# Number Talks with Dot Cards: Subitizing, Number Sense, Facts (Part 2)

Hi!  This is Part 2 regarding ways to do number talks using dot cards. This post will feature random dot cards. See the last post for strategies with ten frame dot cards and some background information about why and how (click HERE).

My pictures below feature dot cards provided via an extra purchase from this great resource regarding Number Talks. I blacked out the number in the small print at the bottom of each card because I was using them online and didn’t want the magnification to show the number.  When showing them in person, the number is too small really for a student to notice or I can use my hand to cover it when showing the card.  Anyway . . . that’s for those of you wondering what the little black smudge was. Here’s an amazon link to the cards which you can get digitally for \$19.95 (279 pages worth): Number Talk Dot Cards

My previous post (linked above) also listed 2 resources for ten frame and random dot cards.  Here is another one you might like and is great to use with partners as well.  I’ll describe an activity with them below.  Dot Cards for Number Sense (\$2 from mathgeekmama.com)

You may like checking out mathgeekmama for other wonderful FREE resources.

Random Dot Cards

While I refer to these as “random” dot cards, it really doesn’t mean the dots are just scattered willy-nilly.  The dots on these cards are still organized, but just not on ten frames.  When using these cards, the goal is for students to “see” patterns with the dots to aid their subitizing and quick recall of number pairs.  You might start with dot dice first, then look for these on the dot cards:

• groups of 2
• groups of 3 (such as triangles)
• groups of 4 (such as squares)
• groups of 5 (like on a dice)
• groups of 6 (like on a dice)
• doubles
• near doubles

I also often point out to students how I mentally “move” a dot to visualize one of the above scenarios. This will be shown in the pictures below with an arrow.

Procedures for whole group (either in person or on Zoom):

1. Flash the card (longer for more dots).
2. Students put thumb up (I prefer thumb in front of chest) when they have decided the amount.
3. Randomly select students to tell you how many they saw. No judgement yet on who is correct and who isn’t.
4. Then ask the VERY important question, “How did you see it?”  This should elicit various responses which will help reinforce different ways numbers can be decomposed.
5. If desired with in-person sessions, you can have students pair-share their response first before calling on students to tell you. This way all students get a chance to share their way with a ready listener.  Click on this link for a way to silently signal  “Me too” in sign language. I find this very helpful especially for those students who want to respond — and helps avoid the “he took my answer” complaint.
6. Record the different responses on a chart tablet.
7. On the occasions where there are limited responses, here are some options:
• Ask students if they see a way another student might have seen it. Be prepared — you might get some amazing (or long-winded) responses.
• If students don’t see something I think it worth mentioning, I might say, “Here’s a way I saw a student think about this one last year.”
• Or you could  just show the card another day to see if there are some new responses then.

What do you see with these?  . . . Plus some examples:

How do you see these? . . . Plus suggested outcomes:

Procedures for individual or partners (great for online tutoring or class center activity)

1. Flash the card (longer if more complicated).
2. Student tells you how many.  If not correct, show the card again.
3. Ask, “How did you see them?”
4. If the card is laminated, circle the parts the child describes.
5. Tell how you (teacher) saw it.
6. Ask, “How might another student see it?”  This gets them to see other possibilities.
7. Record responses.

With the activity I mentioned earlier from mathgeekmama.com, this is a great with partners. I would recommend dot cards with no more than 8 dots for this activity:

• Start with a stack of dot cards (face down).  Provide a blank laminated square to record dots on.
• Partner 1 selects the top card and flashes it to partner 2 (perhaps 2-3 seconds).
• Partner 2 uses a laminated blank square to try to draw the dots (with dry erase marker) to match what partner 1 showed them.
• Both students reveal their dot cards to see if they match.
• Switch roles and repeat.

As an individual activity, provide the laminated dot cards and a dry-erase marker.  Circle the dots.  Write a math problem to match it. Take pictures to record answers. (Recommendation: Do this after you have already modeled it during a Number Talk session.)

Take care. Share your experience with using dot cards for Number Talk sessions. I love success stories!

Interesed in personal professional development, or PD for your grade level team or school? Please contact me for special rates. I can meet via Zoom for just about any need you have (math or reading).  I’d love to help!

