Extending Mathematical Thinking


Lots of children enjoy math-related activities outside of school, and many families are interested in supplementing their school’s math offerings. Below are some recommendations that would be appropriate for children in the middle childhood years, from approximately ages six to 12. These are activities that are meant to build problem solving skills and extend mathematical thinking. They will not necessarily help a student to accelerate in math, nor will such activities replace in-school math. Rather, these are fun things for a mathematically curious child to try out. You might also find that these games and puzzles help to build confidence for children who believe that math is not one of their strengths.

Many of the puzzles and games mentioned below are available directly from the manufacturers' websites as well as other online retailers. Locally you can find a lot of them at the toy store Child’s Play, which has locations in Rockville, DC, McLean, and Arlington. I also recommend having a look at the museum gift shops of the Exploratorium, a hands-on math and science museum in San Francisco, as well as the The National Museum of Mathematics in New York City. Their buyers are always on the lookout for new educational games.

Spatial Puzzles and Games

Children ages eight and older may enjoy puzzles and games that challenge their spatial sense. One such puzzle that can be worked on alone or competitively is Tangoes, a tangram-style puzzle. The object is to use provided plastic tiles to recreate silhouettes pictured on cards within the set. For those looking for a three-dimensional puzzle, Kanoodle or Kanoodle Genius may be of interest. This puzzle has seven interlocking pieces that can be combined to make 202 shapes pictured on challenge diagrams included with the set. The diagrams show how to get started, then it is up to the player to figure out how to place the remaining pieces to complete the pictured design. Easier problems are two-dimensional, while more complicated problems are three-dimensional and involve building pyramidal shapes. Children who like card games may enjoy Swish, which is played with transparent cards featuring colored balls and hoops. During game play, players layer the cards on top of each other to match the balls into hoops of the same color, a “swish.”

Games with Number Operations

Once students are comfortable with addition, subtraction, multiplication, and division, they may enjoy playing games that use those computational skills. One such classic is the 24 Game. There is no limit to the number of players, and individuals can even challenge themselves. The goal is to use the four numbers on a card to make 24. Each number can only be used once. Some may solve a puzzle card in seconds, while others may work on more advanced puzzles for several minutes. If you have two to six players handy and up to 30 minutes to spare, you might enjoy the card game Math Fluxx. The rules are little tricky because the object of the game changes during every turn, but it is a game that one can learn quickly. For those who like board games, there is Equate which is analogous to Scrabble but with number operations. Equate is one that I keep around my own house and occasionally challenge my husband to play. This one takes a little more time for a full game, so it’s a good one for family game night. It also involves fractions, so it’s best for students in the second half of fourth grade and older. Some children may also prefer to play in teams with adults who can assist with trickier operations.

Logic Puzzles

Not only are logic puzzles fun to figure out, they help to build problem solving skills. You may want to try the Mind Benders series. which come in many different levels for all ages. They are also available in formats from ebook to printed. I also like grid-style logic puzzles. In these puzzles a very few clues are given. The puzzle solver must then use deductive reasoning to make several matches based on relatively little information. There are numerous free puzzles at websites such as Brainzilla. If you want to buy book versions, try Amazon, your local toy store, or Teachers Pay Teachers.

Online Math Games

If you pop over to Google to search for “math games,” you might be underwhelmed by the results. Many of the sites that you will find are covered in ads, and some of the games are not particularly fun. So skip the searching and go directly to the Greg Tang Math website where you will find a good assortment of ad-free math . Many of these are designed for younger learners who are mastering subitzing and basic addition skills. Some more advanced first and second graders may enjoy Math Limbo, as it can involve making sums with multiple numbers. If any of the games on the website are a hit with your child there are also resources that you can order from Greg Tang's online store. Families with older children who are ready for pre-algebra may like Calculation Nation. Though one has the option of registering on this site, clicking on “guest pass” gives you unlimited game play without having to offer up any personal information. You will, however, need the latest version of Flash to play. Students in 5th through 7th grades will may enjoy trying out these games that involve adding fractions, summing positive and negative integers, using a coordinate grid, and maximizing area with a given perimeter among other math skills.

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