spencer's blog post - Ask the Teachers: https://spencerauthor.com/ask-the-teachers/
Christopher Emdin's article on 7 Cs of Effective Teaching: https://www.ascd.org/el/articles/seven-cs-for-effective-teaching
Brian Cambourne's Conditions of Learning: http://sydneysclass.weebly.com/uploads/3/8/7/0/38708599/cambourne_relevant_theroy1.pdf
Dave's article: Are they wrong? Or did they just answer a different question? https://pubs.nctm.org/view/journals/tcm/12/4/article-p202.xml

Hosted on Acast. See acast.com/privacy for more information.

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‎Teaching Like Ted Lasso: Be Curious on Apple Podcasts

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Description Dr. Amanda Jansen joins John and Dave on the Teaching Like Ted Lasso Podcast to discuss what it means to BE CURIOUS: in the show and in the classroom. And Dave and John do a play-by-play commentary on an assessment interview featuring a first-grader. Video: https://youtu.be/5TCTYxCQdaw...

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Paint Splatter Arrays (.key)
Paint Splatter Arrays (.pdf)

In Steve Wyborney's Splat!, the total number of dots is given and the number of dots under each splat is unknown. In my Paint Splatter Arrays, the total number of dots is unknown. My paint splatters do cover some dots but how many is beside the point. Also, Steve's dots are scattered; mine are arranged in arrays. (More on that below.) Steve's splats splat. My splatters are there from the get-go. See? Not the same.

h/t Andrew Stadel

Here's why I created this activity...

T: "How many do you see?"

S: "Twenty-five."

T: "How do you see them?"

S: "Two, four, six, ..."

Every. Single. Time.

Not all students. Most students do see and use groups or arrays to figure out how many. Those strategies are described in this post. But some students don't seem to make sense of others' ideas. That's a greater challenge than I'll tackle here. (Recommended: Intentional Talk by Elham Kazemi and Allison Hintz.) Instead, I designed the activity above to (gently) shove students towards looking for and making use of arrays.

The first three are softballs. For example, the second:

Students can still see each dot and count all by ones or twos. But a more efficient strategy is to see 3 × 5 (3 rows, 5 columns).

The next several slides completely cover at least one dot, so students can't count all by counting what they can see. In each, at least one complete row and one complete column is visible. For example:

I had some fun with the last two. In the next-to-last one, the middle column is completely concealed.

In the last one, most of the dots are hidden. A bit of estimation. How many?

How confident are you?

What about now?

I test-drove these on my daughters. (Keira likes Booger Math! over Paint Splatter Arrays, by the way. It is catchier.) I'm looking forward to trying this out in Surrey classrooms. Feedback welcome!

And mine goes ding ding ding di di ding ding DING ding ding ding di di ding ding.

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This isn't Splat! Paint Splatter Arrays (.key) Paint Splatter Arrays (.pdf) In Steve Wyborney's Splat!, the total number of dots is given and the number of dots under each splat is unknown. In my Paint Splatter Arrays, the total number of dots is unknown. My paint splatters do cover some dots but how many is...

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Erikson Institute Early Math Collaborative

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Quantity is a particular amount of something, expressed as a number. Quantity cards for young children can have pictures of small sets such as dots, finger patterns, or 5- or 10- frames.

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I love that the game plays well with even the youngest of children, but some of the included game types scale up to match skills available to slightly older players. I also love that the game includes a brief guide for grownups on how to help kids enjoy and learn as they play. Tiny Polka Dot makes this list for its fun factor, not [just] because of its educational elements.

Matt Miller, Game Informer

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I love that the game plays well with even the youngest of children, but some of the included game types scale up to match skills available to slightly older players. I also love that the game includes a brief guide for grownups on how to help kids enjoy and learn as they play.

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These Savvy Subitizing cards were designed to play a card game I call Savvy Subitizing (modeled after the game Ratuki®). This is a deck of playing card sized cards, not a classroom sized set of cards.

This deck of 68 cards contains six different visuals for each number 0 through 10 plus two instruction cards. Each number 0 through 10 is represented in the deck with tally marks, rekenrek, ten frame, dot pattern, numeral, and finger pattern. The written numerals are in a handwriting font so that the 4 has an open top and the 6 and 9 are easily differentiated.

The cards are bridge size playing cards and come in a box for storage.

In stock (can be backordered)

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These Savvy Subitizing cards were designed to play a card game I call Savvy Subitizing (modeled after the game Ratuki®). This is a deck of playing card sized cards, not a classroom sized set of cards. This deck of 68 cards contains six different visuals for each number 0 through 10 plus two instruction cards.

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Build Math Minds Subitizing Cards Freebie

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Build Math Minds Subitizing Cards Freebie

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Savvy Subitizing Cards

These cards contain the numbers 1-10, but for each number it has a card that shows the numeral, finger pattern, ten frame, rekenrek, tally marks, and dot patterns. If you don't want to make your own, you can purchase a deck of the cards on my shop page.

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These cards contain the numbers 1-10, but for each number it has a card that shows the numeral, finger pattern, ten frame, rekenrek, tally marks, and dot patterns. If you don't want to make your own, you can purchase a deck of the cards on my shop page.

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Decomposition Activities

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IT'S THE NUMBER THAT A STUDENT WORKS WITH UNTIL HE KNOWS IT "UPSIDE DOWN AND BACKWARDS" WITHOUT HESITATION. THAT IS WHY WE CALL IT A "JUST RIGHT NUMBER."

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All Learners Network - I chat with hosts John Tapper and TJ Jemison about Elementary Math October 2022

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All Learners Network - I chat with hosts John Tapper and TJ Jemison about Elementary Math October 2022

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Get to know Spotify for Podcasters, the free, all-in-one podcast platform for every creator.

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Ann Elise Administering the Early Numeracy Assessment

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Ann Elise Administering the Early Numeracy Assessment

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Division Mountain and other resources.  Click on the image below. 

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Division Mountain and other resources.  Click on the image below. 

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Multiplication Mountain and other Resources  Click on the image below. 

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Multiplication Mountain and other Resources  Click on the image below. 

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Dr Nicki Newton's Subtraction Mountain and other resources.  Click on the image below.  

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Dr Nicki Newton's Subtraction Mountain and other resources.  Click on the image below.  

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Addition Fact Progression Mountain Chart and other Resources - just click on the image 

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Addition Fact Progression Mountain Chart and other Resources - just click on the image 

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Dr Nicki Newton's MRR Freebies Folder including progressions resources

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Dr Nicki Newton's MRR Freebies Folder including progressions resources

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Paint Splatter Arrays (.key)
Paint Splatter Arrays (.pdf)

In Steve Wyborney's Splat!, the total number of dots is given and the number of dots under each splat is unknown. In my Paint Splatter Arrays, the total number of dots is unknown. My paint splatters do cover some dots but how many is beside the point. Also, Steve's dots are scattered; mine are arranged in arrays. (More on that below.) Steve's splats splat. My splatters are there from the get-go. See? Not the same.

h/t Andrew Stadel

Here's why I created this activity...

T: "How many do you see?"

S: "Twenty-five."

T: "How do you see them?"

S: "Two, four, six, ..."

Every. Single. Time.

Not all students. Most students do see and use groups or arrays to figure out how many. Those strategies are described in this post. But some students don't seem to make sense of others' ideas. That's a greater challenge than I'll tackle here. (Recommended: Intentional Talk by Elham Kazemi and Allison Hintz.) Instead, I designed the activity above to (gently) shove students towards looking for and making use of arrays.

The first three are softballs. For example, the second:

Students can still see each dot and count all by ones or twos. But a more efficient strategy is to see 3 × 5 (3 rows, 5 columns).

The next several slides completely cover at least one dot, so students can't count all by counting what they can see. In each, at least one complete row and one complete column is visible. For example:

I had some fun with the last two. In the next-to-last one, the middle column is completely concealed.

In the last one, most of the dots are hidden. A bit of estimation. How many?

How confident are you?

What about now?

I test-drove these on my daughters. (Keira likes Booger Math! over Paint Splatter Arrays, by the way. It is catchier.) I'm looking forward to trying this out in Surrey classrooms. Feedback welcome!

And mine goes ding ding ding di di ding ding DING ding ding ding di di ding ding.

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This isn't Splat! Paint Splatter Arrays (.key) Paint Splatter Arrays (.pdf) In Steve Wyborney's Splat!, the total number of dots is given and the number of dots under each splat is unknown. In my Paint Splatter Arrays, the total number of dots is unknown. My paint splatters do cover some dots but how many is...

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Introductory Video Discussing Exploring Multiplication Facts Through Strategies

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Introductory Video Discussing Exploring Multiplication Facts Through Strategies

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Ann Elise's page of just Cuisenaire Rod products on Hand2Mind. Using this link will provide support to Ann Elise's business.

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Ann Elise's page of just Cuisenaire Rod products on Hand2Mind. Using this link will provide support to Ann Elise's business.

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**using this link helps support by business

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Ann Elise's Cuisenaire Rods 3-5 on-demand workshop

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Ann Elise's Cuisenaire Rods 3-5 on-demand workshop

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In my consulting work, one of the biggest frustrations of upper elementary educators is surrounding students' lack of number sense and basic fact fluency. Too often, our students are caught in the additive phase of reasoning of skip counting even within the contexts of multi-digit calculations and work with fractions and decimals. However, there are ways we can explore mathematics with students that will unlock a positive math journey for all!

This workshop will focus on how Cuisenaire Rods have the power to help all our students progress on the development of mathematical reasoning from the additive phase of reasoning into multiplicative reasoning throughout the 3-5 grade span as well as develop fraction number sense. Together we can foster the development of curious, risk-taking, confident, and flexible mathematicians!

