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## Solve It! Student Thinking: Factor Groups

### big solutions to little problems

Solutions to a December 2012/January 2013 Solve It! problem are discussed, and the procedures used with problem solving are explored.

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## Seeing Spots and Developing Multiplicative Sense Making

Cans on a grocery store shelf and Hirst's Capric Acid Amide can illustrate dot arrays, thus helping students understand the distributive property, partial products, and the standard algorithm for multiplication.

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## Mystery Fractions

This activity engages students in problem solving while exploring key concepts of number theory, such as divisibility and divisibility tests, place value, fractions, and scale factors.

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## The Locker Problem: An Open and Shut Case

The Mathematics Teaching Practices open the door to helping students engage with meaningful mathematics.

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## Mathematical Explorations: Moving beyond Factor Trees

An alternative method for teaching prime decomposition explores using tools rather than factor trees.

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## Math Explorations: Hanging in the Balance

A physical balance scale can be a useful tool to help students understand the concept of balancing equations. However, some students may have misconceptions about the concept of balance even when using a physical model, focusing on the amount of weight only and ignoring the placement of the weight. Although most students at some point in their lives have been on a teeter-totter or seesaw, they rarely connect those playground objects with the mathematical principles involved in using a simple tool such as a lever.

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## Designing an Amusement Park Ride

iSTEM (Integrating Science, Technology, Engineering, and Mathematics) authors share ideas and activities that stimulate student interest in these integrated fields in K–grade 6 classrooms. This month, preservice teachers use Polydron® Revolution kits to design and create an amusement park ride that spins. The lesson integrates engineering design processes with mathematics to explore the concepts of proportional reasoning and least common multiple within the context of gears.

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## Doing Mathematics with Spirograph

. Finding GCF and LCM CCSS.MATH.CONTENT.6.NS.B.4: Find the greatest common factor of two whole numbers. Day 3 Task (see table 4 ) Too often, mathematical concepts are introduced to students in a way that emphasizes only the standard algorithm

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## Pruning Trees

### big solutions to little problems

Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.

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## An Exce-L-ent Algorithm for Factors and Multiples

The L-shaped 2-5-3-7 algorithm, combining efficient Singaporean and Korean procedures with divisibility rules of primes 2, 3, 5, and 7, helps students identify LCMs and GCFs.