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Subitizing is not a term that we use often, but it is an important mathematical concept that can greatly benefit student achievement. Subitizing is the ability to " instantly see" how many. This method of teaching is achieved when students can spontaneously recognized and discriminate small numbers of objects. Students who can successfully subitize are able to " just know" a group of numbers and recognize the pattern. We move students on from one by one counting to subitizing.

Let's take a look at the following examples:

HOW DO YOU TEACH SUBITIZING?

We teach subitizing by exposing students to number patterns that they can immediately recognize. We train their brains to see organized groups of numbers. When students can successfully subitize, they are able to mentally compose (bring together) and decompose (break apart) numbers. They are able to quickly add numbers together without counting one by one.

For example, if a student knows that a full ten frame equal ten, and half of a ten frame equals 5, they are able to visually and/or mentally compose the numbers to make 15.

Students use subitizing to decompose numbers....

In effort to make subitizing hands-on, fun and highly effective, I created these engaging NO PREP Subitizing packets!

These subitizing packets allows students to work with consistent patterns of dots, dice, ten frames, counting sticks and other familiar math patterns. Best of all, students get to color and play their way to successful subitizing!

BINGO: Level 1...

Students roll a die. They place a game piece on a matching number. For example, if they roll a three, they look for an item that has three. This pattern can occur in a die, ten frame, tally marks, fingers or any other organized pattern. This fun game helps students train their brain to immediately see and know the number. This simple activity helps students move on from one by one counting. Math becomes more effortless, quicker and FUN! This would be considered Level 1, where the numbers are less than 10.

BINGO: Level 2...

Once you move onto Level 2, the numbers increase and it becomes much more challenging. As you can see...we LOVE this game! I am currently using this as a review for my 2nd grader, who sometimes struggles to "see" the numbers immediately. These fun subitizing games will help us MASTER this concept!

Since the numbers are higher, we move on from dice to spinners. Begin by spinning the spinner with a paperclip and pencil. Cover the number that matches your spin.

We used what we had around the house...bug counters. For two players, each person gets a color for their game pieces. The first person with 5 in a row wins the game!

We worked hard on training our brain to "see" the numbers automatically! The conversation was AMAZING! When she spun a 17 for example, she would search the gameboard for an organized set of numbers that made up 17. She finally found one with a full ten frame plus 7 more! She can calculate pretty well, but this simple review is helping her brain automatically see the numbers!

Color Your Way to Successful Subitizing!

Kids LOVE to color, so why not teach subitizing by coloring? The patterns on the coloring pages are organized in a way that kids can immediately recognize sets of numbers. That being said, if students start off by counting the numbers, that's fine too. However, we want to move them on from one by one counting to be able to visually " chunk" those numbers and immediately KNOW the amount.

Grab the BUNDLE and SAVE! Click HERE

The Fall Subtilizing Packet is available { HERE}.

Subitizing: Winter Edition Subitizing: Spring Edition
The Spring packet is filled with fun ways to make subitizing effective! Kids will be begging to play their subitizing games!

Be the First to Fill Your Board! These games allow students to play by themselves, with a partner or in small groups! Simply flip a card and cover the answer.

Just print the game boards on color paper, print the pieces on color paper, laminate and PLAY!

The great thing about these boards is that you can play AGAIN and AGAIN!

MAZES!!! These are AMAZINGLY FUN! Color your way through the maze, finding only the numbers indicated!

Grab The BUNDLE and SAVE 20%

If you are looking for more basic math activities, Click Here to check out this blog post:

And here is a Free Subitizing Sampler Packet for YOU!!!

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Subitizing is not a term that we use often, but it is an important mathematical concept that can greatly benefit student achievement. Subitizing is the ability to " instantly see" how many. This method of teaching is achieved when students can spontaneously recognized and discriminate small numbers of objects.

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Uploaded by Build Math Minds on 2017-08-31.

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Developing Number Fluency - What, Why and How

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In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

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In recent years there has been a huge shift away from rote memorization of math facts and toward a strategy-based approach for learning math facts. There's a big difference between memorizing and understanding. Sure, we want kiddos to have automaticity with their facts. Knowing math facts is similar to knowing sight words-it frees up the mind to solve real math problems. If a child has to struggle to solve 8 + 3, they have no mental energy (or desire) left to grapple with the types of problems that will increase their capacity as a mathematician.

