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  2. Abacus - Wikipedia

    en.wikipedia.org/wiki/Abacus

    Early 20th century abacus used in Danish elementary school A twenty bead rekenrek. Around the world, abacuses have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic. In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame is common (see ...

  3. Counting board - Wikipedia

    en.wikipedia.org/wiki/Counting_board

    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 ...

  4. Tally stick - Wikipedia

    en.wikipedia.org/wiki/Tally_stick

    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.

  5. Cuisenaire rods - Wikipedia

    en.wikipedia.org/wiki/Cuisenaire_rods

    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.

  6. Manipulative (mathematics education) - Wikipedia

    en.wikipedia.org/wiki/Manipulative_(mathematics...

    To teach integer addition and subtraction, a number line is often used. 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”.

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