Differentiated Instruction in the
Primary Mathematics Classroom
J. Silva
Differentiation Strategies
Content Process Product
According to Students’
Readiness Interest LearningProfile
Teachers Can Differentiate
Adapted from The Differentiated Classroom: Responding to the Needs of All Learners (Tomlinson, 1999)
Environment
Differentiated Instruction Structures and Strategies
Strategies Anticipation Guide Think-Pair-Share Exit Cards Venn Diagrams Mind Maps Concept Maps Metaphors/
Analogies Jigsaw
Structures Cubing Menus Choice Boards RAFTs Tiering Learning Centers Learning Contracts Open Questions Parallel Tasks
CubeJournal Prompts
Face 1: I understand…
Face 2: I don’t understand…Face 3: I find it easy to…
Face 4: I find it difficult to…
Face 5: I learned…
Face 6: I still want to know…
CubeGeometry Compare and Contrast
CubeProbability Prompts
IMPOSSIBLE
LIKELY
CERTAIN
Describe probability as a measure of the likelihood that an event will occur, using mathematical language
Appetizer (Everyone): What is a pattern?Main dish (Choose 1): Create a repeating pattern using pattern blocks. Create a growing pattern using pattern blocks?Side dishes (Choose 2): Describe a pattern that results from repeating an action. Describe a pattern that results from repeating an operation. Describe a pattern that results from using a transformation.Dessert(if you wish) Create a growing pattern. How is it the same as a repeating
pattern? How is it different?
MenuPatterning
Use base ten materials to decompose 327
Use base ten materials to show that the 3 in 324 represents 3 hundreds
Use base ten materials to represent the relationship between a decade and a
centuryShow 60 in as many different
ways as you canShow $1 in as many different
ways as you canDescribe the number 18 in as many different ways as
you can
Use counters to show that 3 groups of 2 is equal to 2 + 2
+ 2
Draw a picture to show that 3 groups of 2 is equal to 3 x
2
Give a real-life example of when you might need to
know that 3 groups of 2 is 3 x 2
Choice BoardNumber Sense and Numeration
ROLE AUDIENCE FORMAT TOPIC
length Teacher Pictures How I help you find the perimeter of a square
height Principal Words How I help you find the perimeter of a rectangle
distance Student Numbers How I help you find the perimeter of a circle
R.A.F.T.
Station 1: Simple “rectangular” or cylinder shape activities
Station 2: Prisms of various sorts
Station 3: Composite shapes involving only prisms
Station 4: Composite shapes involving prisms and cylinders
Station 5: More complex shapes requiring invented strategies
Learning CentersSurface Area
Open Learning Tasks
• have a specific mathematical purpose
• are built on a big idea
• allow students at different levels to participate
Open-Ended Learning Tasks:
Open Learning Task
Choose a type of shape. Tell as many things about it as you can.
Open Learning TasksWhat makes the task open?
The mathematical purpose To reveal what students understand about attributes or properties of the shape.
Big ideaShapes of different dimensions and their properties can be described mathematically.
Student ReadinessIt allows students to tell whatever they know about a shape, whether it is 2D or 3D.
Some “Opening Up Strategies”
Start with the answer instead of the question.
Ask for similarities and differences.
Leave the values in the problem somewhat open.
Start with the Answer
The answer is 42. What is the question?
Num
ber
Sen
se &
N
umer
atio
n
Start with the Answer
A triangle has a perimeter of 10. Make as many different triangles as you can. What are the side lengths.
Geo
met
ry &
S
patia
l Sen
se
Start with the Answer
A container holds about 4litres. Describe its size in other ways.
Mea
sure
men
t
This balance shows that 4 + 2 = 5 + 1.
How could you move the blocks to show other equations that are true?
Start with the AnswerP
atte
rnin
g &
A
lgeb
ra
Start with the Answer
Work in pairs to decide what this graph might be about.
Dat
a M
anag
emen
t &
Pro
babi
lity
0
10
20
30
40
50
60
70
80
90
How are the numbers 10 and 15 alike? How are they different?
Num
ber
Sen
se &
N
umer
atio
nSimilarities and Differences
How are these shapes alike? How are they different?
Similarities and DifferencesG
eom
etry
&
Spa
tial S
ense
Two shapes are the same size. What could they be? How are they different?
Mea
sure
men
tSimilarities and Differences
Jane made the pattern below. Make a pattern that you think is like this.
Tell how the patterns are alike. Tell how they are different.
Pat
tern
ing
&
Alg
ebra
Similarities and Differences
How are these graphs alike and how are they different.
Similarities and DifferencesD
ata
Man
agem
ent
& P
roba
bilit
y
Choose a number for the second mark on the number line.
Mark a third point on the line. Tell what the number name it should have and why.
