Chapter 6: Understanding Division

Domains: Operations & Algebraic Thinking

Danielle Pipolo

Grade 3 - 2015

DPipolo@nyit.edu

6.4 Aim: I can model division with bar models. (3.OA.2)

CCLS 3.OA.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.


Student AIM: I can model division using bar models.

Teaching Point: Students will model division using bar models and equal groups.


Vocabulary: Dividend, divisor, quotient


Essential Question: How can you relate what you learned about division to what you've already learned about multiplication?

Higher Order Thinking Question: How can you use bar models to solve division problems?


Mini Lesson: (Smart Board Slide: Investigate)

Guided Practice: (Smart Board Slide: Guided)


Check For Understanding: (see photos)

Problem 1: 12 ÷ 4=

Draw the given triangles into the given bar model.

Problem 2: Draw a bar model to show 15 ÷ 3=


Group Work:

H: Students are solving, creating their own bar model.

M: Students are solving, with the bar model present.

L: Students are using blocks in a reteach format to solve simple division problems with the teacher.

Smart Board: Station

Laptop learning: ixl- Divide by counting equal groups


Share: How did your group use a bar model to solve? Students will share what their groups worked on during their collaborative group work time.


Independent Practice: (Exit Slip) Rachel has 9 crackers. She puts 3 crackers in each bag. Circle the crackers to show Rachel's bag.

a) Write a division sentence where the answer represent the number of Rachel's bags.

b) Draw a bar model to represent the problem

c) Can you try to use another model to find your answer?

6.5 Aim: I can understand relationship between division and subtraction (3.OA.3)

CCLS 3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.


Student AIM: I can use subtraction to help me divide.

Teaching Point: Students will use repeated subtraction and a number line to relate subtraction to division.

Vocabulary: subtraction, less than


Essential Question: How can you relate what you learned about division to what you've already learned about multiplication?

Higher Order Thinking Question: How can you teach a friend to subtract and divide?

Mini Lesson: (Smart Board Slide: Investigate)

Guided Practice: (Smart Board Slide: Guided)


Check for Understanding

Problem 1: Solve using repeated subtraction. Use the model to check your answer.

12 ÷ 3 = __

Problem 2: Solve using repeated subtraction. Use a model to check your answer.

25 ÷ 5 = ___


Group Work:

H: I can use repeated subtraction to solve division problems.

M: I can relate subtraction and addition by using repeated subtraction

L: Reteach

SB: Station

Laptops: Puzzle Pics Division- solve by using repeated subtraction on white boards.


Share: Students will share what their groups worked on during their collaborative group

Independent Practice: (Exit Slip) Spencer buys 20 strawberries to make smoothies. Each smoothie needs 5 strawberries. Use repeated subtraction to find the number of smoothies Spencer can make. Make a drawing to match your counting.

Did you like this strategy? Why or Why not?

6.6 Aim: I can model division with arrays. (3.OA.3)

CCLS 3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.


Student Aim: I can use arrays to help me divide.

Teaching point: Student will model division with arrays.


Vocabulary: array, row, column


Essential Question: How can you relate what you learned about division to what you've already learned about multiplication?

Higher Order Questions: How can we use arrays to solve division problems? How can making array help you divide? Explain the steps you took to use an array to find the quotient.


Mini Lesson: (Smart Board Slide: Investigate)

Guided Practice: (Smart Board Slide: Guided)

Check for Understanding

Problem 1:Use an array to solve the problem. 15 ÷ 3 = __

Problem 2: Use an array to solve the problem. Deena makes 21 jars of tomato sauce. She puts 7 jars in each box to sell at the market. How many boxes does Deena need?


Group Work:

H: I can use arrays to solve division problems. Students will create the arrays.

M: I can use arrays to solve the division problem

L: Reteach

Smart Board: Station

Laptop learning: ixl- write division sentences for arrays


Share: Students will share what their groups worked on during their collaborative group


Independent Practice: (Exit Slip) Ricky puts 15 tennis balls into cans. Each can holds 3 balls. Circle groups of 3 to show the balls in each can.

Ricky needs ___ cans.

___ x 3 = 15

15 ÷ 3 = _____

Use an array to model the problem.

Is there another strategy you can think of that will help you with this?

6.7 Aim: I can relate multiplication and division (3.OA.6)

CC.3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.


Student AIM: I can use multiplication to help me solve division problems.

Teaching Point: Students will use bar models to relate multiplication and division.

Vocabulary: relate, fact family, inverse operation


Essential Question: How can you relate what you learned about division to what you've already learned about multiplication?

Higher Order Thinking Question: How can we use multiplication to divide?


Mini Lesson: (Smart Board Slide: Investigate)

Guided Practice: (Smart Board Slide: Guided)


Check for Understanding

Problem 1: Write the fact family for 32 ÷ 4 =

Problem 2: Write the fact family for the array:

X X X X X X X X X X

X X X X X X X X X X

X X X X X X X X X X


Group Work:

H: I can use multiplication to help me divide. Students will use bar models.

M: I can use multiplication to help me divide. Students will be given representation of bar models

L: Reteach

Smart Board: Station

Laptop: ixl- relate multiplication and division for arrays


Share: Students will share what their groups worked on during their collaborative group.


Independent Practice: (Exit Slip): Show how multiplication and division are related by drawing an array to show 6 x 3 = 18.

Now draw an array to show 18 ÷ 3 =

How are your arrays similar?

Why do they look the same?

Lesson Support Synopsis

In our integrated collaborative teaching classroom we try our best to reach all of our student's learning needs, styles and preferences in order for them to be successful. Our classroom is lucky and beyond appreciative to have not only laptops and a Smart Board, but TWO Smart Boards to accommodate for parallel teaching and station teaching models. That being said, it is essential that we use technology as much as we can throughout the day.


Smart Board: Allowing students to use the smart board enhances their understanding with visuals and movement. Children have access to various pen tools such as highlighting. They are also able to easily display their mathematical thinking with infinite "math manipulatives". Children in our school have seen the smart boards used before and this year all of our students have opportunity to utilize the tools of the Smart Board several times a day.


Math Resources:

As I build the Smart Board Lessons for the math curriculum team, I search and include games that best serve the importance and of each lesson's skill. Sometimes the functions of the game need to be quickly modeled for the students. Typically if the resource is not student friendly and doesn't pertain to the skill or strategy, it is not selected for use.


Math Playground: Student friendly math games are available at most CCLS skills. The beauty behind this website is that students have been "Playing" on this tool throughout their careers in our school and they have so much fun they forget they are learning.


IXL: Math tasks are set up in a multiple choice / test prep format. I like to have students work on IXL in small partnerships, showing their work on either paper or white boards for each question to I can see their reasoning and process. This site sometimes needs some quick modeling for students but otherwise, displays the content in very concrete (and non distracting) formats.

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