Open-Ended Math Tasks

A powerful, effective and easy way to differentiate in math is through open-ended tasks.  Open-ended math tasks teach your students valuable mathematical problem-solving skills while deepening student engagement, understanding and retention.

Open-ended math tasks…

  • Do not have one right answer
  • May be completed at different levels and in different ways
  • Empower students to make mathematical decisions
  • Engage students in productive struggle to build understanding
  • Encourage student creativity

Open-ended math tasks may be used in guided math lessons where the teacher can support and coach students as they work on the task and share their ideas. Open-ended math tasks may also be used at work stations with students working independently or collaborating with a team. Teachers can also use open-ended math tasks for assessment. The three categories you may use to assess the tasks are:

  • Complexity: The work matches the level of the student
  • Correctness: All math terms, computation and information is correct.
  • Neatness: Completed task is neat and easy to understand

Here are some ways to develop open-ended math tasks that do not take a lot of teacher preparation. You may click here to download the 10 open-ended math task cards shown in the image above.

  1. Compare and Contrast: Students choose two numbers, shapes, graphs, etc and explain in writing and diagrams how they are alike and different.
  2. What’s the Question? Students are given the answer and then they write a word problem with a question for the answer. This task card could be given to students at any grade level.  math task zombies
  3. What’s the Answer and the Question? Students choose a number to put in the blank and create a word problem for their answer.math card marbles
  4. Use These Words and Numbers: A little more challenging open-ended task is to give students some words and numbers to use in their word problem. This is a great way to have students to use math vocabulary.
  5. Modify Closed Word Problems: You can use some of the closed word problems for your grade level and remove some of the values to create open-ended math tasks.
  • Closed: Taylor has 854 baseball cards, and Kyle has 928.  If Taylor and Kyle combine their baseball cards, how many cards will there be? 
  • Open-Ended: Taylor has lots of baseball cards, and Kyle has even more cards than Tyler. If Jade and Kyle combine their baseball cards, how many cards will there be?
  • Closed: Bobby saw 3 cows, 2 horses and 6 chickens at the farm. How many animals did Bobby see at the farm?
  • Open-Ended: Bobby saw some cows, horses and chickens at the farm. How many animals did Bobby see at the farm? 
  • Closed: In the fish tank there are 28 fish. One fourth of the fish are goldfish. How many goldfish are in the tank. 
  • Open-ended: One fourth of the first in the tank are goldfish. Draw a picture of the fish in the tank.

6. Close or Almost: Using these words on math tasks gives students many more possibilities for their answers.   

  • Add two numbers where the sum is almost 25. What could the numbers be?
  • Subtract two numbers then add a third number where the answer is almost 30. What could the numbers be?
  • Multiply two numbers where the product is close to 500. What could the numbers be?
  • Divide two numbers then multiply a third number where the answer is close to 100. What could the numbers be?

I hope your students enjoy using open-ended math tasks!

Happy Teaching!