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An abacus (pl. abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. [1] An abacus consists of a two-dimensional array of slidable beads (or similar objects). In their ...
The counting board is the precursor of the abacus, [1] and the earliest known form of a counting device (excluding fingers and other very simple methods). Counting boards were made of stone or wood, and the counting was done on the board with beads, pebbles etc. [ 2 ] Not many boards survive because of the perishable materials used in their ...
To teach integer addition and subtraction, a number line is often used. A typical positive/negative number line spans from −20 to 20. A typical positive/negative number line spans from −20 to 20. For a problem such as “−15 + 17”, students are told to “find −15 and count 17 spaces to the right”.
Wooden Dienes blocks in units of 1, 10, 100 and 1000 Plastic Dienes blocks in use. Base ten blocks, also known as Dienes blocks after popularizer Zoltán Dienes (Hungarian: [ˈdijɛnɛʃ]), are a mathematical manipulative used by students to practice counting and elementary arithmetic and develop number sense in the context of the decimal place-value system as a more concrete and direct ...
Single and split tallies from the Swiss Alps, 18th to early 20th century (Swiss Alpine Museum) There are two principal forms of tally sticks: the single tally and the split tally. A comparable example of this primitive counting device can be found in various types of prayer beads.
A suanpan (top) and a soroban (bottom). The two abaci seen here are of standard size and have thirteen rods each. Another variant of soroban. The soroban is composed of an odd number of columns or rods, each having beads: one separate bead having a value of five, called go-dama (五玉, ごだま, "five-bead") and four beads each having a value of one, called ichi-dama (一玉, いちだま ...
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Cuisenaire rods illustrating the factors of ten A demonstration the first pair of amicable numbers, (220,284). Cuisenaire rods are mathematics learning aids for pupils that provide an interactive, hands-on [1] way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors.