This Unit Focuses on Multi-Digit Addition and Subtraction As Well As Data Analysis Including

Unit Plan: Using Numbers and Organizing Data From Everyday Math, Grade 4, Unit 2

Alison Keller

This unit focuses on multi-digit addition and subtraction as well as data analysis including collecting, organizing, and graphing. Generally, the addition and subtraction is going deeper into something they should already know how to do. The data information is more complex but they have seen words like mean, mode, etc. and should know what they mean. They have learned the standard algorithm for both addition and subtraction and should have all of their facts memorized (although some students do not). It is the second unit from the fourth grade Everyday Math curriculum. The first unit focused on geometry but began to introduce place value and addition and subtraction concepts. It also featured some graph and table information. The geometry concepts especially focused lines, rays, segments, polygons, angles (obtuse, acute, right) and parallel and perpendicular lines. The next lesson delves into multiplication and division and briefly introduces some algebra concepts. Unit Plan: Using Numbers and Organizing Data Big Ideas and Goals From Everyday Math, Grade 4, Unit 2 Alison Keller Big Ideas Interpreting Data Data is gathered and organized in order to interpret information about something. Different types of graphs and organizations are used to tell different things about data. Instead of seeing data as a collection of numbers, landmarks give the big picture of what the data represents. Place Value and Multi-digit Addition and Subtraction Different strategies can be used to solve multi-digit addition and subtraction problems. The position of digits in numbers determine what each digit represents. Place value determines the meaning of the numbers in multi-digit addition. Place value determines the meaning of the numbers in multi-digit subtraction.

Standards and GLCEs Interpreting Data D.RE.04.01 Construct tables and bar graphs from given data. D.RE.04.02 Order a given set of data, find the median, and specify the range of values. Place Value and Multi-digit Addition and Subtraction N.FL.04.08 Add and subtract whole numbers fluently. N.ME.04.01 Read and write numbers to 1,000,000; relate them to the quantities they represent; compare and order. N.ME.04.02 Compose and decompose numbers using place value to 1,000,000’s, e.g., 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones. N.ME.04.03 Understand the magnitude of numbers up to 1,000,000; recognize the place values of numbers and the relationship of each place value to the place to its right,e.g., 100 is 10 tens. NCTM Process Standard, Communication: Communicate mathematical thinking clearly and coherently to peers, teachers, and others.

These big ideas cover the main themes of the unit. Students do multi-digit addition and subtraction as a major part of the unit. In order to be successful they need to be aware of multiple strategies, and also need to have a firm understanding of place value. The rest of the unit is comprised of data analysis and determining statistical landmarks. Students need to know first of all why landmarks are important and how they communicate information about data. They also need to know that different kinds of graphs tell different types of information. An objective of the lesson is that students can give the statistical landmarks, but as that is more specific information and not crucial to their general big picture understanding for this unit, it is not a big idea. The benchmarks align with these big ideas. Communication is an important process standard for this unit because we are working on trying to express what we know in words. It helps me to see where a child is missing some understanding when they try and explain it in words rather than numbers. Unit Plan: Using Numbers and Organizing Data Assessment Plan From Everyday Math, Grade 4, Unit 2 Alison Keller Summative Assessment Written Assessment 2.10 The summative assessment is a 2 part (Part A and Part B) written assessment. Part A of the written assessment links directly to the learning goals for the unit. The first part includes 3 multi-digit addition and three multi-digit subtraction problems. It reviews old material and asks about polygons, having students name and draw a specific polygon. It also includes a table of information and ask students to find the maximum, minimum, mode, range, and median. It also asks students to communicate how they found the median. Part A ends with a graph of the given data. Part B includes information that the students are not expected to master yet and is a formative assessment for units to come. It is not graded but gives an idea of where the children are as they move forward. It asks students to do some measuring and estimating

Pre-Assessment

Math Box 1.9 The final math box from Unit 1 serves as a pre-assessment for Unit 2. It is a short 6 question sheet. It includes multi-digit addition and subtraction problems, ordering number from greatest to least, and a place value question. The pre-assessment does not evaluate the student’s ability to analyze data because that should be new information for all of the students.

