Partial products and regrouping

Partial Products and Regrouping are alike because both methods are multiplied by one number and if the product of the number has 2 digits it can be carried. Now let us discuss how they are different: Partial Products and Regrouping are different because Partial Products are doing multiplication step by step and regrouping is regular multiplication.

Topic: Multiplying Numbers up to Three Digits by Numbers up to Two Digits without Regrouping Subject: Mathematics Grade Level: Grade 4 Duration: 1 hour. I. OBJECTIVES: At the end of the lesson, the students should be able to: 1. ... Step 7: Add the partial products. When using the long method we follow these steps: Ste p1: Write the …Using partial products to multiply 2- and 3-digit numbers by 1-digit numbers. Using an area model to multiply 2-digit by 2-digit numbers. Using partial products to multiply 2-digit by 2-digit numbers. Multiplying 2-, 3-, and 4-digit numbers by 1-digit numbers with regrouping. Multiplying 2-digit by 2-digit numbers with regroupingPartial Products and Regrouping are alike because both methods are multiplied by one number and if the product of the number has 2 digits it can be carried.Partial Products and Regrouping are different because Partial Products are doing multiplication step by step and regrouping is regular multiplication.Multiply using partial products and the standard algorithm with regrouping (Part 2) Multiply two two-digit numbers with the help of an area model. Break one of the two factors into tens and ones, and multiply each part by the other factor using the standard algorithm. Step 4. Your answer should be. an integer, like 6 ‍. a simplified proper fraction, like 3 / 5 ‍. a simplified improper fraction, like 7 / 4 ‍. a mixed number, like 1 3 / 4 ‍. an exact decimal, like 0.75 ‍. a multiple of pi, like 12 pi ‍ or 2 / 3 pi ‍.The partial products method is a method for multiplying multi-digit numbers. It is typically used as an introductory method to multiplying numbers larger than 10.They are alike because when you multiply with both of these methods, you get the same answer. They are different because with partial products you have to multiply tens …Introduction. Write ‘Partial Product’ on the board and ask students, "What does this mean?" Have students turn and talk to a partner to discuss its meaning. Remind students to think about similar words or math vocabulary they know. Underline product and ask, "In math, what is a product?" Answers should include "the answer to a ...

View Module 3 Notes.pdf from BIOL 2703 at Alfred State College. Grade 4 Module 3 Eureka Math Main ideas : Multiplication (Lessons 1­13, 34­38) Definition of multiplication :Compare partial products and regrouping. Describe how the methods are alike and different. Compare partial products and regrouping. Describe how the methods are alike and different ... Describe the different methods that can be used to find the product: (2x-5)(3x-1). I know there is the. I need to describe three purposes and three methods of ...A reasonable estimate of the product is $420. True False 23b. Using partial products, the products are 42 and 180. True False 23c. Using regrouping, 18 ones are regrouped as 8 tens and 1 one. True False 23d. The product is 438. True False Oqnakdl Rnkuhmf ¤ @ookhb`shnmrOqnakdl Rnkuhmf ¤ @ookhb`shnmr Use the table for 18–19. 18.Math Worksheets. Examples, solutions, and videos to help Grade 3 students learn about multiplication using the partial products method. Partial Products Multiplication. The …Multiply 2-digit numbers. Multiply. Stuck? Review related articles/videos or use a hint. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.Understanding the rubric being used to evaluate our work helps us push ourselves to try to earn the most points possible. We realized that in order to earn maximum points our answers need to be correct and our work needs to show a thorough understanding!Compare partial products and regrouping. Describe how the methods are alike and different. A bag contains 5 green marbles , 8 red marbles, 11 orange marbles, 7 brown marbles, and 12 blue marbles. You choose a marbles, A company offers the following schedule of charges: $30 per thousand for orders of 50,000 or less with the charge per …Oct 2, 2018 · Partial Products and Regrouping are alike because both methods are multiplied by one number and if the product of the number has 2 digits it can be carried. Now let us discuss how they are different: Partial Products and Regrouping are different because Partial Products are doing multiplication step by step and regrouping is regular multiplication.