Here's what you can expect from my two and a half hour on-demand workshop:

Customized workshop notebook to keep track of ideas that resonate, reflections, and record your action items

Discussion of the foundations of elementary mathematics: fluency, problem solving, and grade level content standards.

Introduction to Cuisenaire Rods including the organization of the colors of the rods, managing them in the classroom, and introducing them to the students.

Separate videos for grades 3, 4 and 5 demonstrating ways in which the Cuisenaire rods can help you explore the content standards of your grade level.

Online resources that will enable students to continue to explore Cuisenaire rods virtually during remote instruction.

An access code to a 6-month classroom membership at https://www.brainingcamp.com/and their amazing suite of online manipulatives including Cuisenaire rods!

Closed Captioning for all videos

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In my consulting work, one of the biggest frustrations of upper elementary educators is surrounding students' lack of number sense and basic fact fluency. Too often, our students are caught in the additive phase of reasoning of skip counting even within the contexts of multi-digit calculations and work with fractions and decimals.

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Ann Elise's Cuisenaire Rods K-2 on-demand workshop

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Ann Elise's Cuisenaire Rods K-2 on-demand workshop

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In my consulting work, one of the biggest frustrations is surrounding students' lack of number sense and basic fact fluency. Too often, our students are caught in the counting phase of reasoning even within the contexts of multi-digit calculations and work with fractions and decimals. However, there are ways we can explore mathematics with students that will unlock a positive math journey for all!

This workshop will focus on how Cuisenaire Rods have the power to help all our students progress on the development of mathematical reasoning from the counting phase of reasoning into additive thinking throughout the K-2 grade span. Together we can foster the development of curious, risk-taking, confident, and flexible mathematicians!

Here's what you can expect from my two hour on-demand workshop:

Closed Captioning for all videos

Customized workshop notebook to keep track of ideas that resonate, reflections, and record your action items

Discussion of the foundations of elementary mathematics: fluency, problem solving, and grade level content standards.

Introduction to Cuisenaire Rods including the organization of the colors of the rods, managing them in the classroom, and introducing them to the students.

Separate videos for K, 1, and 2 showing ways in which the Cuisenaire rods can help you explore the content standards of your grade level.

Online resources that will enable students to continue to explore Cuisenaire rods virtually during remote instruction.

An access code to a 6-month classroom membership at https://www.brainingcamp.com/and their amazing suite of online manipulatives including Cuisenaire rods!

Print resources such as an ocean-animal-themed decomposition mats, an anchor chart for your classroom, a mat for students to "build it, draw it, and model it" and recommended additional online and print resources.

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Power and Versatility of Cuisenaire Rods: K-2

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In my consulting work, one of the biggest frustrations is surrounding students' lack of number sense and basic fact fluency. Too often, our students are caught in the counting phase of reasoning even within the contexts of multi-digit calculations and work with fractions and decimals.

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Subtraction is the Achilles' Heel of our students

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Subtraction is the Achilles' Heel of our students

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Subtraction is the Achilles' Heel of our Students: But it Doesn't Need to Be

By Ann Elise Record

In my 20 years as an educator in the role of classroom teacher, Math Coach K-5, and currently independent math consultant, one of the observations I've had is that subtraction takes the students out! For the younger students, I witness them counting back on their fingers to determine a fact like 15 - 8. For the upper elementary students, I witness them doing the exact same thing except this fact is embedded with the subtraction algorithm within a division problem. In this post, I'd like to share with you some ways we can explore subtraction that will help students develop flexible strategies starting with basic facts and the future impact as they apply these same strategies to the numbers appropriate to their grade level. If we dedicate instructional time to subtraction (equal to the other operations), we can ensure access to the mathematics for all our students.

First of all, I want to be clear that students using their fingers to count back isn't what bothers me. They are a "handy" manipulative that students always have with them and I never want any student to feel shame in using them. I would use my fingers, too, if I were counting back a large number like an 8. The issue is that the students are in the counting phase of reasoning. Here is graphic of the K-12 math journey made by Pam Harris of www.mathisfigureoutable.com that has profoundly affected my understanding of students' mathematical development.

Subtraction Basic Facts
In Preschool and Kindergarten, students are in the world of counting and cardinality. There is a lot going on in these grade levels and we definitely expect them to use their fingers to explore quantities and begin to explore addition and subtraction. In grades 1 and 2, though, we want to explore quantities in ways that will help students develop their understanding of number relationships. Not only will we be helping students arrive at their answers more efficiently, but they will be developing their conceptual understanding of the operations as well as their number sense.. There are two keys to developing fluency with subtraction: decomposing numbers and realizing there are two meanings of subtraction.
Subtraction Fluency within 10
The first context we use when we explore subtraction with our youngest students involves the action of removing items so objects get eaten, broken, or given away. Because this action is in the story problem, it becomes natural that students act out the problem and count the objects as they remove them and then count the ones that are left. As our students are introduced to working with larger numbers in grades 1 and 2, we want to help them move past the counting phase of reasoning and into additive thinking. The first step on this journey is to explore the second meaning of subtraction: finding the distance between the two numbers. A context such as Kylynn has 8 cookies and Delia has 6. How many more cookies does Delia need to have the same as Kylynn? This story situation encourages using addition to solve subtraction. So, rather than counting back 6, we can start at the 6 and count up to the 8. This is a tell-tale expression I use when I interview students on their basic facts using Dr. Nicki Newton's Math Running Records ( www.mathrunningrecords.com ). At the same time, we can be exploring the decomposition pairs of all the numbers up to 10 so that if I ask a student 8 - 6 they will know it is 2 because 6 + 2 = 8.

For me, the most powerful and versatile manipulative is CuisenaireⓇ Rods (The name Cuisenaire Rods and the color sequence of the rods are registered trademarks of hand2mind). Since they are not labeled with values, they can represent anything we wish - whole numbers, decimals, and fractions. Since the quantities exist as a group, we can help students focus on the number relationships and move beyond counting with addition and subtraction (and beyond skip counting with multiplication and division). Here is the color coding system of the rods...

They are a perfect manipulative to help students determine all the decomposition pairs of all the numbers up to 10. Here's an example with the number 5.

Subtraction Fluency within 20
As we move into subtraction facts within 20, we want students to use strategies that make sense for their brains. Some prefer the removal thought process while others prefer to think addition. We never want to dictate which strategies students use, but we can show that some strategies are more efficient with certain numbers than others. This is particularly true with subtraction. Our choice of manipulatives can play a crucial role in developing our student's efficiency. Rather than counting back or counting up, students can think in chunks using 10 as a bridge. Here are two examples using Cuisenaire rods and notice the difference in the thinking to arrive at the same difference of 7.

I was interviewing a 2nd grader recently using the Math Running Record and when I asked her 14 - 8, she counted up from the 8 to get up to the 14. Here's a conversation we had together once the interview was done.

If you are interested in learning more about how you can explore the basic facts of addition and subtraction in concrete, pictorial, and abstract ways, check Dr. Nicki Newton, Dr. Alison Mello, and my book called Fluency Doesn't Just Happen with Addition and Subtraction .
Future impact
The power of this work in the basic fact fluency is that those very same strategies can be used when students are working on the content standards of their grade level. Too often our students are getting caught in the counting phase of reasoning within their work with multi-digit numbers. Let's take a moment to think about the thought processes of the students in a traditional algorithm to subtract 102 - 98. Students typically begin in the ones place and realize (not always!) that there aren't enough in the ones place to remove 8. If they are able to successfully regroup across those zeros, they will need to think about 12 - 8. Too often at this point, students have not developed fluency yet and fall back to a comfortable place by counting back the 8 from 12. They then do the same thinking in the other place value positions. So essentially, students have only thought about basic facts and are even counting to determine the differences.

Yet, if they had explored their basic facts by using strategies such as using addition to solve subtraction, they could think about the distance between 98 and 102 which is much easier for their brains. By making the thinking visible within the work of basic facts using manipulatives, students are able to visualize the same thinking process within the context of multi-digit numbers and even decimals and fractions down the road. This is so very powerful! Here's an example of how we can help students develop flexible strategies using Cuisenaire rods with 2-digit subtraction.

Finally, here's a video of a conversation with a 3rd grader about subtraction after a Math Running Records interview. I had asked her 15 - 8 and she had said you can add two to get to 10, then add 5 to get to 15 so the difference was 7. Yet, when I asked her some subtraction problems which could become attainable with mental math using the adding up thought process, she didn't use it.

There truly is nothing elementary about teaching elementary math. In fact, the more I learn, the more I realize I need to learn. Let's work together to help students develop fluency. I'd love to hear from you either through Facebook, Twitter, or by email. Down below, I've included those links. If I've peaked your interest in Cuisenaire rods, I do have two on-demand workshops for K-2 and 3-5 in which I explore how we can use Cuisenaire rods for fluency, problem solving, and the content standards for every grade. You can find there at https://www.anneliserecord.com/courses-new .

Together we can provide access to all our students and will be creating students who are engaged, curious, flexible, risk-taking, and confident mathematicians!
Ann Elise Record is an elementary math specialist/consultant.
Website and newsletter signup: www.anneliserecord.com

Facebook: https://www.facebook.com/annelise.record.94

Twitter: @AnnEliseRecord

Instagram: ann.e.record

Email: aer@anneliserecord.com

Subtraction is the Achilles' Heel of our Students: But it Doesn't Need to Be

By Ann Elise Record

In my 20 years as an educator in the role of classroom teacher, Math Coach K-5, and currently independent math consultant, one of the observations I've had is that subtraction takes the students out! For the younger students, I witness them counting back on their fingers to determine a fact like 15 - 8. For the upper elementary students, I witness them doing the exact same thing except this fact is embedded with the subtraction algorithm within a division problem. In this post, I'd like to share with you some ways we can explore subtraction that will help students develop flexible strategies starting with basic facts and the future impact as they apply these same strategies to the numbers appropriate to their grade level. If we dedicate instructional time to subtraction (equal to the other operations), we can ensure access to the mathematics for all our students.

