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Division Strategies We’ve just begun our division unit! As I introduce new division strategies I’ll add them to this document. Many of the strategies will be stepping stones to another more abstract strategy. In third grade, the students were introduced to the concept of division through problems related to known multiplication facts. The state’s third grade TEKS also specified that all problems were to be supported with pictures because the goal was for the students to learn that division is the process of breaking a total up into equal sized groups. This year students are expected to be able to divide three digit by one digit numbers without the support of pictures. To get them to this point, we introduce them to a variety of strategies that will bridge the gap. Many of the strategies will be stepping stones to another more abstract strategy. 1)Multiplication/Division inverse relationships Students use their knowledge of fact families to solve simple division problems. For example, 63 ÷ 9 = _____ could be interpreted as 9 x ___ = 63. 2)Break the problem apart using known multiplication facts Students will use facts that they know to solve division problems piece by piece. For example: 56 ÷ 4 = _____ Students will choose a 4’s fact that they are comfortable using, such as 4x10 or 4x12. They will then subtract the product of this equation from 56, which should result in another total that they can easily divide by 4 using another known multiplication fact. Step #1: 4x10 = 40 Start with a known 4’s fact. Step #2: 56 – 40 = 16 Subtract the product from step #1 from the dividend. Step #3: 4 x 4 = 16 Identify the 4’s fact that will equal the total from step #2. Step #4: (4x10) + (4x4) = (14x4) Add up the groups of 4. Since there are 14 groups of 4, then 56 ÷ 4 = 14 In the beginning, students often use tile manipulatives or draw arrays on graph paper to represent the problem: 4 x 10 = 40 4 x 4 = 16 Students first arrange the 56 tiles into one array with 4 rows. They then separate the large array into two smaller arrays that represent known facts. Finally, they can add the 10 groups and 4 groups to determine that the array represents 14 groups of 4. This visual representation usually helps them see how to break up a larger dividend into smaller parts. Students can break the array into any combination of facts they are comfortable using.