Browse

You are looking at 1 - 10 of 38 items for :

• Manipulatives
• Refine by Access: All content
Clear All
Full access

Construct It! Introducing Integers with Floats and Anchors

Use the Floats and Anchors context as well as physical and digital materials to help students understand integer addition and subtraction.

Restricted access

Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

Restricted access

Visualizing the Arithmetic Mean

The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.

Restricted access

Playing with Fractions

Constraints for social distancing require teachers to find creative ways to engage students. Consider this fun strategy for exploring fraction equivalence, addition, and subtraction in a game environment where students use self-made or digital manipulatives.

Restricted access

Excerpts from discussion threads on the online MyNCTM community

Restricted access

Using Arrays for Meaningful Multiplication

Use Cuisenaire™ Rods to emphasize the column-and-row structure in arrays for meaningful multiplication.

Restricted access

Building number sense with Lego® robots

Lego Mindstorms™ robotics quickly draws children in and provides ample opportunities for engaging them in robust mathematical learning. Two introductory programming tasks empower children to use their creativity and problem-solving skills to build number sense in a fun, engaging learning environment. Contributors to the iSTEM (Integrating Science, Technology, Engineering, and Mathematics) department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms. Send submissions of no more than 1500 words to this department by accessing http://tcm.msubmit.net. See detailed submission guidelines for all departments at http://www.nctm.org/WriteForTCM.

Restricted access

Delving Deeper: Twists on the Tower of Hanoi

A t a party that I attended, the hosts gave their guests the Tower of Hanoi puzzle with alternating dark and light discs and a challenge to move the 7 discs to a new post. (I disqualified myself because I knew how to solve the challenge.) However, the hosts' son and daughter-in-law misunderstood the directions and moved the dark discs to one side post and the light discs to the other side post. I immediately wondered, “How many moves did they take, assuming that they made the most efficient moves? How can their interpretation of the problem be generalized to n discs?”

Restricted access

Postscript: Knock 'em down

This simple dice game supports students' development of flexibility with numbers, the properties of the four operations (+, −, ×, ÷), and the order of operations. It requires only dice and a game board for each player.

Restricted access

Revisit Pattern Blocks to Develop Rational Number Sense

A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.