First of all, I want to be clear that students using their fingers to count back isn't what bothers me. They are a "handy" manipulative that students always have with them and I never want any student to feel shame in using them. I would use my fingers, too, if I were counting back a large number like an 8. The issue is that the students are in the counting phase of reasoning. Here is graphic of the K-12 math journey made by Pam Harris of www.mathisfigureoutable.com that has profoundly affected my understanding of students' mathematical development.

Subtraction Basic Facts
In Preschool and Kindergarten, students are in the world of counting and cardinality. There is a lot going on in these grade levels and we definitely expect them to use their fingers to explore quantities and begin to explore addition and subtraction. In grades 1 and 2, though, we want to explore quantities in ways that will help students develop their understanding of number relationships. Not only will we be helping students arrive at their answers more efficiently, but they will be developing their conceptual understanding of the operations as well as their number sense.. There are two keys to developing fluency with subtraction: decomposing numbers and realizing there are two meanings of subtraction.
Subtraction Fluency within 10
The first context we use when we explore subtraction with our youngest students involves the action of removing items so objects get eaten, broken, or given away. Because this action is in the story problem, it becomes natural that students act out the problem and count the objects as they remove them and then count the ones that are left. As our students are introduced to working with larger numbers in grades 1 and 2, we want to help them move past the counting phase of reasoning and into additive thinking. The first step on this journey is to explore the second meaning of subtraction: finding the distance between the two numbers. A context such as Kylynn has 8 cookies and Delia has 6. How many more cookies does Delia need to have the same as Kylynn? This story situation encourages using addition to solve subtraction. So, rather than counting back 6, we can start at the 6 and count up to the 8. This is a tell-tale expression I use when I interview students on their basic facts using Dr. Nicki Newton's Math Running Records ( www.mathrunningrecords.com ). At the same time, we can be exploring the decomposition pairs of all the numbers up to 10 so that if I ask a student 8 - 6 they will know it is 2 because 6 + 2 = 8.

For me, the most powerful and versatile manipulative is CuisenaireⓇ Rods (The name Cuisenaire Rods and the color sequence of the rods are registered trademarks of hand2mind). Since they are not labeled with values, they can represent anything we wish - whole numbers, decimals, and fractions. Since the quantities exist as a group, we can help students focus on the number relationships and move beyond counting with addition and subtraction (and beyond skip counting with multiplication and division). Here is the color coding system of the rods...

They are a perfect manipulative to help students determine all the decomposition pairs of all the numbers up to 10. Here's an example with the number 5.

Subtraction Fluency within 20
As we move into subtraction facts within 20, we want students to use strategies that make sense for their brains. Some prefer the removal thought process while others prefer to think addition. We never want to dictate which strategies students use, but we can show that some strategies are more efficient with certain numbers than others. This is particularly true with subtraction. Our choice of manipulatives can play a crucial role in developing our student's efficiency. Rather than counting back or counting up, students can think in chunks using 10 as a bridge. Here are two examples using Cuisenaire rods and notice the difference in the thinking to arrive at the same difference of 7.

I was interviewing a 2nd grader recently using the Math Running Record and when I asked her 14 - 8, she counted up from the 8 to get up to the 14. Here's a conversation we had together once the interview was done.

If you are interested in learning more about how you can explore the basic facts of addition and subtraction in concrete, pictorial, and abstract ways, check Dr. Nicki Newton, Dr. Alison Mello, and my book called Fluency Doesn't Just Happen with Addition and Subtraction .
Future impact
The power of this work in the basic fact fluency is that those very same strategies can be used when students are working on the content standards of their grade level. Too often our students are getting caught in the counting phase of reasoning within their work with multi-digit numbers. Let's take a moment to think about the thought processes of the students in a traditional algorithm to subtract 102 - 98. Students typically begin in the ones place and realize (not always!) that there aren't enough in the ones place to remove 8. If they are able to successfully regroup across those zeros, they will need to think about 12 - 8. Too often at this point, students have not developed fluency yet and fall back to a comfortable place by counting back the 8 from 12. They then do the same thinking in the other place value positions. So essentially, students have only thought about basic facts and are even counting to determine the differences.

Yet, if they had explored their basic facts by using strategies such as using addition to solve subtraction, they could think about the distance between 98 and 102 which is much easier for their brains. By making the thinking visible within the work of basic facts using manipulatives, students are able to visualize the same thinking process within the context of multi-digit numbers and even decimals and fractions down the road. This is so very powerful! Here's an example of how we can help students develop flexible strategies using Cuisenaire rods with 2-digit subtraction.

Finally, here's a video of a conversation with a 3rd grader about subtraction after a Math Running Records interview. I had asked her 15 - 8 and she had said you can add two to get to 10, then add 5 to get to 15 so the difference was 7. Yet, when I asked her some subtraction problems which could become attainable with mental math using the adding up thought process, she didn't use it.

There truly is nothing elementary about teaching elementary math. In fact, the more I learn, the more I realize I need to learn. Let's work together to help students develop fluency. I'd love to hear from you either through Facebook, Twitter, or by email. Down below, I've included those links. If I've peaked your interest in Cuisenaire rods, I do have two on-demand workshops for K-2 and 3-5 in which I explore how we can use Cuisenaire rods for fluency, problem solving, and the content standards for every grade. You can find there at https://www.anneliserecord.com/courses-new .

Together we can provide access to all our students and will be creating students who are engaged, curious, flexible, risk-taking, and confident mathematicians!
Ann Elise Record is an elementary math specialist/consultant.
Website and newsletter signup: www.anneliserecord.com

Facebook: https://www.facebook.com/annelise.record.94

Twitter: @AnnEliseRecord

Instagram: ann.e.record

Email: aer@anneliserecord.com

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The Teacher As Mathematician Guest Post by Ann Elise Record - The Teacher As

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Subtraction is the Achilles' Heel of our Students: But it Doesn't Need to Be By Ann Elise Record In my 20 years as an educator in the role of classroom teacher, Math Coach K-5, and currently independent math consultant, one of the observations I've had is that subtraction takes the students out!

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Flexibility Through Facts Webinar for Global Math Department I facilitated.

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Flexibility Through Facts Webinar for Global Math Department I facilitated.

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Fluency has three aspects: flexibility, efficiency, and accuracy. Let's explore the heart of the strategic thinking for all 4 operations and discuss how we can begin that conceptual understanding while developing students' fact fluency. Not only will students develop fluency for their basic facts, but they will be setting a foundation of flexibility that will naturally progress to their grade level content. Together we can create positive math journeys for ALL our students!

Recommended Grade Level: K - 6

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Fluency has three aspects: flexibility, efficiency, and accuracy. Let's explore the heart of the strategic thinking for all 4 operations and discuss how we can begin that conceptual understanding while developing students' fact fluency. Not only will students develop fluency for their basic facts, but they will be setting a foundation of flexibility that will naturally progress to their grade level content.

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Never Say Anything a Kid Can Say by Steve Reinhart

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Never Say Anything a Kid Can Say by Steve Reinhart

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Dr Nicki and Ann Elise's Top Ten Ways to Get Students Problem Solving - Teacher as podcast discussion

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Dr Nicki and Ann Elise's Top Ten Ways to Get Students Problem Solving - Teacher as podcast discussion

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Episode 64: Top Ten Ways to Get Students Problem Solving with Dr. Nicki Newton and Ann Elise Record - The Teacher As

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Dr. Nicki Newton and Ann Elise Record are back! They each have their own lists of the best ways for students to practice problem solving and they collaborate to create one essential top ten list.

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All Learners Network curated site of Daily Routines

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All Learners Network curated site of Daily Routines

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Launch is how we use the first 5-15 minutes of our math block for purposeful, discussion-rich number sense routines in our classrooms. Learn more!

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Brainingcamp Redeem code for 60 Day Licence:  MATHRR122

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Brainingcamp Redeem code for 60 Day Licence:  MATHRR122

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Division Strategies all with same student!

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Division Strategies all with same student!

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Flexibility Through Facts Webinar for Global Math Department I facilitated.

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Flexibility Through Facts Webinar for Global Math Department I facilitated.

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Fluency has three aspects: flexibility, efficiency, and accuracy. Let's explore the heart of the strategic thinking for all 4 operations and discuss how we can begin that conceptual understanding while developing students' fact fluency. Not only will students develop fluency for their basic facts, but they will be setting a foundation of flexibility that will naturally progress to their grade level content. Together we can create positive math journeys for ALL our students!

Recommended Grade Level: K - 6

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Fluency has three aspects: flexibility, efficiency, and accuracy. Let's explore the heart of the strategic thinking for all 4 operations and discuss how we can begin that conceptual understanding while developing students' fact fluency. Not only will students develop fluency for their basic facts, but they will be setting a foundation of flexibility that will naturally progress to their grade level content.

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Find the connections between the Common Core State Standards for Mathematics

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Google search "wishball place value" or whatever topic you like

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Google search "wishball place value" or whatever topic you like

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Access Google Sites with a personal Google account or Google Workspace account (for business use).

