standard_description: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
problem_activity: Problem 1
Sondra says
$$3\times223=696$$
. Use what you know about the product of two odd numbers to explain why Sondra is wrong.
Problem 2
Explain two ways you could find the next number in the highlighted diagonal below. You don’t need to actually compute it!
{"table": [{"_attributes": {"border": "1", "cellpadding": "1", "cellspacing": "1", "class": ["table", "table-bordered"], "style": "width:100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "strong": [{"_value": "\u00d7"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "10"}]}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "1"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2"}, {"_attributes": {"style": "text-align: center;"}, "_value": "3"}, {"_attributes": {"style": "text-align: center;"}, "_value": "4"}, {"_attributes": {"style": "text-align: center;"}, "_value": "5"}, {"_attributes": {"style": "text-align: center;"}, "_value": "6"}, {"_attributes": {"style": "text-align: center;"}, "_value": "7"}, {"_attributes": {"style": "text-align: center;"}, "_value": "8"}, {"_attributes": {"style": "text-align: center;"}, "_value": "9"}, {"_attributes": {"style": "text-align: center;"}, "_value": "10"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "b": [{"_value": "2"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "2"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "4"}, {"_attributes": {"style": "text-align: center;"}, "_value": "6"}, {"_attributes": {"style": "text-align: center;"}, "_value": "8"}, {"_attributes": {"style": "text-align: center;"}, "_value": "10"}, {"_attributes": {"style": "text-align: center;"}, "_value": "12"}, {"_attributes": {"style": "text-align: center;"}, "_value": "14"}, {"_attributes": {"style": "text-align: center;"}, "_value": "16"}, {"_attributes": {"style": "text-align: center;"}, "_value": "18"}, {"_attributes": {"style": "text-align: center;"}, "_value": "20"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "3"}, {"_attributes": {"style": "text-align: center;"}, "_value": "6"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "9"}, {"_attributes": {"style": "text-align: center;"}, "_value": "12"}, {"_attributes": {"style": "text-align: center;"}, "_value": "15"}, {"_attributes": {"style": "text-align: center;"}, "_value": "18"}, {"_attributes": {"style": "text-align: center;"}, "_value": "21"}, {"_attributes": {"style": "text-align: center;"}, "_value": "24"}, {"_attributes": {"style": "text-align: center;"}, "_value": "27"}, {"_attributes": {"style": "text-align: center;"}, "_value": "30"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "4"}, {"_attributes": {"style": "text-align: center;"}, "_value": "8"}, {"_attributes": {"style": "text-align: center;"}, "_value": "12"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "16"}, {"_attributes": {"style": "text-align: center;"}, "_value": "20"}, {"_attributes": {"style": "text-align: center;"}, "_value": "24"}, {"_attributes": {"style": "text-align: center;"}, "_value": "28"}, {"_attributes": {"style": "text-align: center;"}, "_value": "32"}, {"_attributes": {"style": "text-align: center;"}, "_value": "36"}, {"_attributes": {"style": "text-align: center;"}, "_value": "40"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "5"}, {"_attributes": {"style": "text-align: center;"}, "_value": "10"}, {"_attributes": {"style": "text-align: center;"}, "_value": "15"}, {"_attributes": {"style": "text-align: center;"}, "_value": "20"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "25"}, {"_attributes": {"style": "text-align: center;"}, "_value": "30"}, {"_attributes": {"style": "text-align: center;"}, "_value": "35"}, {"_attributes": {"style": "text-align: center;"}, "_value": "40"}, {"_attributes": {"style": "text-align: center;"}, "_value": "45"}, {"_attributes": {"style": "text-align: center;"}, "_value": "50"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "6"}, {"_attributes": {"style": "text-align: center;"}, "_value": "12"}, {"_attributes": {"style": "text-align: center;"}, "_value": "18"}, {"_attributes": {"style": "text-align: center;"}, "_value": "24"}, {"_attributes": {"style": "text-align: center;"}, "_value": "30"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "36"}, {"_attributes": {"style": "text-align: center;"}, "_value": "42"}, {"_attributes": {"style": "text-align: center;"}, "_value": "48"}, {"_attributes": {"style": "text-align: center;"}, "_value": "54"}, {"_attributes": {"style": "text-align: center;"}, "_value": "60"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "7"}, {"_attributes": {"style": "text-align: center;"}, "_value": "14"}, {"_attributes": {"style": "text-align: center;"}, "_value": "21"}, {"_attributes": {"style": "text-align: center;"}, "_value": "28"}, {"_attributes": {"style": "text-align: center;"}, "_value": "35"}, {"_attributes": {"style": "text-align: center;"}, "_value": "42"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "49"}, {"_attributes": {"style": "text-align: center;"}, "_value": "56"}, {"_attributes": {"style": "text-align: center;"}, "_value": "63"}, {"_attributes": {"style": "text-align: center;"}, "_value": "70"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "8"}, {"_attributes": {"style": "text-align: center;"}, "_value": "16"}, {"_attributes": {"style": "text-align: center;"}, "_value": "24"}, {"_attributes": {"style": "text-align: center;"}, "_value": "32"}, {"_attributes": {"style": "text-align: center;"}, "_value": "40"}, {"_attributes": {"style": "text-align: center;"}, "_value": "48"}, {"_attributes": {"style": "text-align: center;"}, "_value": "56"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "64"}, {"_attributes": {"style": "text-align: center;"}, "_value": "72"}, {"_attributes": {"style": "text-align: center;"}, "_value": "80"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "9"}, {"_attributes": {"style": "text-align: center;"}, "_value": "18"}, {"_attributes": {"style": "text-align: center;"}, "_value": "27"}, {"_attributes": {"style": "text-align: center;"}, "_value": "36"}, {"_attributes": {"style": "text-align: center;"}, "_value": "45"}, {"_attributes": {"style": "text-align: center;"}, "_value": "54"}, {"_attributes": {"style": "text-align: center;"}, "_value": "63"}, {"_attributes": {"style": "text-align: center;"}, "_value": "72"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "81"}, {"_attributes": {"style": "text-align: center;"}, "_value": "90"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "10"}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "10"}, {"_attributes": {"style": "text-align: center;"}, "_value": "20"}, {"_attributes": {"style": "text-align: center;"}, "_value": "30"}, {"_attributes": {"style": "text-align: center;"}, "_value": "40"}, {"_attributes": {"style": "text-align: center;"}, "_value": "50"}, {"_attributes": {"style": "text-align: center;"}, "_value": "60"}, {"_attributes": {"style": "text-align: center;"}, "_value": "70"}, {"_attributes": {"style": "text-align: center;"}, "_value": "80"}, {"_attributes": {"style": "text-align: center;"}, "_value": "90"}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}, "_value": "100"}, {"_attributes": {"style": "text-align: center;"}}]}, {"td": [{"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "text-align: center;"}}, {"_attributes": {"style": "background-color:#eeeeee; text-align: center;"}}]}]}]}]}


aligns: no