1. Planning differentiated lessons in math for grades 1-4
By: Aimee Tyszka
&
Jessica Rinaldi

2. This Is Your Classroom !

3. Planning a Focused Curriculum Means Clarity About What Students Should …
KNOW
Facts
Vocabulary
Definitions
UNDERSTAND
Principles/ generalizations
Big ideas of the discipline
BE ABLE TO DO
Processes
Skills

4. Know
These are the facts, vocabulary, dates, places, names, and examples you want students to give
you.
The know is massively forgettable.
“Teaching facts in isolation is like trying to pump water uphill.” Carol Ann Tomlinson

5. Facts, names, dates, places, information
KNOW
Facts, names, dates, places, information
There are 50 states in the US
Napoleon Bonaparte
1066
The Continental Divide
The multiplication tables

6. Major Concepts and Subconcepts
Understand
Major Concepts and Subconcepts
These are the written statements of truth, the core to the meaning(s) of the lesson(s) or unit. These are what connect the parts of a subject to the student’s life and to other subjects.
It is through the understanding component of instruction that we teach our students to truly grasp the “point” of the lesson or the experience.
Understandings are purposeful. They focus on the key ideas that require students to understand information and make connections while evaluating the relationships that exist within the understandings.

7. UNDERSTAND Essential truths that give meaning to the topic
Stated as a full sentence
Begin with, “I want students to understand THAT…” (not HOW… or WHY… or WHAT)
Multiplication is another way to do addition.
People migrate to meet basic needs.
All cultures contain the same elements.
Entropy and enthalpy are competing
forces in the natural world.
Voice reflects the author.

8. BE ABLE TO DO
Skills (basic skills, skills of the discipline, skills of independence, social skills, skills of production)
Verbs or phrases (not the whole activity)
Analyze
Solve a problem to find perimeter
Write a well supported argument
Evaluate work according to specific criteria
Contribute to the success of a group or team
Use graphics to represent data appropriately

9. KUD’s Count to one hundred in units of ten.
Multiplication is another way to do addition.
Find the missing addend using counters.
Subtraction and addition have an inverse relationship.
The multiplication tables 0-12.
Clue words for addition are sum, and, altogether, in all, combine, join, plus, and total.
The value of a digit depends on its place in the number.
Write the value of the underlined digit in each number.

10. In Other Words: KUDs Matter Because
They create clear learning goals
Allow us to align goals, assessments, teaching,
and learning tasks
They allow us to incorporate standards AND make
meaning for students
They give us a basis for differentiation.
Who needs which K’s & D’s
How do we ensure that every student gets
meaningful access to the U’s
They tell us what strugglers should invest in
They give us a platform for extending for advanced
students

11. Instructional Strategies that Support Differentiated Instruction
Learning Centers – pgs
Cubing – pgs
RAFT – pgs
Graphic Organizers – pgs
Think DOTS – pgs
Learning Contracts – pgs
Web Quests – pgs
*See Marcia Imbeau’s PowerPoint for further explanation of each strategy.

12. Lesson Title: Think Dots Curriculum Area (s): Math Grade Level: 1
Unit Title: Addition
Lesson Title: Think Dots
Curriculum Area (s): Math
Author: Jessica Rinaldi
Grade Level: 1
Author Contact:
Time Required: 3-4 weeks/entire unit
Instructional Groupings: partners
Standards: NOA.1.3 Represent and solve problems involving addition and subtraction.
NOA.1.4 Add and subtract fluently within 20 NOA..1.8 Use addition and subtraction with commutative and associative properties to determine equivalence and solve .
Materials: Think Dot sheets (3 levels), card decks, pencils, worksheet copies, addition bingo, giant number line, desk number lines, connecting cubes, 2 color chips, dice
Overview:   This lesson will provide practice of a concept previously taught. Students will formulate responses to a variety of addition problems.
What will I differentiate? Content and Product
How will I differentiate?    For readiness           
As a result of this lesson/unit students will…
Understand: TSW understand that addition is the joining or combining of items. Also, the commutative properties of addition and its inverse relationship to subtraction.
Know:
TSW know addition vocabulary and how to count to 20
Do (Skills): TSW model, solve, create and evaluate addition problems.
Pre-Assessment:
Students will be given a word problem that must be solved by using addition. Students must show thinking. Think dots will be given after a week of instruction on addition; whole group and small group. Depending on information attained through observation of whole group work, small group work, completed classwork, and exit tickets; student will be given think dot to match their level of readiness.
Steps in the Lesson:
1. Whole class- Explicit instruction on how to use think dots. Explanation of where to find materials. Expectations for work.
Think dots will be used as an anchor activity. Students work on tasks after completion of independent work.
Small group- meetings to reinforce, guide, and make corrections
4. Individual/partners- Think Dot activities
Closure Activity/Wrap up:
Closure will occur at the end of each day. Students will chart progress and notify teacher of which Think Dot activities were completed.
Post-Assessment:
Students may be grouped to new levels after teacher/students consult daily classwork, observations during group meetings, and outcome of Think Dot assignments. Students will have weekly opportunities to share finished products from Think Dot activities.

