In our daily routines we deal with some form of decimals. It could be at the grocery store, at work or trying to figure out how much money we need for a purchase that is $9.76. When I was a student I did not realize how important it was for me to learn about mixed decimals but as an adult I see what my teacher was talking about. It is essential that we educate 5th grade students on mixed decimals and help them realize the importance of working with mixed decimals. Any person that uses money will need the skills to round mixed decimals to the nearest tenth to help them complete a purchase.
There are prerequisite concepts that the 5th graders need to know before attempting rounding mixed decimals. The students will have to master the concepts of rounding numbers. They have learned that 5 is the focal point, if a number is lower than 5 we round down and if the number is 5 or greater we round up. It is crucial for the students to have learned how to round whole numbers in order for them to grasp the concept of rounding decimals and this will also help them with their place values. The student also needs to know how to count to 100 in order to be familiar with the number place values such as tenths, and hundredths.
It is beneficial for them to know their basic addition and subtraction functions to help them work with rounding mixed decimals. The students will be learning the place values and how to round whole numbers that are located on the left side of the decimal and the tenths and hundredths that are located on the right side of the decimal. These skills are essential in everyday life and it is vital that the students grasp the concept of rounding on the right side of the decimal point.
I want to make sure that students know which number is in tenths place so they will draw a box around the number in tenths place. This will help them remember which number is to be rounded. Their attention will be drawn to the number with the box around it because it is the focal point of the rounding exercise. This is when they need to remember the rule of 5 and up round up and 4 and below round down. If the student needs to round up it changes the number in tenths place but if the number is 4 or below the tenths place stays the same. The number is 3.73 so rounding to tenths place would be 3.7 because 3 is below 5 and it will not change the tenths digit but if it would have been 3.76 it would be rounded to 3.8 because 6 is greater than 5 so we round up.
Another helpful lesson would be to have students draw a straight line on blank paper. We would start at the right with 1 and go up to 10 leaving space in between numbers to mark tenths on the line. They would start 1, 1.1, 1.2, 1.3 etc. until they have numbered the complete line up to the number ten. I would give them mixed decimals to round and then have them place them on the number line. We will use 2.85, 6.73, 1.21, and 8.39. The students would then place them on the number line and I will be able to check to see if they have mastered rounding mixed decimals. They should mark 2.9, 6.7, 1.2, and 8.4; if they have any other answers we will need to figure out what concept they are having problems with and reteach that portion.
I would introduce them to money exercises to check their abilities to round mixed decimals because everyone eventually will have to use money. I will have an overhead projector and have them write their answers down on their worksheet. I will give them a problem: your items total $5.67 and you have to figure out if you need $5.60 or if you need $5.70 to make the purchase. The students could use the number line they did on the previous exercise. They would put a box around the 6 in tenths place and since the 7 in hundredths place is above 5 we round up therefore 6 would change to 7. The student can then look at the line and see that 5.67 is larger than 5.6 but less than 5.7 therefore in order to give the clerk enough money the student would give them $5.70.
To make learning fun I will let them play decimal rounding bingo to see what they have retained from the lesson on rounding mixed decimals. The object to the game is to have a decimal that needs rounding and the bingo cards have the rounded decimal and they must round correctly in order to bingo. I may call out 4.87 and the students would have to round to tenths place which would be 4.9. You will have students mark 4.8, because they have forgotten the rounding rules and this would be wrong; at this point you can go over why they were wrong. It is because 7 is in hundredths place and it is greater than 5 so we round up to the next number in tenths place which would be 9. If the number was below 5 we would round down which would be 8.
As the students work on each activity I will be going around the room to make sure the students grasp the procedures and concepts of rounding mixed decimals. Even with all my help as they are working there are still possibilities that some students will still have problems dealing with mixed decimals. We must remember that all students learn at different levels and not all of them will relate to the concepts to start with, they just need reminded as they work until they see the relationship you are trying to build with decimals and rounding to the nearest tenth.
A problem students may have is when they see 1.77 and they round to 1.7. Sometimes the repetition of the sevens confuses the students and you will have to go back and explain why the answer would be 1.8. We look at the 7 in hundredths place is higher than 5 so we round the tenths place to 8 and the answer would be 1.8. They could also look at the line we have numbered earlier and see if 1.77 is closer to 1.7 or 1.8 to determine which is correct. Also remind students we are only looking at the digits on the right side of the decimal because the whole number is not changing in these exercises. They must master this concept before we can move on to rounding decimals to whole numbers.
Another situation would be dealing with mixed decimals and the students rounding the whole number instead of the tenths place. For example you may give the student a decimal of 85.67 and the student fails to identify that the 6 is in tenths place and they round the decimal to 86.0. That is the wrong answer. It should be 85.7 because the 7 in hundredths place is greater than 5 so you round up to the next number which makes your 6 a 7. We will go back and have the students draw a box around tenths place so they will realize which place is tenths place. This is what the lesson is based on teaching to round mixed decimals to the tenths place. I will also have several worksheets the students can take home to practice on to prepare them for a quiz on this lesson. They will have 3 days to prepare for the quiz so I may answer any questions they have about the worksheets to help them understand the lesson.