differentiated instruction in the primary mathematics classroom j. silva

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...