Grades 6–8 Math Activities

Logic problems are fun and challenging, both to create and to solve. Logic problems involve organizing clues and drawing conclusions, being careful to base all conclusions on the information. Logic problems develop great thinking skills and can be a lot of fun!

	Pencil and paper

Begin by working with your child to solve this problem:

John, Jack, Jerry, and James are four brothers who play sports. They all participate in track, basketball, baseball, and football, but each brother has his own favorite sport, which is different from each of the other brothers' favorites. Use the following clues to determine each brother’s favorite sport.

	Jerry doesn’t like sports that begin with “B.”

	Jack likes playing sports with balls, but his favorite ball isn’t perfectly round.

	James’ favorite sport does not involve shooting a ball through a hoop.

It may be possible to just talk through these clues and come up with the answer. However, if your child is struggling, you might want to suggest creating a chart like the one shown here.

This chart can be used to eliminate possibilities, which can lead to more informed and organized conclusions. For example, the chart could be marked as follows to represent the clues. Each “X” means that possibility has been eliminated, and “O” means that possibility has been chosen.

Once the clues have been recorded, you can start to draw conclusions. Jack’s favorite sport is football, since it is the only sport with a ball that is not round. Once you draw this conclusion, all of the other sports can be eliminated for Jack, and football can be eliminated for the rest of the boys. Jerry's favorite then becomes obvious. You can continue in this way until exactly one sport is chosen as each boy's favorite.

Logic problems can range in difficulty from fairly simple to very complex. Here is an example of a problem that is more complicated that the first example.

Four friends – Ally, Ben, Cheryl, and Dan – had a party. Each person brought a game and a snack. At the party, they played Monopoly, chess, checkers, and cards. They snacked on chips, nuts, pretzels, and candy. Unfortunately, they have forgotten what each person brought at the end of the night when it is time to bring the games and leftovers home. Use the following clues to help them figure out what each person brought.

	Dan is allergic to nuts and doesn’t own any board games.

	Ally likes salty snacks and games with red and black circular pieces.

	There were some pieces of candy found in the chess game, so the person who brought chess must have also brought the candy.

	Cheryl loves games that have to do with buying and selling things.

	Neither Dan nor Ally like chips.

For this problem, your child will probably want to make a chart. There is just too much information to be sorted through without using an organizational chart.

Since there are three variables to organize, the chart will be a little more complex as well. Here is one possibility:

After working on these logic problems, you and your child can start making up some of your own. Make sure that you provide enough clues in your problems to make them solvable. The trick is to give just enough information to make a problem solvable without making the solution obvious! (Hint: begin with a solution organized in a chart and work backwards.) Solving and creating logic problems will give your child a helpful foundation in analytic reasoning.

 Grades 6–8 Math Activities