Day 1: Division Strategies-Does it Divide?
Title: Does it Divide?Day One: Content Development / Grade Level:
4-5 / Resources for Lesson:
High Yield Routines:
Origo Fundamentals: Blue Level Pages 24-27
Lesson: Use divisibility rules to divide larger numbers. / Guiding (Focus) Question: How can I determine if a number is divisible by different divisors?
Unit Learning Targets:
Find whole number quotients with single digit divisors.
Success Criteria:
I can determine if a number can be divided by different divisors by applying rules of divisibility.
Mathematical Practices
MP 3
MP 7
MP 8 / Content Standards
4.NBT.B.6
5.NBT.B.5 / Time for Lesson:
Warm Up: 10 Minutes
Content Development: 20 Minutes
Game: 20 Minutes
Reflection: 10 Minutes
Content Objectives:
I can use strategies to divide larger numbers.
I can determine if a number is divisible by different divisors through use of strategies. / Language Objectives:
(Throughout unit make sure all four language modalities, reading, writing, speaking and listening are addressed)
I can discuss my moves during the game using the divisibility rules
Key Vocabulary
- Divisor
- Dividend
- Quotient
- Strategies
Chart with divisibility rules. / Materials:
- Game sheet page 26
- Number cube showing 2, 3, 4, 5, 6 and 9.
- Counters
- Calculator
- White Board/White Board Pens
- EL Achieve Cards
Student Engagement: Leadership
How will this lesson develop leadership skills for our migrant students?
2. I speak and listen well to others. / Strategies to develop leadership skills:
Students work in pairs when playing the game. Students can use EL Achieve Cards to use polite conversation.
Examples include:
Why do you think…
How did you come up with…
Warm Up: High Yield Routines ~ Mystery Number
Have students discover your “mystery number” by giving clues. Example includes…
My number is a multiple of 6.
My number has six factors.
My number is less than 5 x 5.
What is my number?
Content Development:
Review the divisibility rules with students. Give students several three digit numbers and have students work in pairs to determine which numbers are divisible with 2, 3, 4, 5, 6, and 9. Numbers that could be used are 516, 234, and 940. Each of these numbers are divisible by more than one divisor.
Have students predict which numbers the 3 digit numbers would be divisible.
Then have students justify their answers. / Notes:
Have students start questions with EL Achieve Card Ask a Question.
Game Activity:
Explain the rules of the game. The aim of the game is to arrange four in a row either horizontal, vertical or diagonal.
See “How to Play” on page 24 of Blue Fundamentals Book.
After students roll the number cube they find numbers that can be divided by that divisor. Have students justify their answers by calculating numbers on a white board. If students disagree they can use a calculator to verify answers.
As students are playing circulate and ask questions such as, what number will you need to roll to get the number you need.
Reflection:
See After the Game on page 25. Ask students to determine the number with the most and fewest divisors possible. / Review and Assessment:
Exit Ticket- Give students the number 171. Ask student to determine which numbers this three digit number can be divided by without a remainder.
Home School Connection:
Send number cubes and game sheets home for students to play with other family members. / Materials to Send Home:
Game Sheet
Game Directions
Number Cube
Counters
Day 2: Problem Solving
Title: Day Two: Problem Solving-Division Strategies / Grade Level:3-5 / Resources for Lesson:
High Yield Routines:
Illustrative Mathematics-Mental Division Strategy
Origo Fundamentals:
Lesson: Mental Division Strategy-Developing mental strategies for division and the strategy of “compatible numbers.” / Guiding (Focus) Question:
What are other strategies besides divisibility strategies, when thinking about division
Unit Learning Targets:
Using mental strategies and divisibility rules to divide large numbers
Success Criteria: (Student Friendly)
I can use and develop multiple strategies when solving division problems
Mathematical Practices
MP 3
MP 4 / Content Standards
4.NBT.B.6 / Time for Lesson:
Warm Up: 10 Minutes
Content Development: 20 Minutes
Problem Solving: 20 Minutes
Reflection: 10 Minutes
Content Objectives:
(Student Friendly)
I can use strategies to divide larger numbers.
I can determine if a number is divisible by different divisors through use of strategies. / Language Objectives:
(Throughout unit make sure all four language modalities, reading, writing, speaking and listening are addressed)
I can discuss and write my strategies for division including mental math strategies.
Key Vocabulary
- Divisor
- Dividend
- Quotient
- Strategies
- Distributive Property
- Compatible numbers
Review of the divisibility rules
Distributive Property / Materials:
Jillian’s Problem
Area model examples
Student Engagement: Leadership
How will this lesson develop leadership skills for our migrant students?
2. I speak and listen well to others. / Strategies to develop leadership skills:
Students work in pairs when justifying problem solving.
Students can use EL Achieve Cards to use polite conversation.
Examples include:
Why do you think…
How did you come up with…
Warm Up: High Yield Routines-Mystery Number
Have students discover your “mystery number” by giving clues. Example includes…
My number is a three digit number.
My number is more than 5 x 100, but less than 6 x 100.
My number can be divided by 2, 3, 4, 5, 6, and 9.
What is my number? (540)
Content Development:
Provide students with the following question:
I know that 20 times 7 is 140. If I take away 2 sevens that leaves 126. So that means 126 7 = 18.
- Is Jillian’s calculation correct?
- Draw a picture showing Jillian’s reasoning.
- Provide a story problem to match the equation.
- Justify your reasoning with words, pictures and numbers.
Show Area Model as illustrated in the notes from Illustrative Commentary for this task.
Use Jillian’s Problem
Problem Solving Activity:
Use Jillian’s method to find 222 6.
Reflection:
Review the distributive property and discuss other examples. / Review and Assessment:
Home School Connection
Play, Does it Divide Again? In this game your child will need to come up with numbers for the game board. Your child could create 2, 3, 4 or even 5 digit numbers to place on the game board. Make sure they include numbers that could be divided by each of the numbers on the number cube. / Materials to Send Home:
Does it Divide Again Game board
Home School connection page
Divisibility Rules:
[2] A number is divisible by two if the digit in the ones place is divisible by 2.
[3] A number is divisible by three if the sum of its digits is divisible by 3.
[4] A number is divisible by four if the number represented by the digits in the ten’s and one’s place is divisible by 4.
[5] A number is divisible by five if the ones place is either a 0 or 5.
[6] A number is divisible by six if it is divisible by 2 and 3.
[9] A number is divisible by nine if the sum of its digits is divisible by 9.
Home School Connection
Does it Divide?
Goal of Game:
Your child will practice rules for divisibility of larger numbers. Your child will be able to tell if a larger number can be divided by the numbers on the number cube using divisibility rules. Then your child can practice dividing numbers to prove if their thinking is correct.
Materials:
Does it Divide Game Board
Number Cube with 2, 3, 4, 5, 6, and 9
Divisibility Rules
Counters (2 colors)
How to Play:
The goal is to cover four numbers in a row either up and down, across or diagonal.
- The first player rolls the number cube.
- The player chooses a number on the game board that is divisible by the number rolled.
- The number claimed is covered by a counter. (Both players can claim the same number and have different colored counters on only one space.)
- The player has to justify the answer by calculating the number claimed by dividing it by the number rolled.
- If a player cannot find a number that is divisible by the number rolled, they miss a turn.
- The other player has a turn.
- The player who makes the most four in a rows is the winner.
Questions I could ask my child:
If you have three in a row what numbers would you need to win?
What number would that be divisible by?
Are there other numbers you could roll and still get the number you want?
Other Activities:
Play, Does it Divide Again? In this game your child will need to come up with numbers for the game board. Your child could create 2, 3, 4 or even 5 digit numbers to place on the game board. Make sure they include numbers that could be divided by each of the numbers on the number cube.