subitizing Archives - Shelley Gray

Have You Tried This Fun Way to Build Multiplication Flexibility and Fluency?

Shelley Gray — Wed, 19 Oct 2022 01:47:02 +0000

Fact fluency is a critical component of success in the math classroom. But students need to be able to do more than just recall the answer to multiplication facts quickly. A key part of fact fluency is flexibility. That is, can students develop and apply strategies that help them solve a wide range of problems?

Dot talks are a tool that can help build such flexibility. In this routine, the teacher presents students with an image of dots. These dots are often arranged in a certain pattern like the one below. The teacher presents a simple question, “How many?”

Students silently attempt to find an answer. When they find it, they can discreetly signal to the teacher using a thumbs up against their chest. While they wait, they attempt to find their answer in a new way. Each additional strategy they develop can be signalled by raising an additional finger.

At first, the teacher may choose to leave the dot image on the screen for the entire length of the dot talk. However, this may invite students to count the dots one by one. Remember, the goal is to develop efficient and flexible strategies for counting the dots. Many teachers choose to flash the image for a certain amount of time (also called a Quick Look), for example, two seconds. This encourages students to look for patterns that can speed up their counting.

When students are ready to share their answers, model each strategy using a different colored pen. For example, Student A saw four groups of three dots. They used a skip counting strategy to find that four groups of three make twelve.

Student B saw two groups of four, and then two groups of two. They knew that four plus four equals eight, and four more makes twelve.

Student C decided to make two groups of six. They added six plus six to make twelve.

Each of these strategies is unique, but is a valid way of seeing this visual. As dot talks increase in complexity, they can be used to teach multiplication strategies like doubling, doubling and halving, or multiplying by ten!

If your students are in need of flexible multiplication strategies, consider dot talks as one of your computational fluency routines!

Don't have time to create your own dot talks?

Find entire sets of pre-made Dot Talks here!

Click Here

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Here’s an Easy Way to Incorporate Subitizing into Your Math Routine

Shelley Gray — Wed, 24 Aug 2022 00:51:11 +0000

Subitizing – if you teach elementary math you’ve probably heard this word, but may be unsure of what it actually means or how it can be used effectively in the classroom. Before I get into the definition of subitizing and tips for using it to help your students build number sense, let’s try a couple of fun activities.

Let me ask you a question. How many do you see?

Now I want you to think about how you saw them. Chances are good that you didn’t count them one by one. Did you see 4 groups of 3? 2 groups of 6? Are there any other ways you can see them?

Let’s try another one.

How did you see them this time? Do you see 4 diagonal groups of 3? Do you see 3 horizontal rows of 4? Maybe you saw 2 groups of 6. Are there any other ways you can see them?

What you just did is called subitizing. You recognized a quantity of objects without counting them one by one.

When you practice subitizing, you become a flexible thinker, realizing that there are many different ways to make a number. You also build a strong foundation for number sense as you visualize numbers in different ways.

Subitizing is common in kindergarten and grade 1, but did you know it can be just as beneficial to students in older grades? Imagine the conversations you might have with a class of grade 3 or 4 students using subitizing images like this:

Or what about the conversations you might have with a grade 5 or 6 class using a visual like this?

Research supports the relationship between subitizing and strong number sense. But it can be a difficult routine to implement if you don’t have the proper visuals available to you.

Dot Talks are here to support you as you implement this routine in your classroom and work to close the number sense gaps that your students may be struggling with.

Dot Talks are intended as a whole-class, low-floor high-ceiling activity that will get even your most reluctant students involved. There is no wrong answer, as long as you can justify it!

Simple Tips for Getting Started Subitizing with Dot Talks

Begin with visuals that seem “too easy.”

Even though you might think the visuals look too easy, it can be fascinating to hear how different students see the dots. This is also an opportunity to begin with something that seems “low-risk” to students who don’t generally participate in classroom discussions. As students get better at subitizing, use slides with more dots or more complex patterns.

Consider leaving images on the screen before getting into Quick Looks

Often, subitizing activities are done as quick looks. This means that the teacher flashes the image for the students, giving them enough time to see it, but not enough time to count the dots one by one.

But when you first introduce subitizing to your class, you may want to simply leave the dot image on the screen and have a discussion about different ways to see the dots. Then move to quick looks once students are comfortable.

Use Dot Talks as a way to ease into number talks.

If you plan to implement number talks this year for the first time, it can be intimidating to get started. Dot talks are a great way to ease into the number talk routine. It only takes 5 minutes, and your students will beg to do more! When you are ready to get into more complex math talks, your students will be used to the routine and more willing to participate.