13. Using counters, show the many ways to make the number 10.
Think Dots
Addition (Yellow)
Directions: With your partner, roll the dice. Do the box that matches your dice. If you don’t want to do that box you can roll one more time. Then, you must do that activity. Do your best! Put work in your folder when finished.
Using connecting cubes, model and solve addition problems less than 20.   
Using the number line on your desk, solve addition sentences by jumping to count on.
Using counters, show the many ways to make the number 10.
On the giant number line, jump to show the totals.
Solve word problems using colored chips.
Create your own word problems using the objects from the red bin.

14. Roll the dice to make addition sentences.
Think Dots
Addition (Purple)
Directions: With your partner, roll the dice. Do the box that matches your dice. If you don’t want to do that box you can roll one more time. Then, you must do that activity. Do your best! Put work in your folder when finished.
 Use the number line on your desk or the giant number line to show addition problems up to 20.
Roll the dice to make addition sentences.
Write the turn around fact for each number sentence.
 Solve addition word problems using the number line.
 Find the missing addends using counters.
 Create addition word problems that use each vocabulary word: altogether, in all, total, and, join, and combine.

15. Find the missing addend.
Think Dots
Addition (Blue)
Directions: With your partner, roll the dice. Do the box that matches your dice. If you don’t want to do that box you can roll one more time. Then, you must do that activity. Do your best! Put work in your folder when finished.
Flip the deck. Each player flips 2 cards and adds. Compare your answer to your friends. The friend with the greatest sum earns the point. First person to thirty wins.
Find the missing addend.
Write the fact families for each set of numbers.
 Addition Bingo- in a group of 4.
Create at least 5 word problems.
 Are you right or wrong? Correct the homework sheet. Fix any mistakes.

16. Lesson Title: 3- digit Place value centers Curriculum Area (s): Math
Unit Title: Addition
Lesson Title: 3- digit Place value centers
Curriculum Area (s): Math
Author: Jessica Rinaldi
Grade Level: 2
Author Contact:
Time Required: minutes
Instructional Groupings: groups
Standards: NOA 2.1 To represent three digit numbers as groups of hundreds, tens, and ones in the base ten number system.
Materials: Chairs labeled hundreds, tens, and ones, place value charts, base ten blocks
Overview:   Students need to understand that every digit has a different value depending on its position in the number before they can understand quantitative relationships.
What will I differentiate? Process
How will I differentiate?    Using the different modalities           
As a result of this lesson/unit students will…
Understand: TSW understand that every digit has a value depending on its position in the number.
Know:
TSW know10 ones=1 ten, 10 tens=1 hundred, and 10 hundreds= How to count by 1, 10, and 100’s. A digit is the 0,1,2,3,4,5,6,7,8,and 9.
Do (Skills): TSW model and write the value of the digit in the ones, tens, and hundreds place.
Pre-Assessment:
Given a couple days before to see what students prior knowledge of the material is. TSW be assessed on ability to count by 10’s and 100’s. They will also be asked to label the values of each place. TSW also be assessed on ability to identify the value of each digits.
Steps in the Lesson:
Day 1: Whole group: present the knows- identify the digits, the value of each position in the number (represent on chart and using labeled chairs), and counting by 1’s to 10, by 10’s to 100, and 100’s to Explain that only one digit can sit in each chair/place. With Smart Board display 3 digit numbers using the base ten blocks. (Demonstrate how to model numbers each way so tomorrow students already know what to do in their centers.) Guided practice: Students draw base ten blocks to model 3-digit numbers, while others model using the base ten blocks, and another 3 students show the number by sitting in the correct chair.
Day 2: At work station- Students will apply skills learned yesterday about identifying the value of the given digit.
Closure Activity/Wrap up: Groups share how they model 3-digit numbers.
Post-Assessment:
Exit ticket: students will identify value of the underlined digit in 3- digit numbers.