When 4 is multiplied by 1, we get 4. Since there is no other digit left for multiplication, we write 4. So, we have 49200 in the third line as the partial product. Step 7: Add all the 3 partial products to obtain the final product. This means 738 + 6150 + 49200 = 56088. Step 8: Therefore, the final product is 56088. ☛ Related Topics. 2-Digit ...Multiply two 2-digit numbers with this easy format! Included is the regrouping format, as well as an example problem, that will assist your students with mastering this tricky skill! I created a step by step process for my 4th graders to use as practice. This resource would be good to have printed...A product obtained by multiplying a multiplicand by one digit of a multiplier with more than one digit is known as the partial product. When we use the partial products method of multiplication, we are really using the distributive property of multiplication to help us break the factors into smaller parts. Compare partial products and regrouping. Describe how the methods are alike and different. Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify the expression. 4002-2153=1849 how is regrouping thousand shown in the problem above.Example Use the partial products method to find the product of 124 and 3. The expanded form of 124 is 100 + 20 + 4. 3 cannot be further expanded. 100 × 3 = 300 ; 20 × 3 = 60 ; 4 × 3 = 12 300 + 60 + 12 = 372In Regrouping we add the partial products to the next tens,hundreds and so on. We don not write them down and then add later. Lets take the same example and do the multiplication with Regrouping method. 1)2 -----> ( write the number in tenth place here) 47 ×3 ___ __1 -----> ( write the number in ones place here) 2)47 ×3 ___

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Sandra used partial products to find the product of 438 × 17 by multiplying 438 by 1 and 438 by 7 to get 3,066. Find the product; Estimate. Find all the partial products. Then, add to find the final product. Draw an area model if needed. Rounding each; Explain how modeling partial products can be used to find the products of greater numbers6 Oct 2015 ... So instead of using partial products where we do 40 times three plus 6 times three, like we did last week, we're going to multiply the ones ...Everyday Mathematics Virtual Learning Community. Join the Virtual Learning Community to access EM lesson videos from real classrooms, share resources, discuss EM topics with other educators, and more. Oct 2, 2018 · Partial Products and Regrouping are alike because both methods are multiplied by one number and if the product of the number has 2 digits it can be carried. Now let us discuss how they are different: Partial Products and Regrouping are different because Partial Products are doing multiplication step by step and regrouping is regular multiplication. Answer 1 Answer: We get the same answer from both processes.In the end, it is a multiplication process. In partial product we take the values of ones, tens, hundreds in …

Practice worksheets for 2 - digit multiplication. Three strategies are included: area model, partial products and regrouping.This lesson explains the partial products algorithm for multiplying two- or three-digit numbers in columns that can be easier for some students than the standard algorithm of multiplication. It is a complete lesson with explanations and exercises, meant for fourth grade. In a nutshell, students break the number to multiply into parts, multiply ... 2 x 1-digit – Products to 999 e.g. 93 x 4; 2 x 1-digit – regrouping e.g. 73 x 7; 3 x 1-digit e.g. 436 x 7; 2 x 2-digit no regrouping e.g. 42 x 23; 2 x 2-digit regrouping e.g. 57 x 34; 4 x 1-digit e.g. 5316 x 8; Third/ Fourth Grade. Addition & Subtraction Worksheet (Challenging) (4 pages) Worksheet Generator. Partial Products Method ... A reasonable estimate of the product is $420. True False 23b. Using partial products, the products are 42 and 180. True False 23c. Using regrouping, 18 ones are regrouped as 8 tens and 1 one. True False 23d. The product is 438. True False Oqnakdl Rnkuhmf ¤ @ookhb`shnmrOqnakdl Rnkuhmf ¤ @ookhb`shnmr Use the table for 18–19. 18. Then we would have figured out that 36 times 2 is 72, but this 2 isn't just a 2. This is a 20. So 36 times 20 is 720. And now we can add these two things because 36 times 27 is the same thing as 36 times 20 plus 36 times 7. So let's add these two numbers together. 2 …The Partial Products book shows students how to break numbers into parts, multiply those parts, and then add the partial products to find the final product. The Standard Algorithm book shows students the …3-Digit Multiplication Without Regrouping. In order to find the product of a 3-digit number and a 1-digit number, we multiply the 1-digit number by each digit of the 3-digit number. ... The partial products are written one below the other and …Cross out the digit in the tens place, subtract one from it and write that number on top of the digit in the tens place. Write the "1" in front of the zero in the ones place. Explain the same process when subtracting the numbers in the tens, hundreds, thousands and the remainder of digits in the problem. If the digit is a zero to the left of ...

