Grade 3 Operations and Algebraic Thinking OA.5 & OA.6
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1 THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 3 Operations and Algebraic Thinking OA.5 & OA COMMON CORE STATE STANDARDS ALIGNED MODULES
2 THE NEWARK PUBLIC SCHOOLS Office of Mathematics MATHTASKS Operations and Algebraic Thinking - 3.OA.5. & 3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Goal: Students will apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). In addition, students will understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Essential Questions: What is multiplication? What are the properties of multiplication? How can multiplication be used when dividing? Prerequisites: Whole Numbers Simple Counting Addition Subtraction Factors Embedded Mathematical Practices MP.1 Make sense of problems and persevere in solving them MP.2 Reason abstractly and quantitatively MP.3 Construct viable arguments and critique the reasoning of others MP.4 Model with mathematics MP.5 Use appropriate tools strategically MP.6 Attend to precision MP.7 Look for and make use of structure MP.8 Look for and express regularity in repeated reasoning Lesson 5 3. OA.5 & 3.OA.6 Golden Problem Lesson 4 3. OA.6 Using multiplication to divide Lesson 3 3. OA.5 Properties of Multiplication Lesson 2 3. OA.5 Commutative Property and Multiplicative Identity Property of One Lesson 1 3. OA.5Understanding Multiplication Lesson Structure: Introductory Task Prerequisite Skills Focus Questions Guided Practice Homework Journal Question Page 2 of 37
3 Multiplication Concepts Multiplication can be defined in terms of repeated addition. For example, 3 6 can be viewed as More generally, for any positive integer n, n b can be represented as n b = b + b + + b, where the sum on the right consists of n addends. A rectangular array provides a visual model for multiplication. For example, the product 3 6 can be represented as By displaying 18 dots as 3 rows with 6 dots in each row, this array provides a visual representation of 3 6 as An equivalent area model can be made in which the dots of the array are replaced by unit squares. Besides representing 3 6 as an array of 18 unit squares, this model also shows that the area of a rectangle with a height of 3 units and a base of 6 units is 3 6 square units, or 18 square units. Multiplication is a binary operation that operates on a pair of numbers to produce another number. Given a pair of numbers a and b called factors, multiplication assigns them a value a b = c, called their product. Multiplication has certain fundamental properties that are of great importance in arithmetic. The Commutative Property of Multiplication states that changing the order in which two numbers are multiplied does not change the product. That is, for all numbers a and b, a b = b a. The array model can be used to make this plausible. For example, because 3 6 = 6 3, an array with 3 rows and 6 dots in each row has the same number of dots as an array with 6 rows and 3 dots in each row. Another important property of multiplication is the Identity Property of Multiplication. It states that the product of any number and 1 is that number. That is, for all numbers a, a 1 = 1 a = a. The Zero Property of Multiplication states that when a number is multiplied by zero, the product is zero. That is, for all numbers a, a 0 = 0 a = 0. Page 3 of 37
4 Teaching Tips Teaching Tip 1 Digit Name vs. Digit Value Stress place value in multiplication by distinguishing between the name of the digit and the value it stands for. The 2 in 24 stands for 2 10 = 20, not 2. Base-10 blocks and area model diagrams emphasize the value that each digit stands for because they use expanded notation to build the answer. Teaching Tip 2 Drawing Rectangles for an Area Model The area model is an alternative and efficient way to multiply. Encourage students to draw rectangles, even though the rectangles may not be drawn to scale. If students need to use base-10 blocks as a transitional step, change the numbers in the problems to match the quantity of blocks that are available. Teaching Tip 3 Using an Area Model to Record Multiplication Is it okay to permit students to use the area model as a recording method for multiplication? Yes. An area model not only helps to explain why the standard algorithm commonly taught in the United States for multiplication works, it is an efficient recording alternative. Some students (especially visual learners and those who have difficulty keeping numbers lined up in multiplication problems) may prefer it. Furthermore, this method has certain benefits. It illuminates important mathematical concepts (such as the distributive property), allows for computational flexibility (expanded notations allow students to use derived facts), and reinforces the concept of area. Finally, when students take algebra, they are likely to see the area model when they learn to multiply and factor polynomials. Page 4 of 37
