This week we explored combinations to add to certain values. For example, 7 can be thought of as 0+7, 1+6, 2+5, 3+4 4+3, 5+2, 6+1, and 7+0. We saw how the Associative Property of Addition plays out with the order of addends, 4+3 = 3+4. We also looked at the big idea of compensation or give-and-take; if we start with 2+5, take one from the 2 and give it to the 5 we now have 1+6. This type of thinking will help us develop the give-and-take strategy later on when we might add 48+37 as 50+35 by taking 2 from 37 and giving it to the 48.
This week we used a new context of parcels (boxes of 10 presents) and presents (1 unit) to solve story problems involving addition and subtraction of two-digit numbers. We also used number lines to represent our thinking.
This week we continued to explore equivalent fractions. We are spending a significant amount of time on developing equivalent fractional relationships, much the same way we spent our early years building additive relationships in single digit numbers (see the Math 1 paragraph above). We want to develop the sense that 1/2 = 2/4 = 8/16, or 2/3 = 8/12 = 4/6.
This week we used ratio tables to multiply decimal and fractional amounts. We watched a video about Pascal's Triangle and the resulting patterns.
This week we finished the unit Comparing Quantities. We can now solve systems with three variables. We have several models that we can use:
combination chart (2 variables)notebook notation (2 or more variables)equations.
We also are well versed in the different strategies of scaling up/down and adding/subtracting equations to find a unit rate. We also use substitution once we know a unit rate to find the other variables.