-The student will be able to
name whole numbers
from 1 to 100.
-The student will be able to
Identify whole numbers
1 to 100 when given a
run of numbers with
blanks.

Low- Name that Number
Medium- Write that Number
High- Place that Number

Accurately be
able to
compute using
all other
operations.

Procedural

Recall
Apply

-The student will be able to
perform the appropriate
mathematical operation
when presented with a
mixed operation sheet
requiring them to decide
whether to add, subtract,
or multiply to solve.

Low- Mixed Practice
Medium- Mixed Practice
High- Mixed Practice

Division of
Whole numbers

Factual
Procedural

Apply
Remember
Evaluate
Understand

The student will be able to
apply the division process in
order to accurately find
solutions to long division
problems.

Low- Divide it up!
Medium- Division Doubles
High- Crabby Practice

GOAL: The purpose of this differentiated education plan is to teach middle school students the processes needed to divide whole numbers. At this stage of their mathematical understanding it is necessary for students at this age level to be able to successfully multiply in order to prepare for the role division will play in their life and their future math education.
All students should be able to complete the necessary steps to divide whole numbers. All students should be able to memorize and apply the division algorithm in order to meet this goal.
Some students will be able to apply the algorithm to solve division problems.
A limited amount of students will be able to complete a division problem independently through applying the algorithm and interpret the quotient and remainder.
Most students will become familiar and recognize a variety of vocabulary words associated with the process of division.

Teacher Input for Unit:
-Important for everyday life skills (shopping, taxes, bills, future job)
-Necessary skill for higher level math (algebra, calculus, graphing)
-Necessary for working with other operations (inverse, multiplication, addition, subtraction)
-In order to gain knowledge of our next unit, decimals, fractions, and their place value, students must be successful with the division formula and applying it independently to solve problems.
I am ready to teach this unit because I have already distinguished between the students who should be ready to divide with basic grouping skills and smaller numbers and the students who should be able to learn and apply division with multi-digit numbers using the algorithm. I have also taught division before so through pre-assessment and observations I have been able to determine the levels of students prior to the start of the unit. This has enabled me to decide the learning concepts and outcomes. The following sites also gives more ideas for educating yourself as a teacher of mathematics, or ideas to start your own division unit and develop supplementary materials needed for reinforcement of math skills. Start Up TeachingMathIdeas
After the preassessments are complete, and before the first concept is covered, the teacher should have a whole group discussion regarding the goals of the upcoming math "unit" and have students do a written response stating their own feelings on their math capabilities and their strengths and weaknesses they feel they will contribute throughout the unit. This written activity can even be differentiated by giving selective sentence starters to students who need help expressing their opinions and initial understanding of the material.

Student Readiness for Unit:
Division of whole numbers will be a new content area that will be taught to all students. Students need to learn this skill in order to progress onto higher level math. Area's that the students need to understand and have prior experience with is addition, subtraction, and multiplication. Division and the concept of it is built upon the foundations of prior understanding of the formentioned areas. Students will also have to know the multiplication table or how to effectively use the multiplication table. Students will also have to understand the concept that numbers can be divided into groups.

Most students will be interested in this topic because it relates to math they have already been exposed to and are expected to have mastery of. The students who will have limited interested in this area are those that are expected to have lower skills and be more resistant to this math unit.
Since Kindergarten this checklist has been used to track the mathematical conceptual knowledge of each student. The skills in this unit will be mostly focused on those listed under the third and fourth grade expectations. This checklist was also used as a preassessment to see where each students prior knowledge levels lie. Cum Math Checklist

Student Needs
Depending on the academic level and learning style of the learner at hand there will be some of the following needs that may exist throughout the division unit:
1) The most important knowledge that needs to be exhibited throughout this unit is number sense. Students will need the knowledge of the operations, the symbols they represent (+ , - , / , x ), and the vocabulary (sum, dividend, divisor, difference, product) they will see when they are required to apply the operation in a word problem.
2) Students may need to use manipulatives to form groups when evaluating multiplication problems
3) Students may not be prepared for this unit with the concrete knowledge and recall of their multiplication facts. For these students smaller numbers will be used when practicing the operations of addition, subtraction, and multiplication.
4) Some students may already know how to divide. For these students the algorithm of division will be used so they can evaluate problems and learn how to interpret remainders and apply the algorithm to word problems.
5) Some students may need more of a visual explanation of the process and point of division. Understanding that division is the opposite of multiplication is a difficult task if students don't understand that you can break down whole numbers into groups.

Vocabulary: Add or addition: To join two or more numbers (or quantities) to get one number (called the sum or total). Difference-Difference between two numbers (subtraction). Digit-Any symbol of numbers, 0,1,2,3,4,5,6,7,8,9 used to write. Divide- Sharing or grouping into equal parts. Dividend- The number being divided. Divisible- Can be divided without a remainder. Divisor- A number that will divide the dividend exactly. Factor- A number that divides exactly into another number. Grouping- Dividing things into equal groups (sets). Multiply- A mathematical operation where a number is added to itself a number of times. Numbers- Numbers describe quantities or values. Product- the result when two numbers are multiplied. Quotient- The number resulting from dividing one number by another (the answer). Remainder- Amount left over after dividing a number. Subtract- To take one quantity away from another. Sum- The total or whole amount, the result of adding.

How Students Will Acquire the New Skills
Through our differentiation process, we will incorporate learning strategies and techniques that will assist students of all abilities to attend to the materials. We will do this in ways such as, shorter requirements of materials, hands on activities, engaging materials, small group work, and one on one time as needed.

Students will complete the initial assessments first. These initial assessments include:
-Orally demonstrating ability to recognize whole numbers from a number line
-Mad Minute completion in the areas of addition, subtraction, and multiplication
-Independent completion of vocabulary, symbols, and question map. Example:

After the initial assessments are completed students will be learning and practicing the same skills, they will just be completing the practice problems at different levels. The purpose for children practicing the manipulation of the different operations is because when applying the division algorithm all operations are necessary in order to reach the quotient.
1) Low level students will be given less examples with smaller numbers. These students will also be grouped during a certain time period throughout the unit for extra practice on the computer. These students will also be given different forums to respond to a variety of arithmetic practice. They can respond orally or in written form.
2) Medium and High level students will be given the same amount of examples. The difference between these two groups will be the medium level students will have less digits in their practice problems and in their assessments they will have no remainders to their problems.
3) Some students will need additional reinforcement to master basic math skills. The following is an excellent resource to help families and students practice math skills from home. FamilyMathLink

Assessment Explanations: CONCEPT 1: Identify Whole Numbers Between 1-100 PROCESS: Whole Group:
-Oral repetition of reciting numbers.

Small Group based upon ability:
-Identifying specific numbers 1-100 by pointing.
-Writing numbers 1-100 on paper.
-Separating numbers 1-100 from a larger population and identifying them.

Expectations:
The student will be able to name whole numbers from 1 to 100.
Low- Name that Number
Teacher will point to a number 1-100 and the student must be able to verbally identify it.

Medium- Write that number
Teacher will verbally recite a number 1-100 and the student must be able to write it down in standard form.

High- Place that number
Student will be given a paper of ten sets of numbers 1-100 in standard form. Students must be able to write the numbers 1-100 out in word form from least to greatest.

Differentiation:
-Some students may be able to name the whole numbers out of order while others may only be able to do it in order.
-While all students should be able to name whole numbers from 1 to 100 some students may be able to name whole numbers above 100.

PRODUCTS
-Depending upon the student the product must show that a student is able to identify random whole numbers.

Concept 2: The student will be able to accurately compute using operations (+, -, x) PROCESS Whole Group:
-Reviewing the symbols and the words they represent (+ means add, - means to subtract, x- means to multiply)

Small Group based upon ability:
-Begin with single-digit addition, subtraction, and multiplication. Once a student achieves at this level allow them to demonstrate their application skills by trying problems with a variety of multi-digit numbers.
-Students may orally recite their times tables or fact families or they may answer them in written form through a MAD MINUTE format. Expectations:
Low- Mixed Practice
Addition: DoubleDigitAddWithoutRegrouping
Subtraction: DoubleDigitSubtractionWithoutRegrouping
Multiplication: MultiplcationMadMinute
(these students will only do 4 rows at a time when being timed, or they will be given 2.5 minutes to complete the entire sheet)

Differentiation:
-Some students may be able to solve problems with a variety of multi-digit numbers, using all three operations (+,-,x)
-Some students may only be able to do one or two out of the three operations successfully.
-Some students may need a review of the other operations before they are given problems to compute.

PRODUCT
The student will be able to perform the appropriate mathematical operation when presented with a mixed operation sheet requiring them to decide whether to add, subtract, or multiply to solve.

Concept 3: Division of whole numbers PROCESS: Whole Group:
-Using graph paper all students will be able to divide whole numbers into even groups (either 2 or 3 digit dividends).

Independent based upon ability:
-All students will be able to use the algorithm to apply their computation abilities to divide whole numbers in Mad Minute format or when orally prompted
(either 2 or 3 digit dividends).

Differentiation: CONTENT
-All students will be able to apply their knowledge of the other operations to successfully complete the steps needed to divide whole numbers
-Some students will be able to divide a number into groups using figure drawings
-Some students will be able to divide multi-digit whole numbers using the algorithm
-Some students will be able to divide single digit whole numbers into groups using the algorithm
-Some students will be able to divide whole numbers and interpret remainders

PRODUCT
-The student will be able to apply the division process in order to accurately find solutions to long division problems.
*The attached is a link for games to help practice math skills.Practice math skills

LearningConcept (s)(theme or topic)KnowledgeDimensionCognitiveProcessesStudent Learning OutcomeAssessmentnumbers

between

1 and 100.

Apply

name whole numbers

from 1 to 100.

-The student will be able to

Identify whole numbers

1 to 100 when given a

run of numbers with

blanks.

Medium- Write that Number

High- Place that Number

able to

compute using

all other

operations.

Apply

perform the appropriate

mathematical operation

when presented with a

mixed operation sheet

requiring them to decide

whether to add, subtract,

or multiply to solve.

Medium- Mixed Practice

High- Mixed Practice

Whole numbers

Procedural

Remember

Evaluate

Understand

apply the division process in

order to accurately find

solutions to long division

problems.

Medium- Division Doubles

High- Crabby Practice

GOAL:The purpose of this differentiated education plan is to teach middle school students the processes needed to divide whole numbers. At this stage of their mathematical understanding it is necessary for students at this age level to be able to successfully multiply in order to prepare for the role division will play in their life and their future math education.All students should be able to complete the necessary steps to divide whole numbers. All students should be able to memorize and apply the division algorithm in order to meet this goal.

Some students will be able to apply the algorithm to solve division problems.

A limited amount of students will be able to complete a division problem independently through applying the algorithm and interpret the quotient and remainder.

Most students will become familiar and recognize a variety of vocabulary words associated with the process of division.

Teacher Input for Unit:-Important for everyday life skills (shopping, taxes, bills, future job)

-Necessary skill for higher level math (algebra, calculus, graphing)

-Necessary for working with other operations (inverse, multiplication, addition, subtraction)

-In order to gain knowledge of our next unit, decimals, fractions, and their place value, students must be successful with the division formula and applying it independently to solve problems.

I am ready to teach this unit because I have already distinguished between the students who should be ready to divide with basic grouping skills and smaller numbers and the students who should be able to learn and apply division with multi-digit numbers using the algorithm. I have also taught division before so through pre-assessment and observations I have been able to determine the levels of students prior to the start of the unit. This has enabled me to decide the learning concepts and outcomes. The following sites also gives more ideas for educating yourself as a teacher of mathematics, or ideas to start your own division unit and develop supplementary materials needed for reinforcement of math skills.

Start Up

TeachingMathIdeas

After the preassessments are complete, and before the first concept is covered, the teacher should have a whole group discussion regarding the goals of the upcoming math "unit" and have students do a written response stating their own feelings on their math capabilities and their strengths and weaknesses they feel they will contribute throughout the unit. This written activity can even be differentiated by giving selective sentence starters to students who need help expressing their opinions and initial understanding of the material.

Student Readiness for Unit:Division of whole numbers will be a new content area that will be taught to all students. Students need to learn this skill in order to progress onto higher level math. Area's that the students need to understand and have prior experience with is addition, subtraction, and multiplication. Division and the concept of it is built upon the foundations of prior understanding of the formentioned areas. Students will also have to know the multiplication table or how to effectively use the multiplication table. Students will also have to understand the concept that numbers can be divided into groups.

Most students will be interested in this topic because it relates to math they have already been exposed to and are expected to have mastery of. The students who will have limited interested in this area are those that are expected to have lower skills and be more resistant to this math unit.

Since Kindergarten this checklist has been used to track the mathematical conceptual knowledge of each student. The skills in this unit will be mostly focused on those listed under the third and fourth grade expectations. This checklist was also used as a preassessment to see where each students prior knowledge levels lie.

Cum Math Checklist

Student NeedsDepending on the academic level and learning style of the learner at hand there will be some of the following needs that may exist throughout the division unit:

1) The most important knowledge that needs to be exhibited throughout this unit is number sense. Students will need the knowledge of the operations, the symbols they represent (+ , - , / , x ), and the vocabulary (sum, dividend, divisor, difference, product) they will see when they are required to apply the operation in a word problem.

2) Students may need to use manipulatives to form groups when evaluating multiplication problems

3) Students may not be prepared for this unit with the concrete knowledge and recall of their multiplication facts. For these students smaller numbers will be used when practicing the operations of addition, subtraction, and multiplication.

4) Some students may already know how to divide. For these students the algorithm of division will be used so they can evaluate problems and learn how to interpret remainders and apply the algorithm to word problems.

5) Some students may need more of a visual explanation of the process and point of division. Understanding that division is the opposite of multiplication is a difficult task if students don't understand that you can break down whole numbers into groups.

Vocabulary:To join two or more numbers (or quantities) to get one number (called the sum or total).Add or addition:Difference-Difference between two numbers (subtraction).Digit-Any symbol of numbers, 0,1,2,3,4,5,6,7,8,9 used to write.Sharing or grouping into equal parts.Divide-The number being divided.Dividend-Can be divided without a remainder.Divisible-A number that will divide the dividend exactly.Divisor-A number that divides exactly into another number.Factor-Dividing things into equal groups (sets).Grouping-A mathematical operation where a number is added to itself a number of times.Multiply-Numbers describe quantities or values.Numbers-the result when two numbers are multiplied.Product-The number resulting from dividing one number by another (the answer).Quotient-Amount left over after dividing a number.Remainder-To take one quantity away from another.Subtract-The total or whole amount, the result of adding.Sum-How Students Will Acquire the New SkillsThrough our differentiation process, we will incorporate learning strategies and techniques that will assist students of all abilities to attend to the materials. We will do this in ways such as, shorter requirements of materials, hands on activities, engaging materials, small group work, and one on one time as needed.

Students will complete the initial assessments first. These initial assessments include:

-Orally demonstrating ability to recognize whole numbers from a number line

-Mad Minute completion in the areas of addition, subtraction, and multiplication

-Independent completion of vocabulary, symbols, and question map. Example:

After the initial assessments are completed students will be learning and practicing the same skills, they will just be completing the practice problems at different levels. The purpose for children practicing the manipulation of the different operations is because when applying the division algorithm all operations are necessary in order to reach the quotient.

1) Low level students will be given less examples with smaller numbers. These students will also be grouped during a certain time period throughout the unit for extra practice on the computer. These students will also be given different forums to respond to a variety of arithmetic practice. They can respond orally or in written form.

2) Medium and High level students will be given the same amount of examples. The difference between these two groups will be the medium level students will have less digits in their practice problems and in their assessments they will have no remainders to their problems.

3) Some students will need additional reinforcement to master basic math skills. The following is an excellent resource to help families and students practice math skills from home. FamilyMathLink

Assessment Explanations:CONCEPT 1: Identify Whole Numbers Between 1-100PROCESS:Whole Group:-Oral repetition of reciting numbers.

Small Group based upon ability:-Identifying specific numbers 1-100 by pointing.

-Writing numbers 1-100 on paper.

-Separating numbers 1-100 from a larger population and identifying them.

Expectations:The student will be able to name whole numbers from 1 to 100.

Low- Name that Number

Teacher will point to a number 1-100 and the student must be able to verbally identify it.

Medium- Write that number

Teacher will verbally recite a number 1-100 and the student must be able to write it down in standard form.

High- Place that number

Student will be given a paper of ten sets of numbers 1-100 in standard form. Students must be able to write the numbers 1-100 out in word form from least to greatest.

Differentiation:-Some students may be able to name the whole numbers out of order while others may only be able to do it in order.

-While all students should be able to name whole numbers from 1 to 100 some students may be able to name whole numbers above 100.

PRODUCTS-Depending upon the student the product must show that a student is able to identify random whole numbers.

Concept 2:The student will be able to accurately compute using operations (+, -, x)PROCESSWhole Group:-Reviewing the symbols and the words they represent (+ means add, - means to subtract, x- means to multiply)

Small Group based upon ability:-Begin with single-digit addition, subtraction, and multiplication. Once a student achieves at this level allow them to demonstrate their application skills by trying problems with a variety of multi-digit numbers.

-Students may orally recite their times tables or fact families or they may answer them in written form through a MAD MINUTE format.

Expectations:Low- Mixed Practice

Addition: DoubleDigitAddWithoutRegrouping

Subtraction: DoubleDigitSubtractionWithoutRegrouping

Multiplication: MultiplcationMadMinute

(these students will only do 4 rows at a time when being timed, or they will be given 2.5 minutes to complete the entire sheet)

Medium- Mixed Practice

Addition: DoubleDigitAddWithRegrouping

Subtraction: DoubleDigitSubtractionWtihRegrouping

Multiplication: MultiplcationMadMinute

(these students will have to complete the entire sheet in 1.5 minutes)

High- Mixed Practice

Addition: TripleDigitAddWithRegrouping

Subtraction: TripleDigitSubtractionWithRegrouping

Multiplication: MultiplcationMadMinute

(these students will have to complete the entire sheet in 1 minute)

Differentiation:-Some students may be able to solve problems with a variety of multi-digit numbers, using all three operations (+,-,x)

-Some students may only be able to do one or two out of the three operations successfully.

-Some students may need a review of the other operations before they are given problems to compute.

PRODUCTThe student will be able to perform the appropriate mathematical operation when presented with a mixed operation sheet requiring them to decide whether to add, subtract, or multiply to solve.

Concept 3:Division of whole numbersPROCESS:Whole Group:-Using graph paper all students will be able to divide whole numbers into even groups (either 2 or 3 digit dividends).

Independent based upon ability:-All students will be able to use the algorithm to apply their computation abilities to divide whole numbers in Mad Minute format or when orally prompted

(either 2 or 3 digit dividends).

Expectations:Low- Divide it up!

SingleDivisorDivisionNoRemainder

Medium- Division Doubles

DoubleDigitDivideNoRemainder

High- Crabby Practice

3DigitDivisionNoRemainder

Differentiation:CONTENT-All students will be able to apply their knowledge of the other operations to successfully complete the steps needed to divide whole numbers

-Some students will be able to divide a number into groups using figure drawings

-Some students will be able to divide multi-digit whole numbers using the algorithm

-Some students will be able to divide single digit whole numbers into groups using the algorithm

-Some students will be able to divide whole numbers and interpret remainders

PRODUCT-The student will be able to apply the division process in order to accurately find solutions to long division problems.

*The attached is a link for games to help practice math skills.Practice math skills