Mathematics may viewed as a subject that always has one correct solution and one best solution strategy. In order for students to develop conceptual understanding for procedural fluency, building mathematical reasoning is essential through seeing multiple strategies for approaching problems. Open-ended questions can develop children’s number sense and help them be adaptable, problem-solvers, and good communicators. Open-ended problems encourage discussion and exploration. They show that mathematics can involve creativity and also demonstrate how mathematics is relevant and realistic.

For example, one open-ended question is how many ways can you represent 28? There are a number of ways to do this and below are just a few.

Students can develop number sense, estimation, and mathematical reasoning through open-ended questions. They can also help students be curious about the world and learn how to problem solve, which is the basis of good mathematical thinking. Making estimations, predictions, and thinking about other ways that daily things can be done can help students do well in mathematics. The table below has examples of open-ended questions that parents could discuss with their child. Mathematics is not a spectator sport and children should get used to the idea of being an active learner for mathematics. 

This activity integrates children’s literature, engineering design, mathematics, and English language arts. The children’s book I wrote helps students learn more about engineering and biomedical engineering. Biomedical engineering is an interdisciplinary STEM field that combines biology and engineering to create solutions for medicine and healthcare. English language arts standards are incorporated through reading the children’s book and a class discussion about the book. After reading the book, students work on an engineering design challenge to design and build a prosthetic leg. Mathematics is incorporated through measurement.

After readings students the book, The Little Engineer That Could, ​the teacher then leads a class discussion using the following questions. Alternatively, these can be used as individual writing prompts. Describe Cadence and her feelings throughout the story. What was her motivation for helping Danny? How did her actions contribute to the sequence of events in the story. How did Cadence respond to challenges that arose?

To begin the design challenge students watch the following video about the Invictus Games. The Invictus Games is an international sporting event for wounded, injured and sick Servicemen and women. The Games strive to use the power of sports to inspire recovery, support rehabilitation and generate a wider understanding and respect of all those who serve their country.

After watching the video, students answer the following questions.

1. Why do you think the Invictus Games are held? 
2. Do you know anyone who has been injured, sick, or hurt? 
3. Why is important to help and encourage others? 
4. Have you ever done something that was difficult? Why is it important to keep putting forth effort and to not give up?

Challenge
Sergeant Danny Mendez is participating in the Invictus Games. He wants your team to develop a comfortable leg for walking around the games when he is not competing. As a first step you will design and build the leg for one person in your group to test your prototype.
 
Criteria and Constraints
There are three criteria for the design. 1) The leg should be comfortable. 2) The leg should be sturdy and stable. The person in your group must be able to walk 10 feet with the prosthetic leg. 3) The prosthetic leg should be aesthetically pleasing (look good).
 
Rubric for criteria 1)
1 point- leg is not comfortable and causes pain.
2 points- leg is mildly comfortable with little discomfort or pain.
3 points- leg is comfortable with little discomfort and no pain
 
Rubric for criteria 3)
1 point-leg is not aesthetically pleasing
2 points- leg is somewhat aesthetically pleasing
3 points- leg is aesthetically pleasing
 
The constraints are that you can only use the provided materials and that you have 60 minutes to design and build the prosthetic leg.
 
Materials
Your group will have scissors, measuring tape, and a ruler.
 
-Duct tape
-cardboard tube
-pvc plastic pipe
-large rubber bands
-toliet plunger (unused)
-wood board
-sponge
-bubble wrap
-cardboard
-string
-rope

Mathematical discussion is important so that students can learn from each other and explain their thinking. There are 5 practices for teachers to orchestrate productive discussion. A brief description of the 5 practices is below.

1. anticipating likely student response to challenging mathematical tasks;
2. monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups);
3. selecting particular students to present their mathematical work during the whole-class discussion;
4. sequencing the student responses that will be displayed in a specific order;
5. connecting different students’ responses and connecting the responses to key mathematical ideas. (Smith & Stein, 2011)

After implementing a mathematical task teachers can reflect on the implementation using the questions below. 

-What was the big idea we worked on today?

-What did I learn today?

-What good ideas did I have today?

-What did I struggle with today?

-Where could I use the knowledge I learned today?

-What questions do I have about today's work?

-What new ideas do I have that this lesson made me think about?