Task 3 attempt 2

docx

School

Western Governors University *

*We aren’t endorsed by this school

Course

NUMBER SEN

Subject

Computer Science

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by kclinedinst

Kyle Clinedinst Student ID-001029234 AOA2 BNM2-Task 3: Understanding and Teaching Integers and Order of Operations Part A 1. List three content standards from your state that apply to integers or the order of operations for grades K–6. The three selected standards must represent three different grade levels. Grade 3: “. 3.OA.5 Apply properties of operations as strategies to multiply and divide. For example, if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative Property of Multiplication); 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 (Associative Property of Multiplication); knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive Property). Students need not use formal terms for these properties.” -Ohio Learning Standards/Mathematics Grade 3 Grade 4: “4.OA.3 Solve multistep word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.” -Ohio Learning Standards/Mathematics Grade 4 Grade 5: “5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.” -Ohio Learning Standards/Mathematics Grade 5

2. Write a sample problem for each of the three standards to illustrate the evolution of student understanding. Grade 3: “. 3.OA.5 Amy wants to find out how many people can go on the Top Thrill Dragster roller coaster at Cedar Point at a time. She draws the model of the roller coaster below. The train is made up of 4 cars. Each car has 2 rows and there are 2 seats in each row. Use the associative property of multiplication to solve how many people are on each train. 4x2x2= Grade 4: 4.OA.3 There are 427 fourth graders at Mount Vernon Elementary School. 187 students are girls. If half of the 4th grade boys are taking gym class this semester, how many 4th grade students are boys taking gym class this semester? Grade 5: 5.OA.2 A box contains 12 apples. Mr. Jones orders 6 boxes of apples for his restaurant and 9 boxes for his store. a. Write an expression to show how to find the total number of apples Mr. Jones ordered. Solve your expression. b. Next week, Mr. Jones doubles the number of boxes ordered. Write a new expression to show how to find the total number of apples ordered next week. Solve the new expression.

3. Provide a solution for each problem that demonstrates each step or explains the thinking process involved in determining the solution. Grade 3: “. 3.OA.5 Amy wants to find out how many people can go on the Top Thrill Dragster roller coaster at Cedar Point at a time. She draws the model of the roller coaster below. The train is made up of 4 cars. Each car has 2 rows and there are 2 seats in each row. Use the associative property of multiplication to solve how many people are on each train. (4x2)x2= 16 Or 4x(2x2)= 16 Thinking- For this 3rd grade associative property problem, students start to use order of operations. In k-2, students don’t do very many if any multi-step problems. The first thing students need to know about the order of operations is that there are multi-step word problems. For this, I would make a visualization piece for the students to see. Students could either multiply the number of cars (4) by the number of rows in each car (2) first. Then take that product (8) and multiply it by the number of seats in each row (2). Or, the students could multiply the number of rows in each car by the number of seats in each row. Then take that product and multiply it by the number of cars. Learning to do the operation in the parentheses first is the first step of the order of operations. Grade 4: 4.OA.3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

There are 427 fourth graders at Mount Vernon Elementary School. 187 students are girls. If half of the 4th grade boys are taking gym class this semester, how many 4th grade students are boys taking gym class this semester? Thinking- For this problem, students would need to know which operation to do first. Students will need to take the total number of 4th graders and subtract that by the total number of 4th grade girls. 427-187=240. This would give them the number of 4th grade boys. Then they would take 240 and divide it by 2 to find half. The equal may look like: (427-187) /2= 120 Grade 5: 5.OA.2 A box contains 12 apples. Mr. Jones orders 6 boxes of apples for his restaurant and 9 boxes for his store. a. Write an expression to show how to find the total number of apples Mr. Jones ordered. Solve your expression. (6x12)+(9x12) or 12(6+9) 72 + 108 12(15)=12x15 180 180 b. Next week, Mr. Jones doubles the number of boxes ordered. Write a new expression to show how to find the total number of apples ordered next week. Solve the new expression. ((6x12)+(9x12))x2 or ( (12x(6+9) )x2 (72 + 108)x2 (12x15) x2 360 180x2 360 Thinking- For a, the students could start by find how many boxes Mr. Jones orders. 6+9=15. Then they could take this number and multiply it by 12. 15x12=180. For b, students would do the same step as a, but take the total 180 and multiply it by 2. 4. Discuss how the chosen standards and problems build student understanding of integers or the order of operations across the three K–6 grade levels selected in part A1. I chose these standards because they build on the previous year’s prior knowledge of order of operations from grades 3-5. First, the 3rd grade question is a multi-step word problem. For this problem, students learn how to use parentheses and what they mean. Next, the 4th grade question builds

on the use of parentheses. The students have to use different operations, using subtraction first, then division to solve a multi-step word problem. The 3rd grade question used the same operation. The 5th grade question builds on both. For this question, students will use 3 operations. They need to know which operation to use first, and that builds on the 4th grade question. Part B: Watch the “Grade 6 Math: Introduction to Integers” video and do the following: 1. Explain how the introductory activity assesses prior knowledge. The introductory video assesses students' prior knowledge because it shows if the students know how to arrange positive and negative whole numbers and also if the students know how to identify negative numbers. The students obviously did not know where the negative numbers go on a number line. This is great information for the teachers. Also, it seemed that some students had some prior knowledge of negative numbers, understanding the negative symbol, whereas some students may not have any prior knowledge of negative numbers. Also, the introduction activity assessed the students' knowledge of vocabulary words. It seemed that “integer” was a new term for them, but “whole numbers” is a term they may know, but not completely understand. 2. Describe how the teacher effectively integrates relevant vocabulary terms into the lesson using examples from the video. The teacher integrates vocabulary terms directly into the lesson by first explaining the term and its definition. The teacher tells the students the new vocabulary term “integers” and gives a definition. Next, the teacher asks the students to work with their partner and write down any numbers that are not integers. She understands that in order for students to learn the new concept of integers, they must be able to identify numbers that are not integers. The students talk about mixed numbers and decimals as examples of numbers that are not integers. 3. Explain how the visual aids and real-world examples in the observed lesson work together to illustrate the meaning of zero. In this lesson, the teachers use many visual aids and real-world examples to teach the meaning of zero and positive and negative numbers. First, the teachers use multiple number lines. They show positive and negative integers. I liked how they talk about the vertical number line and ask students if they have seen a vertical number line in real life. 2 students give real world examples, one from the fair and the other from a school

