Math News! Focus Area Topic A. 3 rd Grade Math. Grade 3, Module 3, Topic A. Properties of Multiplication and Division


 Garey Kevin Crawford
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1 Grade, Module, Topic A rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69 Topic A. Topic A. Properties of Multiplication and Division Commutative Property Product Tape Diagram Unknown n + Factors Things to Remember!!! What is a tape diagram? A tape diagram uses a rectangle(s) with numbers to represent the number in a word problem. Now that numbers are getting bigger a rectangle is used to represent the number instead of drawing dots or pictures. A tape diagram allows the student to visualize the problem. Focus Area Topic A Properties of Multiplication and Division The commutative property of multiplication means that changing the order of factors does not change the answer or product. This means that 7 x 4 = 4 x 7. By understanding this property students also learn that a majority of their multiplication facts are already known. Learning how to solve multiplication problems by using the commutative property and n+ is also taught in this topic. Solve The commutative property states that factors can change order and still have the same product. 6 x 8 can also be written as 5 x 8 + x 8. By using a multiplication fact that is already known, solving 6 x 8 can be easy. The n+ rule is simply saying to add one more group. In this case we know 5 x 8 is 40 and if more group of 8 is added (repeated addition), then 6 groups of 8 = 6 x 8 = 4. In previous lessons a question mark (?) was used to represent an unknown number. In this topic using a letter to represent the unknown is also introduced. OBJECTIVE OF TOPIC A Study commutatively to find known facts of 6, 7, 8 and 9. Apply the distributive and commutative properties to relate multiplication facts of 5 x n + n to 6 x n and n x 6 where n is the size of the unit. Mrs. James has 48 pencils for her library. Mrs. James placed a pack of 6 pencils on each desk. How many packs of pencils does Mrs. James have? Multiply and divide with familiar facts using a letter to represent the unknown.
2 Grade, Module, Topic B rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69 Topic B. Topic B Multiplication and Division Using Units of 6 & 7 Commutative Property Decompose Distributive Property Things to Remember!!! What is decomposing? Decompose it to break a number apart. When the numbers are not as big it is easier for students to multiply or divide problems. The number 5 can be decomposed into 0 + 5, or Focus Area Topic B Multiplication and Division Using Units of 6 & 7 Using number bonds to decompose and to skip count When adding two numbers together it is easier to add to a ten. Students will decompose numbers to make 0 so it is easier to add and find the answer. In the problem above the student will decompose one of the 7 s in order to combine 7 and another number to make a = 0, so if we decompose 7 into and 4 we can add the 7 and together to make 0 then add the remaining 4 to 0 and the answer is 4. Students will gain a better understanding that multiplying is actually repeated addition. Distributive Property of Multiplication When one of the factors of a product is a sum, multiplying each addend before adding does not change the product. 9 x 7 =? We can decompose the number 9 to create two smaller multiplication problems. Below is a tape diagram that decomposes 9 into 5 and 4. The problem could be written (5 + 4) x 7. If we use the distributive property the problem is written (5 x 7) + (4 x 7) =? We distributed the 7 to both the 5 and the 4. Now we can multiply two smaller problems and add them together to get the answer. OBJECTIVE OF TOPIC B 4 Count by units of 6 to multiply and divide using number bonds to decompose Count by units of 7 to multiply and divide using number bonds to decompose Use the distributive property as a strategy to multiply and divide units of 6 & 7 Interpret the unknown in multiplication and division to model and solve problems using units of 6 & 7 Using number bonds to apply the distributive property.
3 Grade, Module, Topic C rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69 Topic C. Topic C Multiplication and Division Using Units up to 8 Associative Property Mental Math Distributive Property Parentheses Product Unknown Focus Area Topic C Multiplication and Division Using Units up to 8 Solve 6 x This is a difficult problem to solve. Let s simplify the problem. Begin by listing the factors of 6., 4 and 8 are factors of 6. Knowing that 8 x are factors we can rewrite the problem as (8 x ) x. In math the parentheses are used to group important things together, so you always do them first. (8 x ) is in parentheses so you would multiply them first to get 6. This problem is still hard to solve because we are still trying to multiply 6 x. We can use the associative property to help solve the problem. The associative property says that when we are multiplying all numbers together we can multiply the numbers in any order and still get the same answer. So we can move the parentheses to make the problem easier to solve. 8 x ( x ). Drawing an array to solve the problem is a simple solution to the problem. Draw 8 groups of x. Division Word Problem The store sells meter of fabric for $7. Tonya buys some fabric that costs a total of $56. She uses meters to sew a dress. How many meters of fabric does she have left? Students may also realize that the problem can also be written as 8 x 6 or they may use the distributive property to solve the problem. The distributive property says that when one of the factors of a product is a sum, multiplying each addend before adding will not change the product or answer. Moving Parentheses OBJECTIVE OF TOPIC C Understand the function of parentheses and apply to solving problems. Model the associative property as a strategy to multiply. 4 Use the distributive property as a strategy to multiply and divide. Interpret the unknown in multiplication and division to model and solve. The first time we solved this problem the parentheses was around the addition problem. Now the parentheses are around the multiplication problem. The parentheses tell us what problems to solve first. First multiply the problem in the parentheses, 8 x = 4. Next we add 8 to that answer =. It is very important to solve the problems in parentheses first because the answer will not be the same.