17. Place value work stations
Group 1
(Kinesthetic)
1. Pick an index card up with a digit written on it.
2. Pick a chair to sit in.
3. What number did you and your friends make? 4. What is the value of your digit?
5. Write answer on the data sheet.
Group 2
(Visual)
Roll the dice 3 times
Write down each digit to create a 3 digit number.
Draw base ten blocks to show your number.
What is the value of each digit?
Write answer on data sheet.
Group 3
(Tactile)
Pick 3 cards from the deck.
Make a 3-digit number.
3. Build the number using the base ten blocks.
4. Write the value of each digit on your data sheet.

18. What is the value of your digit?
Name: _______________________________ Date: __________________
Place Value
Hundreds
Tens
Ones
What is your digit?
What is the value of your digit? Ex 2 9 20

19. Unit Title: Multiplication (1 digit)
Lesson Title: Think Dots
Curriculum Area (s): Math
Author: Aimee Tyszka
Grade Level: 3/4
Author Contact:
Time Required: 3-4 weeks/entire unit
Instructional Groupings: homogeneous
Standards:  Understand and apply basic concepts of multiplication.
Materials: Think Dot sheets (3 levels), dice, paper (lined and colored), pencils, I-Pad, worksheet copies
Overview:   This lesson will provide practice of a concept previously taught. Students will formulate responses to a variety of multiplication scenarios, touching on Bloom's taxonomy.
What will I differentiate? Content         Product
How will I differentiate?    For readiness           
As a result of this lesson/unit students will…
Understand: TSW understand that multiplication is repeated addition
Know:
TSW know multiplication facts for 0-9
tables.
Do (Skills): TSW show, solve, and describe the multiplication process
Pre-Assessment:
Pre-assessment will take place during observation of whole group work, small group meetings, completed classwork, and mad minutes, etc…
Steps in the Lesson:
1. Whole class- oral/visual review of facts
2. Whole class- mad minute
3. Small group- meetings to reinforce, guide, and make corrections
4. Individual/partners- Think Dot activities
Closure Activity/Wrap up:
Closure will occur at the end of each day. Students will chart progress and notify teacher of which Think Dot activities were completed.
Post-Assessment:
Students may be grouped to new levels after teacher/students consult daily classwork, observations during group meetings, and outcome of Think Dot assignments. Students will have weekly opportunities to share finished products from Think Dot activities.
Additional Resources: Splash Math- on I-pads

20. Multiplication (0-2 times tables)
Think Dots
Multiplication (0-2 times tables)
Directions: At your table group, take turns rolling the dice and complete the learning task from the corresponding dot.
It is alright if more than one person rolls the same number as each person’s response will be individual.
You will practice making arrays. Please get practice page 2 from the blue folder.
Describe how multiplication is like addition. Pick any 0-2 multiplication fact to show as both addition and multiplication. Draw a picture.
Play How Low Can You Go? dice game.
The directions and dice are in the blue basket on the math shelf.
Practice multiplication facts using the I-pads. Be sure to get your numbered
I-pad and log into Splash Math. Have fun!
Discuss and answer the following word problems.
My factors are 2 and 4. What is my product?
My factors are 3 and 1. What is my product?
My product is 0. What must one of my factors be?
Construct your own math worksheet. Make sure you have at least three problems for each times table (0-2). Create an answer key for the teacher.

22. How Low Can You Go? Directions:
Materials:
1 pair of blank dice
(one die labeled 1-6, one die labeled with 3 zeros and 3 ones)
Directions:
Students will take turns rolling the dice, multiply the numbers that come up, and write the product. Each player gets 5 rolls. Players record the product for each roll and then find the sum of their products. The player with the lowest totals wins.

