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Breaking down problems with proportions

100 problems to calmly prepare for lower secondary school

Camillo Bortolato

Product: Book

Trim size in cm: 14,8x21cm

Pages: 224

ISBN: 978-88-590-2609-9

Publication date: 01/09/2021

Suitable for: Primary 2nd level (ages 8-10), Lower secondary 1st level (ages 10-11)


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Breaking down problems with proportions presents a gradual programme of 100 arithmetic problems, in the form of games and puzzles, challenging and self-correcting situations, for children aged 10 and over, to be completed with the guidance of a teacher or alone.
The heart of the proposal is proportional thinking, which respects the way children and young people think, and can be used in any type of problematic situation.
Explanations are reduced to a minimum: suggestions and graphic schemes stimulate pupils to develop strategies to visualize problems, to seek alternative and divergent ways to solve problems.

The topics covered are:

  • ratios and proportions (intuitive, direct and indirect proportionality)
  • fractions and decimal numbers
  • introduction to powers, square roots, accenni a potenze, radice quadrata, LCM and GCD

Suggested for
Breaking down problems with proportions is a foray into the lower secondary school programme for primary school pupils who want to get ahead.  It is also useful for older children, as a recovery and reinforcement tool.


Intuitive proportionality
Direct and inverse proportionality
Fractions and decimals
Problems with dots
Various problems
Solutions
Conclusions



Breaking down problems


 

Sometimes children fail to solve mathematical problems not because they do not possess logical skills but because they get lost in the description of the problem. Teacher Camillo Bortolato, with his intuitive approach at the base of The Analogical Method, has created three mini block pads containing hundreds of problems turned into picture games, inspired by Sudoku and other brain teasers. Primary and lower secondary school children will be able to focus on the logical aspects of the problems, and, bypassing the confusing textual descriptions, anxiety will be dissipated.

 

 

Each problem is designed as an intuitive individual challenge, accompanied by graphic hooks and with a midpoint tip that leads children towards the solution. In class or at home, problems’ anxiety will be dissipated and children will no longer doubt their abilities!

 

Breaking down problems

90 exercises for overcoming your fear of mathematics

Primary 2nd level (ages 8-10), Lower secondary 1st level (ages 10-11), Lower secondary 2nd level (ages 12-13)

Due to the graphic solutions adopted, the problems do not involve any arithmetic and have a therapeutic value for all those children who mistakenly identify mathematics with the operations of the discipline. The problem-solving skills required are the same ones that children use in their daily lives, outside of school, and are related to their experiences. The graphic and illustrated representation of the problem is simple and facilitates resolution through intuition.

Find out more!

Leaf through some pages of the volume which have been translated into English to facilitate your evaluation of the product:

Breaking down problems with a calculator

99 exercises for freeing children's intelligence

Primary 1st level (ages 6-7), Primary 2nd level (ages 8-10), Lower secondary 1st level (ages 10-11), Lower secondary 2nd level (ages 12-13)

The use of a calculator is recommended in order to overcome difficulties in some of the calculations and to create a more rewarding atmosphere of collective study. The calculator allows children to tackle all primary school problems, even the ones with high numbers, right from the first two years of school.

Find out more!

Breaking down problems with proportions

100 problems to calmly prepare for lower secondary school

The volume is an incursion into the secondary school curriculum for primary school pupils who want to discover it in advance. It is also useful for older children, as review and reinforcement material. The problems contained in this proposal stimulate to choose, at first intuitively, strategies and procedures to be used then consciously, restoring confidence and joy in facing mathematical challenges.

Find out more!

Leaf through some pages of the volume which have been translated into English to facilitate your evaluation of the product: