What's happening in Math Class this week
JANUARY 9-10, 2018
We used base ten pieces in class this week to add three-digit numbers with regrouping. Whether your child was in school or missed a day or two, all kids would benefit from continuing this
activity at home. You don’t need to purchase base ten blocks to do this, you can use the free Math Learning Center app - Number Pieces.
Start by giving your child a 3-digit number to build and name verbally.
Some students are unsure how to name numbers over 99 and need continued modeling. Take turns, where you write a number for them to build and name verbally, and have them do the same for you. On your turn, build it wrong sometimes for them to find your error. After you feel your child can build and name the numbers proficiently, give them two 3-digit numbers to build and add. Use the regrouping function to build the “minimal collection” (smallest number of pieces to represent the value).
Kids needs lots of experiences with the regrouping activity to support their understanding of
our place value system.
We reviewed our addition strategies of: splitting by place value, keeping one addend whole
and adding BY a friendly number, keeping one addend whole and adding TO a friendly
number, take-n-give (compensation). Then we added the standard algorithm to our
repertoire of adding strategies. The standard algorithm is also known as stack-n-add and is
what most of us were taught back in the day.
I offer the standard algorithm as one of many strategies to have, but I want kids to have all
the strategies - not just one favorite that they use all the time. We talked about that this
week, and pushing our brains to consider several strategies before choosing how we will solve a particular problem. The standard algorithm is particular efficient when the problem does not require regrouping.
Similar to the Oaks class, we used the base 10 blocks to build the concept of regrouping. The difference being that the Oaks are primarily working on place value understanding and working at the level of concrete objects, while the Elms are working on the standard addition algorithm and transferring from concrete objects to abstract numerical representations.
Break is over and back to fractions! We reviewed our a models for finding common
denominators: money, clocks, the double number line, and ratio tables. We worked to clarify
when each model is useful depending on the denominators in the problem. We added to this
some strategies for when money and clock models are not appropriate.
When one denominator is a factor of the other denominator, you can scale up to use the
larger denominator. When both denominators have a common factor, you can find a
common multiple that is less than the product of the two denominators. Lastly, when the
denominators have no common factors, you can multiply them to find a common multiple.
Our exploration of these relationships is not meant to end in memorized list of when to do
which rule. Kids can certainly construct these rules if they are ready to, but since they can
think through each problem they don’t need to memorize a bunch of rules.
This week we started our third unit - Ratios and Rates. We finished section A about single
number ratios - meaning ratios that could be expressed as 4:1, or 4/1, or 4 to 1. Next week
we will look at ratios involving two numbers, like 4 to 3. We use single number ratios a lot
without even thinking about them as ratios. We looked at gas mileage (miles per 1 gallon)
and speeds (miles per 1 hour). The benefit is that they make comparing easy because the
second value is always 1.
We used ratio tables to take ratios not given as single number ratios and find their equivalent
single number ratio. For example, Bill drove 265 miles in 5 hours, what was his average
Likewise, we started with single number ratios and scaled up to solve other problems. For
example, Sally set her cruise control and drove at 68 mph for 3 1/2 hours. How far did she