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Math Monthly

October 2021:

October’s Standard: Look for and make use of structure

  • Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.
  • It's Important to give students a chance to "play" with these properties, and even to help them discover them for themselves, rather than just memorizing them as a "rule," so that they can transfer their understanding to progressively more complex problems. Use concrete representations such as physical manipulatives or area models whenever possible to help students see these properties at work.

October’s Vocabulary:

Property: feature or features, characteristic or characteristics. A property may relate to numbers, operations, values, shapes and other mathematical items.  The properties of operations are the rules that set down particular properties in relation to operations on numbers.