A-maze-ing Fractions - Mathcounts

N EW! A-maze-ing Fractions Navigate a maze while adding, subtracting, multiplying and dividing fractions. This activity allows students to explore what happens when you add, subtract, multiply or divide fractions greater than and less than 1. Does the value increase or decrease? Operations with fractions are often hard for students to conceptualize. With this activity’s dry erase maze boards and four basic arithmetic operations, students can begin to uncover the secrets of fractions by finding a path that results in the least value or the greatest value. They can try alternative operations, numbers and paths. They will see what makes the value grow and what makes it shrink. MATERIALS NEEDED Maze Board (one per student or group—five are included in your Club in a Box kit) Dry erase marker (one per student or group —included in your Club in a Box kit) Maze handout (optional if not enough Maze Boards—one per student or group)* Scratch paper and pencil (optional) *Included in this Club Activity Book and available for download at www.mathcounts.org/clubleaders OPERATIONS WITH FRACTIONS Depending on how comfortable students are in performing arithmetic operations with fractions, you may want to do a mini lesson or refresher before the students attempt to solve the maze. Discuss what happens with each of the four operations when the number being added, subtracted, multiplied or divided is greater than 1 and when it is less than 1. When will the value increase? When will it decrease? Why is it increasing or shrinking in each case? Perhaps drawing a chart like the one shown here at the right will help. – 1 inc. dec. inc. dec. 1 inc. dec. dec. inc. MAZE INSTRUCTIONS The maze begins with the value inside the hexagon labeled “Start,” at the top of the board. To navigate the maze, students move downward along the diagonal paths and left-to-right or right-to-left along the horizontal paths. Students cannot retrace any paths they have already used and cannot move upward along the diagonals. Using the dry erase marker (or pencil if using a printed handout), students should trace their path through the maze. In each hexagon, they should write the resulting value after performing the operation on the path they just traced. Have the students write their values as common fractions or mixed numbers only. It is also suggested that they perform their operations without the aid of a calculator, but this is at the discretion of the Club Leader. Before starting the maze, encourage students to take a look at all their path options and think about a strategy. Ask them to consider the following questions: What paths will increase their value? What paths will decrease their value? Which path produces the largest increase? Which path produces the largest decrease? MAZE SOLUTIONS Five Maze Boards are included in your Club in a Box kit. On the front of the Maze Board is Maze #1 and on the back of the Maze Board is the Blank Maze. These and the two additional numbered mazes are in this Club Activity Book and are also available for download online. You can print copies of these mazes or have students fill in the Blank Maze to match the additional mazes. The Blank Maze on the dry erase board allows this activity to be used an endless number of times! We have provided the solutions for the path to the largest and the path to the smallest number for each of the three mazes shown on the next two pages. 2016-2017 MATHCOUNTS Club Activity Book 9

Start /2 1 /8 1 /4 /3 1 /2 3 /4 5 /5 2 /6 1 1 – /3 / 2 3 1 /3 / 2 3 1 /5 2 1 3 /4 1 – 3 /4 5 / / 1 3 / 1 10 3 /4 – / 1 10 3 /10 3 /5 1 6 Finish / 2 1 2 1 15 / 2 2 3 / / 1 3 3 /4 / 1 3 /6 – 1 15 1 /4 /8 1 /3 1 / 2 3 / / /3 1/2 – /2 1 /4 3 /2 / 1 3 2 3 / 1 2 / – / or 28/15 38 15 / or 84/9 / or 81/9 –1 3 4 / 2 3 / / or 114/15 3/5 73 9 Start 1 1 3 76 9 – / – 10 /3 Start 29 15 0 Maze #2 Smallest Value Solution: 1/2 1 Finish 1 2 / 1 2 / 2 – –1 3 4 / 29 30 4/3 Finish Maze #2 Largest Value Solution: / / 1 4 2 / or 441/6 4 5 3 1 0 /3 or 422/3 128 1 /4 1/4 2 265 6 Finish / / / 1 2 4/3 32 / 1 2 1 12 2 3 2 3 2 / or 11/2 3 2 1/4 Start 1 3 /10 1 24 Maze #1 Smallest Value Solution: – Maze #1 Largest Value Solution: / 1 9 2016-2017 MATHCOUNTS Club Activity Book

Start /3 2 /10 1 /8 3 /3 1 – /2 1 /8 3 1 /10 1 /3 1 – / 5 6 1 /2 /9 1 – 1/3 2 1 / 7 8 / /9 557 Finish 1 8 / 5 4 4 – 1 /4 7 / 1 8 / 5 6 /18 or 3017/18 /9 2/5 /12 or 115/12 /9 or 304/9 274 / 137 /6 or 11/6 7 1/3 2 / / 5 4 – 1/3 /18 7 7 8 /3 or 112/3 – 1/4 1 6 /6 or 11/6 2 35 / 1 6 7 1/3 Start 1 /3 1 2/5 Maze #3 Smallest Value Solution: Maze #3 Largest Value Solution: /18 11 Finish DO MORE WITH THIS ACTIVITY It is really easy to do more with this activity! Here are some ideas: Play to obtain different values—such as closest to 1 or closest to 2. That way, the same Maze Board can be used over and over again! Change the rules—for example, by allowing path moves to go up! Create your own mazes! We have included template mazes so you can fill in your own numbers and operations. Try decimals or mix decimals and fractions. Also feel free to create new mazes completely from scratch! Make this an outside activity! Draw a large maze with sidewalk chalk outside on the blacktop. Students can solve the maze there and write out their work in chalk! 2016-2017 MATHCOUNTS Club Activity Book 11

A-maze-ing Fractions Start 1 / /2 2 3 1 Navigate a maze while adding, subtracting, multiplying and dividing fractions /8 1 1 –1 / 3 4 /4 1 /3 2 – 3 1 / 1 2 / 1 2 – /4 1/4 3 / 2 3 Finish /2 4/3 – 1 inc. dec. inc. dec. 1 inc. dec. dec. inc.

A-maze-ing Fractions EW! Navigate a maze while adding, subtracting, multiplying and dividing fractions. This activity allows students to explore what happens when you add, subtract, multiply or divide fractions greater than and less than 1. Does the value increase or decrease? Operations with fractions are often hard for students to conceptualize.