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1000s FREE Primary Teaching Resources & Printables - EYFS, KS1 and KS2 - SparkleBox

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1000s of FREE teaching resources for Early Years and Primary School teachers.

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These resources were provided by the University of Kentucky Partnership for Mathematics and Science Education Reform (PIMSER).
Posted January 2008

For more information: https://pimser.eku.edu/

One-to-One Math

One-to-One Math was developed to help teachers, parents and para-professionals, community members, etc. work with students on math facts and critical concepts.

It is based on the beliefs that:

All students can and should learn math.

If children like math and feel successful at math, they will learn math.

For children to like math, it must be fun! Students like to play games, so One-to-One Math is a game-based program.

For children to feel successful at math they must be successful. One-to-One Math starts students with concepts they can quickly master and then builds on that success.

Students need to go through three stages as they learn math:

1. concrete or manipulative,

2. mental or representational,

3. abstract or symbolic

Below are the printable number and computation resources for elementary grades from One-to-One Math.

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These resources were provided by the University of Kentucky Partnership for Mathematics and Science Education Reform (PIMSER).Posted January 2008 For more information: https://pimser.eku.edu/ One-to-One Math was developed to help teachers, parents and para-professionals, community members, etc. work with students on math facts and critical concepts.

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Many webinars facilitated by Ann Elise and a few together with Dr. Nicki Newton

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Many webinars facilitated by Ann Elise and a few together with Dr. Nicki Newton

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The most popular manipulatives at your fingertips. Powerful yet easy-to-use.

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is the ability to recognise a whole quantity as the result of recognising smaller quantities. Sayers and others (2016) suggest that Conceptual subitising conceptual subitising may lead to the later development of arithmetic as it leads to decomposition or partitioning of numbers, the commutativity of addition, and part-whole knowledge. Sayers article is below and is an interesting and easy read.

Conceptual subitising builds upon the ability to subitise perceptually. The previous post explains perceptual subitising and provides activities to support students.

Once children are competent with perceptual subitising they should be gradually introduced to conceptual subitising by adding 1 or 2 more to a standard pattern, as on a die.

Maths Coach's Corner blog about Subitizing: Moving from Perceptual to Conceptual here.

What Does the Research Tells Us?

The Role Of Conceptual Subitising in the Development of Foundational Number Sense by Judy Sayers, Paul Andrews, and Lisa Björklund Boistrup, Stockholm University (2016)

Subitising Through the Years by Valerie Faulkner, North Carolina State University, USA and Jennifer Ainslie, Wake County Public Schools, USA (2017)

Early Spatial Thinking and the Development of Number Sense by Janette Bobis, Australian Primary Mathematics Classroom 13 (1) 2008

Different Ways to Subitise

Video from CE Kindergarten talks about subitising using dot patterns (familiar and unfamiliar), tens frames and Rekenreks.

Using Number Talks to Teach Addition and Subtraction

Not sure what a Number Talk is? The Brown Bag Teacher provides a quick explanation here.

Quick Images from the Teaching Channel
Video of a Number Talk by Jo Boaler
Activities for Conceptual Subitising

John Van de Walle talks about subitising in his book Teaching Student-Centered Mathematics: Grades K-3. He provides blackline masters of dot patterns that can be used with your students. for the blackline masters. Maths Coach's Corner has enlarged versions of Van de Walle's cards so they would be easier to use, and you can grab them .

Find It - Add and Count from Mathematical Thinking

Find It - Bingo from Mathematical Thinking

Subitising Freebie from Natalie Lee Kindergarten

Dog House Dots from A Blog from the Pond

Early Years Focus: 10 Subitising Activities by James A. Russo (Monash University, Melbourne)

Domino Maths Games from Fun Games 4 Learning

' Gone Dotty ' Dominoes - a non-standard version of dominoes

Teacher Mama: FREE Subitizing Dot Cards {After School Linky}

Conceptual Subitising Flash Cards on the Whiteboard

Interactive Whiteboard Resources

Illuminations offers interactive resources for both five and ten frames. Students can use these to answer 'How Many?, Build, Fill and Add.'

iPad Apps (These are great resources but, unfortunately, not free)

Subitising Flash Cards from Little Monkeys

Subitize Tree from Doodle Smith Ink

Quick Images 11 from Tom Patten

Number Flash from Mitchell Mark

Conceptual subitising is one of the most important foundational maths skills children need to support them in developing mental images for addition and subtraction. Its development assists students in moving away from 'counting on' and 'counting back' and from using their fingers as support.

It's important children receive lots of repetition and visualising it in different ways. For students who are having difficulty, stick to the traditional arrangements, gradually introducing non-traditional and ensuring the new arrangements are explicitly taught.

There are lots of resources out there. Fortunately all the resources, except for the iPad apps, are free!!

Until next time,

Carole

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Subitising - Moving from Perceptual to Conceptual - Maths 4 All

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Conceptual subitising involves recognising a whole quantity as the result of recognising smaller quantities using perceptual subitising. Research sugests it supports the later development of arithmetic.

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Build Math Minds Podcast. Host Christina Tondevold interviews Cathy Palkovic about when her students determined how many cards were in 6 boxes of hundreds of decks of cards. Wow!

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Build Math Minds Podcast. Host Christina Tondevold interviews Cathy Palkovic about when her students determined how many cards were in 6 boxes of hundreds of decks of cards. Wow!

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Episode 60: Building Self-Reliance in Math

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Welcome, fellow recovering traditionalist, to episode 60. Today is an interview with third-grade teacher, Cathy Palkovic, and a theme of our conversation is about building self-reliance in math. Christina - In this interview with Cathy, we get into it all kinds of things, from what her distance learning looks like to Math Running Records, to how her third-graders solved 898 x 52 and they did it without any guidance from her.

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Kids Math Talk Podcast interview with Dr. Nicki Newton, Dr. Alison Mello, and Ann Elise Record

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Kids Math Talk Podcast interview with Dr. Nicki Newton, Dr. Alison Mello, and Ann Elise Record

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Exploring Basic Math Fact Fluency - An Interview with Dr. Nicki, Alison, and Ann Elise

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Desiree Harrison 0:00 Fluency is a concept we have talked a lot about on the podcast. We need to keep talking about this because there are so many deep-seated core beliefs about how to best help children with addition and subtraction. We need to move past our feelings and get into the facts.

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Ann Elise's conversation about Math Running Records with Laura and Karina on the Learning Through Math Podcast  Released Oct 17, 2021

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Ann Elise's conversation about Math Running Records with Laura and Karina on the Learning Through Math Podcast  Released Oct 17, 2021

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Learning Through Math with Laura and Karina

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Episode 55: Learning About Math Running Records - Learning Through Math with Laura and Karina

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In this episode, Laura and Karina discuss Math Running Records with Ann Elise Record. CHALLENGE: Give a Math Running Record to one of your students and let us know how it goes!

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Subtraction Multi-Digit (click on arrow to expand and watch video)

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Subtraction Multi-Digit (click on arrow to expand and watch video)

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Division RR Analysis (click on the arrow to expand and see video)

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Division RR Analysis (click on the arrow to expand and see video)

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Division RR G5 S1 - (click on the arrow to expand and see the video)

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Division RR G5 S1 - (click on the arrow to expand and see the video)

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5 Weeks of Daily Routines by Berkeley Everett

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5 Weeks of Daily Routines by Berkeley Everett

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Here are 5 weeks of number sense routines (5-10 minute math talks) tailored to each grade K-5. Every slide deck includes a "how to" and a week each of:

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5 Weeks of Daily Routines by Berkeley Everett

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5 Weeks of Daily Routines by Berkeley Everett

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Here are 5 weeks of number sense routines (5-10 minute math talks) tailored to each grade K-5. Every slide deck includes a "how to" and a week each of:

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Ann Elise and Dr Nicki have done several hour-long webinars for Brainingcamp. All can be viewed for free at www.brainingcamp.com/webinars

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Ann Elise and Dr Nicki have done several hour-long webinars for Brainingcamp. All can be viewed for free at www.brainingcamp.com/webinars

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The most popular manipulatives at your fingertips. Powerful yet easy-to-use.

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Top Ten Manipulatives - Teacher as podcast interview with Dr. Nicki Newton and Ann Elise!

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Top Ten Manipulatives - Teacher as podcast interview with Dr. Nicki Newton and Ann Elise!

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Episode 44: Top Ten Math Manipulatives — The Teacher As

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In this second edition of Top Ten, Dr. Nicki Newton and Ann Elise Record return with their own lists of top ten math manipulatives and collaborate to create one essential top ten list. Dr. Nicki and Ann Elise are so knowledgeable and share their favorite manipulatives and how they like to use them w

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Keep current on topics in math education, and learn from the perspectives and expertise of Black women.

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Making Math Moments that Matter interview with Ann Elise

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Making Math Moments that Matter interview with Ann Elise

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Ann Elise: Well, first of all, we need to define fluency. We need to be all on the same page of what fluency means. So in my presentations I ask people, "What words come to mind when you think about being fluent with your math facts?" And, overwhelmingly, people will put words like 'speed.' Speed, fast, automaticity, all words about speed. And then occasionally, I'll get 'accuracy,' right, because kids can give the right answer but then be wrong. Right? So we want to have the accuracy as well as it being, I call it relatively speedy, because it's the least of the four things I want to talk about. But there are two more pieces of fluency, which is crosstalk.

Jon Orr: Today we speak with Ann Elise Record. Ann Elise is a seasoned educator with a career spanning over two decades of elementary classroom experience. These days, she's a K-5 math coach who works with districts on developing strategies to increase students' fact fluency as well as how to use manipulatives in the classroom.

