Math Mazes
By Michael Naylor

For more of Michael's "Counting Mazes" click here. PDF 9KB

Mazes are not only a lot of fun for students, but they also build spatial sense. You can get even more value from mazes if you combine maze ideas with concepts from number and operation sense.

Counting maze (Kindergarten)
Draw a grid (4 x 4 or 5 x 5) and make a path of counting numbers from one corner to another, moving up, down, right or left. Fill in the empty squares with other numbers to hide the path.

Have your students try to draw the path. They can start with a number other than 1, or have the numbers follow a skip-counting pattern by twos or fives.

Grid maze (Grades 1-8)
For this maze, students are given a 5 x 5 grid of random numbers. They must find a path from the top left corner to the bottom right, moving only down or to the right, so that the sum of all the numbers in the path equals a target number.

Once students have tried this maze, it's easy for them to make their own to challenge their classmates. Start by creating a 5 x 5 grid of random numbers. In this example, we'll use only the numbers 0-5. Draw a path through the maze (moving only down or to the right) and add up all of the numbers on the path. Write this number next to the ending box.

Give your students copies of your maze and challenge them to find a route giving that sum. There may be more than one way to do it!

With younger kids, use just the numbers 0-4. If you have older students, try making a multiplication maze. Students can use their knowledge of factors to help them find the route. For example, in the next maze on page 40, students may notice that 270 has 10 as a factor, so the route must contain a 5 and a 2. This makes it easy to find the proper route!

100-chart maze (Grades 1-3)
In this game, students recreate a mystery path on a hundreds chart by following addition and subtraction directions.
Give your students hundreds charts and a set of small counters they can use to mark the path (this way they won't have to draw on the charts). Ask them to start with a counter on the number 1. If you tell them "+5," they should then place five counters, counting up to the number 6. If your next command is +30, they will then place three counters vertically, counting +10, +20, +30, to reach the number 36. Your students will be building place-value relationships between the ones and tens digits.

Try the following patterns with your students and ask them to describe the pattern afterwards.

Stepping: +2, + 20, +2, +20, repeat
Weaving right and left: +9, +10, -9, +10, repeat
Loops: +3, +30, -1, -10, repeat
Spiral: +9, +90, -9, -80, +8, +70, -7, -60, +6, +50, -5, +40, -4...

100-chart maze (Grades 1-3)
This is a game for two students. One student places 20 counters of one color randomly on the grid (at least one counter in every column) except on the numbers 1 and 100. He or she then places a differently colored counter on 1.

The second player must then give directions to the first player to tell him or her how to move the playing piece to reach 100. Make sure your students know that the directions must be plus or minus in units of ones or tens (for example: "plus 50, minus 2, plus 20, plus 6").

Once the playing piece reaches 100, he or she must now give directions to get back to 1. Players then switch roles. As a variation, have the second player write the directions ahead of time. He or she must now use spatial reasoning along with place-value sense to navigate the maze – a fun challenge!

Decimal maze (Grades 4-8)
Supply a copy of a grid of numbers as shown below or draw a similar grid on the board. Give a starting number and four layers of decimal numbers between 0 and 5. Be sure there are plenty of numbers between 0 and 1.
To navigate this maze, students should be allowed to use the four operations, +, –, ÷ and x, one time each, as they move from number to number. The goal is to create the greatest possible result at the end of the maze. Allow the use of calculators and be sure to have students press the "=" key after each operation.

Discuss strategies afterwards – there will be some surprises! It's obvious that multiplying by a large number is a good move, but it''s less obvious that dividing by a small number is also a good move. This maze helps develop operation sense, especially with multiplying and dividing by decimal fractions.

For more of Michael's "Counting Mazes" click here. PDF 9KB

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.