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.Continue reading →
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:
I have 1 penny in one pocket. I have 6 more pennies in another pocket. This is a Join or “some and some more” story structure.
Many teachers I work with have asked for advice on problem solving in math. Students often don’t know how to approach them or know what operation to use. Should teachers help students focus on key words or not? What about the strategies such as CUBES, draw pictures, make a list, guess and check, work backwards, find a pattern?
While all of those strategies definitely have their purpose, I find we often give kids so many steps to follow (underline this, circle this, highlight that, etc.) that they lose sight of what the problem is basically about.
In this post, I will focus on two basic questions (who and what) and a simple graphic organizer that will help students think about (and visualize) the actions in a one-step Join story problem. KG and first grade students can act out these actions using story mats or ten frames. Late first through 5th grade can use a part-part-whole box. There are two FREE items offered.
These are the types of problems I will focus on in the next few posts.
Join (also referred to as SSM – Some and Some More)
Separate (also referred to as SSWA – Some, Some Went Away)
JOIN problems have 3 versions:
a + b = ___ (The result is unknown.)
a + ____ = c (How the story changed is unknown / missing addend.)
____ + b = c (The start is unknown / missing addend.)
They can also be referred to as “Some and Some More” stories (SSM). This means, you have some and you get some more for a total amount. These present themselves as additive stories, but it doesn’t necessarily mean you have to add to solve them. The second and third version above are often referred to as missing addend problems. Continue reading →
To build number sense, students need frequent exposure or review of concepts you have previously introduced. There are many ways to build number sense on an on-going, informal basis – especially when you can squeeze in 10-15 minutes daily:
by C. Elkins, OK Math and Reading Lady (updated post on 8-12-17)
The term “subitize” means to recognize quantity without counting. It is a concept recently added to the new OAS (Oklahoma Academic Standards). KG students should be able to “recognize without counting the quantity of a small group of objects in organized and random arrangements up to 10.” For first graders, the quantity is increased to 20 of “structured arrangements.” Subitizing is an important pre-requisite skill to learning addition and subtraction number combinations or number bonds.
Suggested items for the teacher to present this concept: