In this unit, students will solidify their understanding of the standard algorithms for addition and subtraction through the use of multistep word problems. Additionally, students will determine the most efficient strategy for each problem type by reasoning about the operation and the numbers involved in the problem. Students will continue to apply this reasoning as they explore strategies for solving multiplication and division problems. Students will explain the type of strategy used and then apply this knowledge by solving multistep word problems. Students will also examine the relationships between numbers when different strategies are used and explain the relationships.
Key Concepts:
 The standard algorithms for addition and subtraction are efficient ways to add and subtract that use place value concepts.
 We can multiply whole numbers of up to four digits using a variety of strategies; the choice of strategy does not change the quantities involved or the relationships between them.
 We can find quotients of whole numbers of up to four digits using a variety of strategies; the choice of strategy does not change the quantities involved or the relationships between them.
 The relationship between multiplication and division holds even when the division results in a remainder. (100 / 40 = 2 R 20: therefore, 100 = 2 x 40 + 20).
Prior Knowledge Needed:
 Use multiplication and division strategies with larger numbers; (Grade 4, Unit 2; 4.OA.A.3, 4.NBT.B.5, and 4.NBT.B.6)
 Solve problems using multiplicative comparison; (Grade 4, Unit 7, 4.OA.A.2)
 Develop strategies for addition and subtraction; (Grade 3, Unit 3, 3.NBT.A.1 and 3.NBT.A.2)
 Solve addition and subtraction problems using measurement; (Grade 3, Unit 6, 3.MD.A.1 and 3.MD.A.2)
Units on the Horizon:
 Develop multiplication and division strategies (Grade 5, Unit 2)
 Finalizing multiplication and division with whole numbers (Grade 5, Unit 15)
Lessons

Lesson objective: Understand that the numbers in an addition or subtraction problem determine the most efficient choice of solution strategy. Students bring prior knowledge of addition and subtraction strategies from 3.NBT.A.1 and 3.NBTA.2. This prior k...

Lesson objective: Fluently add and subtract multidigit numbers while choosing the most efficient solution strategy and justifying the choice. This lesson helps to build fluency with the standard algorithms for addition and subtraction and mental math. ...

Lesson objective: Solve a complex problem using efficient strategy choices for addition and subtraction. This lesson provides an opportunity for students to apply their knowledge and understanding of addition, subtraction, and estimation to a reallife ...

Lesson objective: Understand that the choice of solution strategy for multiplication problems does not affect the answer or the relationships between the numbers involved. Students bring prior knowledge of multiplication solution strategies from 4.OA.A....

Lesson objective: Solve multistep multiplication word problems using various strategies. This lesson helps to build fluency with multidigit whole number multiplication using various strategies. The area model is used here because it supports the devel...

Lesson objective: Solve a complex problem using various strategies for multidigit multiplication. This lesson provides an opportunity for students to apply their knowledge and understanding of multidigit multiplication strategies to a reallife situat...

Lesson objective: Understand that various strategies can be used to solve division problems and the choice of strategy does not affect the outcome or the relationships between the numbers involved. Students bring prior knowledge of division solution str...

Lesson objective: Solve multistep division word problems using various strategies. This lesson helps to build fluency with multidigit whole number division using various strategies. The area model and partial quotients are used here because they suppo...

Lesson objective: Solve a complex problem using various strategies for multidigit division. This lesson provides an opportunity for students to apply their knowledge and understanding of multidigit division to a reallife situation. Students are asked...

Lesson objective: Solve a complex problem using various strategies for multidigit multiplication and division. This lesson provides an opportunity for students to apply their knowledge and understanding of multidigit multiplication and division to a r...

Lesson objective: Understand that the relationship between multiplication and division holds even when the division results in a remainder. (100 ÷ 40 = 2 R 20: therefore, 100 = 2 x 40 + 20). Students bring prior knowledge of being able to solve multipli...

Lesson objective: Use multiplication to check division problems with remainders. This lesson helps to build fluency with checking division problems through multiplication and addition. Picture models are used here because it supports understanding that ...

Lesson objective: Understand that we can represent problem situations with equations, understanding that the operations shown in the equation may not be the operation we use to solve the problem. Students bring prior knowledge of being able to use multi...

Lesson objective: Represent a word problem with an equation. This lesson helps to build procedural skill with taking two equations and combining them into one that represents the entire problem. A tape diagram is used here because it allows students to ...

Lesson objective: Apply skills with combining equations into one equation and representing a word problem with an equation by playing a game. This lesson provides an opportunity for students to apply their knowledge and understanding of representing equ...