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Developing whole-number Place-Value concepts - Coggle Diagram
Developing whole-number Place-Value concepts
Understanding whole-number place-value concepts
Place value understanding
pre-place value
everything is counted by ones to get every number
students cannot conceptualize groups of items as a set of ten
Unitary
grouping
being able to see items as sets of ten and using this knowledge to count how many sets of tens there are
equivalent grouping
representing numbers without the maximum number of groups of tens
base ten grouping
the maximum number of groups of ten that can be made from a quantity
base ten groupings and words
saying the place with the numbers to get students to associate numbers as groups of tens and ones
53= 5 tens and 3 ones
place value understanding
students understanding that tens are written to the left of the ones and the ones place is usually the furthest to the right 53= 5 tens (50 ones) and 3 ones
Base ten models place value concepts and activities
models
groupable
students have to ability to construct the tens group out of singles (ten single cubes connected together to make a ten cube stack)
objects in this group show that a ten is 10x larger than the ones
pregrouped
having things you can't build represent groups of items(prebuilt sets they students can't physically break apart)
certain blocks pre-set groups of items
still maintain the size component being physically 10 or 100x the size of the ones
non-proportional
things that are grouped but don't have the size component
Money, chips, or cards that are no larger than the ones object but are assigned a different value
activities
counting by tens
give students a quantity of items, count the amount of items necessary then group them in as many groups of tens as possible
group tens to make 100
allow students to group tens together and ask how many 10 groups of 10s make
equivalent representations
asks students what other combinations of 10s and 1s can make large numbers
reading and writing numbers
connecting the oral pronunciations and written representations together and to their numerical value
emphasize the place value at first by using base ten language
do not assume once students understand one place value they will apply those generalizations to numbers bigger than that
PV patterns and relation ships: a foundation for computation
students can use the concept of place value to help better understand skip counting
giving the students the understanding that each place value represents 10x the previous place makes comparisons easy in the base ten system
paired with a number chart these students can start to see patterns within the base ten system
students can use their understanding of groupings to help them estimate quantities
numbers beyond 1000
applying the generalization to every place value
every place value is 10 of the place value below it
understanding that a pattern appears every three place values such that it is modeled after the ones tens and 100s (one thousand, ten thousand, hundred thousand)
it is difficult to model such large numbers but some students need to see the relationships can continued to be expressed