07 AUG 2017 by ideonexus

## The Double Multiplicative Nature of Fraction or Ratio Equ...

Most real-world numbers aren’t always so nice and neat, with wholenumber multiples. If, say, Plant A grew from 2 to 3 feet, and Plant B grew from 6 to 8 feet, then we would say that Plant A grew 1/2 of its original height, whereas Plant B only grew 1/3 of its original height. Such reasoning exemplifies multiplicative thinking and necessarily involves rational numbers. Consider a final example. If you ask a rising 6th grader to compare 13/15 and 14/ 16, chances are that the student will say...02 SEP 2016 by ideonexus

## Math Exercise: Multiple Approaches to Problem-Solving

For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-...02 SEP 2016 by ideonexus

## Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...09 AUG 2014 by ideonexus