About the Dot Talks Subitizing Routine

Using Dot Talks for your subitizing routine will help your students:

build number sense
visualize numbers and strategies
become strategic and flexible thinkers
boost math confidence

Dot Talks are available in three different grade level packages and can be found here (be sure to download the free previews using the links below for an in depth look at what’s included):

Or grab them as part of a Number Talk Bundle along with Math Conversations to have your entire year of Math Talks planned out (no prep required)!

Three Fun Math Games Your Students Will Love

Games are a great way to incorporate learning into the classroom. It’s easier to learn when you’re having fun! Here are three low-prep, fun math

Do You Need Help With Number Talks? Here’s The Quick Start Guide.

Number Talks have gained in popularity over the last several years – and for good reason! They are a powerful and collaborative way for students

Ten Important Things to Include in Your Number of the Day Routine

There’s no doubt that students thrive on routine. Using a Number of the Day routine starts your math class off with a predictable activity that

The post Here’s an Easy Way to Incorporate Subitizing into Your Math Routine appeared first on Shelley Gray.

How to Investigate Subitizing Through Games to Spark Early Number Sense

Shelley Gray — Mon, 28 Mar 2022 23:54:11 +0000

Subitize comes from the Latin word “subit(us)”, which means “to appear suddenly.” In my last post, we talked about the Early Number Sense Trajectory that was created from the work of John Van de Walle, Doug Clements, and Julie Sarama. According to the trajectory, subitizing is the first mathematical stage a learner experiences. Students who can subitize are able to visually recognize a quantity of five or less. However, there are multiple levels of subitizing, and recognizing the difference between 1, 2, or 3 objects happens as early as within the first few months of infancy!

It’s important to note that when students call out these number names, they are only matching the number name to a visual pattern. In other words, students do not know what those number names mean as a quantity yet. For instance, suppose I show the following image to a young learner:

The learner yells “3!” Yes, the young mathematician knows the number name of the visual pattern but when asked to count how many, the learner may respond “1,3,5.” This is known as perceptual subitizing: the learner can state the number name of a visual pattern but cannot explain why. At this stage of learning, that is okay! We are working with learners who are beginning with perceptual subitizing.

The next stage is conceptual subitizing. This is a learner who can explain why a number name matches a visual pattern and recognizes subgroups that can be combined together to compose a whole. So for the image above, the student may explain that it’s 3 because 2 and 1 make 3.

With that said, there are many ways to support young learners at home during this stage of learning, and what better way to talk about math than through games! Below are three simple games you can play to practice the concept of subitizing. All you need is a deck of subitizing cards (find them for free down below)!

Subitizing Game #1: How Many?

Two players split the deck and take turns flashing the top card from their pile to their playing partner for 1-3 seconds.
If the player correctly identifies the quantity on the card they keep the card as a point. Otherwise, it goes to the discard pile.
The player with the most points/cards wins the game.

Subitizing Game #2: Memory

Place all the cards face down and players alternate flipping over 2 cards to find a match.
If a player finds a match, they collect the cards as their points. The player with the most points/cards wins the game.

Note: You will have to make two copies of the subitizing cards to ensure that each card has a match. Mounting on colored paper or copying on cardstock may also be necessary so students can’t see through the paper.

Subitizing Game #3: How Many? War

All the cards are kept in a single pile and one card is flipped over.
The first player to say the quantity on the card gets to keep the card as a point.
The player with the most points/cards wins the game.

Differentiation

There are many ways to differentiate these games to meet your learner where he/she is at. If you have a young learner in Pre-K or Kindergarten, subitizing cards within 5, like five frame cards, would be more appropriate. For first and second graders, subitizing cards within 10 and 20, like ten frame and double ten frame cards, are a great fit!

Do you have any subitizing games that you love? Share in the comments below! I’ll be sharing some more games for the next stages in the Early Number Sense Trajectory, so stay tuned! Always remember, we are better together.

Resources to Help

Grab and Go

Remember: Depending on what you are using the subitizing decks for, you may need to make multiple copies.

Five Frame Cards

Ten Frame Cards

Double Ten Frame Cards

K-2 Learning Trajectory Document

Deep Dive

Learning and Teaching with Learning Trajectories- This website will provide a wealth of information on specific learning trajectories for learners of all ages!

Learning and Teaching Early Math: The Learning Trajectories Approach by Clements & Sarama

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