Find whole number quotients and remainders In fourth grade, students build on their third grade work I can find whole number quotients with division within 100. Students need opportunities to with up to four-digit dividends and one-digit and remainders with up to four-digit develop their understandings by using problems in and divisors. dividends and one-digit divisors, and out of context. explain using equations, arrays, or models Examples: A 4th grade teacher bought 4 new pencil boxes. She has Reasoning Targets 260 pencils. She wants to put the pencils in the boxes so Use the strategies based on place value, the that each box has the same number of pencils. How many pencils will there be in each box? properties of operations, and/or the relationship between multiplication and Using Base 10 Blocks: Students build 260 with division. base 10 blocks and distribute them into 4 equal groups. Some students may need to trade the 2 Illustrate and explain the calculation by using hundreds for tens but others may easily recognize that 200 divided by 4 is 50. written equations, rectangular arrays, and/or Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ area models. 4) Using Multiplication: 4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65 Students may use digital tools to express ideas. Continued on next page Using an Open Array or Area Model After developing an understanding of using arrays to divide, students begin to use a more abstract model for division. This model connects to a recording process that will be formalized in the 5th grade. Example: 150 ÷ 6 Students make a rectangle and write 6 on one of its sides. They express their understanding that they need to think of the rectangle as representing a total of 150. Students think, 6 times what number is a number close to 150? They recognize that 6 x 10 is 60 so they record 10 as a factor and partition the rectangle into 2 rectangles and label the area aligned to
Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors. I can find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, and explain using equations, arrays, or models In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context. Examples: A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the boxes so that each box has the same number of pencils. How many pencils will there be in each box? Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups. Some students may need to trade the 2 hundreds for tens but others may easily recognize that 200 divided by 4 is 50. Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4) Using Multiplication: 4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65 Students may use digital tools to express ideas. Continued on next page Using an Open Array or Area Model After developing an understanding of using arrays to divide, students begin to use a more abstract model for division. This model connects to a recording process that will be formalized in the 5th grade. Example: 150 ÷ 6 Students make a rectangle and write 6 on one of its sides. They express their understanding that they need to think of the rectangle as representing a total of 150. Students think, 6 times what number is a number close to 150? They recognize that 6 x 10 is 60 so they record 10 as a factor and partition the rectangle into 2 rectangles and label the area aligned to Reasoning Targets Use the strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using written equations, rectangular arrays, and/or area models.
4th%20Grade%20Units-Revised%20June2014.docx