To review line plots from yesterday, we view Interpret Line Plots. Together, we review what they knew about line plots from Grade 4. Line plots are are useful way to organize and display certain types of data. The line plots in this lesson will represent data with fractional values.
In Fourth Grade, students created line plots and use them to solve real world problems that involved addition and subtraction of fractions. Now, in Grade 5, 5.MD.2 requires the focus to shift to real world problems involving all operations with fractions.
It is important for students to understand that the line plot must be divided into equal intervals and must include the entire range of the data set. A common mistake I've noticed is that some students skip the intervals for values without any data.
To support my ESL Learners, I start by drawing a line plot on the board with tick marks and labels at intervals of 1/4, beginning at 0 and ending at 2. This illustrates the tool we are about to use, and I point to it as I explain, "This drawing called is a line plot. We call it a line plot because we plot (put) data on this number line."
Point to the tick marks that are labeled 0, 1/4, 2/4, 3/4, 1, and on and tell students that these marks divide the number line into intervals of 1/4. We then discuss what interval means. I explain that the interval for a plot is the equal distance between the tick marks. To review this even further, or if students still need additional help, have students look at a ruler or yardstick. How is the yardstick like a line plot? What intervals do you see on the yardstick?
In the second example, I point out that some fractions on the number line have different denominators because they are simplified values. Rather than relying on words to convey the sense of this statement, it may be critical for some students that you illustrate this. Emphasize the intervals are still equal and every interval between 0 and 1 is included even if there are no data values.
Jenn wants to re-distribute the punch so there is the same amount in each pitcher. How much punch will be in each pitcher when she is done?
Students need to follow the order of operations to properly calculate the total gallons of punch. The quotient of two whole numbers can be written as a fraction. I expect my students to understand Order of Operations well at this point, but if your students don't then you can post the order of operations on the board. If students need practice, you may want to use a really fun game from Math-Play - Algebraic Expressions Millionaire Game. It is an eye-popping, interactive game which quickly grabs my students' attention. It is very similar to the old game show "Who Wants To Be A Millionaire?"
For this first independent work problem, I use sunflower seeds because we read Holes by Louis Sachar earlier this school year. My kids loved the book, and will remember the sunflower seeds from the story. As often as possible, I try to tie reading and math instruction together. Students are using MP1 here: make sense of problems and persevere in solving them.
Ms. Field has 10 bags of sunflower seeds. The line plot shows the weight of each bag. Ms. Field wants to redistribute the sunflower seeds so that each bag weighs the same. What will be the weight of each bag?
A.) 1/8 + 2 x __ + 2 x ____ + 2X ______ + 3/4 + 7/8 + 1
B.) Evaluate the expression. This was rather challenging for some students, and I did not expect this.
C.) Divide the total weight by the 10 bags. Put the answer into a fraction. ____ = _____
The weight of each bag will be ____ pound(s).
Using MP3, Construct viable arguments and critique the reasoning of others. Students compare a set of data displayed on a line plot with an expression and determine the reasonableness of the expression. Students work with their table partner to solve:
Chrissy wrote this expression to represent the sum of the data shown on this line plot. Is her expression correct? Explain your reasoning.
1/4 + 1/4 + (3 x 1/2) + (2 x 3/4) + 1
Did Chrissy represent every data value in the line plot in her expression?
What operations should be performed first to find the sum of the data values?
Cassandra is actually correct; There are2 Xs above 1/4, 3 Xs above 1/2, 2 Xs above 3/4, and 1X above 1.
In this lesson we focus on using Mathematical Practice - Construct viable arguments and critique the reasoning of others. Being able to construct the arguments that others make is taking some time.
Each student needs to first understand how to solve the problem, and then think about how to clearly explain it to another person. To think about something twice means that a student will understand it that much better. We didn't get all that far with this practice today, but it was good practice for students to be held accountable for doing this.
To review, I ask students to look back at the I Can Statement.
I can solve real world problems by using line plots.
Two responses are as follows: "I can represent data on a line plot by drawing Xs for each value in the set of data." "I can answer questions about a line plot by using the data values that each X represents."