Kyle Pearce: Stick around as we'll discuss effective strategies to help students build their fact fluency, how to help students with the progression from additive thinking to multiplicative thinking, and, how can we help students with concepts that hold them back from their learning?

Jon Orr: Let's do this, Kyle.

Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast, I'm Kyle Pearce from tapintoteenminds.com.

Jon Orr: And I'm Jon Orr, from mrorrisageek.com. We are two math teachers who, together...

Kyle Pearce: With you, the community of Math Moment-Makers worldwide who want to build and deliver math lessons that spark curiosity...

Jon Orr: Fuel sense-making...

Kyle Pearce: And ignite your teacher action. Are you ready, Jon, to dive in to this awesome conversation with a dear, dear math friend?

Jon Orr: Mm-hmm (affirmative), mm-hmm (affirmative), of course, Kyle. We are honored to bring Ann Elise Record onto this show as we've been looking forward to this conversation.

Kyle Pearce: All right, but before we dive in here, Jon, we want to make sure that you folks at home have taken the time to explore some of our most recent full units of problem-based math lessons.

Jon Orr: Right, right. We've been busy adding full units to our Make Math Moments website. And last episode here, we shared some details about our six day unit called the Wooly Worm Race that was created to help educators address teaching fractions, decimals, and percentages conceptually.

Kyle Pearce: Well, we've also tossed in some more context, rich, problem-based math lesson fun with our unit called Snack Time, where students explore the tapintoteenminds.com classic three-act math task called Cheese and Crackers, to use partitive division to partition and distribute slices of cheese to a specified number of crackers.

Jon Orr: That's definitely a classic I've used with my class, and now I'm set up with a whole unit of connected math talks. Sense-making prompts, purposeful practice, and summative assessments, all scraped from my web browser by visiting our test page at makemathmoments.com/tasks.

Kyle Pearce: Yes, it's super exciting, Jon. We hope to see you over at makemathmoments.com/tasks, so that you can run one of these awesome problem-based units in your classroom today.

Jon Orr: All right, enough from us. Let's get on with our great, great, great, great conversation with Ann Elise.
Hey there, Ann Elise, welcome to the Making Math Moments That Matter podcast. As always, we are super excited to chat with someone we've met, someone we know... How are you doing today?

Ann Elise: I'm doing great, doing fabulous.

Jon Orr: Awesome stuff, awesome stuff. Well, we know you quite well, but maybe there's a few Math Moment-Makers out there who aren't as familiar with Ann Elise Record. Can you help us out? Let's learn a little more about yourself. What's your role in education and how did you get to that part in your learning journey?

Ann Elise: Sure. Currently I'm a consultant. So currently I work for myself out of my home and I was traveling around a lot and working in schools and districts, and also presenting around the country for the Bureau of Education and Research. But then once we had the shutdown, I've been working from home. But I had gone to get to, my undergraduate degree was in sociology. So I was not certified or able to teach. And so I got back to school, once our kids were becoming of school age, I went back to school and got my master's in order to teach. And then I taught grade five for 13 years. And then a math coach position opened up in my district, and so I became the math coach K five.
And that was really the start of my journey to truly understand the trajectories of the learning and progressions of kids from the early numeracy on up, and all those connections. But also at that time, I taught some pre-service college classes, the math methods, I helped people, tutored them to help pass the Praxis test, because I've experienced in this role, working with so many different populations of people. And I've seen the anxiety and the stress and the phobias, firsthand, of people.
And I didn't have that growing up. When I grew up, I could answer things quickly and accurately, so I felt good about myself. But to have seen the phobia up close for a variety of people, it was surprising to me how many of the college kids were terrified of math going into teach elementary. And it just became a passion of mine, the more that I learned, why I wanted to share with people. And my husband got a new job two hours south of where we had been living. And then I'm like, "Well, what am I going to do now?" There weren't any math coaching positions. I loved working with the teachers, and the kids, and everyone. And that's when my two close friends and mentors, Dr. Nicki Newton and Christina Tondevold, said, "Well, why don't you go off on your own?" And that's what I did. So my life has been completely different these last few years, doing this new part of my life.

Jon Orr: Yeah. And I think you've brought up a huge point about math anxiety being a huge thing, and I think still is for so many people, and I'm wondering, what suggestions can you give our listeners right now, and teachers, that can help reduce that anxiety? If you've been recognizing it's a problem in your past, in your career, now I'm wondering, I guess, two things. One is, what can we do now to help kids, and even teachers, reduce some of that math anxiety? But then I'm also wondering about, what did Ann Elise look like as a early teacher? Did you recognize that right from the get-go, that we've got this math anxiety, and it's something that you've been using in your career right from the start? Or is that a progression that built up over time? And so those are, I guess, two things to talk about.

Ann Elise: Yes, okay. So first of all, when I think back to when I first began teaching, so I think we all know what we know at the time and we don't know what we don't know. And so, in my master's program to teach, the only class that I had to take that involved math to become certified K eight was math and literature. So it was a literacy-based math class. So I came out certified K eight, really being no more qualified to understand early numeracy than I was to teach an eighth grade math class. I think the assumption was that you'll be given a textbook of whatever district hires you, and you follow the textbook. So that's what I did. I became the grade five teacher, we had a textbook, I was very procedural in my teaching. It's all that I knew when I grew up learning math. It was a very procedural, rote procedure. There was no open tasks. There was no talking about our thinking or having any kind of flexibility of thought.
And so I gave time test to my classroom, all 13 years I was in the classroom. And over the course of that time, I know I did concrete and pictorial things, but it was leading toward the algorithm. I didn't do flexibility with number sense, I was trying to show them why the algorithms worked. I didn't know anything else. So it definitely was not in play the first many years that I was teaching. But as I learned more, and we had a consultant come to our district that showed me how to teach math in a visual way, that was totally new to me. I had no idea that you could teach math visually, like pattern blocks, refractions. It was a mind-blowing thing to me. I had never seen it before.
So it's been, certainly, I call it a journey because I think we're all on journeys. We as educators, as well as the kiddos, right? As we get to find out where we are on that journey, and then you continue and when, Dr. Maya Angelou says, "When you know more, you do better." And that's exactly what I believe and I've been living, that, I know the more that I learn, the more I realize I have to learn. This is a never-ending process. And so, I think we need, I need to send the message to people, I want to let the people know that there is so much more to mathematics and connections and a beautiful journey to it, so far beyond rote memorization and procedures. Because I think that when we think about giving kids worksheets that are just 20 kill and drill things, that's not going to be encouraging a love of math, nor will it build the flexibility of thought that we need to build our number sense and to develop the confidence to try harder problems.
The idea of the growth mindset messages of Jo Boaler from Stanford, the fact that our brains have the way of growing new parts. There is no such thing as a math brain, but think what happens is people have gone on their journey, and I truly believe time tests have begun, well, research is out there that proves it, but, that it's the start of math anxiety. Kids think that because they're not fast at the math, and they're not good at math, and it begins disassociating themselves from the idea that they can be a mathematician. And then it gets harder over the course of the year, as if we're only doing procedures and formulas. That's the only way they've been exposed to thinking and algorithms... Algorithms take lots of steps. And I think, I'm like, a three digit by two digit multiplication problem, that's a lot of calculational work.
But until we explore these things in more flexible ways, it can make it much easier. And I find that my consulting work, the more that I share these ideas, and that they're seeing the math in a different way. Even the parents, I have my districts do math nights, because I want to talk to the parents. It's huge we get the parents involved. And by the end of that 30 minutes, the parents are like, "Oh my gosh, this is a whole new world to me. That's why my child was doing that this morning." Literally they've said to me, "We were arguing with my child this morning about eight plus six. We just told her, 'It's 14.' She's like, 'But no, mom, that's not the way I was supposed to do it.'" And the parents were like, "But now we know why, and we totally get it. We've seen the future impact of that work."
And so, the whole anxiety piece comes from, not the math, but the feeling of insecurity and embarrassment and humiliation people have felt growing up, that they were not a math person, as if it takes some extra kind of brain to be good at math. And it's not true. We all can grow those parts of our brains, and in fun and engaging ways. I want our students to have no bad stories of math growing up. In all my consulting, I would say probably 80% of the people that I meet tell me the most awful, traumatic math journeys of their lives. It's just always negative. They're always about 20% like, "Oh, it was good. It was fun. I loved it." It's like, "Well, you're like me then, because I got my answers correct, I was able to get them done fast, so I thought I was good." But it wasn't until I really began this deep journey that I realized I didn't have any understanding of mathematics, so I didn't see connections to topics within the math. But now the more that I learn, the more I'm like, "Oh my gosh, that connects to that. And throughout the grade levels, even, it's a beautiful thing, to finally see those connections.

Kyle Pearce: Yeah. Well, and we love asking about these things because I worry that when teachers and educators who are at that place in their own journey where they feel like maybe they don't feel comfortable with the content, or they maybe remember their own math anxiety that they had as a student, or they just think plain out that they're doing it wrong and they see someone like yourself, Ann Elise, or Jon and I, and we are so into thinking about how mathematics develops, and thinking about the conceptual connections, all of those pieces. But yet, most of us, most of us didn't have that same experience growing up. And many of us, as you just mentioned, and it's great to hear, that, many of us actually taught it the way we were taught. And it's okay if that's where someone is as they're listening. So I think that is such a huge message for people to see that it takes time.
And I immediately connected when you were describing how you were teaching very procedurally and you were trying to help kids to understand why the procedure works, which I think is part of that trajectory. If you learned procedurally, you tend to teach procedurally, and then hopefully over time you start to see that, "Oh, connections are important." But then what we do, it seems like for me, anyway, I started to still teach the procedures, but then I tried to explain them afterwards. Instead, now we're realizing, "Oh, we really need to start with kids making meaning, and making sense first, and then working towards and allowing those student-generated algorithms to start popping out and helping them to make their connections so that we can essentially get more efficient along the way, but not with the end goal just being an algorithm or a procedure, right?