# Number Talks with Dot Cards: Subitizing, Number Sense, Facts (Part 1)

Do you see 3 + 4 =7 or perhaps 5 + 2 = 7? Maybe you see 3 + 2 + 2 = 7.

I have been using dot cards for many years with K-2 students as part of my Number Talks routine. I’d like to share some ways to follow this routine using both ten frame dot cards and random dot cards.  These are also easy to use via distance learning situations.

If you haven’t tried this before, you are in for a treat!  It is so nice to listen how students process their thinking. I never cease to be amazed at how developed a child’s thoughts can be expressed . . . and how many children take this as a challenge to see how many ways a dot picture can be explained.  I often feel I learn so much about my students capabilities (or sometimes the deficits) during this type of Number Talk session.  Look for my recommended links below (FREE).

What are the benefits?:

1. Students gain the ability to subitize (tell a quantity without physically counting).
2. Students gain number sense by noticing more dots, less dots, patterns aid counting, the same quantity can be shown different ways, sequencing numbers, skip counting, and many more.
3. Students gain the ability to see many different ways a number can be composed or decomposed which assists with addition and subtraction facts.
4. Students gain practice with strategies such as counting on, add/subtract 1, doubles, near doubles, adding 9, adding 10, missing addends, and equal groups.
5. Teachers are able to observe students’ processing skills in an informal math setting.

Materials needed:

1. Ten frame dot cards:  This set is FREE from TPT and includes ten frame cards as well as random dot cards. Great find!!  https://www.teacherspayteachers.com/FreeDownload/Number-Talks-Early-Level-Starter-Pack-10-Frames-and-Dot-Cards-4448073
2. Random dot cards (not on ten frames)

General procedures:

1. Decide how you are going to show the cards:
• Show to students who are seated near the teacher?
• Show to students via a document camera projected to a screen?
• Show to students online with a split screen?
• Show to students via a ppt?
2. Depending on the grade level, you may want to flash the card quickly to encourage subitizing or shorten/extend the time the card is shown.
• To encourage subitzing to 5, I recommend flashing the card for a couple of seconds for dots from 1-5 for all age groups.
• Depending on the number of dots and the complexity of the dots, you may choose to shorten or extend the time you display the card for amounts more than 5.  The goal is for the students to look for patterns, equal groups, doubles, dots making squares, rectangles, or triangles, determine a quantity, and then explain how they arrived at that amount.
3. Students put a quiet thumbs up when they have decided the quantity.  They should not say the amount outloud at this point. This shows respect for others who are still processing.
4. The teacher observes to see who is counting, who is participating, who uses fingers, who is quick /slow, etc.
5. Teacher asks random students, “How many dots?”
6. Teacher asks random students, “How did you see them?”
7. Results can be stated verbally or written down by the teacher.

Here are some examples with sums less than 10:

Here are examples using 2 ten frames to illustrate quantities greater than 10:

Next post:  I will feature ways to use the random dot cards for your Number Talk sessions.

Do you need professional development for yourself, your team, your school?  Please contact me and we can work out a plan that fits your needs.  I can provide personal help via email or Zoom all the way up to custom made webinars or power point presentations.  Let me know!

Do you know students who need extra help at home via online tutoring?  See my link for Varsity Tutors and mention my name.

Do you want to do some online tutoring yourself at a time that works with your schedule? See my link for Varsity Tutors and mention my name.  Feel free to ask me questions as well.

# Ten Frames Part 1: Number Sense

The focus in this post will be an introduction to ten frames and ways they can help your students gain number sense. Then stay tuned because ten frames can also be a great tool for addition, subtraction, multiplication, and division.

Subitizing: This is the ability to recognize an amount without physically counting. Looking at the picture of red counters: If the top row is full, does the student automatically know there are 5? Doing a Number Talk is a great way to practice subitizing using a ten frame:

• Use your own or pre-made dot cards. Flash the card for 1-2 seconds. Observe students. Are any of them trying to point and count? Or do they seem to know right away? Here’s a great video I recommend: KG Number Talk with ten frames
• Tell students to put their thumb in front of their chest (quietly) to signal they know how many there are.
• Ask a few students to name the amount.
• Then ask this very important question, “How did you know?”
• For the top picture you might hope a child says, “I knew there were 5 because when the top row is full, there are 5.”
• For the bottom picture, you might hope for these types of responses: “I saw 4 (making a square) and 1 more.” or “I saw 3 and 2 more.” or “I pictured the 2 at the bottom moving up to the top row and filling it up, which is 5.”