23. Multiplication (3-5 times tables)
Think Dots
Multiplication (3-5 times tables)
Directions: At your table group, take turns rolling the dice and complete the learning task from the corresponding dot.
It is alright if more than one person rolls the same number as each person’s response will be individual.
You will practice making arrays. Please get review page 2 from the orange folder.
Play the Toss and Talk center activity 3-1.
The instruction sheet and dice (number cubes) are in the orange basket on the math shelf.
Make a multiplication table for facts Use a crayon to mark all products in the row and column for 5. Describe the pattern you see in the ones and tens places.
Practice multiplication facts using the I-pads. Be sure to get your numbered
I-pad and log into Splash Math. Have fun!
Discuss and answer the following riddles.
I am between 9 x 4 and 8 x 4. I am an even number. What number am I?
I am greater than 5 x 4. I am less than 6 x 4. I am an odd number. I am not 21. What number am I?
Construct your own multiplication riddles. Create a riddle for each times table (3-5). Create an answer key for the teacher.

26. Multiplication (6-9 times tables)
Think Dots
Multiplication (6-9 times tables)
Directions: At your table group, take turns rolling the dice and complete the learning task from the corresponding dot.
It is alright if more than one person rolls the same number as each person’s response will be individual.
You will practice drawing arrays. Please get the direction sheet and array chart from the red folder. You may choose any 15 of the numbers given.   
Play the Multiplication Brain Game.
The instruction sheet and playing cards are in red basket on the math shelf.
Make a multiplication table. Fill in all facts up to 9 x 9. Color all the even products red. Describe the product when both factors are odd, even, and when one factor is odd and the other is even.
Practice multiplication facts using the I-pads. Be sure to get your numbered
I-pad and log into Splash Math. Have fun!
Complete the Break the Codes worksheet. It is in the red folder. Try making one of your own coded problems.
Complete the Display the Digits worksheet. Then, construct your own problems like these for a classmate to solve. Create 5 problems, each with a different product.
Make an answer key

29. Multiplication Brain Game
Materials:
1 deck of cards (remove jokers, kings, queens, jacks, and tens)
At least 3 players
Directions:
Students will shuffle the deck of cards and place it facedown between two players. Each player draws a card without looking and places it on her/his ‘brain’ or forehead with the card facing the third player. The third player will say the product of the two cards. The other two players will turn and face each other to see the other’s card. Each player now knows the product and the other factor. The first player to call out his own factor (the missing factor) wins. Players will rotate to each have turns naming the products and guessing the missing factors.

32. Unit Title: Basic Fraction Concepts
Lesson Title: Naming and making equivalent fractions
Curriculum Area (s): Math
Author: Aimee Tyszka
Grade Level: 3/4
Author Contact:
Time Required: 1-2 weeks
Instructional Groupings: homogeneous/small group/partners
Standards:  Extend understanding of fraction equivalence and ordering
Materials: Cubes (3 levels), dice, paper (lined and colored), pencils, worksheet copies
Overview:   This lesson will provide practice of a concept previously taught. Students will formulate responses to a variety of scenarios involving fractions.
What will I differentiate? Content         Product
How will I differentiate?    For readiness           
As a result of this lesson/unit students will…
Understand: TSW understand that fractions are smaller parts of a whole.
Know:
TSW know how to read/say a fraction. TSW know terms such as numerator/denominator.
Do (Skills): TSW show, solve, and describe how fractional amounts are
related and compare fractions.
Pre-Assessment:
Pre-assessment will take place during observation of whole group work, small group meetings, completed classwork, etc…
Steps in the Lesson:
Whole class- oral/visual/written lesson
2. Small group- meetings to reinforce, guide, and make corrections
3. Individual/partners- Cubing activities
Closure Activity/Wrap up:
Closure will occur at the end of each day. Students will chart progress and notify teacher of which Cubing activities were completed.
Post-Assessment:
Students’ work will be evaluated and shared with the class. These activities are meant to be anchor activities, or used to reinforce what is being addressed in whole and small group learning experiences.
Additional Resources:

