We discussed ordering decimals in more depth this week. First, the kids were given a set of decimal cards and were asked to read them as mathematicians. To read a decimal number like a mathematician:
Example) 0.42 "Forty-two HUNDREDTHS" Example) 1.076 "One AND seventy-six THOUSANDTHS" We then reviewed what each place value means by "breaking" apart base ten blocks.
After discussing place value, we modeled various decimals using base ten blocks. Example (Using the large cube as one)- 1.357 (One and three hundred fifty-seven thousandths) Our model looks like this because in the number 1.357 we have: 1 + 0.3 (three tenths) + 0.05 (five hundredths) + 0.007 (seven thousandths) Using the decimal cards and decimal grids (like the ones below), we made pictorial representations of decimals. Then, we ordered them, using the visual representations to help us see which ones were bigger and smaller. Next, we moved into figuring out how to compare decimals without drawing them. We talked about how if we were comparing a decimals like 0.6 and 0.28, a lot of people are tempted to choose the 0.28 as the larger number because it LOOKS larger. We talked about how when we are comparing and ordering decimals, we should always add 0s to the end of the decimals so that they all end in the same place value. For example, 0.28 ends in the hundredths place, so we need to add a 0 to the end of 0.6 to make it end in the hundredths place- 0.60. NOTE: ADDING A ZERO TO THE END OF A DECIMAL DOES NOT CHANGE THE VALUE OF THE DECIMAL! It just means you are cutting the amount into more pieces. When we add a 0 to the end of a decimal, it means we are breaking each piece into 10 more pieces. See below: Picture it like a birthday cake. Let's say you have 6 slices of cake left (out of ten)-you have 0.6 of a cake left (6 total 1/10 size pieces). All of a sudden instead of sharing the remaining cake among 6 people, you have to share it with 60 people! You just cut each slice into 10 pieces and end up with 60. We can now see that 0.6 (0.60) is bigger than 0.28. Here is a picture just so you can see it. After this activity, we had the kids get into two groups- decimals worth between 0 and 0.5 and decimals greater than 0.5. The two groups ordered themselves from least to greatest and then each group checked the other's work. Here is a video of that activity.
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