Displaying Numbers This book introduces three methods of displaying numbers in patterns: the five frame, the ten frame and the ten strip. Placing counters in a frame helps students use pattern recognition rather than counting to see ‘how many’: a skill known as ‘conceptual subitising’. Conceptual subitising helps students move from counting to using part-whole understandings to calculate.
Five Frames The five frame highlights number combinations to five.
Ten Frames The ten frame can show combinations of ten, odd and even numbers, and ‘how many’ from the benchmarks of five and ten depending on how it is filled, explained more thoroughly in the following section. Ten frames can be displayed horizontally or vertically. Multiple ten frames can also show place-value partitions of larger numbers, e.g. 17 as 10 + 7.
Ten Strips The ten strip builds upon the ten frame understandings by showing numbers as a linear strip, which shows magnitude (value) more clearly and aids comparison. Since the primary value of all of these representations is in reducing reliance on counting and encouraging calculating, it is important that time is spent building fluency so that students are not needing to count ‘how many’ when working with the chosen representation, especially for ten frames and ten strips. For example, before students are instructed in how to use ten frames for doubling, they should be able to recognise ‘how many’ are in the frame without counting.
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Teaching with Ten Frames
Ten Strips: Calculation Ten strips can be used for calculation in a similar same manner to ten frames. Most of the games/ activities described for ten frames can also be used with ten strips. Ten strips can be lined up under each other to show doubles very effectively, as for the following depiction of 6+6=12, where the 10+2 can clearly be seen:
For doubles up to 5+5, the result is an equally useful pairwise ten frame pattern:
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Teaching with Ten Frames
Develop understanding of the commutative property of addition, that is 5 + 2 = 2 + 5. The most efficient way to add is to start with the larger number. However, children can be shown that the result is the same, regardless of the order in which the numbers are added. Extend to adding zero (see spinner 2). Children will soon realise that there is no change when zero is added to a number.
Variations: •
Use Unifix Cubes™ in two colours. Join them with the largest amount of cubes on the left. Hold the stick of cubes with the thumb and pointer finger and then count on from the next cube.
hold at this point
hold 5
count 6, 7
hold at this point
hold 5
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count 6, 7
Teaching with Ten Frames