Developing Numeracy With Manipulatives - Ten Frames

Free Math Worksheets - Developing Numeracy With Manipulatives - Ten Frames

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This report is from the 10-article series "Developing Numeracy With Manipulatives". Numeracy-developing manipulatives described in this series: whole lines, 0-99 boards, numeral expanders, base ten blocks, bundling sticks, butcher's paper, Unifix cubes, plastic bears, & plastic chains.

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Ten frames are, hands down, the most beneficial and excellent manipulative ready to the teacher for developing numeracy. Their simple structure and simple use belie the excellent way in which they recite or model numbers up to 100 as collections of ten plus leftover ones.

Teaching With this Manipulative

A ten frame is naturally 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 face paved area. Numbers up to ten are marked using counters or other objects which fit legitimately into the squares. Children use this resource by placing counters into the squares to recite numbers.

Two separate arrangements are possible for this process; counters should be settled beginning at one end, and either settled along one long side first and then the other, or settled along a short edge, building up pairs as the whole increases. So to show the whole 6, it would look something like this:

|*|*|*|*|*|

|*| | | | |

or this:

|*|*|*| | |

|*|*|*| | |

These two alternative arrangements for counters each have advantages, such as showing a whole as even or odd, showing how much more than 5 a whole 6-10 is, and showing how much less than 10 a whole is. It is prominent not to "scatter" counters randomly in the squares, as this has very dinky benefit to students, and will often need counting the counters one by one.

Visualizing Numbers

The process which students will found 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 found also when using ten frames. Basically, the learner will become so familiar with arrangements of counters on the ten frame that after a time the learner can espy at an arrangement, and recognize the whole immediately. At the same time, the learner will recognize the whole of empty spaces on the frame, which is the numbers "complement to ten", an additional one legitimately beneficial piece of information.

As an example when a child becomes familiar with looking the whole 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 whole 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 learner with their own ten frame and ten counters. Ask students to display numbers as speedily as they can. Check that arrangements of counters are "correct" agreeing to the recipe described here. When students have a whole displayed, ask how many empty squares there are - expect students to begin to state this whole 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" whole 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 whole 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 whole learning by adding an additional one ten frame. Using a double manipulative, students can show all the tricky numbers in the middle of 10 and 20, providing exquisite 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 whole represented, the learner 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 convention all their whole facts up to 20, together with all addition and subtraction facts. whole fact families such as the "+ 9" facts can be learned legitimately with this manipulative, since it shows that adding 9 is the same as adding ten and removing one.

Next Article

The next report in this series is "Developing Numeracy With Manipulatives -- 0-99 Boards".

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