Ann Elise: Absolutely, 100%. And in fact, the more learning that I'm doing, I've been trying to work on my own knowledge of middle school mathematics, in terms of the conceptual understanding. I can get right answers, I help people pass the Praxis test. That's not the issue of getting right answers. It's, I want to get the connections that I missed first time around. And so I've been doing a lot of work on that. And the more of the work that I'm doing, I am doing mental math or ratio tables and things of using chunks of numbers that are nothing to do with the algorithm. And I'm getting easy answers really quickly, I'm breaking apart numbers in ways I never had done before, and it's just a matter over time. I do a lot of Pam Harris' Math Strat Chat every week, and inaudible Academy. I took a class with Pam Harris on proportional reasoning, that is just like, I'm learning these ways of thinking about it. When I learned it the first time, I had no idea of those connections, I was just following procedures. And it's just a beautiful extension to what I already know as a foundation of understanding K five, and to extend that to that middle school level.

Kyle Pearce: I love that. And it's actually ironic that, nowadays you'll see, both in your messaging and so many others who come on our show and obviously Jon and I, who, we do not believe, like math fluency is not speed. Yet, when we actually start to help kids become more flexible in their thinking, and start to play with different strategies, and really just give them the freedom to think and use critical thinking in order to reason and solve through problems along a trajectory, along a progression, what I end up seeing is actually kids end up becoming more quick with their math facts than kids who are memorizing the procedure. It's actually mind-blowing when you're saying ,"No, no, we're..." It's not about speed, but then the end goal ends up oftentimes becoming speed anyway, which isn't the holy grail, it's just like a symptom of having flexibility and fluency with number. And I'm hearing that in your voice, I hear that in your message.
So before we dive deeper into fact fluency, because we have a lot of questions for you, we know your connections with Christina Tondevold, as well as Nicki Newton. We know you're big into that, and we'll be diving into those questions, but before we let it get out of hand here and we dive too deep, we've got to hear about a math moment from your past. So you've described a few things about how you began teaching, how you taught for a while, also, a bit about your experience learning in the classroom as a student, but is there a moment that pops out in your mind? It could be defining, maybe it's something that, like a celebratory moment, or it could be one that maybe you remember, and it's one of those memories that you sort of wish you didn't remember. What's a math moment that pops out in your mind that you're willing to share with our audience?

Ann Elise: First of all, I'm just so happy to be able to share you my math moment, because I've been listening to your podcast forever. And I walk my dog listening to it. Whenever you ask your guests, I'm like, "Oh, I would tell this story if I was ever inaudible them." When I became math coach, K five, before I began that part of my job, I took a one-week class with Dr. Mahesh Sharma, on, really, it was K eight type content. And it was the first time I saw the connection between grade levels of things I could do at a lower grade level that affected what came up. It was my eye-opening to that kind of procedure. Well, we did the area model of multiplication, and he loves Cuisenaire rods, they're my favorite math manipulative. I think they're the key to helping our kids move past the counting phase of reasoning and into strategic, additive thinking, multiplicative reasoning.
inaudible we had these Cuisenaire rods and we built area models of basic facts. So in the third grade content, right? Well, over the course of that week, we kept using the area model to do double digit by double digit, or to do decimals by decimals, or mixed numbers by, like the same area model, I was able to use with harder content. Well then he said, "We get to division, and we're using the area model to do division," which I had never, ever thought of before. And we were doing it concurrently with the Cuisenaire rods. And he put on the board 'X squared plus five X plus four.' That's the exact problem that he gave. And he wanted us to divide it by X plus one. Now, I remember my brain saying, "I'm out." I took calculus in high school and again in college, it wasn't like, I really thought I did well with math. But, it had been decades since I had done that before.
So I'm like, "Okay, well I'm out. I'm not even going to attempt this." But then he said, "Try doing the same thinking we've been doing with the division for the area model. Can you make a rectangle that is X plus one by something?" And within 20 seconds, I built the area model, I knew the answer was X plus four, and I could explain to you why. And that was my moment that I went, "Oh my gosh, a model that I can show the thinking with the kids in third grade, can follow them through their entire math journey, and the math journey will make sense." It's not just getting a right answer. And I was sold on the whole idea of, "Wow, this is just a learning progression." And the more that I see that, the more that I know, it's all about that journey.
My husband has been working from home since the shutdown in March, and he says, and after doing a lot of trainings online, he's like, "Hon, you say the word 'journey' all of the time." I'm like, "I know, but it is true." We're all on a journey, right?

Jon Orr: Yeah, yeah, for sure. And I'm glad you brought up the area model because we love using it, we love talking about it, and we think it's...

Kyle Pearce: Didn't we just talk about it last night, Jon?

Jon Orr: Yeah. I was just going to bring that up, Kyle. Kyle and I talked about it last night, but I just had a recent discussion with a friend who couldn't see this new math, and why did their son or daughter have to learn this diagram or this way of multiplying? And when I can show her how to multiply, and get done in 30 seconds, and he referenced that Facebook post that we've all seen crosstalk...

Ann Elise: Oh my gosh, I know...

Jon Orr: Somebody being done in 30 seconds, and then twiddling their thumbs for the rest of the time and...

Ann Elise: Yup, exactly.

Jon Orr: Versus somebody who's drawing the area model. And we had this long conversation about that, and that was exactly what I referenced, Ann Elise, is that this model can carry forward, whereas this algorithm works in this one instance, and... We use it in high school and, listeners of this show know I'm a high school math teacher, and I just helped model my students this morning. And yesterday with completing the square, using the area model, and completing the square for a grade 10 student can be tough. And some teachers think it's one of those procedures you just got to show kids. "They just got to memorize this procedure." And it's hard to explain why it works unless you use a square to model it. And the area model works perfectly. And I love how it carries forward from there. And I really like how you referenced, both Kyle and you referenced that, by using these models, kids can get that fluency.

Kyle Pearce: I was sold on the area model from high school and then downwards. Whereas you went from an area model from lower elementary upwards, because I was sold downwards, because after using the area model to help kids complete the square in high school, they're completing the square in their heads. They didn't have to draw anything, they didn't have to write anything, because they could actually imagine the square and what the dimensions of the square would be. And so that they could write the vertex form of a parabola or quadratic expression, so it is a great tool, and I know that we'll talk about many other things.

Jon Orr: And I'm being a high school teacher and still trying to learn more about elementary math. I know Kyle's been on a journey for that for the last few years, but I don't get a lot of experience into the elementary math unless I do that on my own, or I talk to fantastic teachers like yourself. So I'm really hoping for this episode and the remainder of this episode to be a master class in fluency, and a master class that I can learn from, and all our teachers can learn from. So if we just think about diving into early mathematics in particular, and if we could help educators and parents learn effective strategies to help their children and students with fact fluency, let's think about some practical suggestions, some tips that we can help our teachers with on fact fluency at an early age.