A great resource for strategy-based fact instruction is Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization. There's one for multiplication and division facts, too.

A big problem with teaching kids facts is that we often jump to the abstract (symbolic) level of instruction too fast. This does two things: (1) produces children who can recite their math facts, but have no real understanding of what they mean, and (2) children who get left behind because they can't memorize. I'd be hard-pressed to say which is worse.

Learning facts begins in Kindergarten (or PreK) when students are exposed to dot patterns and five-frames. When a child can see 2 dots and 3 dots on a card and know without counting () that there are 5 dots, that's the foundation of learning math facts.

The concrete for the foundation sets (or doesn't...) in first and second grade. are magical! Not only do they help students see how the ability to compose and decompose numbers helps connect facts they know with facts they are learning, but they also plant the seed for place value.

Students should have extensive exposure to the combinations that make ten using objects or drawings in Kindergarten (CCSSM K.OA.4). This skill goes by many names: friends of 10, making ten, tens partners. But it's an absolutely essential skill-move it up to the top of your to-do list! Raise you right hand and repeat, I will not let my kinders become firsties without knowing their combinations for ten! Why is is so important? In 1st grade students are expected to add and subtract within 20 with fluency to 10 (CCSSM 1.OA.6). That means they should have automaticity of the facts within 10 by the end of 1st grade. Why? Because in 2nd grade the standard is for fluency of facts within 20 (CCSSM 2.OA.2). Do you see that beautiful progression? Do you also see, however, how critical it is that students master their grade level standards? And what happens after 2nd grade? Multiplication, of course, but that's a post for another day.

Which finally brings me to today's activity, which utilizes the Using Tens strategy. We want students to be so familiar with their ten combinations that they automatically use them. When a child is trying to add, for example, 9 + 4, a great strategy is to split () the 4 into 3 and 1, use the 1 with the 9 to make a 10, and then add on the 3 to make 13. Likewise, to add 8 + 3, split the 3 into 2 and 1, use the 2 with the 8 to make 10, and add on the extra 1. All this is a mental process, of course, but it begins with lots of work on ten-frames-first with counters and then by drawing. Look at the picture below that illustrates 9 + 4. Don't you see the splitting of the 4 into 3 and 1?

The paper-and-pencil activity shown below is an assessment I created for my 1st grade teachers. Note that it is an assessment to be used after students have had lots of practice with the concept.

I hope I've given you some food for though today and helped you to better see the progression of fact mastery through the early grades. I'd love to hear your comments! Click to grab the freebie assessment.

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The Path to Automaticity with Addition Facts - Math Coach's Corner

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In recent years there has been a huge shift away from rote memorization of math facts and toward a strategy-based approach for learning math facts. There's a big difference between memorizing and understanding. Sure, we want kiddos to have automaticity with their facts.

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Imagine you're driving somewhere, and discover that a street you were planning to turn onto is blocked off for construction. Your initial plan for reaching your destination obviously isn't going to work. So you instantly come up with a new way to get there.

That's what flexible thinking is about-being able to quickly switch gears and find new approaches to solve problems.

Many children with learning and attention issues struggle with flexible thinking, which plays an important role in how kids learn and adapt to new information in many areas. Here are six ways kids use this skill for learning.

1. Flexible Thinking and Real-Life Learning

Doctors have a term to describe the ability to think about things in a different way. They call it "cognitive flexibility." It uses two skills-flexible thinking and set shifting. Flexible thinking is when kids are able to think about something in a new way. Set shifting is when they can let go of the old way of doing something in order to use a new way.

Here's an example of how those skills work together. Kids often start out learning to tie shoes using the "Bunny Ears" method (making each lace into a loop). They then often progress to the "Squirrel and the Tree" method (making one loop and wrapping the other lace around it). Flexible thinking enables kids to consider this new squirrelly approach. Set shifting helps them "unlearn" the old bunny-ears way in order to use the new method.

Kids who are rigid in their thinking have difficulty moving beyond the more basic ways of doing things. If your child has weak flexible thinking skills, taking on new tasks and responsibilities as she gets older may be tough.

2. Flexible Thinking and Reading

Kids use flexible thinking both for learning to read and for reading to learn. When they're starting out, flexible thinking enables them to understand how the same letter combination can make different sounds (such as the "ough" in words like enough and dough). It's also the skill that helps kids understand how words can be used in more than one way (such as "Don't slip on the banana peel" and "Sign the permission slip ").

