Last week’s focus was on using ten frames to help with students’ number sense and conceptual development of number bonds for amounts 1-10. This post will feature ways to use ten frames to enhance students’ understanding of addition and subtraction. Look for freebies and a video!
There are many addition and subtraction strategies to help students memorize the basic facts such as these below. The ten frame is a very good tool for students of all grade levels to make these strategies more concrete and visual. I will focus on some of these today.
add or take away 1 (or 2)
doubles, near doubles
facts of 10
make a ten
add or sub. 10
add or sub. 9
add or sub. tens and ones
Doubles and near doubles (doubles +1, -1, +2, or -2): If the doubles are memorized, then problems near doubles can be solved strategically.
Show a doubles fact on a single ten frame (for up to 5 + 5). Use a double ten-frame template for 6 + 6 and beyond.
With the same doubles fact showing, show a near doubles problem. This should help students see that the answer is just one or two more or less.
Repeat with other examples.
Help student identify what a doubles + 1 more (or less) problem looks like. They often have a misconception there should be a 1 in the problem. Make sure they can explain where the “1” does come from. Examples: 7 + 8, 10+11, 24+25, 15 +16, etc.
For subtraction, start with the doubles problem showing and turn over the 2-color counters or remove them.
Facts of 10: These are important to grasp for higher level addition / subtraction problems as well as rounding concepts.
Place counters on the ten frame. Determine how many more are needed to fill in the ten frame. This also helps with missing addends. Example: 3 + ___ = 10. Ask, “What goes with 3 to make 10?”
Using 2-color counters, fill the 10 frame with 1 color. Then turn over some to reveal a number bond of 10 (such as 4 and 6).
Shake and Spill
Play “Shake and Spill” with 10 two-color counters. Click on these links for Shake and Spill Directions and a Shake and Spill recording page. Basically, the student puts 10 of these counters in a cup, shakes it, and spills it out (gently). Count how many red and how many yellow. Repeat 10 or more times. Keep track of the spills on a recording sheet. Which combination came up most often? Which combination never came up? What is really nice to observe is if a student spills counters and sees 6 are red, do they know automatically there are 4 yellow, or do they still have to count them?
Since number bonds enable a student to see addition and subtraction problems, the second bullet above will serve subtraction problems very well. Start with 10, turn over 7 to the yellow side. How many counters are red?
Make a Ten: This strategy builds on the above (facts of 10) to help with problems with sums between 10 and 20. Students should readily be able to solve a problem such as 10 + 4 mentally first.
Use 2 ten frames (see Ten Frames part 1 for a link for templates)
Let’s say the problem was 8 + 5. Place 8 counters on one ten frame, place 5 on the other.
Move counters from one ten frame to fill up the other. 8 + 5 is the same as 10 + 3. The problem 10 + 3 should be a mental math problem. Students will need to see that counters were not added, but shifted from one ten frame to the other.
Repeated practice with this concrete activity helps children think more deeply about the relationship of numbers.
Continued practice with these strategies:
During your daily math meeting, flash ten frame dot cards to students in which they must use the above strategies. Use it as a # Talk sessions so students can verbally explain how they solved it.
Try this from NMCT Illuminations sight (National Council for Teachers of Mathematics): Interactive ten frame
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:
Provide a blank ten frame to students along with some counters (beans, cubes, bears, cheerios, two sided counters, etc.). State a number to count and place on their ten frame. This is a much better approach in my opinion than asking studens to randomly place counters on a blank mat (which is what Saxon advises in their KG counting lessons). Random placement means the student might easily miscount and the observing teacher cannot often tell at a glance if the student has the correct amount. OK – that’s my soapbox.
This method allows the teacher to readily determine if the student counted correctly. It also leads to helping students see there are different ways to represent this amount (number bonds).
The teacher can now ask students to show (and/or tell) their result. This is what the process standard of communication is all about! If most students show only 1 way, the teacher asks, “Now, can you show 6 in a different way?”
Use a blank ten frame as part of your daily math meeting time. Select a number of the day or number of the week. Show a way to make that amount. Connect with numbers such as: 2 and 2 is 4 (PreK or KG) or 2 + 2 = 4 (late KG, 1st and up)
4 is 1 away from 5. 4 is 2 and 2 (or like a square).
4 is 2 and 2. 4 is 3 and 1.
5 is 5 and 0. 5 is 4 and 1.
5 is 3 and 2.
Six is 5 and 1. Six is 3 and 3. Or the child may see the bottom as 4 and 2.
Six is 4 and 2. Six is 2 and 2 and 2
Learning station ideas for subitizing and number bonds with ten frames:
Match # cards to ten frames (use mini ten frames in resources above).
Provide # cards, 3-4 blank ten frames, and counters. Student turns over a # card and uses counters to show different ways to make the same amount. This physical concrete method is recommended for preK and KG. As an extension for first or second graders, they can start with the concrete and then record their responses (pictorial method) on blank mini ten frame templates.
Play with a partner: Materials — one large blank ten frame per student, counters, set of # cards, and a screen between the 2 players. Turn over 1 number card that both can see. Each student makes that amount on their own ten frame (hidden from view from their partner by the screen). Then remove the screen and compare results.
Put ten frame dot cards in order (least to greatest, or greatest to least).
Play “war” with ready-made ten frame dot cards. Students start out with an equal stack of cards. Each student turns over 1, tells how many and determines who has more (or less).
Play “Go Fish” with mini ten frame cards. This means you will need some cards that have different ways to show the same amount. I will be on the lookout for some!! If you know of some, please share your link.
Tell us how you use ten frames to build number sense!! Or if you try doing any of the above, what were the results?
Last time I focused on some basics about learning the number bonds (combinations) of 10 as well as adding 10 to any number. Today I want to show the benefits of making a 10 when adding numbers with sums greater than 10 (such as 8 + 5). Then I’ll show how to help students add up to apply that to addition and subtraction of larger numbers. I’ll model this using concrete and pictorial representations (which are both important before starting abstract forms).
Using a 10 Frame:
A ten frame is an excellent manipulative for students to experience ways to “Make a 10.” I am attaching a couple of videos I like to illustrate the point.
Model this process with your students using 2 ten frames.
Put 8 counters on one ten frame. (I love using 2-color counters.)
Put 5 counters (in another color) on the second ten frame.
Determine how many counters to move from one ten frame to the other to “make a 10.” In this example, I moved 2 to join the 8 to make a 10. That left 3 on the second ten frame. 10 + 3 = 13 (and 8 + 5 = 13).
The example below shows the same problem, but this time move 5 from the first ten frame to the second ten frame to “make a 10.” That left 3 on the first ten frame. 3 + 10 = 13 (and 8 + 5 = 13). Continue reading →
I’m sure everyone would agree that learning the addition / subtraction facts associated with the number 10 are very important. Or maybe you are thinking, aren’t they all important? Why single out 10? My feelings are that of all the basic facts, being fluent with 10 and the combinations that make 10 enable the user to apply more mental math strategies, especially when adding and subtracting larger numbers. Here are a few of my favorite activities to promote ten-ness! Check out the card trick videos below – great way to get kids attention, practice math, and give them something to practice at home. Continue reading →