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1)Perhaps the best way to get a feel for other bases is to practice grouping

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1)Perhaps the best way to get a feel for other bases is to practice grouping. First, make a set of place value mats for your group: Take some sheets of paper (not necessarily full-size) and label them as follows: ones (base0), stacks (base1), squares (base2), cubes (base3), stacks of cubes (base4), squares of cubes (base5), cubes of cubes (base6). Now arrange them from right to left in the order given above.
Take thirty-seven counters. Those can be grouped into 3 groups of ten (on the "stacks" mat) and 7 units (on the "ones" mat). That's why this number is written 37 (base ten). But they could also be grouped into 4 groups of eight (on the "stacks" mat) and 5 units (on the "ones" mat). So we could state this number as 45 (base eight), or 45eight. By grouping your counters, what number in the bases two through twelve below.
Can you estimate in which base you will first have to what number three-digit number to represent thirty-seven?
Base twelve:
Base eight:
Base eleven:
Base seven:
Base ten:
Base six:
Base nine:
Base five:
2)Now reflect on how changing the base of your number system system.
Base four:
Base three:
Base two:
Base thirty-seven:
affected the properties of your (a) How many symbols are allowable in a base n place value system? Why? What are they?
(b) What are the values of the places in a base n place value system?
-What is the role of zero in a place value system?
-State general set of instructions for representing multidigit numbers concretely in a base n place value system.
-State general set of instructions for representing multidigit numbers symbolically in a base n place value system.
-Compare the two sets of instructions you wrote above, and identify which steps correspond to each other.