As kids start reading books to get information, they use flexible thinking to understand what information is important and what details are just used to add to a description. Flexible thinking is also what helps them understand the perspectives of different characters in a story. Flexible thinkers have an easier time understanding idioms (such as "keep your ear to the ground") and puns (such as "the joke about the duck quacked me up").

If your child is rigid in her thinking, you may see that she has trouble identifying the correct pronunciation for words and interprets what she reads much too literally.

3. Flexible Thinking and Writing

Writing is a complicated process for kids. They have to organize their thoughts and choose the words for the sentences. They have to add supporting details while keeping track of the main idea. On top of that, they need to be able to check for grammar and spelling mistakes. All of that requires the use of flexible thinking. Kids who are more rigid thinkers can have a hard time shifting among all these things.

If your child has trouble thinking flexibly, her writing may not have enough supporting details. Or it might have lots of errors in it.

4. Flexible Thinking and Language Learning

Flexible thinking is the skill kids use to learn the rules of language. It helps them to know, for instance, that the way to put most words into the past tense is to add "-ed" to the end. Flexible thinkers also understand there are exceptions to those rules. It makes sense to them that the past tense of go is went. These kids can easily use both rules and exceptions of language.

Flexible thinking also plays a role in learning foreign languages. In other languages, letters can have different sounds. Sentences aren't put together the way they are in English.

If your child is not a flexible thinker, it may be hard for her to learn the rules and the exceptions that make up languages. She may learn better by listening to how people speak the language than by sitting down and reading the rules in a textbook.

5. Flexible Thinking and Math

Flexible thinking is a key skill in math. Kids use it to find ways to solve word problems and to understand that a phrase like "how many in all" means that addition is being used. Flexible thinking also helps kids understand that there's more than one way to solve a math problem. They can see how a new type of problem can be solved using a formula they already know.

Without strong flexible thinking skills, your child may struggle with math that requires her to do more than just solve the equation on the page. "Cheat sheets" that connect words or phrases to math operations can be helpful tools for your child. So can checklists of the different things she needs to look at to solve a problem.

6. Flexible Thinking and Studying

Doing homework and studying for a test require flexible thinking, too. Knowing how to switch between different subjects during homework time becomes increasingly important as kids get older and have more work to juggle. Doing math problems requires a very different strategy than doing a writing assignment. Kids need to be able to change their thinking to handle both.

When it comes to studying, kids use flexible thinking to figure out what kind of information they need to pay the most attention to. Do they need to memorize facts and information, such as for a multiple-choice quiz? Or do they need to learn the basic ideas so they can retell the story, such as for an essay test?

If your child has poor flexible thinking skills, switching strategies will not come naturally. This can make homework time a source of frustration. Teaching her note-taking strategies and providing homework planners can ease the stress on both of you.

The Good News: There Are Ways to Help

If your child has trouble with flexible thinking, she's likely to have some problems learning. There are ways to help, though. Your child's teacher can use strategies in the classroom to teach your child in ways that make more sense to her.

You and your child can also play games at home to build flexible thinking skills and come up with ways to make homework more manageable. One of the best things you can do is to help your child learn to make a list of pros and cons, first on paper and then in her head, to determine the best choice.

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6 Ways Kids Use Flexible Thinking to Learn

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Imagine you're driving somewhere, and discover that a street you were planning to turn onto is blocked off for construction. Your initial plan for reaching your destination obviously isn't going to work. So you instantly come up with a new way to get there.

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I am preparing for my presentation at the annual US Math Recovery conference and thought it would be a great time to post about one of my favorite math manipulatives for PreK through 2nd grade; the Rekenrek...which just so happens to be the focus of my presentation at the conference next week. To start, here are my favorite resources for the rekenrek. If you don't know what the heck a rekenrek is, read on past these and then come back.

When you want more detailed lessons that connect to the Common Core Standards and the big ideas in PreK-2 math, check out the book I wrote, Mastering the MathRack.

The Math Learning Center also has a free app, called the Number Rack.

I recommend if you want to purchase some for your class go to www.MathRack.com . (full disclosure, I do consulting work for the MathRack company. But the reason I do is because they make the best rekenreks on the market.)

