During the approximately 5 1/2 hours we spend over three days working on math, we cover some serious ground. Your kids amaze us every day, and we are very excited about their progress!
At the start of the year, students learned that in order to combine (or add), they must have like terms. During this past month, students have connected this knowledge to expressions in which the values that are numerated are unit fractions.
That is to say, we moved from expressions such as:
5(2) + 4(2) **These are like terms because we are counting 2's in each of the two terms.
5(2) + 12(3) **These are unlike terms, but we can substitute so that we DO have like terms.
5(1/2) + 12(1/3) **We had been counting whole numbers, but now we are counting fractions. And we can substitute so that we will have like terms.
Students have explored fraction equivalents so that they can apply the substitution principle in order to create like terms. Once they have like terms, they know they can combine the terms.
Students have also extended their understanding of fractions by considering how fractions relate to a whole. For example, if we have 3 items and we form a group -- or one group of three items -- each item becomes a third of the group. We must now think of each item as 1/3. And following this logic, we now have 1/3 and 1/3 and 1/3, which together create the group (one whole).
Thus, 51 partitioned into groups of three is viewed as 51(⅓). This is the concept of division: 51 divided by three is a count of 51 of ⅓. Creating groups of three one-thirds is the means by which to determine the number of groups.
Next up: Using landmark numbers, such as groups of fives and tens, to facilitate our number reasoning. 3 (10(1/3)) = 30(1/3)=10(1).