Formative Assessment Recognizing Student Achievement 2.1-2.9 Each lesson includes a formative assessment. Mostly it is just evaluating their ability on one problem from their workbook pages and will help me stay on top of students and identify their gaps immediately. 2.1 Mental Math: Can students compute mental math addition patterns? 2.2 Page 30, #6: Can students complete a name collection box? 2.3 Page 33, #1-4: Can students identify what a digit represents in a large number? 2.4 Exit Slip: Can students explain how to solve a place value problem? 2.5 Observation: Can students create tally marks correctly? 2.6 Observations: Can students determine median, range, maximum, minimum, mode? 2.7 Page 42, #4-6: Can students compute multi-digit addition problems? 2.8 Page 46, #4: Can students use landmarks to draw conclusions? 2.9 Page 49, #4-6: Can students compute multi-digit subtraction problems? Unit Plan: Using Numbers and Organizing Data Assessment Analysis From Everyday Math, Grade 4, Unit 2 Alison Keller

My assessment plan includes pre-assessment, formative assessments, and a final summative assessment. The pre-assessment looks at the student’s ability to understand place value and compute multi-digit addition and subtraction problems. The formative assessments occur during each lesson and test the student’s progress. These assessments allow me to see where the students are struggling and focus future lessons and one on one attention on that. They focus on specific goals related to multi- digit addition and subtraction and data analysis. The summative assessment tests the unit objectives, as well as some objectives that spiral from the previous unit. Specifically, it also touches on polygons, a topic that is expected mastery from Unit 1. Each objective is assessed at one time or another throughout the unit. The most important objectives and ones I want to be sure the students carry with them to the next unit are tested in the summative assessment. The children need to know how to add and subtract multi-digit numbers, find statistical landmarks of data and draw polygons. The final assessment is a written test and requires reading directions and answering questions. The formative assessments are varied including both observation and pencil and paper assessments. Students need to be able to communicate their mathematical knowledge with both written words and orally. If students seem to be having trouble because of problems reading or following directions, I will ask them orally to explain their work. This ensure that the student understand the mathematical information. The information spirals through each section and builds as the unit progresses. By the time they are finally assessed, the students have seen each type of questions they will be asked several times. The students will find it most difficult to calculate the range and median on the final test. It will be reviewed several times throughout the unit. Those two calculations take more than one-step and set of information so it will be more challenging. Multi-digit subtraction may also be difficult and extra time will be spent preparing students for those tasks. Students will easily find the maximum and minimum and also do multi-digit addition. These areas most students will likely do well on the test and not need as much reinforcement. Unit Plan: Using Numbers and Organizing Data Students and Participation Structures From Everyday Math, Grade 4, Unit 2 Alison Keller

Who are my students?

I have a diverse group of students both personally and academically. Several of my students are high achieving in math. They can easily catch on to new skills, remember definitions easily, and can apply the new skills they acquire quickly. I also have students for whom math is a definite weakness. Some have trouble with place value, still rely on finger counting for addition and subtraction facts, and generally do poorly in math class. Another problem with math is the rapid pace at which we move and the difficult some students have in keeping up during independent work time on their journal pages. There are also very shy and tentative students, who although they are average or high ability math students, do not participate openly in class.

How can I help marginalized students participate more?

In order to help marginalized students I will encourage them as often as possible. Increasing their confidence in their abilities will help them to participate. I will also focus on asking them questions where their strengths lie. When doing group work I will assign roles with careful consideration for the strengths of the individuals in each group.

How will I support all of my students?

The high achieving students need appropriate challenges and responsibilities during math time. They need to feel like they are not just moving through the information but are really learning as well as offering something to the other students in the class. The lower students need to build both skills and confidence in math. I need to help these students individually and assign them tasks they can be successful on. Students who have trouble staying on task need to be reminded and offered places to sit in the room where they can truly focus. Lesson Plan: Multi-digit Addition From Everyday Math, Grade 4, Section 2.6 Alison Keller

Big Ideas: Instead of seeing data as a collection of numbers, landmarks give the big picture of what the data represents. Data is gathered and organized in order to interpret information about something. Different types of graphs and organizations are used to tell different things about a set of data.

Objective:  Students will be able to construct a line plot.  Students will be able to find the median of a data set.  Students will be able to collect data.

GLCEs and Standards: D.RE.04.01 Construct tables and bar graphs from given data. D.RE.04.02 Order a given set of data, find the median, and specify the range of values.

Materials: Math Journal (pages 40-41) Student Reference Book (page 71) Sticky Notes Study Link 2.6 5 large pieces chart paper.

Introduction 5 min. B E “Today we are going to work on organizing data that Students will remember F we collect and determining the landmark numbers. that a landmark is like O What is a landmark number? What are the when you travel and R landmarks we have talked about? We are going to something stands out. I E start together by organizing data about the number may have to return their of people in your families. Then you will work with thinking to numbers. Ask your group to organize a different set of data that students what numbers you will collect.” stick out.

Model Group Activity 10 min.