Step 4. Your answer should be. an integer, like 6 ‍. a simplified proper fraction, like 3 / 5 ‍. a simplified improper fraction, like 7 / 4 ‍. a mixed number, like 1 3 / 4 ‍. an exact decimal, like 0.75 ‍. a multiple of pi, like 12 pi ‍ or 2 / 3 pi ‍.

in Multiplication With Regrouping Partial Products. Additionally, the owner is granted permission to make multiple copies of the learning sheets and instructional materials found in Appendix A. This book may not be sold or given away to other people. If you would like to share this book with another person, please purchase an additional copy for each reader.Learn to multiply a 3-digit number by a 1-digit number without regrouping. In this video, we will multiply 4x201. Created by Sal Khan.Partial Products and Regrouping are similar because both methods are multiplied by a single number, and if the number’s product has two digits, it can be carried. Partial Products and Regrouping differ in that partial products perform step-by-step multiplication while regrouping is a regular multiplication. You might also wonder, “How do ...Partial products are different in regrouping in terms of how numbers are clustered from a set equation as a whole delivering it individual but naturally to all the numbers involved in the set. Regrouping is just like the commutative or associative property of numbers. Associative property of addition is used when you want to group addends.Compare partial products and regrouping. describe how the methods are alike and different. Answers: 3 Show answers. Answers. Answer from: BilliePaul95. Partail products are like pictures. regrouping is for subtraction. Answer from: Quest. answer: for each 3 girls there is 2 boys . 3: 2. hope this ! (: mark me as brainliest if you can. Answer …Compare partial products and regrouping. Describe how the methods are alike and different. Dorothy and Rosanne are baking cookies for a party. Working alone, Rosanne can finish the cookies in 6 hours. Dorothy can finish. Given that a:b = 8:5 and b:c= 3:4 find the ratio a:b:c Give your answer in its simplest form. Show all working out.This lesson explains the partial products algorithm for multiplying two- or three-digit numbers in columns that can be easier for some students than the standard algorithm of multiplication. It is a complete lesson with explanations and exercises, meant for fourth grade. In a nutshell, students break the number to multiply into parts, multiply ...Compare partial products and regrouping. describe how the methods are alike and different. Answers. Partial product multiplication is the process of multiplying the numbers partially (respectively to ones, tens and hundreds) and adding them together in the end. For example, in order to find the product of 3 8 × 6 we should write that, 1) 3 8 × 6 ___ 4 8 …

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Multiplying 2-digits by 1-digit with partial products. Multiply using partial products. Multiply without regrouping. Multiply with regrouping. Multiplying 3-digit by 1-digit. Multiplying 3-digit by 1-digit (regrouping) Math >. 4th grade >. Multiply by 1-digit numbers >.Partial Products and Regrouping Multiplication Anchor Charts and Posters. by . Simple Little Pocket. 5.0 (1) $2.00. PDF. Help your students remember how to multiply! Keep these colorful posters on your Bulletin Boards as a great reference for your students throughout the year.Let The Little Letters and The Little Numbers Come to Life in your ...Oct 12, 2015 - Engage students in computation practice of standard multiplication algorithm with up to 2-digit by 3-digit problems. 12 Posters in AllPost around the room.Get students up and moving!Students estimate and solve the problems.Self-checking with any QR Code Reader.Answers show as Colorful Displays on an...Multiply with partial products (2-digit numbers) CCSS.Math: 4.NBT.B.5. Google Classroom. Greg tried to evaluate 86 × 37 using partial products, but he made a mistake. His work is below. 86 × 37 ― Step 1 2,400 30 × 80 Step 2 18 3 × 6 Step 3 560 7 × 80 Step 4 + 42 ― 7 × 6 Step 5 3,020. The Strategic Instruction Multiplication With Regrouping Partial Products Algorithm program contains the materials needed to teach the partial products algorithm for multiplication using the Concrete-Representational-Abstract method of instruction, with an emphasis on the Home Work Help. home-work-help. Karthik May 10, 2019, 11:52amAnswer: The comparison and similarity between Partial product and Regrouping is explained below. Step-by-step explanation: Partial Product; Partial Product is a way of multiplication in which you multiply the number in parts depending upon their units respectively and then add them together for a complete answer . for example if we multiply 12 by 12 it will be in parts first it will give us 24 ...Math