Num
ber
Sen
se &
N
umer
atio
nLeaving Values Open
Draw a design or shape made up of three shapes. The design should have symmetry.
Choose two objects in the room. Think about their locations. Tell how to get from location to the other.
Geo
met
ry &
S
patia
l Sen
seLeaving Values Open
Pick a length between 5cm and 10cm. Draw a pencil that is ___cm long.
Mea
sure
men
tLeaving Values Open
The fourth picture in a pattern consists of five squares as shown:
What could the first, second, third, and fifth pictures look like.
Leaving Values OpenP
atte
rnin
g &
A
lgeb
ra
? ? ? ?
Think of something that might be true about most of the students in the class. Conduct a survey to find out if you are correct. Display your data.
Leaving Values OpenD
ata
Man
agem
ent
& P
roba
bilit
y
Let’s Open Up QuestionsFind a closed question.
Create an open question using one of the “Opening-up Strategies”:
Start with the answer instead of the question
Ask for similarities and differences
Leave the values in the problem somewhat open
Resource “Opening-up Strategy”
Start with the answer Ask for similarities and differences Leave the values in the problem
somewhat open
Original Question New Question
Let’s Open Up Questions
Parallel Learning Tasks
Parallel learning tasks are two or more different tasks that:
differ in sophistication possess the same big idea focus have a common set of consolidation questions
Parallel Tasks
Choose a way to sort so that one bar of your graphs is much longer than all of the other bars.
Sort the items the teacher has provided. Create a bar graph to describe the number in each group after you have sorted them.
Choose a way to sort so that the bars are all about the same size.
Consolidation Questions How did you sort your items?
Why was your sorting rule an appropriate one for these items?
Where would this object go (hold up another object) if we used your sorting rule?
How does your graph describe the items?
What can you tell about the number of different types of items by looking at the graph?
Asking the Right Questions
What consolidation questions could we ask for each parallel task?
They must apply equally to both tasks and the big idea we want to
address.
Parallel tasks: Number Sense & Numeration
What is the big idea?There are many ways to represent numbers.
What consolidation questions would you ask?What number did you represent?
How do you know that that number is one that was okay to choose?
What are some of the different ways you represented that number?
Choose a number between 1 and 10. Show that number is as many ways as you can.
Choose a number between 20 and 30. Show that number is as many ways as you can.
Parallel tasks: Geometry
Choose 2D shapes to make two different creatures. Describe the two creatures you made.
Choose 3D shapes to make two different creatures. Describe the two creatures you made.
What is the big idea?Shapes of different dimensions and their properties can be
described mathematically.
What consolidation questions would you ask?What are the names of the shapes you used?
How many of each did you use?Why did you decide those would be good shapes to use?
Parallel tasks: Measurement
A rectangle has sides that are whole numbers of centimetres. The perimeter is 44cm. Draw five possible shapes.
A polygon has a perimeter that is 44cm. Draw five possible shapes.
What is the big idea?The same object can be described using different
measurements.
What consolidation questions would you ask?What does it mean to know that the perimeter of a shape is
44cm?How did you select your first shape?
How do you know that your perimeter is 44cm?
Parallel tasks: Patterning & Algebra
Create a repeating pattern that begins with 3, 5,…
Create an increasing pattern that begins with 3, 5,…
What is the big idea?A group of items form a pattern only if there is an element of
repetition, or regularity, that can be described with a pattern rule.
What consolidation questions would you ask?What is your pattern?
What makes it a pattern?What would be your 10th number?
Parallel tasks: Data Management & Probability
You have these two bags:
You pick one cube from one of the bags and it is blue. You return the cube and pick again from the same bag and it is blue, the one after that is yellow.
Which bag do you think you have? Explain.
You have these three bags:
You pick one cube from one of the bags and it is blue. You return the cube and pick again from the same bag and it is blue, the one after that is yellow.
Which bag do you think you have? Explain.
Parallel tasks: Data Management & Probability
Which bag do you think you have? Explain.
What is the big idea?In probability situations, one can never be sure what will happen
next. This is different from most other mathematical situations.
What consolidation questions would you ask?What colour do you think will be picked on the fourth try?
Why do you think that?Can you be sure?
Some Math
Find different ways to make 120
Hunting on the Hundreds Chart
Find three numbers on the Hundreds chart that form an I and add to give 150.
Record your thinking/strategy on chart paper to share later.
Can you find other letters that will give your sum? Show your work.
Find an L on the Hundreds chart where the numbers add to give 308.
Consolidation Questions
With your table group, come up with a few consolidation questions you could ask that would be appropriate for either task.
The Three Part Lesson
Minds On
Action
After
5-10 minutes
15-25 minutes
15-20 minutes
Ways to make 120?
Summing numbers to make “I” and “L”.
Consolidation,Highlight Key Ideas, Misconceptions, Practice, Next Steps...
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