“I am going to draw what is called a line plot on the board. I know you have all used bar graphs to organize data before, a line plot is a different way to organize data.” Draw line plot on the board. “Now I am going to hand out sticky notes to each of you. I want you to write with your green pen, nice Students may want to ask and big, the number of people in your immediate a lot of questions about family, those people who you live with. Include you. I who to include in their am not going to answer any questions about who to family. Remind them that I include and not. You can each decide on your own am not answering who counts as a member of your family. You can questions about that and include brothers in college, but not cousins in they can use their best Tennessee. Use your judgment.” judgment. Hand out sticky notes and give students 30 seconds to write a number. More than one student may claim to be lowest “Who thinks they have the minimum of our data set? and highest, model how to Anyone lower? We are going to put that number at add tally marks. the left end of our line plot. Who thinks they have the maximum? Anyone higher? That number is how high This will help students see we are going to go. I am going to write the numbers one way of graphing data up here and then call you up by tables to place your and how that works. They sticky note above the number of people in your will get to construct this family. knowledge with a group Write in the numbers and then call each table to and try their ideas with place the numbers. Monitor students as they place each other. The sticky their numbers. notes make finding the median easier and since “Lets find the landmark numbers. Who can tell me this is their first experience what the maximum is? The minimum? The mode? with median it scaffolds The range? How about the median? The median is that learning. the middle number of a data set. One way to figure it out is to line up all the data and count the same way Students should have an from each side. I am going to quickly undo our line easy time with maximum plot to show you how it works. Okay, now that they and minimum but may are all in a line, its easier to see which is the middle need scaffolding to get number. What is it?” mode and range. Ask the Circle the numbers the students say. Move the notes students to refer to their into a straight line. books if they need help and monitor progress. The last landmark number we are going to talk about Slowly introduce median, it the mean. What is another word for the mean? To they have heard the word find the mean you need to add up all of the numbers but not calculated it. and divide by the total number of sticky notes. So in this case how many are we going to divide by? You Mean is not a mastery goal can do this with a calculator. I am going to add it up at this time. If there are a and write the answer up here while you begin your lot of questions try and group task. move on. Calculate the range while they are working. Group Task Instructions 5 min.

You are going to work in your table group to create a line plot and then determine the landmark numbers. I am going to give each member of your group a task The directions may card. You all need to work together, but the task card overwhelm students. Show shows you which part of the task you need to take them the guidelines on the lead on. The cards say: data collector, recorder, their task sheets and tell maximum minimum range and mode, median, and them to confer with their mean. The data collector is in charge of gathering groups. data. You can choose what data you want to collect. Hand out task cards with We will decide right now. special attention to Let students choose between: number of tvs in a students. Give students house, number of pets, number of after school who need more of a activities, number of pencils in desk, number of challenge the mean and ______. median cards, and those To save time, collect data from your table group and who struggle the maximum one other. You do not need to talk to any other and minimum cards. groups and only the data collectors can leave their seats. The maximum, minimum, range, and mode person calculates those and gives them to the recorder. The mean and median person does the same. The recorder is in charge of putting everything on the big paper. Draw a line plot and use sticky notes the same way I did for the family size data. You can have your group help you with the sticky notes.

D Group Task 20 min U R Begin working. I will come around and answer any Look that student are I questions. Make sure you are working with your working together. Check to N group but leading on the task I give you. see if students have drawn G Pass out task sheets. Wander to groups to make a line plot and how they sure they are on the right track. are calculating. Students may become possessive of their task, encourage teamwork. Students may be confused about terms, encourage them to discuss with their groups. Things to say: What does the mean refer to? Remember when we said the median is the middle. How did I solve for the median when I modeled? Find out what ____ is working on and help her along. Share and Discuss 5 min Please put your chart paper up on the board. We are Help students who do not A briefly going to share what each group came up with. know where to find the F The recorder can share what you decided to graph median. Students may T and what the median number was. want to talk a lot, keep E them moving. Ask: R Handout homework 2.6. How did you solve this problem? What did you do I hope you all have confidence in your ability to take to work with your group? data that you have collected it and organize it. When How else might you have you find these landmark numbers it makes it easier figured that out? for you to understand what story the data is telling.

Assessment: Monitor each groups progress as they create the plot and name the landmark numbers. Check their homework number 4 to be sure they are understanding median.

Accommodations: Carefully select which student gets which task card. Those who struggle should be given the maximum, minimum card, and those who need a challenge the median, mean card. Work on the board should be done on Elmo so it shows up on screen and visually impaired student can see it or she can use her CCTV. Lesson Plan: Multi-digit Addition From Everyday Math, Grade 4, Section 2.7 Alison Keller

Big Ideas: Different strategies can be used to solve multi-digit addition and subtraction problems. Place value determines the meaning of the numbers in multi-digit addition.

