1. How To Differentiate Mathematics Instruction Using Math Stations Fulton County School System
Nelly Belinga-Hill
Mathematics Teacher
Math Department Chair
Martin Luther King Jr High School
June 28th, 2011

2. How To Differentiate Mathematics Instruction Using Math Stations
Essential Question
How can I use Math Stations to differentiate instruction in my classroom?
Agenda
1. Opening Activity: Choice Board (30 mins Thinking & 30 mins Sharing)
2. Morning Discussion: The Importance of Problem Solving in Mathematics (30 mins)
3. Connecting The Pieces: From Problem Solving to Station Teaching (30 mins)
Morning Break (10:30 – 10:40 am)
4. Differentiating Instruction: How Math Stations Help Differentiate Instruction (2h)
Lunch Break (12:40 – 1:40 pm)
5. Afternoon Session: Designing Your Own Differentiated Lesson
(2h and 20 mins)

3. 1. Opening Activity Choice Board

4. Problem solving Choice board
Choose 3 activities
You have 30 mins
You must go through the center
Think – Group (optional) - Share
10 mins mins mins
Draw
Move
Around
Sing
Write
a Speech
Math Challenge Questions
Debate
Journal
Entry
Describe the Learning environment
Role-Play
1. Opening Activity: Choice Board

5. How many valentines? Solution To Math Challenge 1
Introduce yourself Share Some of Your Answers
How many valentines? Solution To Math Challenge 1
There are five friends. For Valentine's Day, each friend gives each other friend a valentine. How many valentines are there altogether?
Next, extend your reasoning to a larger number, what if you had 28 friends?
Source:
1. Opening Activity: Choice Board

6. NCTM Standard 2 (1998)
Sets the purpose of patterns, functions, and algebra in mathematics education at all grade levels.
Mathematics instructional programs should include attention to patterns, functions, symbols, and models so that all students:
understand various types of patterns and functional relationships;
use symbolic forms to represent and analyze mathematical situations and structures;
use mathematical models and analyze change in both real and abstract contexts.
Source: NCTM Principles and Standards (1998)
1. Opening Activity: Choice Board

7. Types of solutions List Them All Do Addition Draw Points and Arrows
Make a Star
Make a Grid
Look for a Pattern
Use a formula
Just do it
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

8. Types of solutions List them all Do addition
Suppose the names of the friends are A, B, C, D, and E.
Let's list the valentines that each friend gives, starting with A's valentines.
A–B, A–C, A–D, A–E
B–A, B–C, B–D, B–E
C–A, C–B, C–D, C–E
D–A, D–B, D–C, D–E
E–A, E–B, E–C, E–D
That's 20 valentines.
Suppose the names of the friends are A, B, C, D, and E.
A gives 4 valentines
B gives 4 valentines
C gives 4 valentines
D gives 4 valentines
E gives 4 valentines
Add the numbers.
The total is 20 valentines.
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

9. Types of solutions Draw points Make a star and arrows
This solution is a lot like "Draw Points and Arrows," except we arrange the points differently.
Suppose the names of the friends are A, B, C, D, and E.
Every arrow represents 2 valentines and there are 10 double-headed arrows. Again, that's 10 twice—a total of 20 valentines.
Suppose the names of the friends are A, B, C, D, and E.
Draw an arrow between each pair. Then count the arrows. There are 10 and each one represents 2 valentines. So that's 10 twice—a total of 20 valentines.
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

10. Types of solutions Make a grid
Suppose the names of the friends are A, B, C, D, and E. We make a grid of all the friends. Each pink square is a valentine. The gray squares show that each person does not send a valentine to himself or herself.
Either count the pink squares (20), or notice that there are 5 x 5 = 25 squares in the whole grid, minus 5 gray squares. Thus = 20 valentines.
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

11. Types of solutions Look for a pattern
Here we look at even smaller numbers.
What if there were only one person? Then no valentines are given. Zero.
What if there were only two friends instead of five? Then there would be 2 valentines exchanged.
Three friends, there would be 6 exchanged.
Four friends, there would be 12.
What's the pattern? 0, 2, 6, 12,...?
Between the first and second numbers is a difference of 2.
Between the second and third, a difference of 4.
Between the third and fourth, a difference of 6.
And so on. If the pattern were to continue, the next number would be a difference of 8—and 20 valentines would have been exchanged.
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

12. Types of solutions Use a formula
You know that if there are n people, each will send out (n - 1) valentines.
So the total number of valentines V is
V = n (n - 1)
Since n = 5 in this situation, V = 5 x 4 = 20
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

13. Types of solutions Just do it
Get four friends.
Now there are five of you.
Give valentines to each other.
Then collect all the valentines and count them.
There are 20.
Source: Annhenberg CPB/Math and Science Project
1. Opening Activity: Choice Board

14. Checkpoint question: 5-mins discussions Discuss – Summarize - Share 2 mins 1 mins 2 mins
How do we build this type of reasoning across the grades (K – 12)?
1. Opening Activity: Choice Board

15. Across the grades
The youngest children begin simply by counting. They count by 1s, then by 2s, 5s, and 10s. These patterns give students a natural strategy to understand addition and multiplication. When considering a number pattern such as 2, 4, 6..., a young student will ask herself, By what number can I count (add) to get to the next number in the pattern and the next and the next?
As the student gets older, her knowledge of patterns advances from sums to products. When asked for the 50th number in the pattern, she will know to multiply 2 times 50.
High school students can start to understand functions, such as f(x) = 2x + 2, where x is the numerical sequence 0, 1, 2, 3,…. They begin with simple in-out machines and gradually adapt their understanding to the abstractions of algebra.
Source: NCTM Principles and Standards (2000)
1. Opening Activity: Choice Board

16. 2. Morning Discussion The Importance of Problem Solving In Mathematics

17. Discussion Question
Describe what is meant by “Problem Solving.” Why is this important? How is this different from the problem solving you see in most math books?
2. The Importance of Problem Solving
In Mathematics

18. NCTM Standard (2000) Problem Solving
Problem solving means engaging in a task for which the solution method is not known in advance.
In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings.
Solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking.
Source: NCTM Principles and Standards (2000)
2. The Importance of Problem Solving
In Mathematics

19. Importance of Problem Solving
In everyday life and in the workplace, being a good problem solver can lead to great advantages. Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program.
By learning problem solving in mathematics, students should acquire
ways of thinking
habits of persistence and curiosity
confidence in unfamiliar situations
Problem solving in mathematics should involve all the five content areas described in the NCTM Standard:
build new mathematical knowledge through problem solving;
solve problems that arise in mathematics and in other contexts;
apply and adapt a variety of appropriate strategies to solve problems;
monitor and reflect on the process of mathematical problem solving.
Source: NCTM Principles and Standards (2000)
2. The Importance of Problem Solving
In Mathematics

20. Problem Solving Artifacts Found in Various Classrooms (Cont.)
What to do if you get stuck
Read the problem again
Look back at the lesson
Look back at the previous work
Look in the book
Refer to the reference chart
Ask your partner
Ask the teacher
10 Steps to Success
Just keep trying
Try to determine what’s working
Try to determine what’s not working
Try to find someone who has done it
Try and ask for help
Try again tomorrow
Try it a little differently
Try one more time
Try again
Try
2. The Importance of Problem Solving
In Mathematics

21. Problem Solving Artifacts Found in Various Classrooms (Cont.)
7 Steps to Solving Math Problems
1. Identify the Problem
What is the question asking?
2. Define the Problem
What will the answer look like?
3. Formulate a Strategy
How should I tackle this problem (VANG)?
4. Organize the Information
What information is given?
5. Allocate Resources
Where can I read more or learn more about this?
6. Monitor Progress
How much time do I have?
What are my steps?
Do I need to use a different strategy?
7. Evaluate the Results
Does my answer make sense?
Is this the best possible solution?
5 Steps to Solving Math Problems
Identify Problem- What is the problem asking you for?
Indentify knowns/unknowns- Organize given information
Translate known/unknowns into math symbols/language- Assign variables, subscripts and formulas as necessary
Solve for unknown
Check answer
4 Steps to Solving Math Problems
Look for clues
Establish a Game Plan
Solve the Problem
Recheck and Reflect. 
2. The Importance of Problem Solving
In Mathematics

22. Checkpoint Question
What type of Problem Solving Artifacts do you use in your classroom (or do you plan to modify and use)?
2. The Importance of Problem Solving
In Mathematics

23. 3. Connecting the Pieces From Problem Solving to Station Teaching

24. I Face Book through most of my classes. I do 49% of the reading
I spend
two hours
on my
cell phone.
I Face Book
through most
of my classes.
I read 3
books a
Year.
I spend
3 ½ hours
Online.
I listen to
music 2.5
hours a day.
I do 49%
of the reading
assigned.
MS HS
3. From Problem Solving to Station Teaching 24

25. I hear, and I forget I see, and I remember
I do, and I understand.
Confucius
As teachers, we recognize that we are teaching a different generation with different needs. It is therefore imperative to equip ourselves with tools that will help us address diverse learners, henceforth increase the engagement level.
3. From Problem Solving to Station Teaching

26. I Do and I Understand. What are Math Stations?
Math stations are areas in the classroom where students refine a skill or extend a particular math concept or concepts.
They may also be different places in the classroom where students work on tasks simultaneously, and whose activities are linked.
3. From Problem Solving to Station Teaching

27. Connecting the Pieces Math Stations - Problem Solving
Students should acquire:
Ways of thinking
Habits of persistence and curiosity
Confidence in unfamiliar situations
Math Stations
Math stations are areas in the classroom where students refine a skill or extend a particular math concept or concepts.
They may also be different places in the classroom where students work on tasks simultaneously, and whose activities are linked.
Math Stations
Problem Solving
Source: Carol Ann Tomlinson
“How to Differentiate Instruction in Mixed-Ability Classrooms.”
3. From Problem Solving to Station Teaching

28. Example of a Math Station Lesson Math 1 Probability Lesson Video + Hands-On Experience
3. From Problem Solving to Station Teaching

29. 4 Corner Picture Closing
….Math Stations Are Like….Because…..
4. How Math Stations Help Differentiate Instruction

30. Types of Math Stations
Rotating Stations - rotate students through activities, or rotate activities through groups of students
Individualized Stations - students/groups only use the stations they need or to which they are assigned
Sequential Learning Stations - students must work through the activities in a particular order and proceed with mastery
Thematic Stations - all activities set up to support a specific unit of study
Enrichment Stations - stations that can be selected after assigned stations are completed
3. From Problem Solving to Station Teaching

31. What do stations look like in a math class?
Whole class warm-up
Review station assignments made based on pre-assessment
Pull a group to the teacher’s station for a structured focus lesson.
Other students work at their stations. You move around to monitor their progress when students at the teacher’s station are working in pairs or independently.
Whole class closure activity.
Whole class warm-up
On grade level focus lesson for most of the class
Above grade level students work on an anchor
After focus lesson, students refine their understanding at a specific station or through an anchor activity
Above grade level students receive their focus lesson at the teacher’s station.
Whole class closure activity.
4. How Math Stations Help Differentiate Instruction

32. Station Teaching Be PracticalDo
Begin where students are, not where you think they should be. Pre-assess.
Focus on the essentials so that struggling learners don’t drown in a pool of disjointed facts: Unpack the standard, explain the goal.
Articulate your expectations and spend time modeling the type of work found at each station. Work diligently to ensure that struggling, advanced, and in-between students think and work harder than they meant to; achieve more than they thought they could; and come to believe that learning involves effort, risk, and personal triumph.
Have a strong closing. Give students an opportunity to reflect on their problem solving skills: Math stations are not Math Games; they are learning centers.
Don’t
Do not ask Students to count off from 1 – 4 and form groups. Use your pre-assessment data.
Students do not move from station to station in a round-robin style. You determine which station and when!
Don’t just ask students to “Figure out the instructions.” Give clear instructions regarding material management, time management, direction of the movements, LOTS (Language of the Standard).
Do not sit at your desk and miss out on scaffolding opportunities. Build in time for you to circulate and use your questioning techniques.
Don’t work in isolation. Collaborate with your department to develop tasks for review, practice, and enrichment.
3. From Problem Solving to Station Teaching

33. 4. Differentiating instruction How math stations help differentiate instruction

34. Connecting the Pieces Math Stations - Problem Solving - Differentiated Instruction
4. How Math Stations Help Differentiate Instruction

35. Differentiation is…
GAPSS Instruction Standard 2.2 – All teachers make appropriate use of differentiation, including adjusting content, process, product, and learning environment based upon diagnosis of students’ readiness levels, learning styles, interests and personal goals.
4. How Math Stations Help Differentiate Instruction

36. Differentiation is not….
A class is not differentiated when assignments are the same for all learners and the adjustments consist of varying the level of difficulty of questions for certain students, grading some students harder than others, or letting students who finish early play games for enrichment.
Source: Carol Ann Tomlinson, 1995
4. How Math Stations Help Differentiate Instruction

37. ? Source: Carol Ann Tomlinson, 1995
4. How Math Stations Help Differentiate Instruction 37

38. Differentiate by… Product Content Process
What Students Learn
Materials at varied ability or grade levels in one classroom; Varying the levels of complexity and abstractness
Students may start at different places in the curriculum and/or proceed at different paces
Product
How Students Make
Sense of Learning
Use of diverse activities that are varied to meet student interests or preferences for learning
Recognizes the many learning styles within any group of students.
Process
Students have some choice in how they will demonstrate what they have learned to the teacher, class, or other audience.
Giving different assignments to different students increases motivation and results in an interesting variety of work products.
Source: Calendra Brown, Fulton County Math Coach
4. How Math Stations Help Differentiate Instruction

