## MATHEMATICS FOR KIDS

Collecting thoughts and ideas to foster mathematical learning and mathematical amusement.

This being said, I now present some toys that you can buy (or lend, or share..) if you like them: your kid may like some of them, expecially if everything is kept playful (and if for example the kid decides how long or when to play). The opinions and recommendations are my own, and in general you should try to follow your kid's inclinations and your gut feeling as a parent. If nothing is imposed, then nothing can go really bad: a kid likes presents and colorful stuff, and the worse that it can get is that the toy is not appreciated (if this does not bother you with other kind of toys because it can be a matter of luck, then it should not bother you with mathematical toys as well). Most toys can be used for several kids, and can be sold or given away when not needed anymore. Last but not least you can consider some of these toys as cool presents for a birth or a birthday.

### 1 - Geometry Puzzle

A puzzle with solids. Various prisms have to be inserted into various holes: the correct hole is the one in the shape of the basis of the prism. The bases of the prisms are polygons, stars, ovals and so on.
• Some variants only have three shapes, namely circle, triangle and square.
• Check the parents' recommendations of the toy, because it happens with some versions that a shape fits more than one hole. This is very inconvenient if the kid finds out.
• A variant of this game consists in placing the solids onto a frame rather than inside a box. To vary the toys I recommend the box (for puzzles on a frame animals and numbers are more interesting).

### 2 - Number Puzzle With Frame

Quite popular is a wooden frame where some numbers (usually, from 1 to 10) are carved and they can be taken out as puzzle pieces.
• I recommend a version having for example 8 fishes below the number 8: not only this gives a surprise effect, but it also helps associating a number to a set having that number of elements.
• My favourite is a version with the numbers from 0 to 9 instead, not only because these are precisely all the digits, but also because kids have an occasion to learn the number 0 (and they easily see that zero corresponds to nothing).

### 3 - Two Pieces Number Puzzles

Puzzles again, but with cards. The numbers (usually from 1 to 12) have to be associated to a set with the corresponding number of elements.
• Keep it simple with two pieces! Some puzzles have three or more pieces because they also show some dice with the corresponding number of dots, or hands displaying the correct amount of fingers. The dice cards are not bad, but it is better to put them away until the kid is at ease with associating numbers and sets. The hands cards are in my opinion ugly and unnecessary.
• The first game is associating numbers to sets. The second game is ordering the number puzzles by placing the displayed numbers in increasing order.
• I particularly liked a version in which the cards were quite small, perfect for the small hands of a kid.

### 4 - Matching Game

Objects have to be sorted, or they have to be associated to appropriate sets.
• Anything is allowed to play with sets (strictly mathematically speaking, one is playing with multisets as soon as some elements are indistinguishable). The sets are distinguished by characterizing properties (the color, the kind of animal, and so on).
• If one plays with sets with few elements, then one can also practice numbers and counting.
• Be open to the toys that you find: if you like them (didactically and aesthetically), then you will be happy to play with your kid. And your kid may like them too. But if you don't believe in something, then of course nothing is strictly necessary. For example some parents like to have many small colorful bears and colorful cups for the counting/sorting game, and that's totally OK.

### 5 - The Number Staircase

If you have stairs of your own, then consider number stickers. If you have the occasion to play with a staircase, then place number cards on the steps.
• You can count the numbers while going up. When your kid is confident enough with the number sequence, you can count numbers backwards by going downwards.
• You can experience additions and subtractions by letting your kid for example mount two steps or go down two steps. In the same way, you can make your kid discover even and odd numbers.
• I recommend starting with the number sticker (or the number card) zero placed on the floor in front of the first step.

### 6 - The Numbers Weight Scale

A weight scale with two plates (and number items with the appropriate weights).
• You can practice counting and explore equalities and inequalities with a weight scale with two plates and many small identical objects.
• I like a version where there are numbers as objects: they weigh proportionally to their value, and you have further identical objects weighing like the number 1. It is very easy to explore addition and subtraction (only the correct number on the plate will give balance).
• By having different sets of objects with appropriate weights, one could explore some easy equations. By having weights corresponding to the powers of 2 and 3 one could explore the numeral bases 2 and 3 (working with base 10 is possible but the numbers up to 20 show less variation in basis 10 w.r.t. basis 2 and 3).

# CONTACT

This page is a long-term work-in-progress dedicated to learning material that can be used beyond school.
The recommendations are of mathematical and didactical nature.