Worksheets. Examples, solutions, and videos to help Grade 3 students learn about multiplication using the partial products method. Partial Products Multiplication. The following diagram shows examples of partial products multiplication for 1-digit multiplier and 2-digit multiplier. Scroll down the page for more examples and solutions on ...Apr 19, 2017 · Partial Products. I love using partial sums, partial differences, partial products, and even partial quotients strategies for doing math in my head. It is basically using place value to solve problems. So how does it work with multiplication? Step 1: Take both numbers you will be multiplying and write them out in expanded form. On the right, the first three partial products are \(2 \times 346\) and the second three partial products are \(70 \times 346\). Our standard algorithm is simply a shortening up of the partial products algorithm. We don't write all the zeroes and we doing the carrying involved with adding more than one partial product at a time in our head.In mathematics, regrouping is the reorganization of numbers from one column to another to perform addition and subtraction equations. Typically, regrouping is referred to as “carrying” and “borrowing” a number.We can define regrouping as a process of rearranging groups in order to carry out a mathematical operation. While carrying out multiplication you need to regroup or rearrange the numbers in terms of place value to carry out the operation. ... Now, adding the partial products = 0.12 + 1.8 + 4.8 + 72 = 78.72 ... ….

This lesson explains the partial products algorithm for multiplying two- or three-digit numbers in columns that can be easier for some students than the standard algorithm of multiplication. It is a complete lesson with explanations and exercises, meant for fourth grade. In a nutshell, students break the number to multiply into parts, multiply ...Keep going! Check out the next lesson and practice what you’re learning:https://www.khanacademy.org/math/cc-fourth-grade-math/imp-multiplication-and-division...Partial Products as a Multi-Digit Multiplication Strategy. Most teachers are likely aware of the Partial Products method. In case you are not, it’s really just taking the larger number and breaking it out into expanded form and then having the other factor multiply each of the expanded form factors. Then they are added up to get the final ...Regrouping is the borrowing of a value from one column of numbers to another to aid a mathematical operation. If one is subtracting, it’s necessary to regroup when the number at the top of a column is smaller than the one below it.Multiply using partial products Get 3 of 4 questions to level up! Multiply with partial products (2-digit numbers) Get 3 of 4 questions to level up! Multiply by 1-digit numbers. Learn. Multiplying 2-digit by 1-digit ... Practice. Multiply without regrouping Get 5 of 7 questions to level up! Multiply with regrouping Get 5 of 7 questions to level up! Multi …Compare partial products and regrouping. Describe how the methods are alike and different ~~~What can you look for to help you determine the structure that is being used in an informational text? ... A factory manufactures two products, each requiring the use of three machines. The first machine can be used at most 60Math Worksheets. Examples, solutions, and videos to help Grade 3 students learn about multiplication using the partial products method. Partial Products Multiplication. The following diagram shows examples of partial products multiplication for 1-digit multiplier and 2-digit multiplier. Scroll down the page for more examples and solutions on ... Partial Products and Regrouping are similar because both methods are multiplied by a single number, and if the number’s product has two digits, it can be carried. Partial Products and Regrouping differ in that partial products perform step-by-step multiplication while regrouping is a regular multiplication. You might also wonder, “How do ...Can you compare partial products and regrouping and describe how the methods are alike and different? What is the volume of a spherical water tank whose radius is 19? What does pi stand for when finding the volume of a cylinder? What is four fifths times 2? How much is a no date - p - Indian head nickel - 24 karat gold layered - p mint mark - …National Center on Intensive Intervention. This video describes how to use the partial products strategy with multiplication. The mathematics problem in this video requires regrouping. Although the partial sums strategy eliminates the regrouping during multiplication, regrouping may still be necessary when students add each of the partial ... Partial products and regrouping, compared partial products and regrouping and describe how they are alike and different. heart. 