Edu Everyday

Supporting Ten Structured Thinking(STST) instruction provides conceptual supports to make connections between number words and multi-unit groupings more explicit. The English words used to denote numbers less than one hundred do not support connections as well as the words for larger numbers do. With numbers larger than one hundred, the spoken number words specifically designate the multi-units and the number of each multiunit. We say “eight thousand three hundred” to designate 8 groups of a thousand and 3 groups of a hundred. With numbers less than one hundred the designation of units in European languages is less explicit and is irregular in several ways. The number names do not clearly emphasize the groupings of tens; in English we say “forty” rather than “four ten.” The problems are even more acute for numbers in the teens. Numbers in the teens are designated by a single word, and the first syllable of the word denotes the units rather than the tens. For example, in the word seventeen the number of ones is said before the number of tens, which often results in children writing nineteen as 71.

STST instruction also supports specific solutions of single-digit addition and subtraction that involve grouping by ten. Sums and differences are chunked to make a ten and some ones (e.g. 8 + 5 = 8 + 2 + 3 = 10 + 3). There is a direct connection between these solutions and the Name Ten number system described above (10 + 3 translates directly to one ten three), and they are easily integrated into children’s solutions of multidigit addition and subtraction problems.

Sample Activity – Recording Quantities as Ten-Sticks and Dots

Initially, children make dots in columns of 10 to make a record of objects the class was collecting. They count by ones as they made these columns of 10 dots. When they have fewer than 10 left, they make a horizontal row of dots (often with a space between the first five dots and the last four dots to facilitate seeing how many dots there were).

To check a quantity, children can then count all the dots by ones (unitary conception), count the columns by tens (sequence -tens conception), or count the columns as tens (separate-tens conception). These different ways to count are all modeled by the teacher and by individual children at the chalk-board.

When many children could make such drawings confidently, the columns of 10 dots are connected; children draw a line through them as the counting by tens or of tens is done.

Eventually only the vertical stick is drawn to show a ten.

To facilitate meaning making by children, the teacher can use problem contexts involving packaging for addition and subtraction problems. For example, doughnuts packed in boxes of 10 can be bought and sold, so a new box is packed (addition) or opened (subtraction) as necessary. Children can use either sequence-tens or separate-tens conceptions in adding or subtracting; they counted the “stick and dot” quantities they drew by tens and ones (10, 20, 30, 40, 41, 42, 43) or as tens and as ones (1, 2, 3, 4 tens and 1, 2, 3 ones Usually in addition dots are combined to make another ten when possible; in subtraction, a ten-stick is opened (its 10 dots are drawn within an ellipse or rectangle) when necessary.