33. THINKING CUBE Grade 4 Fractions (below) Play the Toss and Talk game.
Get a gameboad and number cubes from the red folder/basket.
Use fraction strips to show 1/3 and 2/6 of one whole strip. Are 1/3 and 2/6 the same, or equal parts of the strip?
Use 2 more fraction strips to show 2 other fractions that are equal. Label your strips with the fraction you made.
Tom and some of his friends are having a party. Tom’s mother orders a pizza which is cut into 4 pieces. Each boy ate ¼ of the pizza, and the entire pizza was eaten. Explain how to figure out how many boys were at the party. Explain your answer and draw a picture of how the pizza was sliced.
Which fraction is greater, 1/3 or 1/6?
Use words and models to explain your answer.
Create an interesting and challenging word problem that uses fractions.
Show the solution.
You have 6 tiles. 2/6 of the tiles are rectangles. The rest of the tiles are triangles.
Draw a design using the tiles.
THINKING CUBE
Grade 4
Fractions
(below)

35. THINKING CUBE Grade 4 Fractions (average) Play the Toss and Talk game.
Get a gameboad and number cubes from the yellow folder/basket.
Use fraction strips to show 1/2 and 5/10 of one whole strip. Are 1/2 and 5/10 the same, or equal parts of the strip?
Use 2 more fraction strips to show 2 other fractions that are equal.
Label your strips with the fraction you made.
Tom and some of his friends are having a party. Tom’s mother orders a pizza which is cut into 8 pieces. Each boy ate 2/8 of the pizza, and the entire pizza was eaten. Explain how to figure out how many boys were at the party. Explain your answer and draw a picture of how the pizza was sliced.
Which fraction is greater, 4/5 or 4/8?
Use words and models to explain your answer.
Create an interesting and challenging word problem that uses fractions.
Show the solution.
You have 10 tiles. 4/10 of the tiles are rectangles. The rest of the tiles are triangles.
Draw a design using the tiles.
THINKING CUBE
Grade 4
Fractions
(average)

37. THINKING CUBE Grade 4 Fractions (above average)
Play the Toss and Talk game.
Get a gameboad and number cubes from the green folder/basket.
Use fraction strips to show 1/6 and 2/12 of one whole strip. Are 1/6 and 2/12 the same, or equal parts of the strip?
Use 2 more fraction strips to show 2 other fractions that are equal. Label your strips with the fraction you made.
Tom and some of his friends are having a party. Tom’s mother orders a pizza which is cut into 16 pieces. Each boy ate 4/8 of the pizza, and the entire pizza was eaten. Explain how to figure out how many boys were at the party. Explain your answer and draw a picture of how the pizza was sliced.
Which fraction is greater, 2/3 or 4/7?
Use words and models to explain your answer.
Create an interesting and challenging word problem that uses fractions.
Show the solution.
Mary has 23 mables. 7/23 of the marbles are yellow and 13/23 of the marbles are blue. The rest of the marbles are green.
How many marbles are green?
Explain how you know.
THINKING CUBE
Grade 4
Fractions
(above average)

39. Respectful Tasks Equally interesting, appealing, engaging
Focused on the same essential
understandings & skills
Requires all students to work at
high levels of thinking (to apply, argue, defend, synthesize, transform, look at multiple perspectives, associate with, etc.)

40. Respectful or Not-so Respectful?
Scenario 1
Teacher B is assigning math homework. Some of her students are still struggling to master converting fractions to decimals, some understand the process but need more practice, and some are fairly proficient. Because she knows that it will take longer for some students to complete the problems, she decides to assign 10 problems to struggling students, 20 problems to on-grade level students, and 30 problems to advanced students.

41. Respectful or Not-so Respectful?
Scenario 2
One of Teacher K’s students got a 100 on her pre-test, so the teacher has her design homework worksheets that practice the skills that the class learned in that unit.

42. Meet with your grade level to collaborate.
Break out Session
Meet with your grade level to collaborate.
Share ideas
Design math activities

43. Share your thoughts or ask questions.
Open Forum
Share your thoughts or ask questions.

44. Take it one step at a time.
Don’t stress out!
Take it one step at a time.