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April 2012, Volume 17, Issue 8


Less is More
Rong-Ji Chen
Provide less guidance to students and engage them in challenging mathematical tasks.

What Is the Difference? Using Contextualized Problems
Erik S. Tillema
Real-world situations involving layers of subtraction will help students in their future work with algebra.
Second Look:
Subtracting with Integers

Where Are the Congruent Halves?
Samuel Obara
Try this activity that requires creating two polygons from one to apply knowledge of congruency and transformations and develop spatial reasoning.

Putting Mathematical Discourse in Writing
Sararose D. Lynch and Johnna J. Bolyard
A problem-solving pen pal project between preservice teachers and sixth graders presented a lens through which a sixth-grade teacher could view students’ work and her instruction.

Closing in on Proof
David A. Coffland
Questions about closure on sets of numbers provide a context for hypotheses and proofs.

Second Look - Subtracting with Integers

Subtraction of Positive and Negative Numbers: The Difference and Completion Approaches with Chips
An illustration of how the difference and completion (or missing addend) interpretations of subtraction may be used with chips of two colors to understand subtracting negative and positive numbers. Several visual representations are provided.

The Value of Debts and Credits
Promote discussions on integers in real life by using positive and negative numbers in the context of net worth.

Integer Operations Using a Whiteboard
Integrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding.

What Are You Worth?
Use concepts from finance, specifically, assets and debts, to give students a real-world understanding of integer concepts and operations.

Illuminations Lesson: Zip, Zilch, Zero
Positive and negative numbers become more than marks on paper when students play this variation of the card game, Rummy. Engaged in a game involving both strategy and luck, students build understanding of additive inverses, adding integers, and absolute value.

Number and Operations Standard for Grades 6-8

In grades 6–8, students should deepen their understanding of fractions, decimals, percents, and integers, and they should become proficient in using them to solve problems. By solving problems that require multiplicative comparisons (e.g., "How many times as many?" or "How many per?"), students will gain extensive experience with ratios, rates, and percents, which helps form a solid foundation for their understanding of, and facility with, proportionality. The study of rational numbers in the middle grades should build on students' prior knowledge of whole-number concepts and skills and their encounters with fractions, decimals, and percents in lower grades and in everyday life. Students' facility with rational numbers and proportionality can be developed in concert with their study of many topics in the middle-grades curriculum. For example, students can use fractions and decimals to report measurements, to compare survey responses from samples of unequal size, to express probabilities, to indicate scale factors for similarity, and to represent constant rate of change in a problem or slope in a graph of a linear function.