Check out by Graham Fletcher for a very detailed explanation of how the rekenrek helps address many big mathematical ideas as well as the Common Core Content and Practice Standards.

The rekenrek is a tool that was created in the Netherlands and has been translated to be called an arithmetic rack or calculating frame. I personally call them MathRacks because I work with the MathRack company, but more people know them as Rekenreks. So in this post I will call them rekenreks. At first glance many people think it looks like an abacus. There is a slight but powerful difference, the color change. The color of the beads changes after 5 beads so that kids can subitize easier and relate quantities to the benchmarks of 5 and 10.

The rekenrek is a unique tool that allows children to develop number sense at their own pace. With the built-in 5 & 10 structure, rekenreks help children build number relationships that lead to more advanced strategies. In every classroom, there are students of various mathematical abilities, yet as teachers, it is our job to get them all to proficiency. You might have some children who automatically know that 7 + 8 = 15 and others who have to count out seven objects, count out eight objects, and then count them all to determine it makes fifteen. Most manipulatives we use in K-2 classrooms do not help children get past the one-by-one counting and into more efficient strategies.

"In the United States, the manipulatives most commonly used with young children are single objects that can be counted - Unifix cubes, bottle caps, chips, or buttons. While these manipulatives have great benefits in the very early stages of counting and modeling problems, they do little to support the development of the important strategies needed for automaticity. In fact at a certain point they begin to reinforce low-level counting strategies. For example, to solve 6 + 7 with Unifix cubes, children need to count out six, then seven, and then either 'count on' as they combine or (as is most common) count three times - first the two sets, then the total" (Fosnot & Dolk, 2001, p. 103).

With the rekenrek, children can model and solve problems the same as they would with Unifix cubes, but the built-in structure of the rekenrek allows children the flexibility to develop more advanced strategies as well. Here are some examples for how kids might solve 7 + 8 using a rekenrek:

Rekenreks help children develop these more advanced strategies by building number sense. Number sense develops as children have experiences with numbers and they build relationships about numbers. John Van de Walle (2006) describes four relationships that need to be developed for children to gain number sense with numbers up to 20 so they can use those numbers but also understand them:

Spatial relationships - having a visual picture of an amount, also recognizing how many without counting by seeing a visual pattern (subitizing).
One and two more, one and two less - this is not the ability to count on two or count back two, but instead knowing which numbers are one and two less or more than any given number by understanding the pattern of numbers.
Benchmarks of 5 and 10 - because ten plays such an important role in our number system, and two fives make up ten, students must know how numbers relate to five and ten.
Part-Part-Whole - seeing a number as being made up of two or more parts.

Traditional textbooks tend to focus on skills associated with numbers; count to 8, recognize the numeral 8, write the numeral 8, and then operate using the numerals. The relationship building is limited, and sometimes completely missing. If you are looking for a way to build number sense, let them play around with a rekenrek. If you need resources, don't forget the ones I shared at the top of this page.

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I am preparing for my presentation at the annual US Math Recovery conference and thought it would be a great time to post about one of my favorite math manipulatives for PreK through 2nd grade; the Rekenrek...which just so happens to be the focus of my presentation at the conference next week.

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Number Talks for Lower Elementary --Resources

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Number Talks for Lower Elementary --Resources

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Teaching Math With Picture Books, Part 1 | Scholastic

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When we use picture books to support math lessons, students are not only excited to learn math in a different way, but they also come to associate the feel-good joy of re

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Picture books about math are the perfect cross-curricular tool to introduce your kids to complicated concepts and mathematical thinking. We chose some of our favorite authors and stories, both new and old, to add to your classroom library and inspire your students' mathematical minds.

Our picks for the best books about math are listed by grade level and math concept so you can easily find the right selection for your class.

1.by Mac Barnett and Jon Klassen

A sassy story about sneaky Triangle trying to play a trick on his friend Square that turns into a shape showdown. Kids will be mesmerized by this whimsically illustrated tale.

Math concepts: Shapes, relative size

Best for: Grades K-4

2. Place Value by David Adler and Edward Miller

Love the story about monkeys jumping on the bed? You'll adore this version that tells the story of the monkeys at Banana Cafe making one very large banana cupcake.

