Elementary Mathematics

5th Grade Unit 1: NUMBER PUZZLES AND MULTIPLE TOWERS                          Suggested Dates: Aug. 28- Sep. 24

Estimated Duration: 19 days (19 lessons)
*Investigation 1: 4 lessons (1.1-1.4 only)
*Investigation 2: 7 lessons 2.4a (combine 2.4 and 2.5)
*Investigation 3: 8 lessons


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
365 x 20 and 365 x 7 and added the two products. Which one is correct? Explain how you know.

Common Core Clusters and Standards

Standards for Mathematical Practice

Perform operations with multi-digit 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


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. 


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.


Session 2.4a includes work on the order of operations.  After this session, integrate brackets, braces and parenthesis into quick images work *See Quick Images note below.    

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.


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

5.NBT.6- Find whole number quotients using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.  Illustrate and explain using equations, arrays, and area models.
The Language of Mathematics - Words students should use precisely during mathematical conversations.
Product, Quotient, Operations, Multiples, Factors, Reasonableness, Distributive Property, parentheses, brackets, braces, numerical expressions


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 5-6. 

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…

2-digit by 1-digit

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 2-digity by 2-digit multiplication before working with multiplying by a 3-digit 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


This is a great video that uses base-10 blocks to model numbers and them shows how to divide them into groups. Great for visual learners.

This video shows real life examples of using multiplication and division in the sports world.


This video shows real life examples of using multiplication and division in the sports world.

Professional Learning Opportunities

Read the information on Standards 5.NBT.2, .5 and 6  as well as  5.OA.1 and 5.OA.2 in the DPI Unpacking document before teaching this unit.

Unit 1 page 161 in teacher’s edition- Multiplication Strategies. This will explain the different strategies available to students while learning the multiply or divide.

Unit 1 page 171 in teacher’s edition- Developing Computations Strategies that Make Sense. This reading helps to make sense of why we are teaching the students the methods and strategies in this unit.

Read pages with the information on standards 5.NBT.2, .5 and .6, as well as 5.OA.1 and 5.OA.2 in the DPI Unpacking document before teaching this unit.

 Wiki Resources
End of Unit Assessment rubric for Unit 1

5th Grade Vocabulary

Investigations Vocabulary

Investigations Unit Vocabulary

Extension Projects
List of 3-5 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.