5 Multiple Representations to Multiplication In the identity 3(4 + 5) = 3(4) + 3(5), the 3 is distributed over the 4 and the 5. Distributive Property a(b + c ) = ab + ac and (b + c )a = ba + ca Commutative Properties of Multiplication a b = b a 3 4 = 4 3 (3 4) 5 =12 5 = 60 or 3 (4 5) =3 20 = 60 Associative Properties of Multiplication (a c = a (b ) Area Model Array Model Interpret products of whole numbers 5 7 as the total number of objects in 5 groups of 7 objects each Page 5 of 37
6 3.OA.5: LESSON 13.OA.5: LESSON 1 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). Below is an array that shows 6 x 3 = 18. Look at the array below. Design your own array that would depict the problem 8 x 4. What does 8 x 4 equal? Would the answer change if the problem was 4 x 8? Use your array to help you answer these questions. Example 6 x 3=18 Focus Questions Question 1: What is multiplication and what does it tell us? Question 2: How is multiplication related to addition? Journal Question Why is understanding how to multiply useful? Describe one way you could use multiplication in your daily life. Page 6 of 37
7 3.OA.5: LESSON 1 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). Use the arrays below to help you identify the multiplication problems that are being described _X_ or _ X X_ or _ X _ _X_ or _ X X_ or _ X _ _X_ or _ X X_ or _ X _ Page 7 of 37
8 3.OA.5: LESSON 1 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with Create your own array below that identifies the multiplication problems that are listed x 5 or 5 x x 7 or 7 x x 9 or 9 x x 3 or 3 x 10 4 x 5 or 5 x 4 8 x 3 or 3 x 8 Page 8 of 37
9 3.OA.5: LESSON 1 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Name Date_ Below you will need to either identify the multiplication problem that is described by an array, or create your own array to describe a multiplication problem that is given. Use the arrays below to help you identify the multiplication problems that are being described _X_ or _ X X_ or _ X _ _X_ or _ X X_ or _ X _ Page 9 of 37
10 5. 6. _X_ or _ X X_ or _ X _ Create your own array below to that identifies the multiplication problems that are listed x 5 or 5 x x 10 or 10 x x 9 or 9 x x 3 or 3 x 4 4 x 5 or 5 x 4 8 x 3 or 3 x 8 Page 10 of 37
11 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Do the diagrams below show the same quantity of stars? Describe how you can determine the answer using multiplication. Diagram A Diagram B Focus Questions Question 1: What strategies can be used to multiply? Question 2: How do the numbers 1 and 0 effect multiplication? Journal Question In your own words, describe what happens when you multiply two numbers together. Explain what is special about multiplying by 1. Page 11 of 37
12 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Introductory Task Guided Practice Collaborative Homework Assessment Identify the multiplication problems that are pictured below. 1. X _ = or _ X _ = _ X _ = or _ X _ = _ X _ = or _ X _ = _ Page 12 of 37
13 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. 4. X _ = or _ X _ = _ 5. X _ = or _ X _ = _ 6. X _ = or _ X _ = _ 7. X _ = or _ X _ = _ Page 13 of 37
14 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Create pictorial representations of the multiplication problems listed below 8. 1 X 7 = or 7 X _1_ = _ X 6 = or 6 X _4_ = _ 9 X 2 = or 2 X _9_ = _ Page 14 of 37
15 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Name: Date: _ Identify the multiplication problems that are pictured below. 1. X _ = or _ X _ = _ 2. X _ = or _ X _ = _ 3. X _ = or _ X _ = _ Page 15 of 37
16 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. 4. X _ = or _ X _ = _ X _ = or _ X _ = _ X _ = or _ X _ = _ 7. X _ = or _ X _ = _ Page 16 of 37
17 3.OA.5: LESSON 2 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Create pictorial representations of the multiplication problems listed below 8. 1 X 9 = or 9 X _1_ = _ X 5 = or 5 X _4_ = _ 7 X 2 = or 2 X _7_ = _ Page 17 of 37
18 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Zack wants to hang his 8 model airplanes from his bedroom ceiling with wire. Each model airplane needs 6 inches of wire. How many inches of wire will Zack need to hang all 8 of his model airplanes? If Zack bought two more airplanes, how much more wire would he need? Focus Questions Question 1: Does it matter what order the numbers are in when you multiply? Question 2: Is there more than one way to multiply and get the same result? Journal Question If 7x9=63, and 2+5=7, does (2x9)+(5x9)=63? Explain your answer in words or pictures. Page 18 of 37
19 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Look at the example below. Notice how larger groups can be broken into smaller pieces to make multiplying easier. In this case 7x8=56. However, 7 can be broken down into 2+5. So, 2x8=16 and 5x8=40, and 40+16=56. 7x 8 = 56 5 x 8 = 40 2 x 8 = Look at the arrays below. Try to determine what multiplication problem the original array represents. Then try to break it into small pieces like the example Page 19 of 37
20 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision Page 20 of 37
21 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. 4. xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx + 5. OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO OOOOOOOOO + Page 21 of 37
22 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Introductory Task 6. Guided Practice Collaborative Homework Assessment Page 22 of 37
