We finished up in math with the comparing of decimals. Virtually every student understands this though some still make a few errors at times. For the most part, the students in both classes are ready for the next concept, which is ordering decimals. I am confident that this will only take a day and then the focus will shift to rounding decimals by a given place, not necessarily to a decimal place. It might be rounding to the nearest one or a power of ten.
In science, we completed the investigation from Thursday. We are going into the next investigation beginning tomorrow.
In math we are now covering comparing decimals. This lesson was very short since the students grasped it very quickly. Even though they may not have been exposed to it last year, they listened to me when I said to look for a pattern. If they can compare whole numbers, then comparing decimals is a very simple matter.
In science, we had students make a prediction and a conceptual model. Each group had a cup with a bit of butter/margarine, a chocolate chip, some gravel, a sugar cube, and a piece of a birthday candle (wax). They drew a chart in their science notebooks and make the prediction for each material: when it is exposed to hot water, will it melt, dissolve, or will nothing happen?
Once we made the prediction, we had to test it with the experiment. Then, results were noted. On Sunday, we will continue this with drawing conceptual models.
In math, we finished up with breaking down decimal numbers into full expanded notation. We began with an activity that was a variation of Find Your Partner. Students were randomly given a card with either a fraction with a denominator of 10, 100, or 1000; or, they got a card with a decimal number. When given the go-ahead, they went around the room to find the corresponding card. For example, a card with the fraction 13/100 and the card 0.13 are equivalent, so they would match.
in math, we continued with decimals. First, we reviewed place value and did some review exercises that involved finding the value of an underlined number. For example, take the number 847.45. The four is underlined and is in the tenths place, so it is 4 tenths. 4 tenths is expressed as 0.4 or 4/10.
Today's lesson involved full expanded notation. There is a difference between expanded form and full expanded notation. Expanded form is basically the place value of each digit exposed and added together. As an example: 123.45 is broken down to 100+20+3+0.4+0.05.
Full expanded notation shows it in its entirety. What do I mean by this? Take the number 97: it is expressed as 9 x 10. Why, instead of 90+7? Because it really delves into what it means. The nine is in the tens place and there are 9, tens. So, that can be expressed as 9x10+7.
Take the number 456. The four is in hundreds place, so there are four hundreds, or 4x100. The five is in the tens place, so there is five tens, or 5x10. The 6 is in the ones place so there are 6 ones, or 6x1. Since any number multiplied by itself is the same number, it is really unnecessary to write it as 6x1. The full expanded notation of 456 is (4x100) + (5x10) + 6. I use the parentheses to group it together and to make it easier to keep track of.
The key lesson was having decimals. In this case, we will use the number 34.54 as an example. There are 3 tens, so it is 3x10. There are 4 ones, so I write a 4. The five is in the tenths place, so it is 5 tenths, or 5/10. The other 4 is in the hundredths place, so it is 4 hundredths or 4/100. The full expanded notation of 34.54 is: (3x10) + 4 + (5x1/10) + (4x1/100).