Promoting Mathematical Thinking



countingcounting oncounting in twos, threes etc. from zerocounting in twos, threes etc. from a given starting numbercounting in tenscounting on repeatedlycounting in hundredsrepeated additionsequences that go up in equal stepssequences that go down in equal steps'gazzupins'counting the number of stepsenumerating completed arrays using repeated countingrecursive description of additive sequences, i.e. how to get next term from previous termmultiplication of single digit whole numbersmultiplication facts written several waysmultiplication facts known as times tablesundoing multiplication facts (backwards tables)multiplying by tenmultiplying by a hundredenumerating completed arrays using multiplicationarea of rectangles with squared paperenumerating incomplete arrays using countingenumerating incomplete arrays using multiplicationarea of composite rectilinear shapesmultiplying n to get a sequence valuedoubledouble and double again ...how many parts?how much in each part?unit fractions of stuffunit fractions of cakeunit fractions of lengthunits fractions of numbernon-unit fractions <1 of stuff non-unit fractions <1 of cakenon-unit fractions <1 of lengthnon-unit fractions <1 of numbernon-unit fractions >1 of stuff non-unit fractions >1 of cakenon-unit fractions >1 of lengthnon-unit fractions >1 of numberhalf ofhalf of a half of ....dividing whole numbers that go exactly from times tablesdividing whole numbers that do not go exactly but are within times tables scopeunitsmeasuring lengthfractions of lengthmultiplying and dividing lengthsfractions as divisiondivision as fractionshow many ... go into ....?how much more than?how multiplying the unit has same effect as multiplying the whole measurementchanging unitsgrouping non-countable stuffgrouping countable objectssharing countable objectssharing non-countable stuffmeasuring growthshrinking and growing as multiplication/divisioncomparing lengthscomparing liquids (water, lentils)per centrate of changespeed as distance/timegrowth over timeunequal sharing of countable objectsfractions with same denominator that add up to onewet mixturesrecipesso much per so muchconversion rules and graphs'this corresponds to that' problems ................
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