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----
-title: Brainstorming on the mathematical tools required at each level
-published: true
-routable: true
-visible: false
----
-
-<!----------------------------------------------------
-lessons:
-    - slug: define-g12-mathematical-tools
-      order: 2
-    - slug: define-1-mathematical-tools-polyglot
-      order: 3
------------------------------------------------------>
-
-
-#### Define the mathematical tools required at level 1
-
---------------------------------
-
-with a **first classification to sort out** the brainstorming (counting, geometry, etc.).
-It *does not presage chapter titles*.
-
-Feel free to create a new classification if necessary.
-
-
-! *Numeration and operations*
-!
-
-(CME-FR) _Good mastery, with exercises to develop automatisms:_
-
-- *Digits and numbers (base 10)*
-- *Whole numbers, positive and negative*
-- *Real numbers*
-- *The four operations: $`+, -, ×, ÷`$*   
-  and therefore the sign $`=`$
-- *Power of 10 $`(10^p)`$*, power *of any integer n $`(n^p)`$*
-- *$`n^p \times n^q = n^{\,p + q}`$*
-
-RESPOND:
-(XXX-YY) ...
-
---------------------
-(CME-FR) _Good mastery, with exercises to develop automatisms:_
-
- - The *fractions* (related to the Pythagorean theorem in the right-angled triangle, and the cross-multiplication's rule)
-
-RESPOND:
-(XXX-YY) ...
-
----------------------
-(CME-FR) _Good mastery, with exercises to develop automatisms:_
-- *Comparison of numbers: $`\ lt, \ gt, \ le, \ ge`$*
-
-RESPOND:
-... (XXX-YY)
-
----------------------
-(CME-FR) _Simply discovered, or more if it is useful to explain the number system,
-and better understand base 10? It can be very fun with animated figures_
-
-- The *numerical bases* (in connection with the sets)
-
-_Idea: this can be very useful in physics, to introduce ideas very early
-on counting and large numbers._
-
-RESPOND:
-... (XXX-YY)
-
----------------------
-
-(XXX-YY) ...
-
-RESPOND:
-... (XXX-YY)
-
-------------------
-
-! *Sets*
-!
-
-(CME-FR) _Whatever our level, all our life we characterize, classify in categories_
-_and sets. A first approach seems essential to me from this level 1 (with the idea of learning_
-_not to be binary and to relativize). And it can be very visual and very fun, with_
-_thousands of possible examples in everyday life._
-
-_It seems useful to understand: _
-_- base 10 numbering (and the others)._
-_- what is an equation (and therefore later a correlation or a physical law of cause and effect)._
-
-RESPOND:
-... (XXX-YY)
-
----------------------
-(CME-FR)
-- *Elements, characterize* elements
-- *Indistinguishable or distinct elements*
-- *Sets and subsets*.
-- *Union $`\cup`$ and intersection $`\cap`$*
-  
-RESPOND:
-... (XXX-YY)
-
----------------------
-
-(XXX-YY) ...
-
-RESPOND:
-... (XXX-YY)
-
-------------------
-
-! *Geometry*
-!
-
-(CME-FR) _Good mastery, with exercises to develop automatisms:_
-* *Pytahgore's theorem / the cross-multiplication's rule* (in relation to fractions and the right-angled triangle)
-
-RESPOND:
-... (XXX-YY)
-
-------------------
-
-! *The equations*
-!
-
-(CME-FR)
-- *equality $`=`$*
-- *write an equality, maybe true or false*.
-- *equation in mathematics*.
-- *equation in physics (members of the same nature, in the same units)*
-
-
----------------------
-
-(XXX-YY) ...
-
-RESPOND:
-... (XXX-YY)
-
------------------- 
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