Base ten blocks

'''Base ten blocks''', also known as '''Dienes blocks''' after popularizer [[Zoltán Dienes]] ({{IPA|hu|ˈdijɛnɛʃ|lang}}), 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|place-value]] system as a more concrete and direct representation than written [[Hindu–Arabic numeral system|Hindu–Arabic numerals]]. The three-dimensional blocks are made of a solid material such as plastic or wood and generally come in four sizes, each representing a [[power of ten]] used as a place in the decimal system: ''units'' (ones place), ''longs'' (tens place), ''flats'' (hundreds place) and ''blocks'' (thousands place).Van de Walle, John (2008). Elementary and Middle School Mathematics: Teaching Developmentally, p. 191. Pearson Education Inc. USA. {{ISBN|0-205-57352-5}} There are also computer programs available that simulate base ten blocks.

'''Base ten blocks''', also known as '''Dienes blocks''' after popularizer [[Zoltán Dienes]] ({{IPA|hu|ˈdijɛnɛʃ|lang}}), 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|place-value]] system as a more concrete and direct representation than written [[Hindu–Arabic numeral system|Hindu–Arabic numerals]]. The three-dimensional blocks are made of a solid material such as plastic or wood and generally come in four sizes, each representing a [[power of ten]] used as a place in the decimal system: ''units'' (ones place), ''longs'' (tens place), ''flats'' (hundreds place) and ''blocks'' (thousands place).Van de Walle, John (2008). Elementary and Middle School Mathematics: Teaching Developmentally, p. 191. Pearson Education Inc. USA. {{ISBN|0-205-57352-5}} There are also computer programs available that simulate base ten blocks.

Base ten blocks were first described by [[Catherine Stern]] in 1949,{{cite book |last=Stern |first=Catherine |author-link=Catherine Stern |year=1949 |title=Children Discover Arithmetic |publisher=Harper & Row }} ([https://archive.org/details/childrendiscover0000ster/ Revised edition, 1971], with Margaret Stern.) though [[Maria Montessori]] had earlier introduced a similar manipulative, the "golden beads", which were assembled into the same shapes as base ten blocks.{{cite journal |last=Burton |first=Grace M. |year=1984 |title=Teaching the Most Basic Basic |journal=The Arithmetic Teacher |volume=32 |number=1 |pages=20–25 |doi=10.5951/AT.32.1.0020 |jstor=41193944 }} Dienes popularized the idea starting in the 1950s, recommending blocks for several [[Base (group theory)|number bases]] ([[binary number|two]], [[ternary numeral system|three]], etc.), called '''multibase arithmetic blocks''' (MAB), so students could concretely compare different number bases and learn about the decimal place-value system as one arbitrary choice among many possibilities.{{cite book |last=Dienes |first=Zoltán Pál |author-link=Zoltán Pál Dienes |year=1960 |title=Building Up Mathematics |place=London |publisher=Hutchinson |url=https://archive.org/details/buildingupmathem00dien/ |url-access=limited }} {{pb}} {{cite book |last=Dienes |first=Zoltán Pál |year=1963 |title=An Experimental Study of Mathematics Learning |place=London |publisher=Hutchinson |url=https://archive.org/details/isbn_090686500 |url-access=limited }}{{cite journal |last1=Kim |first1=Rina |last2=Albert |first2=Lillie R. |title=The history of base-ten-blocks: Why and who made base-ten-blocks |journal=Mediterranean Journal of Social Sciences |volume=5 |number=9 |year=2014 |pages=356–365 |doi=10.5901/mjss.2014.v5n9p356|doi-access=free }} Multibase blocks found support in the [[New Math]] movement of the 1960s. Today, base ten blocks are widespread while blocks for other bases are rarely found.

Base ten blocks were first described by [[Catherine Stern]] in 1949,{{cite book |last=Stern |first=Catherine |author-link=Catherine Stern |year=1949 |title=Children Discover Arithmetic |publisher=Harper & Row }} ([https://archive.org/details/childrendiscover0000ster/ Revised edition, 1971], with Margaret Stern.) though [[Maria Montessori]] had earlier introduced a similar manipulative, the "golden beads", which were assembled into the same shapes as base ten blocks.{{cite journal |last=Burton |first=Grace M. |year=1984 |title=Teaching the Most Basic Basic |journal=The Arithmetic Teacher |volume=32 |number=1 |pages=20–25 |doi=10.5951/AT.32.1.0020 |jstor=41193944 }} Dienes popularized the idea starting in the 1950s, recommending blocks for several [[Base (group theory)|number bases]] ([[binary number|two]], [[ternary numeral system|three]], etc.), called '''multibase arithmetic blocks''' (MAB), so students could concretely compare different number bases and learn about the decimal place-value system as one arbitrary choice among many possibilities.{{cite book |last=Dienes |first=Zoltán Pál |author-link=Zoltán Pál Dienes |year=1960 |title=Building Up Mathematics |place=London |publisher=Hutchinson |url=https://archive.org/details/buildingupmathem00dien/ |url-access=limited }} {{pb}} {{cite book |last=Dienes |first=Zoltán Pál |year=1963 |title=An Experimental Study of Mathematics Learning |place=London |publisher=Hutchinson |url=https://archive.org/details/isbn_090686500 |url-access=limited }}{{cite journal |last1=Kim |first1=Rina |last2=Albert |first2=Lillie R. |title=The history of base-ten-blocks: Why and who made base-ten-blocks |journal=Mediterranean Journal of Social Sciences |volume=5 |number=9 |year=2014 |pages=356–365 |doi=10.5901/mjss.2014.v5n9p356|doi-access=free }} Multibase blocks found support in the [[New Math]] movement of the 1960s. Today, base ten blocks are widespread while blocks for other bases are rarely found. No Official 10,000 base ten blocks have been found, if there is one, it is likely either a 3D print or a handmade version.

==Use in mathematics instruction==

==Use in mathematics instruction==