fundraiser. They also discuss how and why they do not see negative numbers with these examples. The teacher also uses 2 number lines, one on top of the other to show a real world example of the meaning of zero. The teacher uses the green number line as a football field. He then uses the white number line to show positive and negative “runs from a running back” and what it means if the running back starts at the 40 yard line and gets tackled at the 40 yard line. Before telling the students what it means, he has them discuss with a partner. The teachers did a great job of showing the students that zero doesn’t always mean “zero”, rather that zero may mean a starting point. 4. Describe how the concluding activity reinforces the content of the lesson. The concluding activity reinforces the content of the lesson by having the students show a number line with positive and negative integers. It was the same activity they did to start the lesson, but this time the students did much better. It shows the teachers what the students have learned and if they have activated the learning targets. I also really like how it gives the students direct feedback and satisfaction. The students are able to see what they have learned and will feel successful from this lesson. Part C: Provide two original learning activities that address student misconceptions about integers and order of operations by doing the following: 1. Describe a student misconception about adding and subtracting positive and negative integers. One misconception about adding and subtracting positive and negative integers deals with the negative symbol. At this level, students know how to solve addition and subtraction problems with positive integers. For example, 3+5=8 or 8-5=3. They have misconceptions when adding and subtracting negative numbers. Students may not understand that subtracting a negative number makes the number increase in numeric value. For example 7 – -4 = 11. They also may not understand that adding a negative number makes the value decrease. 7 + -4= 3. a. Describe an interesting and engaging original activity that would clarify the student misconception about adding and subtracting positive and negative integers identified in part C1. For this activity, I will pass out positive and negative numbers on construction paper. On yellow construction paper will be positive 1. Red paper will have negative 1. This

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

will help the students visualize adding and subtracting integers. I will call the paper “chips”. After introducing the vocabulary needed and modeling adding and subtracting positive and negative integers, I would show an addition problem with positive and negative numbers. 5 + (-2) For this problem, I would give 5 students 1 positive chip each and have them stand in the front of the room. . Then I would give 2 students each a -1 chip. Next, they would pair the positive and negative chips and eliminate the pairs. This would show that there are 3 positive chips left giving them the answer. I would do the same thing for -5 + -3. This would show that we would be adding more negative chips to get -8. We would do a few more examples. -8 + 5, 7 + -7,... They would do the same activity for subtraction. For example -4 – -2 . When they are to subtract negative chips, we would say (remove). They would start with 4 -4 chips. Then they would “remove” or subtract 2 -2 chips. This is a good way to describe and visualize subtracting negative numbers. I would do the same thing with the following examples. -4 – -5, -3 – -7. b. Explain how the activity would deepen student understanding of the concept. The activity would deepen the students' understanding by addressing the misconceptions. The students would be able to visualize and manipulate the positive and negative chips because they would be pairing them together with their classmates. The students would be able to see that when we add a negative number to a positive number, it’s like subtracting two positive numbers. Also, when subtracting two negative numbers, the students would “remove” negative chips and the numeric value would become greater. They would be involved because they would physically be removing and/or adding the chips for each problem. 2. Describe a student misconception about order of operations. A common misconception about order of operations is that the p and e in “pemdas” are interchangeable like the (m and d) and the (a and s). a. Describe an interesting and engaging activity that would clarify the student misconception about order of operations identified in part C2.

For this activity, I would use visualization charts and letters to help the students understand the order of operations. I would first pass out 6 big letters to 6 students. P, E, M, D, A, S. Each would be a bubble letter that is white. Next, I would have the class explain each letter in terms of order of operations. Now I would have the students with the letters organize themselves to show the order of operations. While doing this, I would have the students match the letters that are interchangeable. I would be expecting the students with the P and E to match. This is when I would explain the misconception and show an anchor chart like this. We would talk about the misconceptions. Next, I would have the students color in the letters, but use the same colors for the interchangeables. For example, the P could be green, the E red, M and D both be blue, and the A and S both be yellow. I would then post the letters in the room so the students have a class visual to refer to. It would be a visual that they made and/or were a part of. b. Explain how the activity would deepen student understanding of the concept. This activity would deepen the students' understanding because it first lets the students make a mistake. I often tell my class that we learn by making mistakes. Then, we would address this mistake or misconception and I would show a visual. Then, the class would be a part of creating a new visual to help address this misconception. This would be something that the students made and help them feel a part of the lesson and of the classroom decor.

Part D : Acknowledge sources, using in-text citations and references, for content that is quoted, paraphrased, or summarized. Ohio Learning Standards Mathematics . (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/ Ohio-s-Learning-Standards-in-Mathematics/MATH-Standards-2017.pdf.aspx? lang=en-US

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Task 3 attempt 2

Related Documents