View Standards
**Standard(s): **
[MA2015] (5) 2 :

[MA2019] (4) 3 :

2 ) Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5-OA2]

Examples: Express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.

[MA2019] (4) 3 :

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.

In this interactive activity, students will be led through steps to identify missing or extra information in word problems in order to create appropriate equations. By identifying missing or extra information in word problems, students will be able to correctly interpret and solve multistep word problems. There are teaching activities as well as practice activities available. Students will write mathematical equations and expressions when completing the teaching and practice problems. A handout that reviews the strategies taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.

View Standards
**Standard(s): **
[MA2019] (3) 8 :

[MA2019] (4) 9 :

8. Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.

[MA2019] (4) 3 : 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) 9 :

9. Round multi-digit whole numbers to any place using place value understanding.

In this interactive activity, students will be led through steps to estimate numbers by rounding in order to make problems easier to solve. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.

View Standards
**Standard(s): **
[MA2019] (4) 1 :

[MA2019] (4) 2 :

[MA2019] (4) 3 :

[MA2019] (4) 11 :

1. Interpret and write equations for multiplicative comparisons.

[MA2019] (4) 2 :

2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

[MA2019] (4) 3 :

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) 11 :

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Module 3, Topic D gives students the opportunity to apply their new multiplication skills (4.NBT.5). In Lesson 12, students extend their work with multiplicative comparison from Topic A to solve real-world problems (4.OA.2). As shown on the next page, students use a combination of addition, subtraction, and multiplication to solve multi-step problems in Lesson 13 (4.OA.3).

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

[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.

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.

[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.

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.

View Standards
**Standard(s): **
[MA2019] (4) 3 : 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) 11 :

[MA2019] (4) 11 :

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Module 3 closes with Topic H as students multiply two-digit by two-digit numbers. Lesson 34 begins this topic by having students use the area model to represent and solve the multiplication of two-digit multiples of 10 by two-digit numbers using a place value chart. Practice with this model helps to prepare students for two-digit by two-digit multiplication and builds the understanding of multiplying units of 10. In Lesson 35, students extend their learning to represent and solve the same type of problems using area models and partial products. In Lesson 36, students make connections to the distributive property and use both the area model and four partial products to solve problems. Lesson 37 deepens students’ understanding of multi-digit multiplication by transitioning from four partial products with the representation of the area model to two partial products with the representation of the area model and finally to two partial products without representation of the area model. Topic H culminates at the most abstract level with Lesson 38 as students are introduced to the multiplication algorithm for two-digit by two-digit numbers. Knowledge from Lessons 34–37 provides a firm foundation for understanding the process of the algorithm as students make connections from the area model to partial products to the standard algorithm (4.NBT.5). Students see that partial products written vertically are the same as those obtained via the distributive property: 4 twenty-sixes + 30 twenty-sixes = 104 + 780 = 884.

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

In this interactive activity, students will be led through steps to solve problems that have more than one operation. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the activity can be printed. A karaoke song with printable lyrics will help students learn and review the steps taught during the activity. After utilizing this resource, the students can complete the short quiz to assess their understanding.