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 Grade 8 Math Activities

Logic Problems

Logic problems are fun and challenging, both to create and to solve. They 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!

Here's what you need:
Pencil and paper
Here's what you do:

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 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 talk through these clues and come up with the answer. However, if your child is struggling, suggest creating a chart like the one shown below.

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 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 range in difficulty from fairly simple to very complex. Here's an example of a more complicated problem:

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, at the end of the night when it was time to bring the games and leftovers home, they had forgotten what each person had brought. Use the following clues to help them figure it out.

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 involve buying and selling things.
Dan and Ally both don’t like chips.

For this problem there is much information to sort through, so it is best if your child makes a chart.

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

Keep going...

After working on these logic problems, you and your child can make some of your own. Make sure that you provide enough clues to make the problems 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.

 Grade 8 Math Activities

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