“Today we thought about different ways to find the values of sums and differences of fractions and mixed numbers, and whether it is helpful to decompose one of the numbers or to write equivalent fractions.”
“In the last activity, how did you sort the expressions? How did you know, without doing any computation, whether it would be necessary or helpful to decompose a number?” (For subtraction expressions: We looked at the numerators of the first and second numbers. If the first number is greater, there is no need to decompose. If the first number is a whole number, it is helpful to decompose it. For addition expressions: We looked at whether the fractional part of each number would add up to more than 1. If so, it may be necessary to decompose the sum to write a mixed number.)
Highlight that there are numerous ways to start adding and subtracting fractions. Depending on the numbers at hand, it might make sense to decompose or write an equivalent fraction for one or both numbers, to count up or count back, to add or subtract in parts, and so on.
