## Monday, October 13, 2014

### Implement The Core: 'Dates' and 'Figs' - Middle School Investigation

Yesterday's date here in the US was 10-12-14: an arithmetic sequence.

(a) List the other 5 such dates this year

(b) List them for 2015 & 2016

(c) Observations & Explanations

In your group make at least 5 observations and/or conjectures. Explain/prove or show they are false.

Examples...

(1) Observation: There are fewer such dates in 2016 than in 2015.
Possible Explanation: In 2015, the months are the 7 odd numbers  from 1 through 13; in 2016, the months are the 6 evens from 2-12 . There is no 14-15-16.
Note:Would the same be true for all even years from 2014 on?

(2) Conjecture: The middle number in the date is the average (arithmetic mean) of the other 2.
Possible Explanation for Algebra Students: The 3 numbers can be expressed as n,n+k,n+2k. The average of n and n+2k is (2n+2k)/2 or n+k.

COREFLECTIONS
(1) Ask students about the phrase "here in the US".
(2) Arithmetic sequences a middle school topic in the Common Core? What about patterns and linear relationships?
(3) Rich discussion of odds and evens
(4) Connections to Geometry: Find a "Pythagorean Triple" date!
(5) ***WARNING--RANT
Does anyone find the recycled arguments against Common Core Math as ironic and sad as I do? 1960? 1990? 2014? 'Dejá vu all over again' as Yogi would say. Meanwhile students in other countries are bemused as they pass us in the fast lane...