Math Multi-Digit Division Grade Created By: The Owl Teacher
A Note to the Teacher As you progress through this unit, please keep in mind that it s important for your students to have the multiplication foundational skills mastered such as arrays and groupings. It s also just as important that they are fluent in their basic multiplication facts. In this unit you will see that I have discussed the two different types of division, partitive and quotative. This is a common core requirement. While it may be tempting to skip it, I strongly recommend that you do not. These two different types of division will help students grasp the various strategies as you move along throughout the unit. This foundation will also be critical when you approach fractions. I have extensively researched the strategies for division and chosen the ones in this unit based on their flow and how they help students move progressively from concrete to more abstract. I have also discovered along with my research that there are many mistaken names floating around with confusion on what each strategy is actually called. Ultimately, allow students to use whichever strategy that they feel most comfortable with. Don t feel that you must teach each of these lessons in this particular order. These were just the order I felt most comfortable teaching them in to help scaffold the information. You are welcome to skip lessons or add in lessons. However, you may need more time than just one day for each lesson depending on your class. I don t know your class and how long they need with each concept. That is why the pretest is absolutely critical. Never move forward until the large majority of your class understands and is ready for the next lesson. Additionally, continuously review the previously taught areas to keep it fresh in your students minds. I wish you best of luck during this unit!
Standards Addressed.NBT.A. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 0 by applying concepts of place value and division..nbt.b. Find whole-number quotients and remainders with up to four-digit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. SOURCE: National Governors Association Center for Best Practices & Council of Chief State School Officers. (00). Common Core State Standards for Mathematics. Washington, DC: Authors.
Unit Overview Lesson What is division? (Partitive Division) Lesson What are remainders? Lesson? (Quotative Division) Lesson How do we estimate with compatible numbers? Lesson 5 multi-digit numbers that are multiples of ten? pg. 7 Lesson How can I use the relationship between multiplication & division to divide? pg. 0 pg. 8 pg. 8 pg. 55 Lesson 7 multi-digit numbers using the area model (with base ten blocks)? Lesson 8 multi-digit numbers using the area model? Lesson 9 multi-digit numbers using the box model method? Lesson 0 multi-digit numbers with the box model method? pg. pg. 7 pg. 78 pg. 90 pg. 99 Lesson multi-digit numbers using the distributive property? Lesson multi-digit numbers using the distributive property? Lesson multi-digit numbers using the partial quotients method? Lesson multi-digit numbers using the partial quotients method? Lesson 5 How can I demonstrate all that I have learned? (Show what I know) pg. pg. 8 pg. pg. 8 pg. 5 Pretest pg. - Post-Test pg. 50-5 Vocabulary Covered Dividend Divisor Quotient Division Fair Sharing Partitive Division Remainder Quotative Division Decompose Inverse Operation Area Model Array Box Model Method Distributive Property Partial Quotients Method Estimate Compatible Numbers Strategy
Lesson :? (Quotative) I Can Statement I can explain what division is. CCSS.NBT. (Quotative) Vocabulary Dividend; Divisor; Quotient; Division; Remainder; Quotative Division Materials Quotative Division Anchor Chart; Quotative Interactive Notebook Piece; Division Quilt Squares and Division Quilt Problems; Color Pencils/Markers Mini-lesson Alright boys and girls, we have been spending a lot of time talking about fair sharing or partitive division. Today, I want to introduce you to a another type of division called Quotative. These types of division have fancy names, but they really aren t that much different. Instead of distributing our dividend into equal groups, we are going to actually create sets of the divisor. I m going to show you what I mean. Imagine that I have the division problem 8. The first thing I m going to do is take a piece of graph paper and box out 8 squares. The reason I m boxing out 8 squares is because that is my dividend. Now I m going to color in a set of six in red. I chose because that is my divisor right here in the problem. Now I m going to color in another set of six in a different color, just so I can see the different sets. I m going to keep doing this until I can t make another set of six. Each set I m going to change the color with. Once I get to the end here where I can t color a full set, I know these are my remainders. I m going to number them. Now I have my answer. I m going to count each colored set to find the total and then add in my remainder. Now I know that 8 is R. (Continue demonstrating again using the Quotative Division Anchor Chart, helping students understand the difference between Partitive Division and Quotative Division.) Active Engagement Now, I m going to give you a chance to try this way! I have this quotative division interactive notebook piece that you will glue into your math notebook. Then you will take the grid that you are provided and color in the sets based on the divisor just like I did today during the mini-lesson. I ll be around to assist. (Have students get started. You can have them work on it alone or independently. I have provided two different options; one with the divided exactly on the grid and the other with a 00 piece grid so that students have to count out the dividend. You can decide which you prefer. Take note of any students who are struggling. After a few minutes, check it together.) Link and Independent Practice Today we are going to create division quilts. You will continue practicing quotative division and when you are finished, we are going to put all of our squares together to create a fancy quilt. Before we get started, are there any questions about quotative division? Alright, let s get started. (Copy the Division Quilt Problems on to the back of the Division Quilt Squares. Just like before, there is the option of doing the squares using the actual dividend number or the 00 piece and having students count out the dividend.) Intervention Some students may need some additional practice with this type of division. Consider using manipulatives and smaller numbers to start. Extension Have students compare and contrast the differences between quotative and partitive division. Closing Have students share with a neighbor which type of division, quotative or partitive, they like best and why.
Quotative Division Anchor Chart Quotative Division Finding the answer by creating sets of the divisor. 8 =? sets of (the colored pieces) as a remainder (the numbered) 8 = R 7 9 =? 8 sets of 9 (the colored pieces) 5 7 8 7 9 = 8 R as a remainder (the numbered)
Quotative Division Interactive Notebook Piece glue here Quotative Division 7 = 8 5 = Directions: Cut out the interactive notebook above. Cut along the solid black lines and fold on the dotted. Then glue it into your notebook. Next, cut out the grids below and glue them inside the interactive notebook pieces underneath the appropriate flap. Finally, solve the problems using quotative division and write the answer on the line.
KEY Quotative Division Interactive Notebook Piece glue here Quotative Division 7 = 8 5 = R Directions: Cut out the interactive notebook above. Cut along the solid black lines and fold on the dotted. Then glue it into your notebook. Next, cut out the grids below and glue them inside the interactive notebook pieces underneath the appropriate flap. Finally, solve the problems using quotative division and write the answer on the line. 589 7 5 0
Quotative Division Interactive Notebook Piece glue here Quotative Division 7 = 8 5 = Directions: Cut out the interactive notebook above. Cut along the solid black lines and fold on the dotted. Then glue it into your notebook. Next, cut out the grids below and glue them inside the interactive notebook pieces underneath the appropriate flap. Finally, solve the problems using quotative division and write the answer on the line.
Division Quilt Squares
Division Quilt Squares
Division Quilt Problems = 9 9 = 5 7 = 8 7 = 87 9 = = 5 = 7 5 = 5 = 8 = 95 5 = 7 =
Division Quilt Squares 5 5 0 9 8 7 9 8 57 5 7 9 5 8 0 5 8 7 0 5 8 7 9 5 5 7 8 0 5 7 9 8 5 7 9 5 5 5 0 98 7 8 5 7 8 5 7 9 KEY 7 8 5
KEY Division Quilt Problems = 8 R 9 9 = 0 R 5 7 = 9 R R R5 8 7 = 87 9 = 9 R = 5 = 8 7 5 = 7 R 5 = 8 = 8 R 95 5 = 9 7 = R
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