Objective:  Students will be able to calculate multi-digit additon problems using multiple strategies.  Students will be able explain how they solved multi-digit addition problems.

GLCEs and Standards: N.FL.04.08 Add and subtract whole numbers fluently. NCTM Process Standard, Communication: Communicate mathematical thinking clearly and coherently to peers, teachers, and others.

Materials: Math Journal (Pages 42-44) Student Reference Book Study Link 2.7 Math Notebooks

Math Message 5 min. B “Please open your math notebooks and do the E following problems. I want you to think about the Most students will solve F steps you are taking to solve the problems.” the problem using the O 47+37 and 233+158. standard algorithm. Note R students who solve it E another way. Some students may estimate, others may use the standard algorithm. Some will add the biggest numbers first. Introduction to Strategies 10 min.

“Today we are going to look at multiple strategies for solving addition problems. We are going to talk about Ballpark Estimates, the Partial Sums method, and the Column-addition method. Then we are going to have a classroom discussion. While we are talking about the strategies I want you to be thinking about how the strategies work and how they are related to each other and be prepared to talk about how they work and what you think of them.”

Ballpark Estimates: Students will probably say “What is an estimate? We can use ballpark that an estimate is a estimates to see if our answers make sense. We are guess. Ask what the not getting an exact answer but estimates can help difference is between an make sure we are on the right track. We can change estimate and a guess and the numbers to “close but easier” numbers. Lets look remind them of the raisin at 23+77. How could we estimate the sum?” activity, an activity with Do the same for 147+56. graphing that required an estimate and a guess. 25+75 or 20+80 Partial Sums Method: 150+50 “A method for getting the exact sum is called the Partial Sums method. Turn to page 10 of the Student Students may want to start Reference Book. That explains the method if you are with the ones. Remind having trouble, but lets try the problem 46+37.” them that with this method Add the tens: 40+30=70 you start with the largest Add the ones 6+7=13 number so the first sum Then add the partial sums: 70+13=83. gets close to the answer. Let them try 233+158.

The Column-Addition Method: “This is the method most of you use. I am going to review it quickly and we are going to practice it. Do 76+38 and have students try 647+936. Go through each step of the algorithm slowly and clearly.

Discussion Instructions 5 min. “Now we are going to have a class discussion. I Make connections to book want to try something new where the discussion club discussions, which does not go through me. I am going to start by they are familiar with. They asking a question and calling on the first person. may find a math After that person speaks her or she can call on the discussion strange but will next person to respond. I am going to write some be more comfortable with things on the board that will help us with our that connection, discussion. What kind of words should we hear during the discussion, how can you help make the discussion better? Write on the board: Ask a question, Say I agree or I disagree, give an example, Say, I would like to add. “In this discussion we are going to compare and contrast the three methods we discussed. Before we begin I would like everyone to take 1 minute and write quick notes in your notebook. Write anything you can think of about how these methods are alike or different so you can be ready for the discussion. I would like everyone to participate.”

Wait 1 minute and then get attention back. Write the following problem on the board 469+946.

D Discussion 10 min. U Questions: Students will want to be R What is different about solving this problem with specific to the numbers I Ballpark estimate and Partial Sums? given. That is fine to start N What is the same? with but push excelling G Contrast Partial Sum and Column addition? students to be more What is the same? general. They will notice What is different between Ballpark and Column where you start and stop addition? What is the same? ask them to think about What else do you notice about these strategies? place value. Which is the easiest? When would you use each method? When wouldn’t Students should see that you? the steps are different but they get the same Allow students to discuss between themselves, answers. Students might direct the conversation and add additional questions notice where you start for rather than giving answers. each is different. They may need more help to see how they are the same. A Independent Work 15 min. F Students should complete pages 42-44. When they T are finished distribute homework 2.7. These sheets E are practice with each of the methods discussed. R Walk around and check the studen’ts work. Pay special attention to numbers

Assessment: Record conversation and note any insightful comments or any comments revealing misconceptions or miscommunications. Look at journal page 42 numbers 2-6. Students should be able to use one of the given strategies to calculate the correct sums. (94, 1381, 12404)

Accommodations: Keep an eye on students who do not participate readily in group conversations. Prepare them before the lesson begins and encourage them to add their thoughts. Writing down ideas first will help. Solve problems on paper on Elmo rather than on board so that visually impaired student can use her screen.