Update textbook.en.md

00.brainstorming-pedagogical-teams/45.synthesis-structuring/10.math-tools/10.n1/textbook.en.md

@@ -1,10 +1,137 @@
 ---
-title: Brainstorming on the mathematical tools required at each level
+title: Define the mathematical tools required at level 1
 published: true
 routable: true
 visible: false
+lessons:
+    - slug: define-g12-mathematical-tools
+      order: 2
+    - slug: define-1-mathematical-tools-polyglot
+      order: 3
 ---
 
-#### Brainstorming on the mathematical tools required at level 1
+#### 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)
+
+------------------