Learning Activities (4) | Classroom Resources (4) |

View Standards
**Standard(s): **
[MA2019] (4) 12 :

12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

This activity can be used as an introduction or engagement activity to a lesson on division with large numbers. Students will participate in a mathematical conversation that allows them to express their thinking on the relationship between multiplication and division.

*This activity results from the ALEX Resource Development Summit.*

12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

This activity can be used as an introduction to using the area model to divide large numbers. Students will complete a real-world division task that guides their thinking to use the area model.

*This activity results from the ALEX Resource Development Summit.*

12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

This activity should be used at the end of a lesson or unit on the division of whole numbers. This activity should be used as an exit slip to check students' understanding of how to find quotients of larger numbers using strategies based on place value.

*This activity results from the ALEX Resource Development Summit.*

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

Students will complete a division word problem activity that requires them to find whole-number quotients and quotients with remainders. This activity should be used after the students have been taught division strategies. This activity can be used as an assessment or extra practice for solving division word problems.

*This activity results from the ALEX Resource Gap Project.*

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

In this interactive activity, students will be led through steps to easily divide multi-digit numbers by learning divisibility rules and patterns. There are teaching activities as well as practice activities available. A handout that describes strategies taught during the interactive is available to be printed. There is a karaoke song with printable lyrics that will help students learn and remember the divisibility rules taught during the activity. After utilizing this resource, the students can complete the short quiz to assess their understanding.

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

In this interactive activity, students will be led through steps to divide a number into equal groups. There are teaching activities as well as practice activities available. Practice problems can be printed as a handout. There is a karaoke song with printable lyrics to help students remember the strategies taught during the activity. After utilizing this resource, the students can complete the short quiz to assess their understanding.

View Standards
**Standard(s): **
[MA2019] (4) 3 :

[MA2019] (4) 12 :12. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends.

3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

[MA2019] (4) 12 :

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

In Module 3, Topic E, students synthesize their Grade 3 knowledge of division types (group size unknown and number of groups unknown) with their new, deeper understanding of place value. Students focus on interpreting the remainder within division problems both in word problems and long division (4.OA.3). A remainder of 1, as exemplified below, represents a leftover flower in the first situation and a remainder of 1 ten in the second situation. While we have no reason to subdivide a remaining flower, there are good reasons to subdivide a remaining ten. Students apply this simple idea to divide two-digit numbers unit by unit: dividing the tens units first, finding the remainder (the number of tens unable to be divided), and decomposing remaining tens into ones to then be divided. Lesson 14 begins Topic E by having students solve division word problems involving remainders. In Lesson 15, students deepen their understanding of division by solving problems with remainders using both arrays and the area model. Students practice dividing two-digit dividends with a remainder in the ones place using place value disks in Lesson 16 and continue that modeling in Lesson 17 where the remainder in the tens place is decomposed into ones. The long division algorithm is introduced in Lesson 16 by directly relating the steps of the algorithm to the steps involved when dividing using place value disks. Introducing the algorithm in this manner helps students to understand how place value plays a role in the steps of the algorithm. The same process of relating the standard algorithm to the concrete representation of division continues in Lesson 17. Lesson 18 moves students to the abstract level by requiring them to solve division problems numerically without drawing. In Lesson 19, students explain the successive remainders of the algorithm by using place value understanding and place value disks. Finally, in Lessons 20 and 21, students use the area model to solve division problems and then compare the standard algorithm to the area model (4.NBT.6). Lesson 20 focuses on division problems without remainders, while Lesson 21 involves remainders.

3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

[MA2019] (4) 12 :

a. Illustrate and/or explain quotients using equations, rectangular arrays, and/or area models.

Module 3, Topic G extends to division with three- and four-digit dividends using place value understanding. Students begin the topic by connecting multiplication of 10, 100, and 1,000 by single-digit numbers from Topic B to division of multiples of 10, 100, and 1,000 in Lesson 26. Using unit language, students find their division facts allow them to divide much larger numbers. In Lesson 27, place value disks support students visually as they decompose each unit before dividing. This lesson contains a first-use script on the steps of solving long division using place value disks and the algorithm in tandem for three- and four-digit dividends (4.NBT.6). Students then move to the abstract level in Lessons 28 and 29, recording long division with place value understanding, first of three-digit, then four-digit numbers using small divisors. In Lesson 30, students practice dividing when zeros are in the dividend or in the quotient. Lessons 31 and 32 give students opportunities to apply their understanding of division by solving word problems (4.OA.3). In Lesson 31, students identify word problems as a number of groups unknown or group size unknown, modeled using tape diagrams. Lesson 32 allows students to apply their place value understanding of solving long division using larger divisors of 6, 7, 8, and 9. Concluding this topic, Lesson 33 has students make connections between the area model and the standard algorithm for long division.