### Planning Differentiated Lessons in Math

```By: Aimee Tyszka
[email protected]
&
Jessica Rinaldi
[email protected]
PLANNING A FOCUSED CURRICULUM
STUDENTS SHOULD …
KNOW
Facts
 Vocabulary
 Definitions

• UNDERSTAND
– Principles/
generalizations
– Big ideas of the
discipline
• BE ABLE TO DO
–Processes
–Skills
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
KNOW
Facts, names, dates, places,
information
 There
are 50 states in the US
 Napoleon Bonaparte
 1066
 The Continental Divide
 The multiplication tables
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.
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.




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
KUD’S
1. Count to one hundred in units of ten.
2. Multiplication is another way to do addition.
3. Find the missing addend using counters.
4. Subtraction and addition have an inverse
relationship.
5. The multiplication tables 0-12.
6. Clue words for addition are sum, and, altogether, in
all, combine, join, plus, and total.
7. The value of a digit depends on its place in the
number.
8. Write the value of the underlined digit in each
number.
They create clear learning goals
Allow us to align goals, assessments, teaching,
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
They tell us what strugglers should invest in
They give us a platform for extending for advanced
students
INSTRUCTIONAL STRATEGIES THAT
SUPPORT DIFFERENTIATED
INSTRUCTION
1.
2.
3.
4.
5.
6.
7.
Learning Centers – pgs. 23-31
Cubing – pgs. 31-34
RAFT – pgs. 34-46
Graphic Organizers – pgs. 46-50
Think DOTS – pgs. 54-60
Learning Contracts – pgs. 60-64
Web Quests – pgs. 64-66
*See Marcia Imbeau’s PowerPoint for further explanation of each strategy.
Lesson Title: Think Dots
Curriculum Area (s):
Math
Author: Jessica Rinaldi
Author Contact: [email protected]
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?
How will I differentiate?
Content and Product
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.
2.
3.
4.
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
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.
Think Dots
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,
problems less than 20.
Using the number line
jumping to count on.
Using counters, show
the many ways to make
the number 10.
On the giant number
totals.
Solve word problems
using colored chips.
problems using the
objects from the red bin.
Think Dots
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
giant number line to
problems up to 20.
problems using the
number line.
Roll the dice to make Write the turn around
fact for each number
sentence.
Find the missing
counters.
problems that use
each vocabulary word:
altogether, in all,
total, and, join, and
combine.
Think Dots
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
with the greatest sum earns
the point. First person to
thirty wins.
group of 4.
Find the missing
Write the fact
families for each set
of numbers.
Are you right or
Create at least 5 word wrong? Correct the
problems.
homework sheet. Fix
any mistakes.
Lesson Title: 3- digit Place value centers
Curriculum Area (s):
Math
Author: Jessica Rinaldi
Author Contact: [email protected]
Time Required: 20-30 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?
How will I differentiate?
Process
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=1000. 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 1000. 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.
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
4. What is the value of
data sheet.
1.
2.
3.
4.
5.
Group 2
(Visual)
Roll the dice 3 times
Write down each digit
to create a 3 digit
number.
Draw base ten blocks
What is the value of
each digit?
sheet.
Group 3
(Tactile)
1. Pick 3 cards from
the deck.
2. Make a 3-digit
number.
3. Build the number
using the base ten
blocks.
4. Write the value of
sheet.
Name: _______________________________ Date: __________________
Place Value
Hundreds
Ex.
5
Tens
Ones
What is your
digit?
What is the value
2
9
2
20
Unit Title: Multiplication (1 digit)
Lesson Title: Think Dots
Curriculum Area (s):
Math
Author: Aimee Tyszka
Author Contact: [email protected]
Time Required: 3-4 weeks/entire unit
Instructional Groupings: homogeneous
Standards:
Materials:
Understand and apply basic concepts of multiplication.
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?
How will I differentiate?
Content
Product
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.
2.
3.
4.
Whole class- oral/visual review of facts
Small group- meetings to reinforce, guide, and make corrections
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.
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
Describe how multiplication
Play How Low Can You Go?
dice game.
page 2 from the blue folder. multiplication fact to show The directions and dice are
in the blue basket on the
multiplication. Draw a
math shelf.
picture.
Practice multiplication facts
using the I-pads. Be sure to
Math. Have fun!
word problems.
1.
My factors are 2 and 4.
What is my product?
2.
My factors are 3 and 1. What
is my product?
3.
My product is 0. What must
one of my factors be?
worksheet. Make sure you
have at least three
problems for each times
table (0-2). Create an
How Low Can You Go?
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.
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
page 2 from the orange
folder.
Play the Toss and Talk
center activity 3-1.
The instruction sheet and
dice (number cubes) are in
math shelf.
Make a multiplication table
for facts 0-5. Use a crayon
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
Math. Have fun!
riddles.
1.
I am between 9 x 4 and 8 x 4.
I am an even number. What
number am I?
2.
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?
multiplication riddles.
Create a riddle for each
times table (3-5). Create an
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
direction sheet and array
chart from the red folder.
You may choose any 15 of
the numbers given.
Practice multiplication facts
using the I-pads. Be sure to
Math. Have fun!
Make a multiplication table. Fill
Play the Multiplication Brain in all facts up to 9 x 9. Color all
Game.
the even products red. Describe
The instruction sheet and
the product when both factors
are odd, even, and when one
playing cards are in red
factor
is odd and the other is
even.
Complete the Break the
Codes worksheet. It is in
the red folder. Try making
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.
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.
Unit Title: Basic Fraction Concepts
Lesson Title: Naming and making equivalent fractions
Curriculum Area (s):
Math
Author: Aimee Tyszka
Author Contact: [email protected]
Time Required: 1-2 weeks
Instructional Groupings: homogeneous/small group/partners
Standards:
Materials:
Extend understanding of fraction equivalence and ordering
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?
How will I differentiate?
Content
Product
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:
1. 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.
Play the Toss and Talk
game.
number cubes from the
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
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
and draw a picture of how
the pizza was sliced.
You have 6 tiles. 2/6
of the tiles are
rectangles. The rest of
the tiles are triangles.
Draw a design using the
tiles.
Which fraction is
greater, 1/3 or 1/6?
Use words and models
Create an interesting
and challenging word
problem that uses
fractions.
Show the solution.
THINKING
CUBE
Fractions
(below)
Play the Toss and Talk
game.
number cubes from the
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.
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
picture of how the pizza was
sliced.
You have 10 tiles. 4/10
of the tiles are
rectangles. The rest of
the tiles are triangles.
Draw a design using the
tiles.
Which fraction is
greater, 4/5 or 4/8?
Use words and models
Create an interesting
and challenging word
problem that uses
fractions.
Show the solution.
THINKING
CUBE
Fractions
(average)
Play the Toss and Talk
game.
number cubes from the
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
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
and draw a picture of how
the pizza was sliced.
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.
Which fraction is
greater, 2/3 or 4/7?
Use words and models
Create an interesting
and challenging word
problem that uses
fractions.
Show the solution.
THINKING
CUBE
How many marbles are
green?
Explain how you know.
Fractions
(above average)
•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.)
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
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.