1. verified. Verified answer. Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is Jennifer. star. 4.6/5. heart. 4. verified. Verified answer. What is the present value of a cash inflow of 1250 four …, Regrouping, or borrowing, in subtraction is best explained with an example. Let’s show you how with this example: 24 – 16. Now, let’s put them in columns: Look at the ones – we’re trying to take 6 away from 4. That’s not possible, so we have to borrow 10 from the tens column. Now we can now take 6 away from 14. The answer is 8., Oct 19, 2023 · Long Multiplication Example: Multiply 234 by 56. Long Multiplication Steps: Stack the numbers with the larger number on top. Align the numbers by place value columns. Multiply the ones digit in the bottom number by each digit in the top number. 6 × 4 = 24. Put the 4 in Ones place. Carry the 2 to Tens place. , Your students will LOVE this 2-digit partial product multiplication matching activity! Students can use any method, such as area model, partial product, or regrouping, making this an extremely versatile 4th grade math center. They will be so motivated to match their eggs ang bacon!, Different: Partial products are specifically used for multiplication while regrouping is mainly used in addition and subtraction. Partial products involve multiplying each digit to get partial results, while regrouping involves carrying or borrowing digits to ensure accuracy in calculations. Learn more about the multiplication visit:, The students were assessed on their knowledge of lessons 3.1, 3.2, and 3.4. As we come close to Thanksgiving Break, the students will be introduced to the regrouping (traditional) method of multiplication for multi-digit numbers. We will continue to practice both the partial products and regrouping methods after the break., When 4 is multiplied by 1, we get 4. Since there is no other digit left for multiplication, we write 4. So, we have 49200 in the third line as the partial product. Step 7: Add all the 3 partial products to obtain the final product. This means 738 + 6150 + 49200 = 56088. Step 8: Therefore, the final product is 56088. ☛ Related Topics. 2-Digit ..., All that regrouping can be confusing. Which number goes where? And better yet, why? Help students master multiplication with regrouping using the two latest books from KUCRL: Multiplication With Regrouping: Partial Products and Multiplication with Regrouping: Standard Algorithm., Oct 27, 2015 · Different: Partial products are specifically used for multiplication while regrouping is mainly used in addition and subtraction. Partial products involve multiplying each digit to get partial results, while regrouping involves carrying or borrowing digits to ensure accuracy in calculations. Learn more about the multiplication visit: , Research has shown that teaching the standard U.S. algorithms fails with large numbers of children, and that alternative algorithms are often easier for children to understand and learn. For this reason, Everyday Mathematics introduces children to a variety of alternative procedures in addition to the customary algorithms. Examples of a couple ..., The full and partial equity methods are two of three main ways of dealing with the problem of producing accounts when one company has invested in another company. The third method is simple equity. The problem arises because there is often ..., Oct 19, 2023 · Long Multiplication Example: Multiply 234 by 56. Long Multiplication Steps: Stack the numbers with the larger number on top. Align the numbers by place value columns. Multiply the ones digit in the bottom number by each digit in the top number. 6 × 4 = 24. Put the 4 in Ones place. Carry the 2 to Tens place. , What are the partial products that result from multiplying 15 × 32? Type below: _____ Answer: Partial products are 300, 150, 20, 10. Explanation: Partial products are 300, 150, 20, 10. Question 27. A city bus company sold 39 one-way tickets and 20 round-trip tickets from West Elmwood to East Elmwood. One-way tickets cost $14. …, compared partial products and regrouping and describe how they are alike and different. heart. 1. verified. Verified answer. Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is Jennifer. star. 4.6/5. heart. 4. verified. Verified answer. What is the present value of a cash inflow of 1250 four …, Learn to multiply a 3-digit number by a 1-digit number without regrouping. In this video, we will multiply 4x201. Created by Sal Khan., Represent the following expressions with disks, regrouping as necessary. To the right, record the partial products vertically. Question 1. 