39. Differentiating by Learning Profile Choice Board Revisited
Group 3
Group 2
Group 1
Visual
Spatial Intelligence
Draw
Tactile
Bodily Kinesthetic
Move Around
Auditory
Musical
Sing
Linguistic
Write a Speech
Logical
Math Challenge Questions
Debate
Intrapersonal
Journal Entry
Naturalist
Describe the Learning environment
Interpersonal
Role-Play
Group 4

40. What type of differentiation are we implementing
What type of differentiation are we implementing? Send a Reporter in 5 mins to the other group.
Group 1
Breakout Activity
Handout #10a
Circumference Problem
Group 3
Error Analysis
Group 4
Vocabulary in Math
Group 2
Develop Sensitivity For
Struggling Learners
1 Min Challenges
Anchor
Scaffolding Problem
Solving: Focus on the
Process rather than
Arithmetic
Source: Dr. Riccomini “RTI in Math”
4. How Math Stations Help Differentiate Instruction

41. Differentiating by Interest Questions to ask yourself
How will students use this topic in their worlds?
How will the topic help students explain their own experiences?
How will the topic contribute to or deepen students/ current interests?
How can the topic help students fulfill their aspirations?
How can the topic help alleviate students’ fears and concerns?
What will students gain if they learn this topic or lose if they do not?
What will happen if students use this new skill or knowledge well and what will happen if they do not?
Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 47
4. How Math Stations Help Differentiate Instruction

42. Differentiating by Readiness Level
Drain the Pool Learning Task
Question: If tasks at stations are the same for all students, are all students needs being met?
4. How Math Stations Help Differentiate Instruction

43. Lunch Break (1h)

44. 5. Designing Your Own Differentiated Lesson
Afternoon Session

45. This Morning We learned that…
…and they DEFINITELY
don’t learn alike!
Source: Calendra Brown, Fulton County Math Coach
5. Designing Your Own Differentiated Lesson

46. Designing Your Own Differentiated Lesson Unpacking the Standard
Content Goal
Emphasize content knowledge. The main focus is on what students need to know or understand.
Example: Knowing the Meaning of Rate of Change within a real life context.
Key Verbs: “know, understand,…”
Process Goal
Emphasize students’ learning or developing a skill. “Do it, and do know how and why!”
Example: Knowing how to compute the rate of change given 2 points, a linear or non-linear function.
Key Verbs: “Analyze, conduct, write…”
Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 59
5. Designing Your Own Differentiated Lesson

47. Designing Your Own Differentiated Lesson
Include the 5Cs
Curiosity
Collaboration
Creativity
Choice
Take a minute to think about the activities on your list.
Apply 5 C’s to both lists.
To what degree are they present in the things you love to do and absent in those things that you would rather not do?
Call on participants to share
I would try to add hand motions to help them recall the 5 C’s quickly.
Curiosity: touch brain
Collaboration: Motion with hands “come here motion”
Creativity: swirl hand
Choice: hands showing either/ or
Competence: Hands across heart
These same 5 factors are important to remember as we design instruction that promotes understanding, interest, and excellence through a high level of student engagement.
According to Harvey Silver and Richard Strong, our level of interest in and engagement with anything depends on 5 factors.
Competence
I said so
Source: Hanson, Silver, Strong “The 5 C’s of Interest and Engagement”
5. Designing Your Own Differentiated Lesson 47

48. Which Standard? How will you differentiate the lesson using station teaching?
5. Designing Your Own Differentiated Lesson

49. Remember: Station teaching should produce “strategic learners”…
Able to analyze a problem and develop a plan.
Able to organize multiple goals and switch flexibly from simple to more complicated goals.
Access their background knowledge and apply it to novel problem.
Develop new organizational or procedural strategies as the assignment becomes more complex.
Use effective self-regulated strategies while completing a assignment.
Attribute high grades to their hard work and good study habits.
Review the goals and determine whether they have been met.
Source:
5. Designing Your Own Differentiated Lesson

50. Closing Activity Please explain ________1
Very low 2
low 3
medium 4
high
My understanding of math stations before the presentation
My understanding of math stations after the presentation
Please explain ________
EQ: What are several ways that math stations can be used to differentiate instruction in your math classroom?
5. Designing Your Own Differentiated Lesson

51. Make and Take… To Create 1 Folder Game, you will need: 1 folder
4 pockets
1 folder game hand-out
Scissors
Glue sticks
5. Designing Your Own Differentiated Lesson

52. Thank You Fulton County.
Nelly Belinga-Hill
Math Stations Website:
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