Level: CE2 - CM Xavier is writing a dictionary. His publisher told him:
- When you deposit your manuscript, I'll give you an advance. It will be based on the number of pages of the manuscript.
- That is to say?
- I'll add all the numbers that were needed to paginate your manuscript. This sum corresponds to the amount of the advance in euros. For example, if your manuscript has 20 pages, the amount of the advance would be: 1 + 2 + 3 + 4 + ... + 9 + 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3 + ... + 1 + 9 + 2 + 0. That would give you 102 euros.
When the manuscript was finished, he had 599 pages. Xavier
How much did he get his editor?
References:
We find this problem and many others on the site http://www.recreomath.qc.ca/ under "Challenges"
worked Skills:
- involving oral and written descriptions of numbers
- calculate sums of integers
mentally - to organize and process additive calculations
long - make good use of his calculator
procedure possible:
- reading the statement, discussion around the understanding of the method used to calculate in advance
- check with what has been understood that there are good € 102 for the 20
first pages - calculation of the amount corresponding to the 20
following pages - search for a possible organization to carry out research (methods, work allocation)
- final addition and verification of the result
Extensions possible:
We want to write all the numbers from 0 to 285. How many times will he use the number 7?
"Printer": A printer publishes a book of "a" pages. Each page is numbered 1, 2, 3 ... "a". How many digits have been printed for numbering the book?
"a" is chosen to be close to 500.
This is page 159 in "digital learning and problem solving CM2" team in ERMEL Hatier
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