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:
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?
One-to-one correspondence: The ability to count objects so each object counted is matched with one number word.
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?
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.
Subitizing:Recognize an amount without physically counting (ie on dice, dot cards, fingers).
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?
Part / Part / Whole: Compose and decompose sets by looking at the whole and the parts that make up the whole.
7 is the “focus number”
1 and 6 are bonds of 7
Unitizing: The child is able to move from counting by ones to count by sets / groups: fives, tens, etc.
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:
Days of the Week
Months of the Year
Graphing (weather, etc.)
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:
The above plus . . .
Number Bonds (How can we break apart this number? Such as 10 = 3 + 7 or 6 + 4)
Place Value and skip counting using a 100 chart
Number of the Day (word form, base ten form, place on a numberline, tally marks, on a ten frame, expanded form, etc.)
Ordinal Numbers (using the calendar)
Counting money (add one cent each day and exchange pennies for nickels, nickels for dimes, etc.)
4 is 1 away from 5. 4 is 2 and 2 (or like a square).
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 →
A Number Talk is an opportunity to review number sense and operations by making it part of your daily math routine — so that what has previously been taught is not easily forgotten.
In this post I will expand on 2 methods for conducting a Number Talk session for KG-1st grade students (Subitizing and Number Bonds). Refer to a previous post (Sept. 10 – Daily Practice to Build Number Sense), in which I mentioned several other ways to review math concepts on a daily basis such as calendar topics, weather graphs, counting # of days of school, using a 100 chart, Choose 3 Ways, etc. Continue reading →