Begin with the End in Mind: By the end of this unit, students should be able to respond to the following prompts: 

Journal Task: While multiplying 365 x 27, Monica multiplied 365 x 9 and then multiplied the product by 3. Sebastian multiplied 

Common Core Clusters and Standards 
Standards for Mathematical Practice 

Perform operations with multidigit whole numbers and with decimals to hundredths. 5.NBT.5 and 5.NBT.6 Write and interpret numerical expressions. 5.OA.1 and 5.OA.2 Understand the place value system. 5.NBT.2 
What opportunities can you give students to model with mathematics in this unit?
How can looking for and making use of place value structures lead students to understand strategies?


Take Note! Notes about each Investigation 

1 
During this Investigation, students work with standard 5.NBT.5 and 5.NBT.6. Make sure to read this portion of the DPI Unpacking document before teaching this unit for detailed examples of solving problems using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Spend the first few lessons making sure that students are successful with the numbers in Investigations before moving students to larger numbers. 

2 
During this Investigation, students work with standard 5.NBT.5 in their work halving and doubling factors. Many students use the open array with little understanding about the connection to the distributive property. Record representations for 18x14 as (18x10)+(18x4). Explicitly remind students about the term “distributive property” and model it throughout this unit. Using arrays for multiplication... why not just teach students the algorithm? *Arrays help students develop mental pictures for larger numbers and visualize complex multiplication problems. These representations help students rely on their sense of number to estimate quantities. 

3 
Creating multiple towers will help students reason about the magnitude of number (5.NBT.1) The doubling and halving work directly relates to standard 5.NBT.5 

The Language of Mathematics  Words students should use precisely during mathematical conversations. 

Product, Quotient, Operations, Multiples, Factors, Reasonableness, Distributive Property, 

Routine 
Corresponding Common Core State Standards and Notes 

Quick Images  As students solve quick images, record their solutions using parenthesis, brackets, and braces (5.OA.1) where applicable. For example, if a student says, “I saw 3 groups of 8 dots which is 24, then 6 more dots” record as (8x3)+6. Ask students if the solution would be the same if you solved it like this: 8 x (3+6). The goal is to introduce parenthesis, brackets, and braces so that students realize why they are used. See DPI Unpacking document pages 56. 

Today’s Number 
Teacher will assign a number of the day and students will write as many numerical expressions as possible with that solution. Encourage students to use parentheses and brackets in these.  
When students struggle, have them... 
When students clearly understand, have them… 

USE: 2digit by 1digit Array cards (gr 3) Big array/small array (gr 4) Open array breaking numbers apart by place value 
Avoid moving to working with larger numbers during this unit. Students should have extensive experiences with 2digity by 2digit multiplication before working with multiplying by a 3digit number. If students are proficient with 1 strategy, ask them to respond to questions like, “How is your strategy similar to, or different from, ___’s?” 

Technology Connections 



Professional Learning Opportunities 



Wiki Resources  
End of Unit Assessment rubric for Unit 1 5th Grade Vocabulary Investigations Vocabulary Investigations Unit Vocabulary Extension Projects List of 35 Children's Literature that go with each unit. *Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math. 
