This article is from the 10-article series "Developing Numeracy With Manipulatives". Numeracy-developing manipulatives described in this series: number lines, 0-99 boards, numeral expanders, base ten blocks, bundling sticks, butcher's paper, Unifix cubes, plastic bears, & plastic chains.
Ten frames are, hands down, the most useful and powerful manipulative available to the teacher for developing numeracy. Their simple structure and uncomplicated use belie the powerful way in which they represent or model numbers up to 100 as collections of ten plus leftover ones.
MISSIONS TRIPS
Teaching With this Manipulative
A ten frame is simply a rectangle, 5 units long and 2 units wide, divided evenly into squares, in a five by two arrangement. The resource may be drawn on a piece of paper, part of a PowerPoint slide show, drawn by hand or marked out on the classroom floor or outside paved area. Numbers up to ten are marked using counters or other objects which fit easily into the squares. Children use this resource by placing counters into the squares to represent numbers.
Two different arrangements are possible for this process; counters should be placed starting at one end, and either placed along one long side first and then the other, or placed along a short edge, building up pairs as the number increases. So to show the number 6, it would look something like this:
|*|*|*|*|*|
|*| | | | |
or this:
|*|*|*| | |
|*|*|*| | |
These two alternative arrangements for counters each have advantages, such as showing a number as even or odd, showing how much more than 5 a number 6-10 is, and showing how much less than 10 a number is. It is important not to "scatter" counters randomly in the squares, as this has very little benefit to students, and will often require counting the counters one by one.
Visualizing Numbers
The process which students will develop when using this resource is called "subitization", a technical word used by math professors to refer to being able to say how many objects are in a small set without counting. This is something adults do subconsciously every day, and a skill children can develop also when using ten frames. Basically, the student will become so familiar with arrangements of counters on the ten frame that after a time the student can glance at an arrangement, and recognize the number immediately. At the same time, the student will recognize the number of empty spaces on the frame, which is the numbers "complement to ten", another really useful piece of information.
As an example when a child becomes familiar with seeing the number 6 arranged as two rows of three counters, the following facts about 6 would be readily apparent:
6 is an even number 6 is double 3 6 is 4 less than 10
Similarly, when the number 6 is arranged as a row of five and one more counter, a child can see straight away that:
6 is one more than 5 6 is over half of ten 5 + 1 = 6
Activities
Provide every student with their own ten frame and ten counters. Ask students to display numbers as quickly as they can. Check that arrangements of counters are "correct" according to the method described here. When students have a number displayed, ask how many empty squares there are - expect students to begin to state this number without counting, once they get used to visualizing the numbers on the manipulative. Link this to "ten take away ___" questions. Ask students to show "doubles" number facts on their manipulative, using two colors. Ask questions about the facts, such as "What is double 3?"; "What is half of 4?". Ask students to show a number on their ten frame, ask if it is closer to ten or to zero, as a prelude to rounding activities.
Extension: Double Ten Frames
The above understandings and activities can be extended into the next phase of number learning by adding another ten frame. Using a double manipulative, students can show all the tricky numbers between 10 and 20, providing excellent exposure to teen numbers. Place the manipulative so that the long edges are vertical, and fill the left-hand frame first, so that when writing the number represented, the student can see that the "1" lines up with the group of ten, and the extra ones line up with the corresponding digit.
A double ten frame allows students to practice all their number facts up to 20, including all addition and subtraction facts. Number fact families such as the "+ 9" facts can be learned easily with this manipulative, since it shows that adding 9 is the same as adding ten and removing one.
Next Article
The next article in this series is "Developing Numeracy With Manipulatives -- 0-99 Boards".
Developing Numeracy With Manipulatives - Ten Frames MISSIONS TRIPS
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