Ann Elise: Well, first of all, we need to define fluency. We need to be all on the same page of what fluency means. So in my presentations I ask people, "What words come to mind when you think about being fluent with your math facts?" And, overwhelmingly, people will put words like 'speed.' Speed, fast, automaticity, all words about speed. And then occasionally, I'll get 'accuracy,' right, because kids can give the right answer but then be wrong. Right? So we want to have the accuracy as well as it being, I call it relatively speedy, because it's the least of the four things I want to talk about. But there are two more pieces of fluency, which is flexibility and efficiency. Those are the four pillars of math fact fluency. And I want to honor the fact, also, that there may be some of our students that are not ever going to fast, but they are using gray strategies and number sense.
I have to mention to you right off the bat, that, a lot of my consulting work has been focusing around what's called a math running record. It was a protocol designed by Dr. Nicki Newton. She did 10 years of research on math affluency, and created this interview protocol for us to talk to our kids about their thinking. I believe it is the key to transform schools and districts and the mathematical journey for our kids, because it's looking for that flexibility of thought. And if we explore flexibility with our different operations with the kiddos, it'll set a foundation for thinking that will then apply to the actual grade level content we're trying to teach. Without having to go to algorithms, they'll become much more efficient problem-solvers, and with their fluency, with the calculations, because they're using strategies and number relationships, which will build their number sense.
It's the start of everything. I've found it's been my key to educate people on early numeracy, because myself, having gotten, honestly, a master's degree, certified K eight, I had no idea the world of early numeracy, until I took a course from Dr. Sharma, that whole beginning of that journey. But then I also took the Number Sense 101 course with Christina Tondevold. And that was like, "Oh my gosh, what is this world?" And then Dr. Nicki as well, and it filled in more information. And then I just continued to learn about the early numeracy. So I want us to think, first of all, about that, there are developmental journeys our kids go through. Typically what our kids do for math inaudible journey is they begin counting on their fingers, right? Fingers are very important for the brain, very important for kids to do that.
But there's also something called finger agnosia, which is the discrimination of the fingers, but not finger counting. So the idea that the kids are going to start by counting, they usually count all, our youngest kiddos. If you ask them three plus two, in a context, I like putting all the fluency work in context, but you ask them three plus two, they put out three fingers and two fingers, and they would count them all, starting at one. Then kids developed to count on. So they may have all five fingers up, but they know this hand has three, and it's four or five. That progresses to head counting on. So the three isn't even out anymore, they might finger count four or five, or then, in their head, go, "four or five."
Then we have a whole section of derived facts. And that's typically the phase people skip. They tend to go, "Okay, you're counting on." So kids are counting on their fingers when they do their teen sums, because how else do you count on eight without keeping track on your fingers? And then we tell them, "Memorize them. I want you to play games with all the math facts, I want you to memorize these." As the kids are waiting for numbers to pop in their brain, when you ask them the questions, so that they don't know what it is. If they don't know what the answer is, that nothing pops in their head, what do they do? They count on their fingers, which is their comfort level, to find out what the sum is. And then when you think about a double digit addition problem, where we have raised to put the algorithm in front of the kids so soon in their journey, they're usually grade one, I find, a lot. Well, within the algorithm, it's just single digit basic facts. And in each of those basic facts, they're counting on their fingers. So they're in a counting phase of reasoning, within the context of addition problem.
I love this work of Pam Harris on the development of mathematical reasoning. That image of her graphic that she has, to go from the counting phase into additive thinking, and then by grade three, the multiplicative reasoning, before the proportional, and then the functional, the whole K-12 journey. So when I try to think about the math the kids are doing, what phase of reasoning is it? And the algorithms, adding and subtracting, are usually, kids are counting, they're counting on their fingers. So how can we get that? Well, we can work on the flexibility of thought. The idea that I could ask kids what's eight plus five, and that the kids could break apart that five and give two to the eight to make a 10, and then I can rename eight plus five as 10 plus three. That's a lot easier for my brain.
So the heart of that addition of breaking apart numbers and putting them back together in flexible ways will be the key, because I can then forward that to 48 plus five, or 98 plus five, or 98 plus 25. I can take two from it to make a 100, so 100 plus 23. It progresses all the way through their journey, including to fractions. Adding four fifths and three-fifths... Rather than adding numerators, keep denominators the same, uh oh, it feels weird, this large number on top, right? Break apart the three fifths and give one fifth to the four fifths and rename it as a whole plus two-fifths. It just will affect everything down their journey, starting with the basic facts.
So the Math Running Record allows us, when we're interviewing our kids, to be aware of that learning journey. Because there are codes for that. This is all based on Carpenter and Moser's research, inaudible research of the developmental trajectories, that the kiddos, we ask them sets of facts as a benchmark inaudible question for each of the set of facts. So you find which set of facts are causing a super slowdown, inaccuracies, or inefficient strategies, like just counting on. And then within that zone, where are they on that trajectory of the having no strategy to even try it, the counting all, the counting on, the head counting, the derived strategies, and the automaticity. Because we can't take kids from counting all to automaticity in one step, that's not how kids learn and develop. So it's a protocol that allows us to learn about the expertise needed for early numeracy. It's a brilliant protocol, and it's been a lot of my consulting work, because Dr. Nicki is just brilliant and she's so prolific, and she just talks about all different areas of mathematics. But I've latched on to this Math Running Record of the fluency piece, because I really feel it's my gateway to get people to understand, teachers and the parents, to understand the foundations of the operations, and to build the fluency through flexibility. And it alters everything, because it applies to every other content that you're doing.

Kyle Pearce: I love how you reference, even, how, we jump the gun on the memorization of those derived facts, right? They're not really memorizing derived facts or memorizing facts, when we skip all of these parts, and composing and decomposing number is so important. And I'm hearing that in what you're saying here, and this idea of equivalence pops out. And as you're working with young kids and, my son, who's an SK and my daughter who's in grade two, I get to have fun with these things, by playing with numbers and using strategies and seeing the strategies that they're using. And it really is pretty magical when you see them thinking.
And I just had this, I guess, a bit of a sad moment there, reflecting, as you had mentioned, like a student who's sitting there trying to bring up a fact that they've tried to memorize, but now it's like they're recalling facts they haven't derived themselves, so they don't have a connection. They also don't have a path to help them get out of a jam. And we talk about that a lot on this podcast and it continues to cause more and more problems down the road, because if students don't have a understanding of how they got to where they are, which I think many of us are like, as adults, many of us are like that, right? Those adults, like Jon, you had mentioned that friend who was thinking of the algorithm like, "I can multiply two digit by two digit numbers, no problem." But could they do it any other way? Or if they forgot one step of that algorithm, well, how are they going to get themself out of that jam?
And this is happening to so many young children, because I think for so long, we've made them take that leap, and the students who had the memory, the ability to memorize a little more easily or fluently than some other students, they were rewarded in the schooling system, but not necessarily rewarded with any sort of extra reasoning skills in mathematics. They just got the big gold star, and that was about it. Jon always references his puffy stickers that he used to get as a child. So I love that you're referencing this trajectory. And when this episode comes out, it'll be a few weeks after we had Doug Clements on, and his work.

Ann Elise: Oh, my goodness.

Kyle Pearce: Yeah, how fantastic.

Ann Elise: Clements and Sarama, they're just like the king and queen of early numeracy.

Kyle Pearce: Exactly. She was stuck out of town and we wanted to have both on the show.

Ann Elise: Oh, my goodness.

Kyle Pearce: I'm telling you right now, hearing you and your passion about this trajectory, it's so, so critical. And again, I know Nicki Newton thinks so highly, as well, of Doug Clements and Julie Sarama, and...

Ann Elise: Absolutely.

Kyle Pearce: It really all does come back full circle. So whether you're sitting at home right now, and you're thinking to yourself, "Maybe this episode isn't for me, I'm a middle school teacher, or I'm a high school teacher..." I hope that people are seeing the connections, and you brought up Pam Harris and the development of mathematical reasoning that, way down the road in high school, some of our students that are struggling the most, their struggles began way down here in this area where we didn't help them make those connections and really start to use reasoning to get themself through number fluency. And that's really hindered them.
And it makes me think, "What do we do?" Do you have any thoughts, if someone's sitting there thinking, and maybe I have a vision of a specific student in their class, and they're like, "Oh, this student is really struggling." What might be a get started tip for someone who, maybe this is a new idea for them, what are you going to say to them? Where might they begin? Might it be PD of some type, or might it be just a website to get them going? What are your thoughts on that?

Ann Elise: Well, I typically go right back to the Math Running Record, honestly, because it's going to help you understand where each child is on their journeys. You can develop instructional response derived for the kid, and then to get a sense of where all of your kiddos are. Because typically what I find, I'm training districts to implement this and then to do the next steps of how we explore fluency with our kids, in concrete, pictorial, and abstract ways. That's what our book is about. Dr. Nicki, Dr. Alison Mello, and I collaborated on a book about fluency doesn't just happen with addition and subtraction. So the idea that, now I know where I need to begin working with each kid, what can I do then to explore these concretely pictorial and abstract, and develop this fluency program for my kiddos?
So the Math Running Record, I have a Math Running Record Facebook group that I began close to three years ago now, because Dr. Nicki, she's doing so much all the time. I said, "Yo, do you mind if I make a group, of a support group for those of us that are really going in depth of implementing these?" She's like, "Oh, go right ahead." So there are videos in there of she and I talking for an hour about Running Records, and I have a whole Padlet of resources for the group that has all kinds of information, great resources on fluency as well. So it's a wealth of knowledge in one place that you can learn all about this. And I'm always right there. A lot of my time is online, providing advice to people within Facebook, because it's a great platform to be able to share things like that. And so a lot of my life is being in there, and providing advice, and guiding people along.
inaudible beginning a book study starting next Monday, but I know this will not be out in time for that, but all the information in the book study is going to be within the Facebook group. So no matter when anyone joins the group, it'll be there for you. So you can see the posting, and the questions, and the comments, and all. Because until we understand that trajectory of learning, and, then you can't really be looking for that, right? We've got to know, "Oh, that child is counting on. They're counting all." Now, what I want to make sure I'm clear about a derived strategy. So, for example, one really important fact for me is when I get to the progression, the beginning of the progression, say to add zero, and add one to numbers, and then counting on within five, and then within 10... But then I'm going to get you teen numbers, you have the doubles, and then doubles plus one.
So when I ask kids five plus six, most kids tell me that they know it's an 11, because five and five is 10, and one more is an 11. So it's a derived fact. The using a fact that they know to figure out one that they don't know. But the very next question in part two gives them more problems in that zone. The very next question is six plus seven. And that's where I can tell the kids who have begun using strategies, and breaking apart numbers in flexible ways, versus the counting on, because the kids will count on six from the seven. So the very same student that tells me five and five is 10, one more makes an 11, so they know five plus six makes an 11, will count on their fingers, six, higher than the seven. So I can tell that there's no strategy thought there.
So for that kiddo, I'd want them to go on to explore what doubles plus one is. And I would show them like a rekenrek. So a rekenrek is a tool that, one version of the tool, you can have two rows of 10, and the beads are color-coded in each five. So I can slide six beads over and seven down in the bottom row, so kids can see that amount of the 13. And I'll ask them, "What do you see? How do you know?" And some kids will count all the beads. So I know they're in a counting all phase, some count on the six from the sevens, they're in counting on, but other kids will say, "Well, I'm seeing five and five red, and that's 10. And then I see one white and two white, that's three. So I see ten plus three, which is a 13." But other kids say, "Well, I see six and six is 12, and one more makes 13." Other kids say, "I see seven and seven is 14, I take away one is 13." And still other kids say, "Take three from the six and make a 10 with the seven. So it's 10 plus three."
So I'm aware of all these different look fors to then develop my own instructional response with them. Because the kiddo that tells me that six plus seven is 13, because they could break apart that six to be a 10 and a three? They go to the end, they do all their math facts, and do whatever strategies they want with any of the addition math facts. But the kiddos that are counting on their fingers at that point? They go to just having visuals, to see the quantities, and describe what flexible ways can we get to that total, and make it easier for our brain. So that's where I find it's a great place to begin the journey.