23 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision Page 23 of 37
24 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Name _ Date Look at the arrays that follow. Try to determine what multiplication problem the original array represents. Then try to break it into small pieces like the example Page 24 of 37
25 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx + 5. OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO + + Page 25 of 37
26 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision. Introductory Task 6. Guided Practice Collaborative Homework Assessment Page 26 of 37
27 3.OA.5: LESSON 3 Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication) 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) = = 56. (Distributive property). MP: Make sense of problems and persevere in solving them, Reason abstractly and quantitatively, Model with mathematics, Use appropriate tools strategically, and attend to precision Page 27 of 37
28 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by 8. Farmer Fahy was rounding up his sheep when a thunderstorm came rolling in. He was not sure if he had all of the sheep herded into the barn. He knows that he has 12 sheep. When he looked under the stall in the barn, he counted 48 feet. Tell Farmer Fahy if he has all of his sheep, or if he needs to go back outside in the thunderstorm to look for any that are missing. Focus Questions Question 1: How can multiplication help with division? Question 2: What does division really mean? Journal Question What are we doing with number when we divide? Write a journal entry as if you were trying to explain division to another student. Use examples. Page 28 of 37
29 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by 8. Determine the missing number in these division problems by using multiplication Page 29 of 37
30 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by Page 30 of 37
31 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by Page 31 of 37
32 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by 8. Name _ Date Determine the missing number in these division problems by using multiplication Page 32 of 37
33 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by Page 33 of 37
34 3.OA.6: LESSON 4 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by Page 34 of 37
35 3.OA.5-6: LESSON 5 Understand division as an unknown-factor problem. For example, find32 8 by finding the number that makes 32 when multiplied by 8. Juan is having his birthday party at the amusement park. He and his friends have broken up into two equal groups of four, so that their parents can chaperone them easily. His mom has bought a total of 72 ride tickets for Juan and each of his friends. How many tickets will each group get? Use pictures, mathematical operations, and words to explain your answer. Focus Questions Question 1: What strategies can be used to find answer to a multiplication problem? Question 2: Can you determine the answer to a division problem by multiplying? If so, how? Journal Question If you had to explain how to multiply to a 2 nd grader, how would you do it? Provide examples so that they can understand. Page 35 of 37
36 LESSON 5 RUBRIC Score GOLDEN PROBLEM Description 3 Student has an understanding of multiplication and division. Student correctly determines the amount of children (including Juan) to be 8. In addition, the student correctly identifies the total number of tickets needed to be is 72. The student correctly determines the amount of tickets each group gets is 36 (72 total tickets divided by 2 groups). The student then identifies that the amount of tickets per group (36) must be divided by the amount of people in each group (36/4). The students identifies that each person will get 9 tickets in each group (9x4 = 36). All of the information and explains his/her conclusion through the use of mathematical language, pictures and diagrams, and/or mathematical processes. 2 Student has an understanding of multiplication and division, however the student does not identify each the amount of tickets each student is to receive. Student has an understanding of dividing the amount of tickets (72) by 2 for the 2 groups, however does not identify what each student should get. The student shows his/her work, however, has limited explanation through the use of language, pictures, diagrams, and/or mathematical processes. 1 Student may determine how many children are at the party, but fails to figure out the total number of tickets that are needed. The student does not show work and has flaws in their approach to answer the problem. 0 Does not address task, unresponsive, unrelated or inappropriate. Page 36 of 37
37 Third Grade CCSSM Fluencies Skills Multiply/divide within 100 (By end of year, know from memory all products of two one digit numbers) Add/subtract within 1000 Skill builders for the above fluencies. 1. Addition Worksheet Two Plus Two Digit Addition Version 3 Answer Key 2. Addition Worksheet Three Plus Two Digit Addition Version 3 Answer Key 3. Multiplication M + N Two Minute Test Version 1 Answer Key 4. Multiplication M + N Two Minute Test Version 2 Answer Key Page 37 of 37
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