The idea is to keep building on this.

• What if I showed 4 in the top row? Can the student rationalize that it was almost 5? Do they see 2 and 2?
• What if I showed 5 in the top row and 1 in the bottom row? Can the student think “5 and 1 more is 6?”

Here are some resources you might like to help with subitizing using ten frames.

Number Bonds: Using ten frames to illustrate number bonds assists students with composing and decomposing numbers. Students then see that a number can be more than a counted amount or a digit on a jersey or phone number. Here is an example of number bonds for 6:

• 6 is 5 and 1 (or 1 and 5).
• 6 is 4 and 2 (or 2 and 4).
• 6 is 6 and 0 (or 0 and 6).
• 6 is 3 and 3.

Teaching strategies for number bonds using ten frames: Continue reading

# Addition and Subtraction Part 1: Numerical Fluency

To be able to add and subtract, students normally pass through several phases as they build readiness for these operations with numbers.  As teachers, we know oral counting does not necessarily indicate an understanding of numbers and sets, just like reciting the alphabet doesn’t necessarily mean a child can recognize letters and sounds. Read ahead for freebies in the Part-Part-Whole section.

Numerical Fluency Continuum:  There are 7 steps to numerical fluency. If a child gets stuck on any of these steps, it may very likely halt their progress. Hopefully children move through these by the end of 2nd grade, but many students beyond that level have a breakdown which is likely because they missed one of these stages. Can you determine which of these stages your students are in?

1. One-to-one correspondence: The ability to count objects so each object counted is matched with one number word.
2. Inclusion of set: Does a child realize that the last number counted names the number of objects in the set? A child counts 5 objects.  When you ask how many, can they state “5.” If you mix them up after they just counted them, do they realize there are still 5?
3. Counting on: If a child counts 5 objects and the teacher then puts 2 more objects for the child to count, do they start all over or continue counting from 5?  5 . . . 6, 7.
4. Subitizing:Recognize an amount without physically counting (ie on dice, dot cards, fingers).
5. More Than / Less Than / Equal To:  Can a child look at two sets of objects and tell whether the second set is more, less, or equal to the first set. Can a child build a second set with one more, one less, or equal to the first set?
6. Part / Part / Whole: Compose and decompose sets by looking at the whole and the parts that make up the whole.
7. Unitizing: The child is able to move from counting by ones to count by sets / groups: fives, tens, etc.

# Daily Math Meeting Part 2: The basics and subitizing (KG-2nd)

In the next few posts, I will show various ways to conduct daily math meetings which you can incorporate into your daily schedule (as part of your normal morning meeting routine, or at the beginning of your daily math lesson). Daily Math Meetings (10-15 minutes) are vital for quickly reviewing math concepts and number sense in more visual and discussion based format. With primary students, this math meeting might center around the calendar bulletin board (or SMARTboard presentation). With intermediate students, it begins to take on the aspects of a “Number Talk” with a variety of computational strategies being the focus.

PreK – KG Level Components:

1. Counting
2. Subitizing
3. Days of the Week
4. Months of the Year
5. Graphing (weather, etc.)
6. Place Value (tens and ones: ten frames, straws, sticks, etc. to keep track of the days of school – working toward the 100th day)

1st – 2nd Grade Level Components:

1. The above plus . . .
2. Number Bonds (How can we break apart this number? Such as 10 = 3 + 7 or 6 + 4)
3. Place Value and skip counting using a 100 chart
4. Number of the Day (word form, base ten form, place on a numberline, tally marks, on a ten frame, expanded form, etc.)
5. Ordinal Numbers (using the calendar)
6. Counting money (add one cent each day and exchange pennies for nickels, nickels for dimes, etc.)

Subitizing

See my updated post on this topic by clicking here: https://cindyelkins.edublogs.org/2016/09/03/subitizing-what-does-that-mean/

This is such an important process in the continuum of counting, adding, and subtracting numbers. It means students can recognize certain quantities without physically counting each one. Continue reading