I begin today by inviting students to help me complete a line plot graph. The line plot has the lengths of rocks to be recorded on the plot. rock graph.pdfThis type of graph is new for students so I complete the graph on the board as they complete it on their papers. I help them to draw the 2 side lines on a blank piece of graph papers. Next they number up the side and then write the 3 sizes across the bottom. Once the data has been entered I invite students to use think of a strategy to tell me how long all 3 of the 5 inch rocks would be together if we put them end to end. I ask them to do the same with the 5 7 inch rocks and the 2 9 inch rocks.. We compare our answers and determine how we reached these answers. I expect students will use repeated addition so they would write 5 + 5 + 5 = 15 (which they would probably quickly see is counting by 5s). For the 5 7 inch rocks most students will add 7 + 7 + 7 + 7 + 7 = and then group 7 + 7 = 14, and 7 + 7 = 14 so that is 14 + 14 or 28 and then count up 7 more to get 35. I encourage students to share the different strategies they used.
This quick mini lesson introduces the idea of a line plot graph rather than the familiar bar graph and it also allows students to practice with repeated addition.
I ask students to stand up and count how many jumping jacks they can do while I count to 20 out loud. I ask them to jot down their number on a piece of scrap paper for use later in the lesson. Now I ask students to sit back down and be ready to continue.
I ask students to take the slip of paper with their jumping jacks on it and to be ready to share their number. I go around and ask each student to tell his/her number. I record them on the board. Next I ask each student to arrange the data on a sentence strip, starting with the lowest number and going to the highest. I tell them that if there is more than one of the same number, they should record them next to each other.
I hand out the sentence strips and give students a few minutes to organize the data. Next I ask students to find the number that is the most common, and I remind them that it is called the mode. I ask them to circle that number. I introduce the term mode here because it is a district expectation and not a Common Core expectation. You could still have the students work on organizing data, possibly for graphing or answering questions and you would not need to introduce the terms mode or median as I did.
Next I ask them to find the middle number - the median. I remind them that we need to cross out the highest number and the lowest number, and keep repeating until we get to the middle. I ask them to do this with a yellow crayon so we can still see the numbers for later.
We compare the mode and the median number of jumping jacks in 20 seconds.
Next I ask the students if we could find a total for jumping jacks in the class. How might we do it? I listen to suggestions. If no one suggests using repeated addition for the numbers that are the same, I suggest that we might begin there. We do the repeated addition first and get a total. Next we look for partners of 10, or add the ones and then the tens, depending on student suggestion. We work together to get a total with students doing the computations on their papers as I do them on the board. (I delay my work slightly to give students a chance on their own first, but providing support for struggling students at the same time.)
At the end, I tell students that today they will be using repeated addition to help me figure out how many of different items I have in my cupboard, because I need to know if I should order more for next year.
I rearrange the students into groups of 3 and I bring out full boxes of class markers, board markers, pencils, crayons and colored pencils that I have in my cupboard. (I bring out 4 - 6 boxes of each item). I ask students how I might figure out how many of each item I have. I tell them I want to know how many markers (not boxes of markers because I can see I have 5 boxes). I take suggestions from the class.
I tell them that each group will get one item and will need to figure out how many there are. I would like them to write a number sentence to show me how they found their answer.
I remind students that they will need to find the total, and to create a number sentence to show me what they did to find the answer. (They will need a number sentence to match what they have, even if they count every single item to get a total.)
I tell students they will have 10 minutes to figure out what they have, to write the number sentence and to make a picture to show their item. I tell them they will be presenting their work to the rest of the class.
I give students time to work and I circulate around to make sure they are creating a number sentence that matches what they have. If they write 1 + 1 + 1 + 1, I ask them if they can find a more efficient way to show how many they have? I remind them about how we found the total number of inches the 5 inch rocks were at the beginning of class today. I provide scaffolding as needed to help students get to the idea of repeated addition, or multiplication.
I invite the students to come to the rug to share their solutions and totals. I invite one group at a time to share their solutions. I allow other groups to ask questions or make comments after the group presents.
I expect students to be able to talk about how they used some form of repeated addition to solve the problems. Often students would group the numbers together into doubles and then add the doubles together such as 8 + 8 + 8 + 8 = They know that 8 + 8 = 16 and another 8 + 8 = 16, so 16 + 16 = 32. A few students are already multiplying lower numbers so I also expect a few groups to show how they may have used multiplication as well. I expect students to be able to express how the numbers are repeating in a regular fashion so they can use strategies such as doubles to complete their problems (MP8).