4 Grade, Module, Topic D rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69 Topic D. Focus Area Topic D Multiplication and Division Using Units of 9 Students will use the distributive property to establish the 9 = 0 pattern for multiplication. Understanding this pattern will enable students to see this method of multiplication as a tool, rather than a trick. What is easier to solve, 9 x 6 or 0 x 6? 0 x 6 How many sixes are in 0 x 6? 0 sixes Topic D Multiplication and Division Using Units of 9 9 = 0 Strategy Unit Division Word Problem Joey has 54 trading cards and shares them with 7 of his friends. He is so excited he drops his box of cards and looses 4 trading cards. How many trading cards will Joey and each of his friends get? First find out how many trading cards Joey has left = c c = 40 Next divide the trading cards that are left into 8 people. d = 5 Joey and each of his 7 friends get 5 trading cards. OBJECTIVE OF TOPIC D How many sixes are in 9 x 6? 9 sixes x 6 = (0 x 6) ( x 6) 9 x 6 = 60 6 What is 60 6? 54 They will also learn to break up 9 into 5 and 4. 9 x 6 = (5 + 4) x 6 Now use the distributive property to distribute the 6 9 x 6 = (5 x 6) + (4 x 6) 9 x 6 = x 6 = 54 Kim has 9 packs of cookies with 5 in each pack. After giving to each classmate she has 5 left. How many cookies did Kim give away? First find out how many cookies Kim has. 9 x 5 = h h = 45 Apply the distributive property and the fact 9 = 0 as a strategy to multiply. Next subtract 5 from the total to see how many she gives away. Identify and use arithmetic patterns to multiply = g g = 0 Interpret the unknown multiplication and division to model and solve problems. How many classmates does Kim have? 0
5 Grade, Module, Topic E rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69 Topic E. Topic E Analysis of Patterns and Problem Solving Including Units of 0 and Multiplication Table Focus Area Topic E Analysis of Patterns and Problem Solving Including Units of 0 and In Lesson 6, students use patterns to understand: n x 0 = 0 and n x = n they will also understand that when dividing 0 by another number results in 0 but when dividing a number by 0 the answer is undefined. In Lesson 7, students use a multiplication table to explore patterns of multiplication. They will recognize the patterns of particular factors and make connections to multiplication and division. In Lesson 8, students apply the tools, representation, and concepts they have learned to solve twostep word problems using all four operations. (+, , x, ) They will also use the rounding skills learned in prior lessons to assess the reasonableness of the answers. Troy has $05 in the bank. He earns the same amount of money each week for 7 weeks and puts this in money in the bank also. Now Troy has $7 in the bank. How much does Troy earn each week? How much money did Troy put in the bank in 7 weeks? 7 05 = m m = 68 w = the number of dollars earned each week w = $4 Troy earns $4 a week, OBJECTIVE OF TOPIC E Reason about and explain arithmetic patterns using units of 0 and as they relate to multiplication and division. Identify patterns in multiplication and division facts using the multiplication table. Solve twostep word problems involving all four operations and assess the reasonableness of solutions. Tammy does homework for 4 minutes. She then does 7 chores. Each chore took 4 minutes. How many minutes does it take for Tammy to finish all of her chores and her homework? How long does it take to complete chores? How many minutes total? 7 x 4 = c c = = t t = 7 minutes
6 Grade, Module, Topic F rd Grade Math Module : Multiplication and Division with Units of 0,, 69, covers Multiplication and Division with Units of 0,, 69, Topic F. Focus Area Topic F Multiplication of SingleDigit Factors In Lessons 9 students will use the place value chart to multiply multiples of 0. For example, to solve x 40, they begin modeling x 4 in the ones place. Students relate this to multiplying x 4 tens, locating the basic fact in the tens column. They see that when multiplied by 0, the product shifts one place value to the left. In Lesson 9, students will multiply by multiples of 0 using a place value chart. Topic F: Multiplication of SingleDigit Factors and Multiples of 0 array tape diagram associative property Things to Remember!!! In Lesson 0, students will use the associative property to multiply multiples of 0. x 0 = ( x 0) = ( x ) x 0 = 4 x 0 = 40 There are 60 seconds in minute. Use a tape diagram to find the total number of seconds in 5 minutes and 45 seconds. OBJECTIVE OF TOPIC F Multiply by multiples of 0 using the place value chart. Use place value strategies and the associative property n x (m x 0)= (n x m) x 0 (where n and m are less than 0) to multiply by multiples of 0. Solve twostep word problems involving multiplying singledigit factors and multiples of 0. In Lesson, students will solve twostep word problems involving multiplying singledigit factors and multiples of 0.
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