Math concept: Place value

Best for: Grades 1-5

Also by this author: Fraction Fun, Mystery Math: A First Book of Algebra, How Tall ,How Short, How Far Away, Shape Up!: Fun with Triangles and Other Polygons, Perimeter, Area and Volume: A Monster Book of Dimensions, Millions, Billions and Trillions: Understanding Big Numbers, and more.

Mr. and Mrs. Comfort are having a family reunion and need to arrange the tables so that everyone in the family can enjoy their fabulous spaghetti and meatballs. A witty tale by math guru Marilyn Burns.

Math concepts: Area and perimeter

Best for: PreK-Grade 3

Also by this author: The Greedy Triangle, Math for Smarty Pants, The $1.00 Word Riddle Book, This Book is About Time, and more.

Brave knights, a strong ruler, and a dilemma that needs to be solved using math. This book about math is great for introducing geometry concepts in a fun and accessible way.

Math concepts: radius, diameter, circumference

Best for: Grades 2-7

Also by this author: The Sir Cumference series has more than 10 books that explore math concepts from algebra and geometry to measurement and fractions.

Delightful illustrations and a dreamy young girl pondering the vastness of the universe make a very difficult concept approachable and interesting in this book about math.

Math concept: Limitless numbers and infinity

Best for: Grades K-5

Watch as this busy construction crew creates impressive structures by grouping bricks by twos, fives, and tens. Kids will love the catchy repetitive verse and charming illustrations.

Math concept: Counting in quantities

Best for: PreK-Grade 2

Ethan wakes up one morning with a strange cat on his head and the only way it will agree to get it off is if Ethan agrees to play a game of probability with it. This kooky book about math will entertain your students as it teaches a difficult concept.

Math concept: Probability

Best for: Grades 2-5

Also by this author: Fractions in Disguise: A Math Adventure

Kids will love this fun story with delightful cartoon illustrations that teach the importance of zero as a placeholder in our number system. Without Zero the Hero, we wouldn't be able to count beyond the number nine!

Math concept: Concept of zero

Best for: Grades 1-5

A beautifully illustrated book about math that shows how flips, slides, and turns can create amazing symmetrical images.

Math concept: Geometry, symmetry

Best for: Grades 1-3

A playful book with silly characters and perfect rhyming that teaches not just the basics of telling time, but the tricky concept of relative time.

Math Concept: Time

Best for: Grades 1-4

Also by this author: Cleary has written a whole series of books called Math is CATegorical, including The Mission of Addition, The Action of Subtraction, A Dollar, a Penny, How Much and How Manym, A Fraction's Goal- Parts of a Whole, and more.

Mouse and her friends want to play a game of tug-of-war but have a hard time making the sides fair. This charming story teaches the concept of balance and equality.

Math concept: Equality

Best for: Kindergarten-Grade 3

Two more rhyming tales with colorful, busy illustrations that kids will love. In each of these books about math, a boy wakes up one day and finds that things are kookily out of order. Great as a read-aloud or for independent readers who will love hunting through the detailed pictures to find the odd or even items.

Math concepts: Odd and even

Best for: Kindergarten-Grade 3

Your students will love quirky Henry and his wild imagination as he uses his dog Frank as a unit of measure. Henry thinks about real life objects and how they can take up specific spaces. This story will get kids thinking creatively about numbers and many other math concepts.

Math concepts: Problem-solving, measurement, estimation, and calculatio n.

Best for: PreK-Grade 3

Colorful fish bob, glide, and swish through the ocean until POP, a shark appears! Kids not only love hearing and seeing this story, it will get them interested in learning and creating their own patterns.

Math concepts: Patterns and variations of pattern types

Best for: Kindergarten-Grade 2

16. A Remainder of One by Eleanor Pinczes and Bonnie MacKain

The 25th Beetle Army Corp is trying to solve the problem of how to divide their troops into equal groups for the parade march without leaving any stragglers. A fun, rhyming book about math that will get kids thinking about how numbers are put together and pulled apart.

Math concept: Grouping, division

Best for: Preschool-Grade 3
What picture books have you used in your math lessons? Come and share in our WeAreTeachers HELPLINE group on Facebook. Plus, Why It's Important to Honor All Math Strategies.

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16 Picture Books About Math to Inspire Curious Kids - We Are Teachers

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Picture books about math are the perfect cross-curricular tool to introduce your kids to complicated concepts and mathematical thinking. We chose some of our favorite authors and stories, both new and old, to add to your classroom library and inspire your students' mathematical minds.