The current reality in education is that as teachers we have a lot to teach in a short period of time. It is not feasible to give up large chunks of math instruction in order to prepare students for math workshop. Rather, minilessons are designed to complement your math instruction.
Overview
In this lesson, students are given the opportunity to explore and discuss the various tools and manipulatives they might use in math workshop.
Math tools are items that are used for a specific purpose (e.g., ruler to measure length, protractor to draw/measure an angle). Understanding the use of tools is a valuable part of mathematical thinking; this is emphasized in the fifth Common Core State Standards for Mathematical Practice, which reads “Use appropriate tools strategically” (National Governors Association Center for Best Practices and Council of Chief State School Officers 2010).
Manipulatives are items that will help support a student’s thinking by representing an abstract math concept in a concrete way. Manipulatives should be available for students in many, if not all, settings in their elementary, middle, and high school years. Don’t be tempted to show students exactly what to do with manipulatives or even which ones to use in all situations. Doing so may result in you having taught students a procedure rather than allowing them the opportunity to explore. Van de Walle and colleagues in Elementary and Middle School Mathematics: Teaching Developmentally, warn us that, “A natural result of overly directing the use of models is that children begin to use them as answer-getting devices rather than as tools used to explore a concept” (2010, 29).
That being said, providing a student with a calculator or a manipulative does not mean that they know how to use them. Students may not use tools and manipulatives strategically, efficiently, or effectively without an appropriate introduction to them. Students need time to explore using tools and manipulatives before using them as part of learning. This lesson provides an opportunity for students to get to know these items, recognize the differences in them, explore the items just as students explore a math concept, and determine when they would be useful.
Materials
- math tools: collection of calculators, rulers, protractors, compasses, multiplication charts, and any other grade level- appropriate tools
- math manipulatives: collection of blocks, counters, dice, connecting cubes, geoboards, cards, and any other grade level-appropriate manipulatives
Directions
Whether you are working collaboratively or independently, you may choose to use tools or manipulatives to help you with math. A math tool could be a calculator, ruler, protractor, and so on. A math manipulative is something that you use to create a visual representation of a mathematical concept. For example, you might use counters or cubes to help you think through a concept or a problem. What are some math tools or manipulatives that you have used in the past? Have students generate a list.
There are times that tools and manipulatives can support our mathematical thinking and there are times that tools and manipulatives will not be needed. It is important that we talk about how we use these items so you can determine what items help you learn the best.
Today, we will look at one or two tools/manipulatives that I know we will be using this year.
Select the appropriate content from the following to address the specific tool or manipulative being introduced to students.
Math Tools
Let’s think about how a ruler and calculator can be helpful to us in math. Tell your partner about the value of these two tools. What are some things that we need to remember and think about when using these tools? For example, are all rulers the same? All calculators? Is the answer on the calculator always going to be correct? How will we know?
Ask students to share with a partner about a time that they used a tool to help them in mathematics.
Math Manipulatives
While manipulatives may remind you of toys, they’re not for pretend play or games. They’re useful tools for understanding complex concepts in mathematics. Let’s take time to investigate some of the math manipulatives that we will be using this year so when we use them in class, you will be ready to use them properly.
Please take the next five minutes (adjust time to fit the needs of your class) to explore the manipulatives that have been placed at your table. As you explore each manipulative, think about what it looks like, feels like, and what it can do to help you. Have you ever used something like this before? If so, when and how?
Once students have had an opportunity to explore, ask them to share with the group what they noticed about the manipulatives and how they might use them in the future.
