Use Appropriate Tools Strategically

The Standard

The fifth standard of mathematical practice, use appropriate tools strategically, is often thought of as a very obvious practice to utilize. Students are using tools in classrooms nearly every single day. However, there is a level of metacognition required to successfully implement this mathematical practice that is above just using a tool to solve a problem. However, tools do not have to be used only for problem solving. They can also be used to represent an equation or to simply explore mathematics. Tools are a natural part of any classroom, any grade level and aren’t only for students that are struggling. All students benefit from the use of tools in a mathematics classroom, no matter where their current level of understanding is. 

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It is important to understand that in this mathematical practice, the word tools represents anything that a student could use to help with their task which could be an exhaustive list. Illustrative Mathematics recognizes that tools can be clustered together and Mike Flynn (2017) has clustered them farther into five distinct categories: supplies, manipulatives, representational tools, digital tools and mathematical tools (p. 107).

• Supplies - school supplies: paper, pencils, whiteboards, scissors, tape, rulers, string, sticky notes
• Manipulatives - tangible, physical objects: interlocking cubes, blocks, geoboards, counters
• Representational Tools - tools that help students see structure within our number system: number charts, number lines, ten frames, line plots, tally marks, number racks
• Digital Tools - these tools could replicate a physical tool or may allow students to show their work in multiple way: calculators, interactive whiteboards, virtual manipulatives, apps, digital scales
• Mathematical Tools - abstract tools category: estimation, counting, place value, derived facts, numerical reasoning

Digital tools can be extremely beneficial in the classroom but also need to be thought about before utilizing all of the time. When they are effectively used, they can streamline the classroom but they can also become a distraction. The last category, mathematical tools, was added because the Elementary Elaborations of the Standards of Mathematical Practices specifically state that estimation, strategies and algorithms are examples of mathematical tools. This abstract concept can be thought of as a student’s mental toolbox that is developed over time.

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Finally, reflection is an important piece of the fifth mathematical practice. After the use of a tool, students should reflect on if it worked the way they thought it would, if it helped them build knowledge and if it was the best one for the job. Constant reflection will continue to build understanding of the different tools that could be used at any given time.

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The Classroom

It is important that students have access to many different types of tools to use for their mathematical practice. However, they need to be taught how to choose the correct tool for their problem as well as how to use it in order to reach their goal. This means that students need to have explicit instruction about what tools are available, the purpose of the tools, and how to use them strategically and flexibly. This does NOT mean that we show them exactly which tools to use in any given situation because as Mike Flynn says in Beyond Answers (2017), “If we make all the decisions for them, we remove the critical component of MP5 where students make decisions based on their knowledge and understanding of the tools and the task at hand.” (p. 106).

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Math discussions are a great way for students to talk about potential tools they can use as well as reflect on the tools that they chose and why they did or did not work. Involve students in discussions about what tools they might choose so that those that have a hard time getting started can see an entry point while those that already know what tool they want to use may hear another strategy. Thinking about what tools to use can be overwhelming for students so teachers can help by being mindful about the tasks that they choose as well as the tools that are available to students for each task. The time we spend discussing how to choose tools and what their purpose is can also be helpful for students. The creation of a tool chart may be beneficial so that students have a reference when thinking about how to get started on a problem.

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Setting an intention and reflection when utilizing a tool are essential for the fifth mathematical practice. Students can ask themselves three questions when problem solving to set an intention and reflect on their task:

1. Do I need a tool for this?
2. Which makes the most sense?
3. Did it work?

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Question Stems

• What tool could you use to find your answer?
• Is there another tool you could use?
• What information do you have?
• What estimate did you make for the solution?
• What do you know that is not stated in the problem?

Picture Books

• How Big Is A Foot? by Rolf Myller
• Gather Your Tools! by Mama B
• The Brilliant Calculator by Jan Lower
• Tooling Around: Crafty Creatures and the Tools They Use by Ellen Jackson

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Next Steps

Now that you’ve got a basic understanding of the fifth Standard of Mathematical Practice, there are many places that you can dive deeper to learn even more. First, “Use Appropriate Tools Strategically, Huh?” by Annie Fetter is from the Math Forum and AMTNJ Ignite event in 2014 at Drexel University from The Math Forum at NCTM’s YouTube page. It is a very short discussion about how we need to teach students how to conceptually understand mathematics using not only paper and pencil but also the digital tools that they have access to. This graphic organizer is a great resource to help plan for the fifth mathematical practice. If you need to help your students with estimation skills, the Esti-Mysteries from Steve Wyborney’s Blog allows you to work through an estimation mystery through Google Slides and he has many available. Finally, Polypad and Desmos are both digital tools that can and should be utilized when it makes sense.

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Sara VanDerWerf, MDE, will also be hosting a webinar for the fifth mathematical practice on December 18th, 2024 at 7:00 AM which you can find by registering here.

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If you’d like more information, support, or guidance on developing a better understanding of Mathematical Practice #1, please reach out to our Math Team here at Resource Training and Solutions.

Mindy Strom

Math Lead

Email: mstrom@resourcecoop-mn.gov

Phone: (612) 505-7997

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Megan Klaphake

Math Coach

Email: mklaphake@resourcecoop-mn.gov

Phone: (218) 770-0026

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References:

^{SanGiovanni, J. (2019). Using the mathematical practices effectively in the classroom. https://www.mheducation.com/unitas/school/explore/research/reveal-math-using-mathematical-practices-effectively-classroom.pdf} 

^{Illustrative Mathematics. (2014, February 12). Standards for mathematical practice: Commentary and elaborations for K–5. Tucson, AZ. Retrieved December 29, 2018 from http:// commoncoretools.me/wp-content/uploads/2014/02/Elaborations.pdf}

^{Flynn, M. (2017). Beyond answers: Exploring mathematical practices with young children. Stenhouse.}