Kyle Pearce: Right? And, forgive me, I'm not an elementary school teacher, haven't had experience working, other than with my own kids, talking about numeracy at that level... I'm wondering, if I'm a teacher who wants to have that interaction, that lesson with my students, and, what do I do beforehand? How do I prepare for that? We often talk about, that preparation is so important. Another quote that we've used from Tom Schimmer is that you want to plan with precision, so that you can proceed with great flexibility. In that preparation, we can't underestimate that. So I'm wondering, what does a teacher do to help prepare so that when they get in a conversation like that, they know to look for those strategies, and they know, "If I have that strategy, I'm going to push them this way." What would you suggest the teacher can do to help get ready for something like that?

Ann Elise: Well, I think it's a matter of us building our own knowledge about that. Dr. Nicki has a class, an online class, on her site. I've also, on my Padlet, have created videos for each of the strategies, and how we can explore them with math tools. And there's no cost to any of this. The protocols to interview the kids are free, there's no cost to the Running Records. But really it's a matter of us learning what we're looking for, right? And so how do we do that? Well, her Math Running Record book describes all the four operations, and the thought behind each of the operations, and the strategies.
And then our book we've written so far, the addition/subtraction, we are currently working on a multiplication and division book to go along with it. But that's a matter of learning about it, the matter of just building our own... Christina Tondevold, building our math minds, so we can then build the math minds of the kids, right? Because if you don't know what you're looking for... I ask people all the time, when kids are counting. You put eight objects in front of a student and ask them to count - what are you looking for? And very basically I always hear about one-to-one correspondence, and saying the numbers in the correct order, and that's pretty much it.
Well, Clements and Sarama has 20 levels of counting, right? So their site, learningtrajectories.org, I send all my participants to that site, because it is the most wealth of information about, from birth to grade three, of early numeracy and mathematics. But until you know there are 20 things you could be looking for with counting, you're going to look for one-to-one correspondence and if they say it in the right order, right? So it's a journey.

Kyle Pearce: I know. And I love that response because I think that's where the content knowledge piece is so important. And I think in mathematics, I mean, in education in general, oftentimes teachers, we have this drive to find new pedagogical moves. And while they are important, and they are a huge part of how you're going to organize and run your lessons, the content knowledge is key because if you don't have that, then it doesn't matter how hard you try to prepare, you're underprepared, because that look for is not there. Being able to notice and name, and then being able to, essentially, once you've noticed and named what a student has done, to know what comes next. And Jon and I are constantly talking about that with our igniting the next moves piece of the framework, which is this idea of really understanding that trajectory of math learning that students travel down. And that's something that we continue to try to do, and, clearly, you are also an advocate for that, continuing to try to grow your own math mind as well.
And we're just thrilled that we've got some great ideas and some great links to share. We're going to definitely get that Facebook group up there in the resource page. We'll throw in learningtrajectories.org, which is a great resource. And we'll also grab some of those Running Records links, as well as to the book, so... I'm wondering, before we wrap up though, is there anywhere that the Math Moment-Makers can learn more about you specifically in your work, some of which that you've already mentioned here, but where can they find more about you and get connected?

Ann Elise: Sure. I have a webpage, anneliserecord.com. You can check that out, and check out all the different offerings and things I have for you there. And honestly, I have found that connection in the Facebook community because I was living in Northern New Hampshire for over 20 years, and I found this amazing collection of people online. So they're just brilliant and generous and kind. And so, I began in Twitter a little bit, and then in Facebook, creating communities of people willing to learn. So I run a Facebook group of my own called Elementary Math with Ann Elise, and that's any math topic, K five is on the table, anything you want to talk about to give advice and all.
And then I facilitate the Math Running Records one. We have over 13,000 people in there right now. And so that group is focused on fluency. So that's the fluency piece. So the Elementary Math with Ann Elise is that, anything, like fractions or any other topic on mathematics, but the Math Running Records is that fluency one. So joining in those groups or following me on Facebook... I have a growth mindset tree as my picture, because that's my math profile on Facebook. So I only share math things there. So if you follow me there on Facebook, you could continue learning about me.
And I also have a newsletter that I do because I know and respect the fact that people may not want to be on Facebook or social media, so they can subscribe to my newsletter, and I send it out but once every week or two, with all the links and the great things that I come along.

Kyle Pearce: Awesome stuff, thanks for sharing that. We'll make sure that all of that is in the show notes page for this particular episode. Ann Elise, we want to thank you for taking time out of your day to share your expertise with us and our listeners. And we hope you enjoy the rest of your day. And we really appreciate talking to you and hopefully we can catch you at a face-to-face conference sometime in the future.

Ann Elise: Let's hope, absolutely. Thank you so much for having me, I really appreciate it.

Kyle Pearce: Thanks so much, we'll talk to you soon.

Ann Elise: Okay, take care.

Kyle Pearce: It was awesome to finally welcome Ann Elise onto the show to chat with us about her amazing efforts in conceptualizing mathematics.

Jon Orr: Hopefully this conversation has inspired you to dive into your next math class using a problem-based approach.

Kyle Pearce: Right? So be sure to check out the Wooly Worm Race, the Snack Time unit, or any of the other problem-based units that are available for you to dive into right now over at makemathmoments.com/tasks.

Jon Orr: Absolutely, Kyle. Get on over to makemathmoments.com/tasks to run one of these awesome problem-based units in your class today.

Kyle Pearce: In order to ensure you don't miss out on new episodes, make sure that you smash that subscribe button on Apple Podcasts or on your favorite podcast platform. And, did you know that these episodes are also on our YouTube channel? And you know what, Jon? We've been doing a lot of these YouTube lives lately, so be sure...

Jon Orr: Yeah, we're getting ready...

Kyle Pearce: To subscribe over on YouTube, because we got some pretty cool little tricks up our sleeve that we're hoping to do each and every week.

Jon Orr: Yeah, we've got some new stuff coming. Also, if you're liking what you're hearing, please share the podcast with a colleague, help us reach our wider audience by leaving a review on Apple Podcasts, and tweet us over at Make Math Moments on Twitter, or Instagram, or on Facebook.

Kyle Pearce: Show notes and links to resources, including full transcripts that can be downloaded or read right from the web for this episode, and all the other episodes can be found over at makemathmoments.com/episode113. Again, that's makemathmoments.com/episode113. Well, my friends, until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us...and a big high five for you.

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Episode #113: Fluency Doesn't Just Happen - An Interview with Ann Elise Record - Make Math Moments

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Today we speak with Ann Elise Record. Ann Elise is a seasoned educator with a career spanning over two decades of elementary classroom experience. These days she's a K-5 math coach who works with districts on developing strategies to increase students' fact fluency as well as how to use manipulatives in the classroom.

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Teacher as....podcast. Dr Nicki and Ann Elise join host Melissa Milner to discuss our Top 10 Daily Routines.

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Teacher as....podcast. Dr Nicki and Ann Elise join host Melissa Milner to discuss our Top 10 Daily Routines.

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Dr icki Newton and I joined podcast host Melissa Milner to create a List of 10 favorite math daily routines. Such fun!

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The Teacher As...Top Ten episodes are a new addition to the podcast. Dr. Nicki Newton and Ann Elise Record collaborate to create one top ten list of math routines. The collaboration gets a bit intense when the two disagree as they get closer to the top five picks. These math educators have so much to share in this episode.

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030: The Teacher As...Top Ten Math Routines with Dr. Nicki Newton and Ann Elise Record - The Teacher As...

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The Teacher As...Top Ten episodes are a new addition to the podcast. Dr. Nicki Newton and Ann Elise Record collaborate to create one top ten list of math routines. The collaboration gets a bit intense when the two disagree as they get closer to th...

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Brainingcamp Webinar I hosted on Addition K-5

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Brainingcamp Webinar I hosted on Addition K-5

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Fun story mats for problem solving by Dr. Nicki

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Fun story mats for problem solving by Dr. Nicki

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Dr. Nicki Newton's Story Mat Activities.pdf

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KY Center for Math Companion site to Jennifer Bay-Williams and Gina Kling's Math Fact Fluency

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KY Center for Math Companion site to Jennifer Bay-Williams and Gina Kling's Math Fact Fluency

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games available in Word, PDFs, and Jamboard!

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Google has announced that Jamboards will become "read-only" on October 1, 2024 and will disappear completely on December 31, 2024 ( https://support.google.com/jamboard/answer/14084927?hl=en). While we are disappointed in this news, KCM is dedicated to providing resources to support teachers. All KCM Jamboards will remain available for the 2023-2024 academic year. We have begun the process of researching options for converting or updating our current Jamboards to a new format and plan to have the revised resources available in the fall of 2024.

Chapter 1. The Five Fundamentals

Chapter 2. Foundational Addition and Subtraction Facts

Chapter 3. Derived Fact Strategies for Addition and Subtraction

Chapter 4. Foundational Multiplication and Division Facts

Chapter 5. Derived Fact Strategies for Multiplication and Division

Chapter 6. Assessing Foundational Facts

Chapter 7. Assessing Derived Fact Strategies and All Facts

Chapter 8. Families and Facts

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Google has announced that Jamboards will become "read-only" on October 1, 2024 and will disappear completely on December 31, 2024 ( https://support.google.com/jamboard/answer/14084927?hl=en). While we are disappointed in this news, KCM is dedicated to providing resources to support teachers. All KCM Jamboards will remain available for the 2023-2024 academic year.