4 × 513 Answer: Explanation: Represented the following expression 4 X 513 = …, Step 4. Your answer should be. an integer, like 6 ‍. a simplified proper fraction, like 3 / 5 ‍. a simplified improper fraction, like 7 / 4 ‍. a mixed number, like 1 3 / 4 ‍. an exact decimal, like 0.75 ‍. a multiple of pi, like 12 pi ‍ or 2 / 3 pi ‍., We can multiply larger numbers by multiplying by the tens and ones separately, then adding the products together. Multiplying with partial products is one way we use the distributive property. Created by Sal Khan ., 57 × $43 Use partial products. Use regrouping. $ 4 3 × ___ 5 7 $ 4 3 × 5 7 1. How do you know your answer is reasonable? 2. Look at the partial products and regrouping methods above. How are the partial products 2,000 and 150 related to 2,150? How are the partial products 280 and 21 related to 301?, Compare partial products and regrouping. Describe how the methods are alike and different. Compare partial products and regrouping. Describe how the methods are alike and different ... Describe the different methods that can be used to find the product: (2x-5)(3x-1). I know there is the. I need to describe three purposes and three methods of ..., These activities will work for any math textbook chapter covering the fourth grade skill of multiplying one digit by two, three, and four digits and covering the strategies of distributive property, area models, expanded form, partial products, and regrouping. Each of the 15 activities (listed below) is self grading and has around ten questions., Check out these related 4th Grade Math Workshop Units! Multiplication & Division Basics Guided Math Workshop Grade 4. $12.00. Add to cart. Multi-Digit Division Guided Math Workshop. $12.00. Add to cart. Multiplication Strategies with Larger Numbers Guided Math Workshop Unit. $12.00., Partial Product is for multiplication and regrouping is for addition. Hope that helped:), May 3, 2023 · 3 Digit Multiplication Examples: Example 1: Multiply 123 123 by 3 3. Write the given multiplication of 123 × 3 123 × 3 as shown below where 123 123 is the multiplicand and 3 3 is the multiplier. After multiplying these numbers we get the product as 269 269. Example 2: Multiply 211 211 by 3 3. , Compare partial products and regrouping. Describe how the methods are alike and different. 4002-2153=1849 how is regrouping thousand shown in the problem above. Which inverse operations could you use to solve the equation m/5 - 8 = -6? Select two answers A. Add 8 to each side and then., 57 × $43 Use partial products. Use regrouping. $ 4 3 × ___ 5 7 $ 4 3 × 5 7 1. How do you know your answer is reasonable? 2. Look at the partial products and regrouping methods above. How are the partial products 2,000 and 150 related to 2,150? How are the partial products 280 and 21 related to 301?, Multiply with partial products (2-digit numbers) CCSS.Math: 4.NBT.B.5. Google Classroom. Greg tried to evaluate 86 × 37 using partial products, but he made a mistake. His work is below. 86 × 37 ― Step 1 2,400 30 × 80 Step 2 18 3 × 6 Step 3 560 7 × 80 Step 4 + 42 ― 7 × 6 Step 5 3,020. , This HUGE operations bundle will send your students off on rigorous digital adventures where they will practice:Multi-Digit Addition with Regrouping 4.NBT.4Multi-Digit Subtraction with Borrowing & Subtracting Across Zeros 4.NBT.4Multiplicative Comparisons 4.OA.1 & 4.OA.2Multi-Digit Multiplication with up to 4 by 1 digit numbers (estimation, area model, …, Use area model /partial products. Partial products; patterns of zeros; regrouping; 2-digit number Write a problem multiplying a 3-digit number by a 2-digit number. Show all the steps to solve it by using place value and regrouping and by using partial products. 1.8 Relate Multiplication to Division (*Save this lesson for the . 5.NBT.6 Companion ..., Use area model /partial products. Partial products; patterns of zeros; regrouping; 2-digit number Write a problem multiplying a 3-digit number by a 2-digit number. Show all the steps to solve it by using place value and regrouping and by using partial products. 1.8 Relate Multiplication to Division (*Save this lesson for the . 5.NBT.6 Companion ... , In math, regrouping can be defined as the process of making groups of tens when carrying out operations like addition and subtraction with two-digit numbers or larger. To regroup means to rearrange groups in place value to carry out an operation. We use regrouping in subtraction, when digits in the minuend are smaller than the digits in the ..., Both partial products and regrouping involve breaking down a multiplication problem into smaller, more manageable parts. In partial products, you multiply each digit of one number by each digit of the other number, and then add the products together to get the final answer., Understanding the rubric being used to evaluate our work helps us push ourselves to try to earn the most points possible. We realized that in order to earn maximum points our answers need to be correct and our work needs to show a thorough understanding!